
                    Persistence of Vision(tm) Ray-Tracer
                                (POV-Ray(tm))

                          User's Documentation 3.0

                         Copyright 1997 POV-Team(tm)


1                Introduction
   1.1              Notation
2                Program Description
   2.1              What is Ray-Tracing?
   2.2              What is POV-Ray?
   2.3              Which Version of POV-Ray should you use?
      2.3.1            IBM-PC and Compatibles
         2.3.1.1          MS-DOS
         2.3.1.2          Windows
         2.3.1.3          Linux
      2.3.2            Apple Macintosh
      2.3.3            Commodore Amiga
      2.3.4            SunOS
      2.3.5            Generic Unix
      2.3.6            All Versions
      2.3.7            Compiling POV-Ray
         2.3.7.1          Directory Structure
         2.3.7.2          Configuring POV-Ray Source
         2.3.7.3          Conclusion
   2.4              Where to Find POV-Ray Files
      2.4.1            POV-Ray Forum on CompuServe
      2.4.2            Internet
      2.4.3            PC Graphics Area on America On-Line
      2.4.4            The Graphics Alternative BBS in El Cerrito, CA
      2.4.5            PCGNet
      2.4.6            POV-Ray Related Books and CD-ROMs
3                Quick Start
   3.1              Installing POV-Ray
   3.2              Basic Usage
      3.2.1            Running Files in Other Directories
      3.2.2            INI Files
      3.2.3            Alternatives to POVRAY.INI
      3.2.4            Batch Files
      3.2.5            Display Types
4                Beginning Tutorial
   4.1              Our First Image
      4.1.1            Understanding POV-Ray's Coordinate System
      4.1.2            Adding Standard Include Files
      4.1.3            Adding a Camera
      4.1.4            Describing an Object
      4.1.5            Adding Texture to an Object
      4.1.6            Defining a Light Source
   4.2              Using the Camera
      4.2.1            Using Focal Blur
   4.3              Simple Shapes
      4.3.1            Box Object
      4.3.2            Cone Object
      4.3.3            Cylinder Object
      4.3.4            Plane Object
      4.3.5            Standard Include Objects
   4.4              Advanced Shapes
      4.4.1            Bicubic Patch Object
      4.4.2            Blob Object
         4.4.2.1          Component Types and Other New Features
         4.4.2.2          Complex Blob Constructs and Negative Strength
      4.4.3            Height Field Object
      4.4.4            Lathe Object
         4.4.4.1          Understanding The Concept of Splines
      4.4.5            Mesh Object
      4.4.6            Polygon Object
      4.4.7            Prism Object
         4.4.7.1          Teaching An Old Spline New Tricks
         4.4.7.2          Smooth Transitions
         4.4.7.3          Multiple Sub-Shapes
         4.4.7.4          Conic Sweeps And The Tapering Effect
      4.4.8            Superquadric Ellipsoid Object
      4.4.9            Surface of Revolution Object
      4.4.10           Text Object
      4.4.11           Torus Object
   4.5              CSG Objects
      4.5.1            What is CSG?
      4.5.2            CSG Union
      4.5.3            CSG Intersection
      4.5.4            CSG Difference
      4.5.5            CSG Merge
      4.5.6            CSG Pitfalls
         4.5.6.1          Coincidence Surfaces
   4.6              The Light Source
      4.6.1            The Ambient Light Source
      4.6.2            The Pointlight Source
      4.6.3            The Spotlight Source
      4.6.4            The Cylindrical Light Source
      4.6.5            The Area Light Source
      4.6.6            Assigning an Object to a Light Source
      4.6.7            Light Source Specials
         4.6.7.1          Using Shadowless Lights
         4.6.7.2          Using Light Fading
         4.6.7.3          Light Sources and Atmosphere
   4.7              Simple Texture Options
      4.7.1            Surface Finishes
      4.7.2            Adding Bumpiness
      4.7.3            Creating Color Patterns
      4.7.4            Pre-defined Textures
   4.8              Advanced Texture Options
      4.8.1            Pigment and Normal Patterns
      4.8.2            Pigments
         4.8.2.1          Using Color List Pigments
         4.8.2.2          Using Pigment and Patterns
         4.8.2.3          Using Pattern Modifiers
         4.8.2.4          Using Transparent Pigments and Layered Textures
         4.8.2.5          Using Pigment Maps
      4.8.3            Normals
         4.8.3.1          Using Basic Normal Modifiers
         4.8.3.2          Blending Normals
      4.8.4            Finishes
         4.8.4.1          Using Ambient
         4.8.4.2          Using Surface Highlights
         4.8.4.3          Using Reflection and Metallic
         4.8.4.4          Using Refraction
         4.8.4.5          Adding Light Attenuation
         4.8.4.6          Using Faked Caustics
            4.8.4.6.1        What are Caustics?
            4.8.4.6.2        Applying Caustics to a Scene
            4.8.4.6.3        Caustics And Normals
         4.8.4.7          Using Iridescence
      4.8.5            Halos
         4.8.5.1          What are Halos?
         4.8.5.2          The Emitting Halo

            4.8.5.2.1        Starting with a Basic Halo
            4.8.5.2.2        Increasing the Brightness
            4.8.5.2.3        Adding Some Turbulence
            4.8.5.2.4        Resizing the Halo
            4.8.5.2.5        Using Frequency to Improve Realism
            4.8.5.2.6        Changing the Halo Color
         4.8.5.3          The Glowing Halo
         4.8.5.4          The Attenuating Halo
            4.8.5.4.1        Making a Cloud
            4.8.5.4.2        Scaling the Halo Container
            4.8.5.4.3        Adding Additional Halos
         4.8.5.5          The Dust Halo
            4.8.5.5.1        Starting With an Object Lit by a Spotlight
            4.8.5.5.2        Adding Some Dust
            4.8.5.5.3        Decreasing the Dust Density
            4.8.5.5.4        Making the Shadows Look Good
            4.8.5.5.5        Adding Turbulence
            4.8.5.5.6        Using a Coloured Dust
         4.8.5.6          Halo Pitfalls
            4.8.5.6.1        Where Halos are Allowed
            4.8.5.6.2        Overlapping Container Objects
            4.8.5.6.3        Multiple Attenuating Halos
            4.8.5.6.4        Halos and Hollow Objects
            4.8.5.6.5        Scaling a Halo Container
            4.8.5.6.6        Choosing a Sampling Rate
            4.8.5.6.7        Using Turbulence
   4.9              Working With Special Textures
      4.9.1            Working With Pigment Maps
      4.9.2            Working With Normal Maps
      4.9.3            Working With Texture Maps
      4.9.4            Working With List Textures
      4.9.5            What About Tiles?
      4.9.6            Average Function
      4.9.7            Working With Layered Textures
         4.9.7.1          Declaring Layered Textures
         4.9.7.2          Another Layered Textures Example
      4.9.8            When All Else Fails: Material Maps
      4.9.9            Limitations Of Special Textures
   4.10             Using Atmospheric Effects
      4.10.1           The Background
      4.10.2           The Sky Sphere
         4.10.2.1         Creating a Sky with a Color Gradient
         4.10.2.2         Adding the Sun
         4.10.2.3         Adding Some Clouds
      4.10.3           The Fog
         4.10.3.1         A Constant Fog
         4.10.3.2         Setting a Minimum Translucency
         4.10.3.3         Creating a Filtering Fog
         4.10.3.4         Adding Some Turbulence to the Fog
         4.10.3.5         Using Ground Fog
         4.10.3.6         Using Multiple Layers of Fog
         4.10.3.7         Fog and Hollow Objects
      4.10.4           The Atmosphere
         4.10.4.1         Starting With an Empty Room
         4.10.4.2         Adding Dust to the Room
         4.10.4.3         Choosing a Good Sampling Rate
         4.10.4.4         Using a Coloured Atmosphere
         4.10.4.5         Atmosphere Tips
            4.10.4.5.1       Choosing the Distance and Scattering Parameters
            4.10.4.5.2       Atmosphere and Light Sources
            4.10.4.5.3       Atmosphere Scattering Types
            4.10.4.5.4       Increasing the Image Resolution
            4.10.4.5.5       Using Hollow Objects and Atmosphere
      4.10.5           The Rainbow
         4.10.5.1         Starting With a Simple Rainbow
         4.10.5.2         Increasing the Rainbow's Translucency
         4.10.5.3         Using a Rainbow Arc
      4.10.6           Animation
         4.10.6.1         The Clock Variable: Key To It All
         4.10.6.2         Clock Dependant Variables And Multi-Stage Animation
         4.10.6.3         The Phase Keyword
         4.10.6.4         Do Not Use Jitter Or Crand
         4.10.6.5         INI File Settings
5                POV-Ray Reference
6                POV-Ray Options
   6.1              Setting POV-Ray Options
      6.1.1            Command Line Switches
      6.1.2            Using INI Files
      6.1.3            Using the POVINI Environment Variable
   6.2              Options Reference
      6.2.1            Animation Options
         6.2.1.1          External Animation Loop
         6.2.1.2          Internal Animation Loop
         6.2.1.3          Subsets of Animation Frames
         6.2.1.4          Cyclic Animation
         6.2.1.5          Field Rendering
      6.2.2            Output Options
         6.2.2.1          General Output Options
            6.2.2.1.1        Height and Width of Output
            6.2.2.1.2        Partial Output Options
            6.2.2.1.3        Interrupting Options
            6.2.2.1.4        Resuming Options
         6.2.2.2          Display Output Options
            6.2.2.2.1        Display Hardware Settings
            6.2.2.2.2        Display Related Settings
            6.2.2.2.3        Mosaic Preview
         6.2.2.3          File Output Options
            6.2.2.3.1        Output File Type
            6.2.2.3.2        Output File Name
            6.2.2.3.3        Output File Buffer
         6.2.2.4          CPU Utilization Histogram
            6.2.2.4.1        File Type
            6.2.2.4.2        File Name
            6.2.2.4.3        Grid Size
      6.2.3            Scene Parsing Options
         6.2.3.1          Input File Name
         6.2.3.2          Library Paths
         6.2.3.3          Language Version
         6.2.3.4          Removing User Bounding
      6.2.4            Shell-out to Operating System
         6.2.4.1          String Substitution in Shell Commands
         6.2.4.2          Shell Command Sequencing
         6.2.4.3          Shell Command Return Actions
      6.2.5            Text Output
         6.2.5.1          Text Streams
         6.2.5.2          Console Text Output
         6.2.5.3          Directing Text Streams to Files
         6.2.5.4          Help Screen Switches
      6.2.6            Tracing Options
         6.2.6.1          Quality Settings
         6.2.6.2          Radiosity Setting
         6.2.6.3          Automatic Bounding Control
         6.2.6.4          Anti-Aliasing Options
7                Scene Description Language
   7.1              Language Basics
      7.1.1            Identifiers and Keywords
      7.1.2            Comments

      7.1.3            Float Expressions
         7.1.3.1          Float Literals
         7.1.3.2          Float Identifiers
         7.1.3.3          Float Operators
      7.1.4            Vector Expressions
         7.1.4.1          Vector Literals
         7.1.4.2          Vector Identifiers
         7.1.4.3          Vector Operators
         7.1.4.4          Operator Promotion
      7.1.5            Specifying Colors
         7.1.5.1          Color Vectors
         7.1.5.2          Color Keywords
         7.1.5.3          Color Identifiers
         7.1.5.4          Color Operators
         7.1.5.5          Common Color Pitfalls
      7.1.6            Strings
         7.1.6.1          String Literals
         7.1.6.2          String Identifiers
      7.1.7            Built-in Identifiers
         7.1.7.1          Constant Built-in Identifiers
         7.1.7.2          Built-in Identifier 'clock'
         7.1.7.3          Built-in Identifier 'version'
      7.1.8            Functions
         7.1.8.1          Float Functions
         7.1.8.2          Vector Functions
         7.1.8.3          String Functions
   7.2              Language Directives
      7.2.1            Include Files
      7.2.2            Declare
         7.2.2.1          Declaring identifiers
      7.2.3            Default Directive
      7.2.4            Version Directive
      7.2.5            Conditional Directives
         7.2.5.1          IF ELSE Directives
         7.2.5.2          IFDEF Directives
         7.2.5.3          IFNDEF Directives
         7.2.5.4          SWITCH CASE and RANGE Directives
         7.2.5.5          WHILE Directive
      7.2.6            User Message Directives
         7.2.6.1          Text Message Streams
         7.2.6.2          Text Formatting
   7.3              POV-Ray Coordinate System
      7.3.1            Transformations
         7.3.1.1          Translate
         7.3.1.2          Scale
         7.3.1.3          Rotate
         7.3.1.4          Matrix Keyword
      7.3.2            Transformation Order
      7.3.3            Transform Identifiers
      7.3.4            Transforming Textures and Objects
   7.4              Camera
      7.4.1            Type of Projection
      7.4.2            Focal Blur
      7.4.3            Camera Ray Perturbation
      7.4.4            Placing the Camera
         7.4.4.1          Location and Look_At
         7.4.4.2          The Sky Vector
         7.4.4.3          The Direction Vector
         7.4.4.4          Angle
         7.4.4.5          Up and Right Vectors
            7.4.4.5.1        Aspect Ratio
            7.4.4.5.2        Handedness
         7.4.4.6          Transforming the Camera
      7.4.5            Camera Identifiers
   7.5              Objects
      7.5.1            Empty and Solid Objects
         7.5.1.1          Halo Pitfall
         7.5.1.2          Refraction Pitfall
      7.5.2            Finite Solid Primitives
         7.5.2.1          Blob
         7.5.2.2          Box
         7.5.2.3          Cone
         7.5.2.4          Cylinder
         7.5.2.5          Height Field
         7.5.2.6          Julia Fractal
         7.5.2.7          Lathe
         7.5.2.8          Prism
         7.5.2.9          Sphere
         7.5.2.10         Superquadric Ellipsoid
         7.5.2.11         Surface of Revolution
         7.5.2.12         Text
         7.5.2.13         Torus
      7.5.3            Finite Patch Primitives
         7.5.3.1          Bicubic Patch
         7.5.3.2          Disc
         7.5.3.3          Mesh
         7.5.3.4          Polygon
         7.5.3.5          Triangle and Smooth Triangle
      7.5.4            Infinite Solid Primitives
         7.5.4.1          Plane
         7.5.4.2          Poly, Cubic and Quartic
         7.5.4.3          Quadric
      7.5.5            Constructive Solid Geometry
         7.5.5.1          About CSG
         7.5.5.2          Inside and Outside
         7.5.5.3          Inverse
         7.5.5.4          Union
         7.5.5.5          Intersection
         7.5.5.6          Difference
         7.5.5.7          Merge
      7.5.6            Light Sources
         7.5.6.1          Point Lights
         7.5.6.2          Spotlights
         7.5.6.3          Cylindrical Lights
         7.5.6.4          Area Lights
         7.5.6.5          Shadowless Lights
         7.5.6.6          Looks_like
         7.5.6.7          Light Fading
         7.5.6.8          Atmosphere Interaction
         7.5.6.9          Atmospheric Attenuation
      7.5.7            Object Modifiers
         7.5.7.1          Clipped_By
         7.5.7.2          Bounded_By
         7.5.7.3          Hollow
         7.5.7.4          No_Shadow
         7.5.7.5          Sturm
   7.6              Textures
      7.6.1            Pigment
         7.6.1.1          Solid Color Pigments
         7.6.1.2          Color List Pigments
         7.6.1.3          Color Maps
         7.6.1.4          Pigment Maps
         7.6.1.5          Image Maps
            7.6.1.5.1        Specifying an Image Map
            7.6.1.5.2        The map_type Option
            7.6.1.5.3        The Filter and Transmit Bitmap Modifiers
            7.6.1.5.4        Using the Alpha Channel

         7.6.1.6          Quick Color
      7.6.2            Normal
         7.6.2.1          Slope Maps
         7.6.2.2          Normal Maps
         7.6.2.3          Bump Maps
            7.6.2.3.1        Specifying a Bump Map
            7.6.2.3.2        Bump_Size
            7.6.2.3.3        Use_Index and Use_Color
      7.6.3            Finish
         7.6.3.1          Ambient
         7.6.3.2          Diffuse Reflection Items
            7.6.3.2.1        Diffuse
            7.6.3.2.2        Brilliance
            7.6.3.2.3        Crand Graininess
         7.6.3.3          Highlights
            7.6.3.3.1        Phong Highlights
            7.6.3.3.2        Specular Highlight
            7.6.3.3.3        Metallic Highlight Modifier
         7.6.3.4          Specular Reflection
         7.6.3.5          Refraction
            7.6.3.5.1        Light Attenuation
            7.6.3.5.2        Faked Caustics
         7.6.3.6          Iridescence
      7.6.4            Halo
         7.6.4.1          Halo Mapping
         7.6.4.2          Multiple Halos
         7.6.4.3          Halo Type
            7.6.4.3.1        Attenuating
            7.6.4.3.2        Dust
            7.6.4.3.3        Emitting
            7.6.4.3.4        Glowing
         7.6.4.4          Density Mapping
            7.6.4.4.1        Box Mapping
            7.6.4.4.2        Cylindrical Mapping
            7.6.4.4.3        Planar Mapping
            7.6.4.4.4        Spherical Mapping
         7.6.4.5          Density Function
            7.6.4.5.1        Constant
            7.6.4.5.2        Linear
            7.6.4.5.3        Cubic
            7.6.4.5.4        Poly
         7.6.4.6          Halo Color Map
         7.6.4.7          Halo Sampling
            7.6.4.7.1        Number of Samples
            7.6.4.7.2        Super-Sampling
            7.6.4.7.3        Jitter
         7.6.4.8          Halo Modifiers
            7.6.4.8.1        Frequency Modifier
            7.6.4.8.2        Phase Modifier
            7.6.4.8.3        Transformation Modifiers
      7.6.5            Special Textures
         7.6.5.1          Texture Maps
         7.6.5.2          Tiles
         7.6.5.3          Material Maps
            7.6.5.3.1        Specifying a Material Map
      7.6.6            Layered Textures
      7.6.7            Patterns
         7.6.7.1          Agate
         7.6.7.2          Average
         7.6.7.3          Bozo
         7.6.7.4          Brick
         7.6.7.5          Bumps
         7.6.7.6          Checker
         7.6.7.7          Crackle
         7.6.7.8          Dents
         7.6.7.9          Gradient
         7.6.7.10         Granite
         7.6.7.11         Hexagon
         7.6.7.12         Leopard
         7.6.7.13         Mandel
         7.6.7.14         Marble
         7.6.7.15         Onion
         7.6.7.16         Quilted
         7.6.7.17         Radial
         7.6.7.18         Ripples
         7.6.7.19         Spiral1
         7.6.7.20         Spiral2
         7.6.7.21         Spotted
         7.6.7.22         Waves
         7.6.7.23         Wood
         7.6.7.24         Wrinkles
      7.6.8            Pattern Modifiers
         7.6.8.1          Transforming Patterns
         7.6.8.2          Frequency and Phase
         7.6.8.3          Waveform
         7.6.8.4          Turbulence
         7.6.8.5          Octaves
         7.6.8.6          Lambda
         7.6.8.7          Omega
         7.6.8.8          Warps
            7.6.8.8.1        Black Hole Warp
            7.6.8.8.2        Repeat Warp
            7.6.8.8.3        Turbulence Warp
         7.6.8.9          Bitmap Modifiers
            7.6.8.9.1        The once Option
            7.6.8.9.2        The "map_type" Option
            7.6.8.9.3        The interpolate Option
   7.7              Atmospheric Effects
      7.7.1            Atmosphere
      7.7.2            Background
      7.7.3            Fog
      7.7.4            Sky Sphere
      7.7.5            Rainbow
   7.8              Global Settings
      7.8.1            ADC_Bailout
      7.8.2            Ambient Light
      7.8.3            Assumed_Gamma
         7.8.3.1          Monitor Gamma
         7.8.3.2          Image File Gamma
         7.8.3.3          Scene File Gamma
      7.8.4            HF_Gray_16
      7.8.5            Irid_Wavelength
      7.8.6            Max_Trace_Level
      7.8.7            Max_Intersections
      7.8.8            Number_Of_Waves
      7.8.9            Radiosity
         7.8.9.1          How Radiosity Works
         7.8.9.2          Adjusting Radiosity
            7.8.9.2.1        brightness
            7.8.9.2.2        count
            7.8.9.2.3        distance_maximum
            7.8.9.2.4        error_bound
            7.8.9.2.5        gray_threshold
            7.8.9.2.6        low_error_factor
            7.8.9.2.7        minimum_reuse
            7.8.9.2.8        nearest_count
            7.8.9.2.9        radiosity_quality

            7.8.9.2.10       recursion_limit
         7.8.9.3          Tips on Radiosity

                             *** APPENDICES ***

A                Copyright
   A.1              General License Agreement
   A.2              Usage Provisions
   A.3              General Rules for All Distributions
   A.4              Definition of "Full Package"
   A.5              Conditions for On-Line Services and BBS's Including Inter
   A.6              Online or Remote Execution of POV-Ray
   A.7              Conditions for Distribution of Custom Versions
   A.8              Conditions for Commercial Bundling
   A.9              Retail Value of this Software
   A.10             Other Provisions
   A.11             Revocation of License
   A.12             Disclaimer
   A.13             Technical Support
B                Authors
C                Contacting the Authors
D                Postcards for POV-Ray Team Members
E                Credits
F                Tips and Hints
   F.1              Scene Design Tips
   F.2              Scene Debugging Tips
   F.3              Animation Tips
   F.4              Texture Tips
   F.5              Height Field Tips
   F.6              Converting "Handedness"
G                Frequently Asked Questions
   G.1              General Questions
   G.2              POV-Ray Options Questions
   G.3              Include File Questions
   G.4              Object Questions
      G.4.1            Height Field Questions
      G.4.2            Text Questions
   G.5              Atmospheric Questions
      G.5.1            Atmosphere Questions
      G.5.2            Fog Questions
H                Suggested Reading
I                Help on Help


1                Introduction

This document details the use of the Persistence of Vision(tm) Ray-Tracer
(POV-Ray(tm)). It is broken down into four parts: the installation guide, the
tutorial guide, the reference guide and the appendix. The first part (see
chapter "Program Description" and chapter "Quick Start") tells you where to
get and how to install POV-Ray. It also gives a short introduction to
ray-tracing. The tutorial explains step by step how to use the different
features of POV-Ray (see chapter "Beginning Tutorial"). The reference gives a
complete description of all features available in POV-Ray by explaining all
available options (set either by command line switches or by INI file
keywords) and the scene description language (see chapter "POV-Ray Reference"
, chapter "POV-Ray Options" and chapter "Scene Description Language"). The
appendix includes some tips and hints, suggested reading, contact addresses
and legal information.


1.1              Notation

Throughout this document the following notation is used to mark keywords of
the scene description language, command line switches, INI file keywords and
file names.

  name  scene description keyword
  name  command line option
  name  INI file keyword
  name  file name
  name  Internet address, Usenet group


In the plain ASCII version of the document there is no difference between the
different notations.

2                Program Description

The Persistence of Vision(tm) Ray-Tracer creates three-dimensional,
photo-realistic images using a rendering technique called ray-tracing. It
reads in a text file containing information describing the objects and
lighting in a scene and generates an image of that scene from the view point
of a camera also described in the text file. Ray-tracing is not a fast
process by any means, but it produces very high quality images with realistic
reflections, shading, perspective and other effects.

2.1              What is Ray-Tracing?

Ray-tracing is a rendering technique that calculates an image of a scene by
shooting rays into the scene. The scene is built from shapes, light sources,
a camera, materials, special features, etc.

For every pixel in the final image one or more viewing rays are shot into the
scene and tested for intersection with any of the objects in the scene.
Viewing rays originate from the viewer, represented by the camera, and pass
through the viewing window (representing the final image).

Every time an object is hit, the color of the surface at that point is
calculated. For this purpose the amount of light coming from any light source
in the scene is determined to tell whether the surface point lies in shadow
or not. If the surface is reflective or translucent new rays are set up and
traced in order to determine the contribution of the reflected and refracted
light to the final surface color.

Special features like inter-diffuse reflection (radiosity), atmospheric
effects and area lights make it necessary to shoot a lot of additional rays
into the scene for every pixel.

2.2              What is POV-Ray?

The Persistence of Vision(tm) Ray-Tracer was developed from DKBTrace 2.12
(written by David K. Buck and Aaron A. Collins) by a bunch of people, called
the POV-Team(tm), in their spare time. The headquarters of the POV-Team is in
the POVRAY forum on CompuServe (see "POV-Ray Forum on CompuServe" for more
details).

The POV-Ray(tm) package includes detailed instructions on using the
ray-tracer and creating scenes. Many stunning scenes are included with
POV-Ray so you can start creating images immediately when you get the
package. These scenes can be modified so you don't have to start from
scratch.

In addition to the pre-defined scenes, a large library of pre-defined shapes
and materials is provided. You can include these shapes and materials in your
own scenes by just including the name of the shape or material and their name
of their appropriate source file.

Here are some highlights of POV-Ray's features:

  * Spotlights, cylindrical lights and area lights for sophisticatedre.ures.
  * Basic shape primitives such as ... spheres, boxes, quadrics, cylinders,
  * Advanced shape primitives such as ... torii (donuts), bezier patches,
    height fields (mountains), blobs, quartics, smooth triangles, text,
    fractals, superquadrics, surfaces of revolution, prisms, polygons, lathes
  * Shapes can easily be combined to create new complex shapes using
    Constructive Solid Geometry (CSG). POV-Ray supports unions, merges,
  * Objects are assigned materials called textures (a texture describes the
  * Built-in color and normal patterns: Agate, Bozo, Bumps, Checker, Crackle,
    Dents, Granite, Gradient, Hexagon, Leopard, Mandel, Marble, Onion,
    Quilted, Ripples, Spotted, Sprial, Radial, Waves, Wood, Wrinkles and
  * Users can create their own textures or use pre-defined textures such as
  * Combine textures using layering of semi-transparent textures or tiles of
  * Display preview of image while computing (not available on all
  * Continue rendering a halted partial scene later.

2.3              Which Version of POV-Ray should you use?

POV-Ray can be used under MS-DOS, Windows 3.x, Windows for Workgroups 3.11,
Windows 95, Windows NT, Apple Macintosh 68k, Power PC, Commodore Amiga,
Linux, UNIX and other platforms.

The latest versions of the necessary files are available over CompuServe,
Internet, America Online and several BBS's. See section "Where to Find
POV-Ray Files" for more info.

2.3.1            IBM-PC and Compatibles

Currently there are three different versions for the IBM-PC running under
different operating systems (MS-DOS, Windows and Linux) as described below.

2.3.1.1          MS-DOS

The MS-DOS version runs under MS-DOS or as a DOS application under Windows
95, Windows NT, Windows 3.1 or Windows for Workgroups 3.11. It also runs
under OS/2 and Warp.

Required hardware and software:

  - About 6 meg disk space to install and 2-10 meg or more beyond that for
  - A text editor capable of editing plain ASCII text files. The EDIT program
  - Graphic file viewer capable of viewing GIF and perhaps TGA and PNG
formats.


Required POV-Ray files:

  - POVMSDOS.EXE - a self-extracting archive containing the program, sample
    scenes, standard include files and documentation in a hypertext help
    format with help viewer. This file may be split into smaller files for
    easier downloading. Check the directory of your download or ftp site to
    see if other files are needed.


Recommended:

  - SVGA display preferably with VESA interface and high color or true color
ability.


Optional: The source code is not needed to use POV-Ray. It is provided for
the curious and adventurous.

  - POVMSD_S.ZIP - The C source code for POV-Ray for MS-DOS Contains generic
    parts and MS-DOS specific parts. It does not include sample scenes,
    standard include files and documentation so you should also get the
  - A C compiler that can create 32-bit protected mode applications. We
    support Watcom 10.5a, Borland 4.52 with DOS Power Pack and limited
    graphics under DJGPP 1.12maint4. DJGPP 2.0 not supported.

2.3.1.2          Windows

The Windows version runs under Windows'95, Windows NT and under Windows 3.1
or 3.11 if Win32s extensions are added. Also runs under OS/2 Warp.

Required hardware and software:

  - About 12 meg disk space to install and 2-10 meg or more beyond that for
    working space.


Required POV-Ray files:

  - User archive POVWIN3.EXE - a self-extracting archive containing the
    program, sample scenes, standard include files and documentation. This
    file may be split into smaller files for easier downloading. Check the
    directory of your download or ftp site to see if other files are needed.


Recommended:

  - SVGA display preferably with high color or true color ability and drivers
installed.


Optional: The source code is not needed to use POV-Ray. It is provided for
the curious and adventurous.

  - POVWIN_S.ZIP --- The C source code for POV-Ray for Windows. Contains
    generic parts and Windows specific parts. It does not include sample
    scenes, standard include files and documentation so you should also get
  - POV-Ray can only be compiled using C compilers that create 32-bit Windows
    applications. We support Watcom 10.5a, Borland 4.52/5.0 compilers. The
    source code is not needed to use POV-Ray. It is provided for the curious
    and adventurous.

2.3.1.3          Linux

Required hardware and software:

  - About 6 meg disk space to install and 2-10 meg or more beyond that for
  - Any recent (1994 onwards) Linux kernel and support for ELF format
  - ELF libraries libc.so.5, libm.so.5 and one or both of libX11.so.6 or
libvga.so.1.


Required POV-Ray files:

  - POVLINUX.TGZ or POVLINUX.TAR.GZ - archive containing an official binary
    for each SVGALib and X-Windows modes. Also contains sample scenes,
    standard include files and documentation.


Recommended:

  - Graphic file viewer capable of viewing PPM, TGA or PNG formats.


Optional: The source code is not needed to use POV-Ray. It is provided for
the curious and adventurous.

  - POVUNI_S.TAR.GZ or POVUNI_S.TGZ - The C source code for POV-Ray for
    Linux. Contains generic parts and Linux specific parts. It does not
    include sample scenes, standard include files and documentation so you
  - The GNU C compiler and (optionally) the X include files and libraries and
    KNOWLEDGE OF HOW TO USE IT. Although we provide source code for generic
    Unix systems, we do not provide technical support on how to compile the
program.

2.3.2            Apple Macintosh

The Macintosh versions run under Apple's MacOS operating system version 7.0
or better, on any 68020/030/040-based Macintosh (with or without a floating
point coprocessor) or any of the Power Macintosh computers.

Required hardware and software:

  - A 68020 or better CPU without a floating point unit (LC or Performa or
  - A 68020 or better CPU *with* a floating point unit (Mac II or Quadra
  - About 6 meg free disk space to install and an additional 2-10 meg free).
  - Graphic file viewer utility capable of viewing Mac PICT, GIF and perhaps
    TGA and PNG formats (the shareware GIFConverter or GraphicConverter
    applications are good.)


Required POV-Ray files:

  - POVMACNF.SIT or POVMACNF.SIT.HQX - a Stuffit archive containing the
    non-FPU 68K Macintosh application, sample scenes, standard include files
  - POVMAC68.SIT or POVMAC68.SIT.HQX - a Stuffit archive containing the FPU
    68K Macintosh application, sample scenes, standard include files and
  - POVPMAC.SIT or POVPMAC.SIT.HQX - a Stuffit archive containing the native
    Power Macintosh application, sample scenes, standard include files and
documentation.


Recommended:

  - 8 meg or more RAM for 68K Macintosh; 16 meg or more for Power Macintosh
  - Color monitor preferred, 256 colors OK, but thousands or millions of
    colors is even better.


Optional: The source code is not needed to use POV-Ray. It is provided for
the curious and adventurous. POV-Ray can be compiled using Apple's MPW 3.3,
Metrowerks CodeWarrior 8 or Symantec 8.

  - POVMACS.SIT or POVMACS.SIT.HQX - The full C source code for POV-Ray for
    Macintosh. Contains generic parts and Macintosh specific parts. It does
    not include sample scenes, standard include files and documentation so
    you should also get the executable archive as well.

2.3.3            Commodore Amiga

The Amiga version comes in several flavors: 68000/68020 without FPU (not
recommended, very slow), 68020/68881(68882), 68030/68882 and 68040. There are
also two sub-versions, one with a CLI-only interface, and one with a GUI
(requires MUI 3.1). All versions run under OS2.1 and up. Support exists for
pensharing and window display under OS3.x with 256 color palettes and CybeGFX
display library support.

Required:

  - at least 2 meg of hard disk space for the necessities, 5-20 more
  - an ASCII text editor, GUI configurable to launch the editor of your
  - Graphic file viewer - POV-Ray outputs to PNG, Targa (TGA) and PPM
    formats, converters from the PPMBIN distribution are included to convert
    these to IFF ILBM files.


Required POV-Ray files:

  - POVAMI.LHA - a LHA archive containing executable, sample scenes, standard
    include files and documentation.


Recommended:

  - 24-bit display card (CyberGFX library supported)


As soon as a stable compiler is released for Amiga PowerPC systems, plans are
to add this to the flavor list.

Optional: The source code is not needed to use POV-Ray. It is provided for
the curious and adventurous.

  - POVLHA_S.ZIP - The C source code for POV-Ray for Amiga. Contains generic
    parts and Amiga specific parts. It does not include sample scenes,
    standard include files and documentation so you should also get the
    executable archive as well.

2.3.4            SunOS

Required hardware and software:

  - About 6 meg disk space to install and 2-10 meg or more beyond that for
  - SunOS 4.1.3 or other operating system capable of running such a binary
    (Solaris or possibly Linux for Sparc).


Required POV-Ray files:

  - POVSUNOS.TGZ or POVSUNOS.TAR.GZ - archive containing an official binary
    for each text-only and X-Windows modes. Also contains sample scenes,
    standard include files and documentation.


Recommended:

  - preferably 24-bit TrueColor display ability, although the X display code
  - Graphic file viewer capable of viewing PPM, TGA or PNG formats..


Optional: The source code is not needed to use POV-Ray. It is provided for
the curious and adventurous.

  - POVUNI_S.TGZ or POVUNI_S.TAR.GZ - The C source code for POV-Ray for UNIX.
    Contains generic UNIX parts and Linux specific parts. It does not include
    sample scenes, standard include files and documentation so you should
  - A C compiler and (optionally) the X include files and libraries and
    knowledge of how to use it.


Although we provide source code for generic Unix systems, we do not provide
technical support on how to compile the program.

2.3.5            Generic Unix

Required:

  - POVUNI_S.TGZ or POVUNI_S.TAR.GZ - The C source code for POV-Ray for Unix.
    Either archive contains full generic source, Unix and X-Windows specific
  - POVUNI_D.TGZ or POVUNI_D.TAR.GZ or any archive containing the sample
    scenes, standard include files and documentation. This could be the Linux
  - A C compiler for your computer and KNOWLEDGE OF HOW TO USE IT. Although
    we provide source code for generic Unix systems, we do not provide
  - A text editor capable of editing plain ASCII text files.


Recommended:

  - Graphic file viewer capable of viewing PPM, TGA or PNG formats.


Optional:

  - You will need the X-Windows include files as well. If you're not familiar
    with compiling programs for X-Windows you may need some help from someone
    who is knowledgeable at your installation because the X include files and
    libraries are not always in a standard place.

2.3.6            All Versions

Each executable archive includes full documentation for POV-Ray itself as
well as specific instructions for using POV-Ray with your type of platform.

All versions of the program share the same ray-tracing features like shapes,
lighting and textures. In other words, an IBM-PC can create the same pictures
as a Cray supercomputer as long as it has enough memory.

The user will want to get the executable that best matches their computer
hardware. See the section "Where to Find POV-Ray Files" for where to find
these files. You can contact those sources to find out what the best version
is for you and your computer.

2.3.7            Compiling POV-Ray

The following sections will help you to compile the portable C source code
into a working executable version of POV-Ray. They are only for those people
who want to compile a custom version of POV-Ray or to port it to an
unsupported platform or compiler.

The first question you should ask yourself before proceeding is Do  I really
need to compile POV-Ray at all? Official POV-Ray Team executable versions are
available for MS-DOS, Windows 3.1x/95/NT, Mac 68k, Mac Power PC, Amiga, Linux
for Intel x86, and SunOS. Other unofficial compiles may soon be available for
other platforms. If you do not intend to add any custom or experimental
features to the program and if an executable already exists for your platform
then you need not compile this program yourself.

If you do want to proceed you should be aware that you are very nearly on
your own. The following sections and other related compiling documentation
assume you know what you are doing. It assumes you have an adequate C
compiler installed and working. It assumes you know how to compile and link
large, multi-part programs using a make utility or an IDE project file if
your compiler supports them. Because makefiles and project files often
specify drive, directory or path information, we cannot promise our makefiles
or projects will work on your system. We assume you know how to make changes
to makefiles and projects to specify where your system libraries and other
necessary files are located.

In general you should not expect any technical support from the POV-Ray Team
on how to compile the program. Everything is provided here as is. All we can
say with any certainty is that we were able to compile it on our systems. If
it doesn't work for you we probably cannot tell you why.

There is no technical documentation for the source code itself except for the
comments in the source files. We try our best to write clear, well- commented
code but some sections are barely commented at all and some comments may be
out dated. We do not provide any technical support to help you to add
features. We do not explain how a particular feature works. In some
instances, the person who wrote a part of the program is no longer active in
the Team and we don't know exactly how it works.

When making any custom version of POV-Ray or any unofficial compile, please
make sure you read and follow all provisions of our license in "Copyright".
In general you can modify and use POV-Ray on your own however you want but if
you distribute your unofficial version you must follow our rules. You may not
under any circumstances use portions of POV-Ray source code in other
programs.

2.3.7.1          Directory Structure

POV-Ray source code is distributed in archives with files arranged in a
particular hierarchy of directories or folders. When extracting the archives
you should do so in a way that keeps the directory structure intact. In
general we suggest you create a directory called povray3 and extract the
files from there. The extraction will create a directory called source with
many files and sub-directories.

In general, there are separate archives for each hardware platform and
operating system but each of these archives may support more than one
compiler. For example here is the directory structure for the MS-DOS archive.


  SOURCE
  SOURCE\LIBPNG
  SOURCE\ZLIB
  SOURCE\MSDOS
  SOURCE\MSDOS\PMODE
  SOURCE\MSDOS\BORLAND
  SOURCE\MSDOS\DJGPP
  SOURCE\MSDOS\WATCOM


The source directory contains source files for the generic parts of POV-Ray
that are the same on all platforms. The source\libpng contains files for
compiling a library of routines used in reading and writing PNG (Portable
Network Graphics) image files. The source\zlib contains files for compiling a
library of routines used by libpng to compress and uncompress data streams.
All of these files are used by all platforms and compilers. They are in every
version of the source archives.

The source\msDOS directory contains all source files for the MS-DOS version
common to all supported MS-DOS compilers. The pmode sub-directory contains
source files for pmode.lib which is required by all MS-DOS versions. The
borland, djgpp, and watcom sub-directories contain source, makefiles and
project files for C compilers by Borland, DJGPP and Watcom.

The source\msDOS directory is only in the MS-DOS archive. Similarly the
Windows archive contains a source\windows directory. The Unix archive
contains source/unix etc.

The source\msDOS directory contains a file cmpl_msd.doc which contains
compiling information specific to the MS-DOS version. Other platform specific
directories contain similar cmpl_xxx.doc files and the compiler specific
sub-directories also contain compiler specific cmpl_xxx.doc files. Be sure to
read all pertinent cmpl_xxx.doc files for your platform and compiler.

2.3.7.2          Configuring POV-Ray Source

Every platform has a header file config.h that is generally in the platform
specific directory but may be in the compiler specific directory. Some
platforms have multiple versions of this file and you may need to copy or
rename it as config.h. This file is included in every module of POV-Ray. It
contains any prototypes, macros or other definitions that may be needed in
the generic parts of POV-Ray but must be customized for a particular platform
or compiler.

For example different operating systems use different characters as a
separator between directories and file names. MS-DOS uses back slash, Unix a
front slash or Mac a colon. The config.h file for MS-DOS and Windows contains
the following:

  #define FILENAME_SEPARATOR ''


which tells the generic part of POV-Ray to use a back slash.

Every customization that the generic part of the code needs has a default
setting in the file source\frame.h which is also included in every module
after config.h. The frame.h header contains many groups of defines such as
this:

  #ifndef FILENAME_SEPARATOR
  #define FILENAME_SEPARATOR '/'
  #endif


which basically says if we didn't define this previously in config.h then
here's a default value. See frame.h to see what other values you might wish
to configure.

If any definitions are used to specify platform specific functions you should
also include a prototype for that function. The file source\msDOS\config.h,
for example, not only contains the macro:

  #define POV_DISPLAY_INIT(w,h) MSDOS_Display_Init ((w), (h));


to define the name of the graphics display initialization function, it
contains the prototype:

  void MSDOS_Display_Init (int w, int h);


If you plan to port POV-Ray to an unsupported platform you should probably
start with the simplest, non-display generic Unix version. Then add new
custom pieces via the config.h file.

2.3.7.3          Conclusion

We understand that the above sections are only the most trivial first steps
but half the fun of working on POV-Ray source is digging in and figuring it
out on your own. That's how the POV-Ray Team members got started. We've tried
to make the code as clear as we can.

Be sure to read the cmpl_xxx.doc files in your platform specific and compiler
specific directories for some more minor help if you are working on a
supported platform or compiler.


2.4              Where to Find POV-Ray Files

The latest versions of the POV-Ray software are available from the following
sources.

2.4.1            POV-Ray Forum on CompuServe

The headquarters of POV-Ray are on CompuServe in the POVRAY forum, that is
managed by some of the team members. We meet there to share information,
useful programs and utilities and graphics created by POV-Ray. Everyone is
welcome to join in on the action on CIS:POVRAY. Hope to see you there! You
can get information on joining CompuServe by calling (800)848-8990 or visit
the CompuServe home page http://www.compuserve.com. Direct CompuServe access
is also available in Japan, Europe and many other countries.

2.4.2            Internet

The internet home of POV-Ray is reachable on the World Wide Web via the
address http://www.povray.org and via ftp as ftp.povray.org. Please stop by
often for the latest files, utilities, news and images from the official
POV-Ray internet site.

The comp.graphics.rendering.raytracing newsgroup has many competent POV-Ray
users that are very willing to share their knowledge. They generally ask that
you first browse a few files to see if someone has already answered the same
question, and of course, that you follow proper "netiquette". If you have any
doubts about the qualifications of the folks that frequent the group, a few
minutes spend at the Ray Tracing Competition pages at www.povray.org will
quickly convince you!

2.4.3            PC Graphics Area on America On-Line

There's an area now on America On-Line dedicated to POV-Ray support and
information. You can find it in the PC Graphics section of AOL. Jump keyword
POV (the keyword PCGRAPHICS brings you to the top of the graphics related
section). This area includes the Apple Macintosh executables also. It is best
if messages are left in the Company Support section. Currently, Bill Pulver
(BPulver) is our representative there.

2.4.4            The Graphics Alternative BBS in El Cerrito, CA

For those on the West coast, you may want to find the POV-Ray files on The
Graphics Alternative BBS. It's a great graphics BBS run by Adam Shiffman. TGA
is high quality, active and progressive BBS system which offers both quality
messaging and files to its 1300+ users.

  510-524-2780 (PM14400FXSA v.32bis 14.4k, Public)
  510-524-2165 (USR DS v.32bis/HST 14.4k, Subscribers)


2.4.5            PCGNet

The Professional CAD and Graphics Network (PCGnet) serves both the CAD and
Graphics communities by making information useful to them widely available.

Formerly known as ADEnet, PCGnet is a new network created from the ground up,
incorporating new nodes and focusing evenly on both CAD and graphics related
topics, including, but not limited to the following topics: design, drafting,
engineering, 2d and 3d modeling, multimedia, systems, raster imaging,
raytracing, 3d rendering and animation.

PCGnet is designed to serve the needs of all callers by stimulating interest
and generating support forums for active users who have an interest in the
CAD and graphics related topics previously mentioned; interest and support is
generated through PCGnet's message conferences, file sharing across the
network, and industry news and press releases. PCGnet's message conference
are moderated forums designed to accommodate friendly, yet professional and
informative discussion of CAD and graphics related subjects.

TGA BBS serves as the central hub for a large network of graphics-oriented
BBS systems around the world. Following is a concise listing of active PCGNet
nodes at the time of this writing. The POV-Team can not vouch for the
currency of this information, nor verify that any of these boards may carry
POV-Ray.

USA and Canada
  411-Exchange                 Alpharetta        GA      404-345-0008
  Autodesk Global Village      San Rafael        CA      415-507-5921
  CAD/Engineering Services     Hendersonville    TN      615-822-2539
  Canis Major                  Nashville         TN      615-385-4268
  CEAO BBS                     Columbus          OH      614-481-3194
  CHAOS BBS                    Columbia          MO      314-874-2930
  Joes CODE BBS                West Bloomfield   MI      810-855-0894
  John's Graphics              Brooklyn Park     MN      612-425-4436
  PC-AUG                       Phoenix           AZ      602-952-0638
  SAUG BBS                     Bellevue          WA      206-644-7115
  Space Command BBS            Kennewick         WA      509-735-4894
  The CAD/fx BBS               Mesa              AZ      602-835-0274
  The Drawing Board BBS        Anchorage         AK      907-349-5412
  The Graphics Alternative     El Cerrito        CA      510-524-2780
  The Happy Canyon             Denver            CO      303-759-3598
  The New Graphics BBS         Piscataway        NJ      908-271-8878
  The University               Shrewsbury Twp    NJ      908-544-8193
  The Virtual Dimension        Oceanside         CA      619-722-0746
  Time-Out BBS                 Sadsburyville     PA      610-857-2648

Australia
  MULTI-CAD Magazine BBS       Toowong QLD              61-7-878-2940
  My Computer Company          Erskineville NSW         61-2-557-1489
  Sydney PCUG Compaq BBS       Caringbah NSW            61-2-540-1842
  The Baud Room                Melbourne VIC            61-3-481-8720

Austria
  Austrian AutoCAD User Group  Graz                    43-316-574-426

Belgium
  Lucas Visions BBS            Boom                     32-3-8447-229

Denmark
  Horreby SuperBBS             Nykoebing Falster        45-53-84-7074

Finland
  DH-Online                    Jari Hiltunen           358-9-40562248
  Triplex BBS                  Helsinki                358-9-5062277

France
  CAD Connection               Montesson                33-1-39529854
  Zyllius BBS!                 Saint Paul                 33-93320505

Germany
  Ray BBS Munich               Munich                    49-89-984723
  Tower of Magic               Gelsenkirchen            49-209-780670

Netherlands
  BBS Bennekom: Fractal Board  Bennekom                 31-318-415331
  CAD-BBS                      Nieuwegein               31-30-6090287
                                                        31-30-6056353
  Foundation One               Baarn                    31-35-5422143

New Zealand
  The Graphics Connection      Wellington               64-4-566-8450
  The Graphics Connection II   New Plymouth             64-6-757-8092
  The Graphics Connection III  Auckland                 64-9-309-2237

Slovenia
  MicroArt                     Koper                     386-66-34986

Sweden
  Autodesk On-line             Gothenburg                46-31-401718

United Kingdom
  CADenza BBS                  Leicester, UK          44-116-259-6725
  Raytech BBS                  Tain, Scotland         44-1862-83-2020
  The Missing Link             Surrey, England        44-181-641-8593


Country or long distance dial numbers may require additional numbers to be
used. Consult your local phone company.

2.4.6            POV-Ray Related Books and CD-ROMs

The following items were produced by POV-Team members. Although they are only
current to POV-Ray 2.2 they will still be helpful. Steps are being taken to
update the POV-Ray CDROM to version 3.0, with a new version expected around
October 1996.

The books listed below have been recently listed as out-of-print but may
still be found in some bookstores or libraries (Visit
http://www.dnai.com:80/waite/ for more details).

  Ray Tracing Creations, 2d Ed.
  Chris Young and Drew Wells
  ISBN 1-878739-69-7
  Waite Group Press 1994
    700 pages with color insert and POV-Ray 2.2 on 3.5" MS-DOS disk.

  Ray Tracing Worlds with POV-Ray
  Alexander Enzmann, Lutz Kretzschmar, Chris Young,
  ISBN 1-878739-64-6
  Waite Group Press 1994
    Includes Moray 1.5x modeller and POV-Ray 2.2 on 3.5" MS-DOS disks.

  Ray Tracing for the Macintosh CD
  Eduard Schwan
  ISBN 1-878739-72-7
  Waite Group Press, 1994
    Comes with a CD-ROM full of scenes, images, and QuickTime movies,
    and an interactive keyword reference. Also a floppy with POV-Ray for
    those who don't have a CD ROM drive.


'The Official POV-Ray CDROM' The Official POV-Ray CDROM: The Official POV-Ray
CDROM is a compilation of images, scene source, program source, utilities and
tips on POV-Ray and 3D graphics from the Internet and Compuserve. This CD is
aimed not only at those who want to create their own images or do general 3D
programming work, but also at those who want simply to experience some
high-quality renderings done by some of the best POV-Ray artists, and to
learn from their source code. The CDROM contains over 500 ray-traced images.

It's a good resource for those learning POV-Ray as well as those who are
already proficient, and contains a Microsoft Windows-based interactive
tutorial. The disk comes with a fold-out poster and reference sheet. The CD
is compatible with DOS/Windows and Macintosh formats.

The CDROM is available for free retrieval and browsing on the World Wide Web
at http://www.povray.org/pov-cdrom. For more details you may also visit
http://www.povray.org/povcd.

3                Quick Start

The next section describes how to quickly install POV-Ray and render sample
scenes on your computer. It is assumed that you are using an IBM-PC
compatible computer with MS-DOS. For other platforms you must refer to the
specific documentation included in archive that contains POV-Ray.

3.1              Installing POV-Ray

Specific installation instructions are included with the executable program
for your computer. In general, there are two ways to install POV-Ray.

[ Note that the generic word "directory" is used throughout. Your operating
system may use another word (subdirectory, folder, etc.) ]

1) The messy way: Create a directory called POVRAY and copy all POV-Ray files
into it. Edit and run all files and programs from this directory. This method
works, but is not recommended.

Or the preferred way:

2) Create a directory called POVRAY and several subdirectories called
INCLUDE, DEMO, SCENES, UTIL. The self-extracting archives used in some
versions of the program will create subdirectories for you. If you create
your own, the file tree for this should look something like this:

    \--
      |
      +POVRAY --
               |
               +INCLUDE
               |
               +DEMO
               |
               +SCENES
               |
               +UTIL


Copy the executable file and docs into the directory POVRAY. Copy the
standard include files into the subdirectory INCLUDE. Copy the sample scene
files into the subdirectory SCENES. And copy any POV-Ray related utility
programs and their related files into the subdirectory UTIL. Your own scene
files will go into the SCENES subdirectory. Also, you'll need to add the
directories \POVRAY and \POVRAY\UTIL to your "search path" so the executable
programs can be run from any directory.

Note that some operating systems don't have an equivalent to the multi-path
search command.

The second method is a bit more difficult to set-up, but is preferred. There
are many files associated with POV-Ray and they are far easier to deal with
when separated into several directories.

3.2              Basic Usage

Notice: If you did not install the program using the install.exe system, the
examples and instructions given here may not work! The installation process
configures povray.ini and several important batch files. Without these files
configured, the examples herein may not work.

POV-Ray's basic purpose is to read a scene description written in the POV
language and to write an image file. The scene files are plain ASCII text
files that you create using a text editor. Dozens of sample files are
included with this package to illustrate the various features.

You invoke POV-Ray by typing a command at the MS-DOS prompt. The command is
povray and it must be followed by one or more command line switches. Each
switch begins with a plus or minus sign. Blanks separate the switches. The
switches may be upper or lower case.

Note: The examples in this documentation assume you installed POV-Ray in the
c:\povray3 directory. The installer will let you install POV-Ray anywhere and
will properly configure it for the drive and directory you specified. You
just substitute that drive and directory anywhere we tell you to use
c:\povray3. Change to that directory now. Then type the following command
line and press [ENTER]

  POVRAY +ISHAPES +D1


The +I command (for input) tells the program what file to read as input. If
you don't give an extension on the file name, .pov is assumed. Thus +Ishapes
tells it to read in shapes.pov to be rendered.

The +D switch (for display) tells the program to turn the graphic preview
display on. A -D would turn it off. The number "1" tells it what type of
display to use. Type "1" is the old fashioned standard generic VGA at 320 by
200 resolution and just 256 colors. This is pretty much guaranteed to work on
any VGA video system.

There are other options in effect besides those you typed on the command
line. They are stored in a file called povray.ini which was created by the
install system. POV-Ray automatically looks for this file in the same
directory where povray.exe resides. See "INI Files" and "Using INI Files" for
more information on povray.ini and other INI files.

When you enter the command shown above, you will see brightly colored
geometric shapes begin to appear as POV-Ray calculates the color of each
pixel row by row. You will probably be disappointed with the graphic display
results. That is because this is only a preview display. The actual image is
in full 24-bit color but we cannot display that high quality using simple VGA
with a fixed set of 256 colors. If your hardware supports the VESA interface
standard or you have a VESA TSR driver loaded, try running with +DG rather
than +D1. This will give you access to all of the various modes your video
hardware can use. If you have 15-bit or 16- bit high color capability try
+DGH or if you have 24-bit true color capability try +DGT to see the image in
all its glory. See section "Display Types" below for more information on
graphics preview.

When the program finishes, you will hear beeps. After admiring the image,
press [ENTER]. You will see a text screen of statistics. If the text is too
much to fit on the screen you may press [CURSOR UP] or [CURSOR DOWN] keys to
read more text. Notice that there are tabs at the bottom of the screen. Press
[CURSOR LEFT] or [CURSOR RIGHT] keys to view other interesting text
information. Press [ENTER] again to exit POV-Ray.

If you do not have high color or true color ability you will have to view the
image file to see the real colors. The image file shapes.tga is written to
your current directory. By default POV-Ray creates files in TGA format. This
is a standard format for storing 24-bit true-color images. You will need an
image viewing program to view the file. Such programs are usually available
from the same place where you obtained POV-Ray but a viewer is not included
in this package.

If you cannot view TGA files you may add the switch +FN and POV-Ray will
output PNG (Portable Network Graphic) format. If PNG format viewer is not
available then type the following

  T2G SHAPES


and press [ENTER]. This will run a batch file that invokes the tga2gif
program. The program will read your shapes.tga file, create an optimal 256
color palette and write a GIF format file shapes.gif. Most image viewing
programs support GIF.

3.2.1            Running Files in Other Directories

Normally POV-Ray only looks in the current directory for the files it needs.
It does not search your MS-DOS path for data files; it only searches for
programs. In the sample scene you just ran, file shapes.pov was in the
current directory so this was no problem. That scene also needed other files
but your povray.ini file tells POV-Ray other places to search for necessary
files.

If you allowed the install system to update your autoexec.bat file, then you
can change to any drive or directory and can run POV-Ray from that directory.
You will also be able to use the batch files and utilities that came with
this package in any directory. For future reference let's call the
"use-c:\povray3-in-your-path-plan" as plan one.

There are some circumstances where you may not want to put c:\povray3 in your
path. There is a limit of 128 characters in your path statement and you may
not have room for it. Try rendering the shapes example from a different
directory. If it doesn't work, then you forgot to re-boot your system so the
new path takes effect. If after re-booting it still doesn't work, it probably
means your path is too full. You will have to adopt a different plan.

Chances are, you already have several directories in your path. Most systems
have c:\DOS, c:\windows or some directory such as c:\utility already in the
path. We have provided several small batch files that you can copy to that
directory. For future reference we'll call the
"put-batch-files-in-a-directory-already-on-the-path-plan" as plan  two.

At any DOS prompt, type the word path and press [ENTER]. It will show you
what directories are already on your path. Then copy the following files from
your c:\povray3 directory to any of the directories already on your path. The
files are:

  RUNPOV.BAT RERUNPOV.BAT RUNPHELP.BAT T2G.BAT


Once you have copied these files, try the following example. In this case, do
not invoke the program with the command povray. Instead use runpov as
follows:

  cd \POVRAY3\POV3DEMO\SHOWOFF
  RUNPOV +ISUNSET3 +D1


This changes to the \povray3\pov3demo\showoff directory where the file
sunset3.pov is found. It runs the file runpov.bat. That batch file is set up
to run POV-Ray even if it is not on the DOS path. It also passes the switches
along to POV-Ray. These batch files have other uses, even if you are using
plan one as described above or plan three as described below. For more on
these batch files, see "Batch Files".

All of the early examples in this document assumed you were running POV-Ray
from the directory where it was installed such as c:\povray3. This approach
of always using the installation directory is in fact plan three. If you are
using this method, you need to tell POV-Ray where else to look for files. In
the case of sunset3.pov you could do this:

  POVRAY +IC:\POVRAY3\POV3DEMO\SHOWOFF\SUNSET3 +D1


However some scenes need more than one file. For example the directory drums2
that can be found under \povray3\povscn\level3 contains three files:
drums.pov, drums.inc and rednewt.gif all of which are required for that one
scene. In this case you should use the +L switch (for library) to add new
library paths to those that POV-Ray will search. You would render the scene
with this command.

  POVRAY +L\POVRAY3\POVSCN\LEVEL3\DRUMS2 +IDRUMS +D1


3.2.2            INI Files

There were more options used in these renderings than just the switches +I,
+D, and +L that you specify. When you run the program, POV- Ray automatically
looks for the file povray.ini in whatever directory that povray.exe is in.
The povray.ini file contains many options that control how POV-Ray works. We
have set this file up so that it is especially easy to run your first scene
with minimal problems. The file should be placed in the same directory as
povray.exe and it will automatically read when POV-Ray is run. If you ever
move povray.exe to a different directory, be sure to move povray.ini too.

Complete details on all of the available switches and options that can be
given on the command line or in povray.ini are given in "POV-Ray Options".

You may also create INI files of your own with switches or options similar to
povray.ini. If you put a file name on the command line without a plus or
minus sign before it, POV-Ray reads it as an INI file. Try this...

  POVRAY RES120 +ISHAPES +D1


This causes POV-Ray to look for a file called res120.ini which we have
provided. It sets your resolution to 120 by 90 pixels for a quick preview.
The following INI files have been provided for you.

  SLOW.INIII           Turns on radiosity and anti-aliasing; very slow but
  ZIPFLI.INI ZIPFLC.INICreate an FLI/FLC animation from zipped images. See
                       "ANIMATION TIPS" below.


You can create your own custom INI's which can contain any command in the
reference guide.

3.2.3            Alternatives to POVRAY.INI

The povray.ini file is supposed to hold your favorite global default options
that you want to use all the time. You should feel free to edit it with new
options that suit your needs. However it must be located in the same
directory as povray.exe or it won't be found. The DOS path isn't searched nor
will +L commands help because povray.ini is processed before any command line
switches.

If your povray.exe resides on a CD-ROM then you can't edit the povray.ini on
the CD. There is an alternative. You may use an environment variable to
specify an alternative global default.

In your autoexec.bat file add a line similar to this:

  set POVINI=D:\DIRECT\FILE.INI


which sets the POVINI environment variable to whatever drive, directory and
INI file you choose. If you specify any POVINI environment variable then
povray.ini is not read. This is true even if the file you named doesn't
exist. Note that you are specifying an entire path and file name. This is not
a pointer to a directory containing povray.ini. It is a pointer to the actual
file itself.

Note that the POVRAYOPT environment variable in previous versions of POV-Ray
is no longer supported.

3.2.4            Batch Files

We've already described how the file runpov.bat can be used as an alternative
to running POV-Ray directly. runpov.bat also has one other use. It uses the
+GI switch to create a file called rerun.ini. This makes it very easy to run
the same file over again with the same parameters. When creating your own
scene files you will probably make dozens of test renders. This is a very
valuable feature. Here is how it works... Suppose you render a scene as
follows:

  RUNPOV +IMYSCENE +D1 RES120


This renders myscene.pov at 120 by 90 resolution. Note there is no such
scene. This is hypothetical. After viewing it, you noticed a mistake which
you fixed with your text editor. To rerun the scene type:

  RERUNPOV


and that's all. It will rerun the same scene you just ran. Suppose you want
more detail on the next run. You can add more switches or INI files. For
example:

  RERUNPOV RES320


will rerun at higher resolution. Subsequent uses of rerunpov will be at 320
by 200 until you tell it differently. As another example, the +A switch turns
on anti-aliasing. Typing "rerunpov +A" reruns with anti- aliasing on. All
subsequent reruns will have it on until you do a "rerunpov -A" to turn it
off. Note if you do another runpov it starts over from your povray.ini
defaults and it overwrites the old rerun.ini.

Two other batch files are included. runphelp.bat is only used as an
alternative way to run povhelp from another directory. If you used
installation plan two then use runphelp.bat rather than povhelp.exe. This
batch file serves no other purpose.

Finally t2g.bat invokes the tga2gif.exe program for converting TGA files to
GIF files. You could run \FILE {tga2gif} directly but its default parameters
do not generally produce the best results. If you use T2G instead, it adds
some command line switches which work better. For a full list of switches
available for tga2gif, type tga2gif with no parameters and it will display
the available switches and options.

3.2.5            Display Types

You have already seen how to turn on graphics preview using +D1. Here are
details on other variations of the +D switch. Use -D to turn the display off.
If you use -D then you will probably want to add the +V switch to turn on
verbose status messages so you can monitor the progress of the rendering
while in progress.

The number "1" after the +D tells it what kind of video hardware to use. If
you use +D alone or +D0 then POV-Ray will attempt to auto detect your
hardware type. Use +D? to see a message about what type of hardware POV-Ray
found.

You may also explicitly tell POV-Ray what hardware to use. The following
chart lists all of the supported types.

  +DIDiamond Computer Systems SpeedSTAR 24X


The most common type is a VESA standard card which uses +DG. VESA is a
standard software interface that works on a wide variety of cards. Those
cards which do not have VESA support directly built-in, generally have a
video driver that you can load to provide VESA support. The program UniVBE is
a high quality universal VESA driver that may work for you. It can be found
at http://www.povray.org or possibly other POV-Ray sites.

The options listed above had been tested worked under earlier versions of
POV-Ray but there have been many changes in the program and we cannot
guarantee these all still work. If you can use VESA then do so. It has been
well tested and will give you the most flexibility.

After the +D and the type, you may specify a 3rd character that specifies the
palette type.

  +D?3Use 332 palette with dithering (default and best for VGA systems). This
      is a fixed palette of 256 colors with each color consisting 3-bits of
  +D?0Use HSV palette option for VGA display. This is a fixed palette of 256
      colors where colors are matched according to hue, saturation and
  +D?HUse HiColor option. Displays more than 32,000 colors with dithering.
      Supported on VESA, SpeedSTAR 24X, ATI XL HiColor and Tseng 4000 based
  +D?TFor Truecolor 24 bit cards. Use 24 bit color. Supported on the Diamond
      SpeedSTAR 24X and cards with 24-bit VESA support only.


Here are some examples:

   +D0H Auto detect the VGA display type and display the image to the
        screen as it's being worked on. Use the 15-bit HiColor chip and
        dithering to display more than 32,000 colors on screen.
   +D4  Display to a TSENG 4000 chipset VGA using the 332 palette option.
   +D4H Display to a TSENG 4000 chipset VGA using the HiColor option.
   +DG0 Display to a VESA VGA adapter and use the HSV palette option.
   +DG3 Display to a VESA VGA adapter and use the 332 palette option.
   +DGH Display to a VESA VGA adapter and use the HiColor option for
        over 32,000 colors.
   +DGT Display to a VESA VGA adapter and use the TrueColor option for
        over 16 million colors.


Note that your VESA BIOS must support these options in order for you to use
them. Some cards may support HiColor and/or TrueColor at the hardware level
but not through their VESA BIOS.

4                Beginning Tutorial

The beginning tutorial explains step by step how to use POV-Ray's scene
description language to create own scenes. The use of almost every feature of
POV-Ray's language is explained in detail. We will learn basic things like
placing cameras and light sources. We will also learn how to create a large
variety of objects and how to assign different textures to them. The more
sophisticated features like radiosity, halos and atmospheric effects will be
explained in detail.

The following sections explain the features in roughly the same order as they
are described in the reference guide.

4.1              Our First Image

We will create the scene file for a simple picture. Since ray-tracers thrive
on spheres, that is what we will render first.

4.1.1            Understanding POV-Ray's Coordinate System

First, we have to tell POV-Ray where our camera is and where it is looking.
To do this, we use 3D coordinates. The usual coordinate system for POV-Ray
has the positive y-axis pointing up, the positive x-axis pointing to the
right, and the positive z-axis pointing into the screen as follows:

          ^+Y
          |   /+Z
          |  /
          | /
  -X      |/        +X
  <-------|-------->
         /|
        / |
       /  |
    -Z/   |
          v-Y
The left-handed coordinate system (the z-axis is pointing away).

This kind of coordinate system is called a left-handed coordinate system. If
we use our left hand's fingers we can easily see why it is called
left-handed. We just point our thumb in the direction of the positive x-axis,
the index finger in the direction of the positive y-axis and the middle
finger in the positive z-axis direction. We can only do this with our left
hand. If we had used our right hand we would not have been able to point the
middle finger in the correct direction.

The left hand can also be used to determine rotation directions. To do this
we must perform the famous Computer Graphics Aerobics exercise. We hold up
our left hand and point our thumb in the positive direction of the axis of
rotation. Our fingers will curl in the positive direction of rotation.
Similarly if we point our thumb in the negative direction of the axis our
fingers will curl in the negative direction of rotation.

           ^
         +Y|   +Z/ _
           |    /_| |_  _
           |   _| | | |/ \
           |  | | | | |  |
           | /| | | | |  V
 -X        |/ | | | | |    +X
<----------+--|-|-|-|-|------>
          /|  |       ____
         / |  |         ___|
        /  |          /
       /   |   |      /
    -Z/  -Y|
     /     |
"Computer Graphics Aerobics" to determine the rotation direction.

In the above illustration, the left hand is curling around the x-axis. The
thumb points in the positive x direction and the fingers curl over in the
positive rotation direction.

If we want to use a right-handed system, as some CAD systems and modellers
do, the right vector in the camera specification needs to be changed. See the
detailed description in "Handedness". In a right-handed system we use our
right hand for the Aerobics.

There is some controversy over whether POV-Ray's method of doing a
right-handed system is really proper. To avoid problems we stick with the
left-handed system which is not in dispute.

4.1.2            Adding Standard Include Files

Using our personal favorite text editor, we create a file called demo.pov. We
then type in the following text. The input is case sensitive, so we have to
be sure to get capital and lowercase letters correct.

  #include "colors.inc"    // The include files contain
  #include "shapes.inc"    // pre-defined scene elements
  #include "finish.inc"
  #include "glass.inc"
  #include "metals.inc"
  #include "stones.inc"
  #include "woods.inc"


The first include statement reads in definitions for various useful colors.
The second include statement reads in some useful shapes. The next read
pre-defined finishes, glass, metal, stone and wood textures. It is a good
idea to have a look through them to see but a few of the many possible shapes
and textures available.

We should only include files we really need in our scene. Some of the include
files coming with POV-Ray are quite large and we should better save the
parsing time and memory if we don't need them. In the following examples we
will only use the colors.inc, finish.inc and stones.inc include files so we
will better remove the appropriate lines from our scene file.

We may have as many include files as needed in a scene file. Include files
may themselves contain include files, but we are limited to declaring
includes nested only ten levels deep.

Filenames specified in the include statements will be searched for in the
current directory first and, if not found, will then be searched for in
directories specified by any +L or Library_Path options active. This would
facilitate keeping all our "include" (.inc) files such as shapes.inc,
colors.inc and textures.inc in an "include" subdirectory, and giving an +L
switch on the command line to where our library of include files are.

4.1.3            Adding a Camera

The camera declaration describes where and how the camera sees the scene. It
gives x-, y- and z-coordinates to indicate the position of the camera and
what part of the scene it is pointing at. We describe the coordinates using a
three-part vector. A vector is specified by putting three numeric values
between a pair of angle brackets and separating the values with commas.

We add the following camera statement to the scene.

  camera {
    location <0, 2, -3>
    look_at  <0, 1,  2>
  }


Briefly, location <0,2,-3> places the camera up two units and back three
units from the center of the ray-tracing universe which is at <0,0,0>. By
default +z is into the screen and -z is back out of the screen.

Also look_at <0,1,2> rotates the camera to point at the coordinates <0,1,2>.
A point 5 units in front of and 1 unit lower than the camera. The look_at
point should be the center of attention of our image.

4.1.4            Describing an Object

Now that the camera is set up to record the scene, let's place a yellow
sphere into the scene. We add the following to our scene file:

  sphere {
    <0, 1, 2>, 2
    texture {
      pigment { color Yellow }
    }
  }


The first vector specifies the center of the sphere. In this example the x
coordinate is zero so it is centered left and right. It is also at y=1 or one
unit up from the origin. The z coordinate is 2 which is five units in front
of the camera, which is at z=-3. After the center vector is a comma followed
by the radius which in this case is two units. Since the radius is half the
width of a sphere, the sphere is four units wide.

4.1.5            Adding Texture to an Object

After we have defined the location and size of the sphere, we need to
describe the appearance of the surface. The texture block specifies these
parameters. Texture blocks describe the color, bumpiness and finish
properties of an object. In this example we will specify the color only. This
is the minimum we must do. All other texture options except color will use
default values.

The color we define is the way we want an object to look if fully
illuminated. If we were painting a picture of a sphere we would use dark
shades of a color to indicate the shadowed side and bright shades on the
illuminated side. However ray-tracing takes care of that. We pick the basic
color inherent in the object and POV-Ray brightens or darkens it depending on
the lighting in the scene. Because we are defining the basic color the object
actually has rather than how it looks the parameter is called pigment.

Many types of color patterns are available for use in a pigment statement.
The keyword color specifies that the whole object is to be one solid color
rather than some pattern of colors. We can use one of the color identifiers
previously defined in the standard include file colors.inc.

If no standard color is available for our needs, we may define our own color
by using the color keyword followed by red, green and blue keywords
specifying the amount of red, green and blue to be mixed. For example a nice
shade of pink can be specified by:

  color red 1.0 green 0.8 blue 0.8


The values after each keyword should be in the range from 0.0 to 1.0. Any of
the three components not specified will default to 0. A shortcut notation may
also be used. The following produces the same shade of pink:

  color rgb <1.0, 0.8, 0.8>


4.1.6            Defining a Light Source

One more detail is needed for our scene. We need a light source. Until we
create one, there is no light in this virtual world. Thus we add the line

  light_source { <2, 4, -3> color White}


to the scene file to get our first complete POV-Ray scene file as shown
below.

  #include "colors.inc"

  background { color Cyan }

  camera {
    location <0, 2, -3>
    look_at  <0, 1,  2>
  }

  sphere {
    <0, 1, 2>, 2
    texture {
      pigment { color Yellow }
    }
  }

  light_source { <2, 4, -3> color White}


The vector in the light_source statement specifies the location of the light
as two units to our right, four units above the origin and three units back
from the origin. The light source is invisible, it only casts light, so no
texture is needed.

That's it! We close the file and render a small picture of it using the
command

  povray +w160 +h120 +p +x +d0 -v -idemo.pov


If our computer does not use the command line, we have to read the platform
specific docs for the correct command to render the scene.

We may also set any other command line options we like. The scene is written
to the image file demo.tga (or some suffix other than .tga if our computer
uses a different default file format).

The scene we just traced isn't quite state of the art but we will have to
start with the basics before we soon get to much more fascinating features
and scenes.

4.2              Using the Camera


4.2.1            Using Focal Blur

Let's construct a simple scene to illustrate the use of focal blur. For this
example we will use a pink sphere, a green box and a blue cylinder with the
sphere placed in the foreground, the box in the center and the cylinder in
the background. A checkered floor for perspective and a couple of light
sources will complete the scene.

We create a new file called focaldem.pov and enter the following text

  #include "colors.inc"
  #include "shapes.inc"
  #include "textures.inc"

  #version 3.0

  global_settings {
    assumed_gamma 2.2 // for most PC monitors
    max_trace_level 5
  }

  sphere { <1, 0, -6>, 0.5
    finish {
      ambient 0.1
      diffuse 0.6
    }
    pigment { NeonPink }
  }

  box { <-1, -1, -1>, < 1,  1,  1>
    rotate <0, -20, 0>
    finish {
      ambient 0.1
      diffuse 0.6
    }
    pigment { Green }
  }

  cylinder { <-6, 6, 30>, <-6, -1, 30>, 3
    finish {
      ambient 0.1
      diffuse 0.6
    }
    pigment {NeonBlue}
  }

  plane { y, -1.0
    pigment {
      checker color Gray65 color Gray30
    }
  }

  light_source { <5, 30, -30> color White }

  light_source { <-5, 30, -30> color White }


Now we can proceed to place our focal blur camera to an appropriate viewing
position. Straight back from our three objects will yield a nice view.
Adjusting the focal point will move the point of focus anywhere in the scene.
We just add the following lines to the file:

  camera {
    location <0.0, 1.0, -10.0>
    look_at  <0.0, 1.0,  0.0>

  //  focal_point <-6, 1, 30>    // blue cylinder in focus
  //  focal_point < 0, 1,  0>    // green box in focus
    focal_point < 1, 1, -6>    // pink sphere in focus

    aperture 0.4     // a nice compromise
  //  aperture 0.05    // almost everything is in focus
  //  aperture 1.5     // much blurring

  //  blur_samples 4       // fewer samples, faster to render
    blur_samples 20      // more samples, higher quality image
  }


The focal point is simply the point at which the focus of the camera is at
its sharpest. We position this point in our scene and assign a value to the
aperture to adjust how close or how far away we want the focal blur to occur
from the focused area.

The aperture setting can be considered an area of focus. Opening up the
aperture has the effect of making the area of focus smaller while giving the
aperture a smaller value makes the area of focus larger. This is how we
control where focal blur begins to occur around the focal point.

The blur samples setting determines how many rays are used to sample each
pixel. Basically, the more rays that are used the higher the quality of the
resultant image, but consequently the longer it takes to render. Each scene
is different so we have to experiment. This tutorial has examples of 4 and 20
samples but we can use more for high resolution images. We should not use
more samples than is necessary to achieve the desired quality - more samples
take more time to render. The confidence and variance settings are covered in
section "Focal Blur".

We experiment with the focal point, aperture, and blur sample settings. The
scene has lines with other values that we can try by commenting out the
default line with double slash marks and un-commenting the line we wish to
try out. We make only one change at a time to see the effect on the scene.

Two final points when tracing a scene using a focal blur camera. We needn't
specify anti-aliasing (the \Clo{+A} switch) because the focal blur code uses
its one sampling method that automatically takes care of anti-aliasing. Focal
blur can only be used with the perspective camera.

4.3              Simple Shapes

So far we have just used the sphere shape. There are many other types of
shapes that can be rendered by POV-Ray. The following sections will describe
how to use some of the more simple objects as a replacement for the sphere
used above.

4.3.1            Box Object

The box is one of the most common objects used. We try this example in place
of the sphere:

  box {
    <-1, 0,   -1>,  // Near lower left corner
    < 1, 0.5,  3>   // Far upper right corner

    texture {
      T_Stone25     // Pre-defined from stones.inc
      scale 4       // Scale by the same amount in all
                    // directions
    }

    rotate y*20     // Equivalent to "rotate <0,20,0>"
  }


In the example we can see that a box is defined by specifying the 3D
coordinates of its opposite corners. The first vector must be the minimum x-,
y- and z-coordinates and the 2nd vector must be the maximum x-, y- and
z-values. Box objects can only be defined parallel to the axes of the world
coordinate system. We can later rotate them to any angle. Note that we can
perform simple math on values and vectors. In the rotate parameter we
multiplied the vector identifier y by 20. This is the same as <0,1,0>*20 or
<0,20,0>.

4.3.2            Cone Object

Here's another example showing how to use a cone:

  cone {
    <0, 1, 0>, 0.3    // Center and radius of one end
    <1, 2, 3>, 1.0    // Center and radius of other end

    texture { T_Stone25 scale 4 }
  }


The cone shape is defined by the center and radius of each end. In this
example one end is at location <0,1,0> and has a radius of 0.3 while the
other end is centered at <1,2,3> with radius=1. If we want the cone to come
to a sharp point we must use radius=0. The solid end caps are parallel to
each other and perpendicular to the cone axis. If we want an open cone with
no end caps we have to add the keyword open after the 2nd radius like this:

  cone {
    <0, 1, 0>, 0.3    // Center and radius of one end
    <1, 2, 3>, 1.0    // Center and radius of other end
    open              // Removes end caps

    texture { T_Stone25 scale 4 }
  }


4.3.3            Cylinder Object

We may also define a cylinder like this:

  cylinder {
    <0, 1, 0>,     // Center of one end
    <1, 2, 3>,     // Center of other end
    0.5            // Radius
    open           // Remove end caps

    texture { T_Stone25 scale 4 }
  }


4.3.4            Plane Object

Let's try out a computer graphics standard - The Checkered Floor. We add the
following object to the first version of the demo.pov file, the one including
the sphere.

  plane { <0, 1, 0>, -1
    pigment {
      checker color Red, color Blue
    }
  }


The object defined here is an infinite plane. The vector <0,1,0> is the
surface normal of the plane (i.e. if we were standing on the surface, the
normal points straight up). The number afterward is the distance that the
plane is displaced along the normal from the origin - in this case, the floor
is placed at y=-1 so that the sphere at y=1, radius=2, is resting on it.

We note that even though there is no texture statement there is an implied
texture here. We might find that continually typing statements that are
nested like texture {pigment} can get to be tiresome so POV-Ray let's us
leave out the texture statement under many circumstances. In general we only
need the texture block surrounding a texture identifier (like the T_Stone25
example above), or when creating layered textures (which are covered later).

This pigment uses the checker color pattern and specifies that the two colors
red and blue should be used.

Because the vectors <1,0,0>, <0,1,0> and <0,0,1> are used frequently, POV-Ray
has three built-in vector identifiers x, y and z respectively that can be
used as a shorthand. Thus the plane could be defined as:

  plane { y, -1
    pigment { ... }
  }


Note that we do not use angle brackets around vector identifiers.

Looking at the floor, we notice that the ball casts a shadow on the floor.
Shadows are calculated very accurately by the ray-tracer, which creates
precise, sharp shadows. In the real world, penumbral or "soft" shadows are
often seen. Later we will learn how to use extended light sources to soften
the shadows.

4.3.5            Standard Include Objects

The standard include file shapes.inc contains some pre-defined shapes that
are about the size of a sphere with a radius of one unit. We can invoke them
like this:

  #include "shapes.inc"

  object {
    UnitBox
    texture { T_Stone25 scale 4 }
    scale 0.75
    rotate <-20,25,0>
    translate y
  }


4.4              Advanced Shapes

After we have gained some experience with the simpler shapes available in
POV-Ray it is time to go on to the more advanced, thrilling shapes.

We should be aware that the shapes described below are not trivial to
understand. We needn't be worried though if we do not know how to use them or
how they work. We just try the examples and play with the features described
in the reference chapter. There is nothing better than learning by doing.

4.4.1            Bicubic Patch Object

Bicubic or Bezier patches are useful surface representations because they
allow an easy definition of surfaces using only a few control points. The
control points serve to determine the shape of the patch. Instead of defining
the vertices of triangles, we simply give the coordinates of the control
points. A single patch has 16 control points, four at each corner, and the
rest positioned to divide the patch into smaller sections. For ray-tracing
(or rendering) the patches are approximated using triangles. Bezier patches
are almost always created using a third party modeller so for this tutorial,
we will use moray (any other modeller that supports Bezier patches and
POV-Ray can also be used). We will use moray only to create the patch itself,
not the other elements of the scene.

Bezier patches are actually very useful and, with a little practice, some
pretty amazing things can be created with them. For our first tutorial, let's
make a sort of a teepee/tent shape using a single sheet patch.

First, we start moray and, from the main edit screen, we click on "CREATE".
We Name our object Teepee. The "CREATE BEZIER PATCH" dialogue box will
appear. We have to make sure that "SHEET" is depressed. We click on "OK,
CREATE". At the bottom of the main edit screen, we click on "EXTENDED EDIT".

We hold the cursor over the "TOP" view and right click to make the pop-up
menu appear. We click on "MAXIMIZE". We [ALT]-drag to zoom in a little. We
click on "MARK ALL", and under the transformation mode box, "UFRM SCL". We
drag the mouse to scale the patch until it is approximately four units wide.
We click on "TRANSLATE", and move the patch so that its center is over the
origin. We right click "MINIMIZE" and "UNMARK ALL".

We [SHIFT]-drag a box around the lower right control point to mark it. We
[ALT]-zoom into the "FRONT" view so that we can see the patch better. In the
"FRONT" view, we "TRANSLATE" that point 10 units along the negative z-axis
(we note that in MORAY z is up). We "UNMARK ALL". We repeat this procedure
for each of the other three corner points. We make sure we remember to
"UNMARK ALL" once each point has been translated. We should have a shape that
looks as though it is standing on four pointed legs. We "UNMARK ALL".

Working once again in the "TOP" view, we [SHIFT]-drag a box around the four
center control points to mark them. We right-click over the "TOP" view and
"MAXIMIZE". We click on "UFRM SCL" and drag the mouse to scale the four
points close together. We [ALT]-drag to zoom closer and get them as close
together as we can. We [ALT]-drag to zoom out, right click and "MINIMIZE".

In the "FRONT" view, we "TRANSLATE" the marked points 10 units along the
positive z-axis. We "UNMARK ALL". The resulting shape is quite interesting,
was simple to model, and could not be produced using CSG primitives. Now
let's use it in a scene.

We click on "DONE" to return to the main edit screen. We note that U_STEPS
and V_STEPS are both set to 3 and flatness is set to 0.01. We leave them
alone for now. We click on "FILES" and then "SAVE SEL" (save selection). We
name our new file teepee1.mdl. We press [F3] and open teepee1.mdl. There is
no need to save the original file. When teepee1 is open, we create a quick
"dummy" texture (moray will not allow us to export data without a texture).
We use white with default finish and name it TeePeeTex. We apply it to the
object, save the file and press [CTRL-F9]. moray will create two files:
teepee1.inc and teepee1.pov.

We exit moray and copy teepee1.inc and teepee1.pov into our working directory
where we are doing these tutorials. We create a new file called bezdemo.pov
and edit it as follows:

  #include "colors.inc"

  camera {
    location <0, .1, -60>
    look_at 0
    angle 40
  }

  background { color Gray25 }  //to make the patch easier to see

  light_source { <300, 300, -700> White }

  plane { y, -12
    texture {
      pigment {
        checker
        color Green
        color Yellow
      }
    }
  }


Using a text editor, we create and declare a simple texture for our teepee
object:

  #declare TeePeeTex = texture {
    pigment {
      color rgb <1, 1, 1,>
    }
    finish {
      ambient .2
      diffuse .6
    }
  }


We paste in the bezier patch data from teepee1.pov (the additional object
keywords added by moray were removed):

  bicubic_patch {
    type 1 flatness 0.0100 u_steps 3 v_steps 3,
    <-5.174134, 5.528420, -13.211995>,
    <-1.769023, 5.528420, 0.000000>,
    <1.636088, 5.528420, 0.000000>,
    <5.041199, 5.528420, -13.003932>,
    <-5.174134, 1.862827, 0.000000>,
    <0.038471, 0.031270, 18.101474>,
    <0.036657, 0.031270, 18.101474>,
    <5.041199, 1.862827, 0.000000>,
    <-5.174134, -1.802766, 0.000000>,
    <0.038471, 0.028792, 18.101474>,
    <0.036657, 0.028792, 18.101474>,
    <5.041199, -1.802766, 0.000000>,
    <-5.174134, -5.468359, -13.070366>,
    <-1.769023, -5.468359, 0.000000>,
    <1.636088, -5.468359, 0.000000>,
    <4.974128, -5.468359, -12.801446>
    texture {
      TeePeeTex
    }
    rotate -90*x  // to orient the object to LHC
    rotate 25*y   // to see the four "legs" better
  }



We add the above rotations so that the patch is oriented to POV-Ray's
left-handed coordinate system (remember the patch was made in moray in a
right handed coordinate system), so we can see all four legs. Rendering this
at 200x150 -a we see pretty much what we expect, a white teepee over a green
and yellow checkered plane. Let's take a little closer look. We render it
again, this time at 320x200.

Now we see that something is amiss. There appears to be sharp angling, almost
like faceting, especially near the top. This is indeed a kind of faceting and
is due to the U_STEPS and V_STEPS parameters. Let's change these from 3 to 4
and see what happens.

That's much better, but it took a little longer to render. This is an
unavoidable tradeoff. If we want even finer detail, we must use a U_STEPS and
V_STEPS value of 5 and set flatness to 0. But we must expect to use lots of
memory and an even longer tracing time.

Well, we can't just leave this scene without adding a few items just for
interest. We declare the patch object and scatter a few of them around the
scene:

  #declare TeePee = bicubic_patch {
    type 1 flatness 0.0100 u_steps 3 v_steps 3,
    <-5.174134, 5.528420, -13.211995>,
    <-1.769023, 5.528420, 0.000000>,
    <1.636088, 5.528420, 0.000000>,
    <5.041199, 5.528420, -13.003932>,
    <-5.174134, 1.862827, 0.000000>,
    <0.038471, 0.031270, 18.101474>,
    <0.036657, 0.031270, 18.101474>,
    <5.041199, 1.862827, 0.000000>,
    <-5.174134, -1.802766, 0.000000>,
    <0.038471, 0.028792, 18.101474>,
    <0.036657, 0.028792, 18.101474>,
    <5.041199, -1.802766, 0.000000>,
    <-5.174134, -5.468359, -13.070366>,
    <-1.769023, -5.468359, 0.000000>,
    <1.636088, -5.468359, 0.000000>,
    <4.974128, -5.468359, -12.801446>
    texture {
      TeePeeTex
     }
     rotate -90*x // to orient the object to LHC
     rotate 25*y  // to see the four "legs" better
  }

  object { TeePee }

  object { TeePee translate <8, 0, 8> }

  object { TeePee translate <-9, 0, 9> }

  object { TeePee translate <18, 0, 24> }

  object { TeePee translate <-18, 0, 24> }


That looks good. Let's do something about that boring gray background. We
delete the background declaration and replace it with:

  plane { y, 500
    texture {
      pigment { SkyBlue }
      finish { ambient 1 diffuse 0}
     }
     texture {
       pigment {
         bozo
         turbulence .5
         color_map {
           [0 White]
           [1 White filter 1]
         }
       }
       finish { ambient 1 diffuse 0 }
       scale <1000, 250, 250>
       rotate <5, 45, 0>
    }
  }


This adds a pleasing cirrus-cloud filled sky. Now, let's change the checkered
plane to rippled sand dunes:

  plane {y,-12
    texture {
      pigment {
        color <.85, .5, .15>
      }
      finish {
        ambient .25
        diffuse .6
        crand .5
      }
      normal {
        ripples .35
        turbulence .25
        frequency 5
      }
      scale 10
      translate 50*x
    }
  }


We render this at 320x240 -a. Not bad! Let's just add one more element. Let's
place a golden egg under each of the teepees. And since this is a bezier
patch tutorial, let's make the eggs out of bezier patches.

We return to moray and create another bezier patch. We name it Egg1 and
select "CYLINDRICAL 2 - PATCH" from the "CREATE BEZIER PATCH" dialogue box.
We click on "EXTENDED EDIT". We "MARK ALL" and rotate the patch so that the
cylinder lays on its side. We "UNMARK ALL". In the "FRONT" view, we
[SHIFT]-drag a box around the four points on the right end to mark them. In
the "SIDE" view, we right click and "MAXIMIZE". We [ALT]-drag to zoom in a
little closer. We "UFRM SCL" the points together as close as possible. We
zoom in closer to get them nice and tight. We zoom out, right click and
"MINIMIZE".

We click on "TRANSLATE" and drag the points to the left so that they are
aligned on the z-axis with the next group of four points. This should create
a blunt end to the patch. We repeat this procedure for the other end. We
"UNMARK ALL".

In the "FRONT" view, the control grid should be a rectangle now and the patch
should
be an ellipsoid. We [SHIFT]-drag a box around the upper right corner of the
control grid to mark those points. We then [SHIFT]-drag a box around the
lower right corner to mark those points as well. In the "SIDE" view, we "UFRM
SCL" the points apart a little to make that end of the egg a little wider
than the other. We "UNMARK ALL".

The egg may need a little proportional adjustment. We should be able to "MARK
ALL" and "LOCAL SCL" in the three views until we get it to look like an egg.
When we are satisfied that it does, we "UNMARK ALL" and click on done.
Learning from our teepee object, we now go ahead and change U_STEPS and
V_STEPS to 4.

We create a dummy texture, white with default finish, name it EggTex and
apply it to the egg. From the FILES menu, we "SAVE SEL" to filename egg1.mdl.
We load this file and export ([CTRL F9]). We exit moray and copy the files
egg1.inc and egg1.pov into our working directory.

Back in bezdemo.pov, we create a nice, shiny gold texture:

  #declare EggTex = texture {
    pigment { BrightGold }
    finish {
      ambient .1
      diffuse .4
      specular 1
      roughness 0.001
      reflection .5
      metallic
    }
  }


And while we're at it, let's dandy up our TeePeeTex texture:

  #declare TeePeeTex = texture {
    pigment { Silver }
    finish {
      ambient .1
      diffuse .4
      specular 1
      roughness 0.001
      reflection .5
      metallic
    }
  }


Now we paste in our egg patch data and declare our egg:

  #declare Egg = union { // Egg1
    bicubic_patch {
      type 1 flatness 0.0100 u_steps 4 v_steps 4,
      <2.023314, 0.000000, 4.355987>,
      <2.023314, -0.000726, 4.355987>,
      <2.023312, -0.000726, 4.356867>,
      <2.023312, 0.000000, 4.356867>,
      <2.032037, 0.000000, 2.734598>,
      <2.032037, -1.758562, 2.734598>,
      <2.027431, -1.758562, 6.141971>,
      <2.027431, 0.000000, 6.141971>,
      <-1.045672, 0.000000, 3.281572>,
      <-1.045672, -1.758562, 3.281572>,
      <-1.050279, -1.758562, 5.414183>,
      <-1.050279, 0.000000, 5.414183>,
      <-1.044333, 0.000000, 4.341816>,
      <-1.044333, -0.002947, 4.341816>,
      <-1.044341, -0.002947, 4.345389>,
      <-1.044341, 0.000000, 4.345389>
    }
    bicubic_patch {
      type 1 flatness 0.0100 u_steps 4 v_steps 4,
      <2.023312, 0.000000, 4.356867>,
      <2.023312, 0.000726, 4.356867>,
      <2.023314, 0.000726, 4.355987>,
      <2.023314, 0.000000, 4.355987>,
      <2.027431, 0.000000, 6.141971>,
      <2.027431, 1.758562, 6.141971>,
      <2.032037, 1.758562, 2.734598>,
      <2.032037, 0.000000, 2.734598>,
      <-1.050279, 0.000000, 5.414183>,
      <-1.050279, 1.758562, 5.414183>,
      <-1.045672, 1.758562, 3.281572>,
      <-1.045672, 0.000000, 3.281572>,
      <-1.044341, 0.000000, 4.345389>,
      <-1.044341, 0.002947, 4.345389>,
      <-1.044333, 0.002947, 4.341816>,
      <-1.044333, 0.000000, 4.341816>
    }
    texture { EggTex }
    translate <0.5, 0, -5>  // centers the egg around the origin
    translate -9.8*y        // places the egg on the ground
  }


We now place a copy of the egg under each teepee. This should require only
the x- and z-coordinates of each teepee to be changed:

  object { Egg }

  object { Egg translate <8, 0, 8> }

  object { Egg translate <-9, 0, 9> }

  object { Egg translate <18, 0, 24> }

  object { Egg translate <-18, 0, 24> }


Scene build with different Bezier patches.

We render this at 320x240 -A. Everything looks good so we run it again at
640x480 +A. Now we see that there is still some faceting near the top of the
teepees and on the eggs as well. The only solution is to raise U_STEPS and
V_STEPS from 4 to 5 and set flatness to 0 for all our bezier objects. We make
the changes and render it again at 640x480 +A.

4.4.2            Blob Object

Blobs are described as spheres and cylinders covered with "goo" which
stretches to smoothly join them (see section "Blob"). Ideal for modelling
atoms and molecules, blobs are also powerful tools for creating many smooth
flowing "organic" shapes.

A slightly more mathematical way of describing a blob would be to say that it
is one object made up of two or more component pieces. Each piece is really
an invisible field of force which starts out at a particular strength and
falls off smoothly to zero at a given radius. Where ever these components
overlap in space, their field strength gets added together (and yes, we can
have negative strength which gets subtracted out of the total as well). We
could have just one component in a blob, but except for seeing what it looks
like there is little point, since the real beauty of blobs is the way the
components interact with one another.

Let us take a simple example blob to start. Now, in fact there are a couple
different types of components but we will look at them a little later. For
the sake of a simple first example, let us just talk about spherical
components. Here is a sample POV-Ray code showing a basic camera, light, and
a simple two component blob (this scene is called blobdem1.pov):

  #include "colors.inc"

  camera {
    angle 15
    location <0,2,-10>
    look_at <0,0,0>
  }

  light_source { <10, 20, -10> color White }

  blob {
    threshold .65
    sphere { <.5,0,0>, .8, 1 pigment {Blue} }
    sphere { <-.5,0,0>,.8, 1 pigment {Pink} }

    finish { phong 1 }
  }


A simple, two-part blob.

The threshold is simply the overall strength value at which the blob becomes
visible. Any points within the blob where the strength matches the threshold
exactly form the surface of the blob shape. Those less than the threshold are
outside and those greater than are inside the blob.

We note that the spherical component looks a lot like a simple sphere object.
We have the sphere keyword, the vector representing the location of the
center of the sphere and the float representing the radius of the sphere. But
what is that last float value? That is the individual strength of that
component. In a spherical component, that is how strong the component's field
is at the center of the sphere. It will fall off in a linear progression
until it reaches exactly zero at the radius of the sphere.

Before we render this test image, we note that we have given each component a
different pigment. POV-Ray allows blob components to be given separate
textures. We have done this here to make it clearer which parts of the blob
are which. We can also texture the whole blob as one, like the finish
statement at the end, which applies to all components since it appears at the
end, outside of all the components. We render the scene and get a basic
kissing spheres type blob.

The image we see shows the spheres on either side, but they are smoothly
joined by that bridge section in the center. This bridge represents where the
two fields overlap, and therefore stay above the threshold for longer than
elsewhere in the blob. If that is not totally clear, we add the following two
objects to our scene and re-render (see file blobdem2.pov). We note that
these are meant to be entered as separate sphere objects, not more components
in the blob.

  sphere { <.5,0,0>, .8
    pigment { Yellow transmit .75 }
  }

  sphere { <-.5,0,0>, .8
    pigment { Green transmit .75 }
  }


The spherical components made visible.

Now the secrets of the kissing spheres are laid bare. These semi-transparent
spheres show where the components of the blob actually are. If we have not
worked with blobs before, we might be surprised to see that the spheres we
just added extend way farther out than the spheres that actually show up on
the blobs. That of course is because our spheres have been assigned a
starting strength of one, which gradually fades to zero as we move away from
the sphere's center. When the strength drops below the threshold (in this
case 0.65) the rest of the sphere becomes part of the outside of the blob and
therefore is not visible.

See the part where the two transparent spheres overlap? We note that it
exactly corresponds to the bridge between the two spheres. That is the region
where the two components are both contributing to the overall strength of the
blob at that point. That is why the bridge appears: that region has a high
enough strength to stay over the threshold, due to the fact that the combined
strength of two spherical components is overlapping there.

4.4.2.1          Component Types and Other New Features

The shape shown so far is interesting, but limited. POV-Ray has a few extra
tricks that extend its range of usefulness however. For example, as we have
seen, we can assign individual textures to blob components, we can also apply
individual transformations (translate, rotate and scale) to stretch, twist,
and squash pieces of the blob as we require. And perhaps most interestingly,
the blob code has been extended to allow cylindrical components.

Before we move on to cylinders, it should perhaps be mentioned that the old
style of components used in previous versions of POV-Ray still work. Back
then, all components were spheres, so it was not necessary to say sphere or
cylinder. An old style component had the form:

  component STRENGTH, RADIUS, <CENTER>


This has the same effect as a spherical component, just as we already saw
above. This is only useful for backwards compatibility. If we already have
POV-Ray files with blobs from earlier versions, this is when we would need to
recognize these components. We note that the old style components did not put
braces around the strength, radius and center, and of course, we cannot
independantly transform or texture them, so if we are modifying an older work
into a new version, it may arguably be of benefit to convert old style
components into spherical components anyway.

Now for something new and different: cylindrical components. It could be
argued that all we ever needed to do to make a roughly cylindrical portion of
a blob was string a line of spherical components together along a straight
line. Which is fine, if we like having extra to type, and also assuming that
the cylinder was oriented along an axis. If not, we would have to work out
the mathematical position of each component to keep it is a straight line.
But no more! Cylindrical components have arrived.

We replace the blob in our last example with the following and re-render. We
can get rid of the transparent spheres too, by the way.

  blob {
    threshold .65

    cylinder { <-.75,-.75,0>, <.75,.75,0>, .5, 1 }

    pigment { Blue }
    finish { phong 1 }
  }


We only have one component so that we can see the basic shape of the
cylindrical component. It is not quite a true cylinder - more of a sausage
shape, being a cylinder capped by two hemi-spheres. We think of it as if it
were an array of spherical components all closely strung along a straight
line.

As for the component declaration itself: simple, logical, exactly as we would
expect it to look (assuming we have been awake so far): it looks pretty much
like the declaration of a cylinder object, with vectors specifying the two
endpoints and a float giving the radius of the cylinder. The last float, of
course, is the strength of the component. Just as with spherical components,
the strength will determine the nature and degree of this component's
interaction with its fellow components. In fact, next let us give this fellow
something to interact with, shall we?

4.4.2.2          Complex Blob Constructs and Negative Strength

Beginning a new POV-Ray file called blobdem3.pov, we enter this somewhat more
complex example:

  #include "colors.inc"

  camera {
    angle 20
    location<0,2,-10>
    look_at<0,0,0>
  }

  light_source { <10, 20, -10> color White }

  blob {
    threshold .65

    sphere { <-.23,-.32,0>,.43, 1 scale <1.95,1.05,.8> }   //palm
    sphere { <+.12,-.41,0>,.43, 1 scale <1.95,1.075,.8> }  //palm
    sphere { <-.23,-.63,0>, .45, .75 scale <1.78, 1.3,1> } //midhand
    sphere { <+.19,-.63,0>, .45, .75 scale <1.78, 1.3,1> } //midhand
    sphere { <-.22,-.73,0>, .45, .85 scale <1.4, 1.25,1> } //heel
    sphere { <+.19,-.73,0>, .45, .85 scale <1.4, 1.25,1> } //heel

    cylinder { <-.65,-.28,0>, <-.65,.28,-.05>, .26, 1 }    //lower pinky
    cylinder { <-.65,.28,-.05>, <-.65, .68,-.2>, .26, 1 }  //upper pinky

    cylinder { <-.3,-.28,0>, <-.3,.44,-.05>, .26, 1 }      //lower ring
    cylinder { <-.3,.44,-.05>, <-.3, .9,-.2>, .26, 1 }     //upper ring

    cylinder { <.05,-.28,0>, <.05, .49,-.05>, .26, 1 }     //lower middle
    cylinder { <.05,.49,-.05>, <.05, .95,-.2>, .26, 1 }    //upper middle

    cylinder { <.4,-.4,0>, <.4, .512, -.05>, .26, 1 }      //lower index
    cylinder { <.4,.512,-.05>, <.4, .85, -.2>, .26, 1 }    //upper index

    cylinder { <.41, -.95,0>, <.85, -.68, -.05>, .25, 1 }  //lower thumb
    cylinder { <.85,-.68,-.05>, <1.2, -.4, -.2>, .25, 1 }  //upper thumb

    pigment { Flesh }
  }


A hand made with blobs.

As we can guess from the comments, we are building a hand here. After we
render this image, we can see there are a few problems with it. The palm and
heel of the hand would look more realistic if we used a couple dozen smaller
components rather than the half dozen larger ones we have used, and each
finger should have three segments instead of two, but for the sake of a
simplified demonstration, we can overlook these points. But there is one
thing we really need to address here: This poor fellow appears to have
horrible painful swelling of the joints!

A review of what we know of blobs will quickly reveal what went wrong. The
joints are places where the blob components overlap, therefore the combined
strength of both components at that point causes the surface to extend
further out, since it stays over the threshold longer. To fix this, what we
need are components corresponding to the overlap region which have a negative
strength to counteract part of the combined field strength. We add the
following components to our blob (see file blobdem4.pov).

  sphere { <-.65,.28,-.05>, .26, -1 } //counteract pinky knuckle bulge
  sphere { <-.65,-.28,0>, .26, -1 }   //counteract pinky palm bulge

  sphere { <-.3,.44,-.05>, .26, -1 }  //counteract ring knuckle bulge
  sphere { <-.3,-.28,0>, .26, -1 }    //counteract ring palm bulge

  sphere { <.05,.49,-.05>, .26, -1 }  //counteract middle knuckle bulge
  sphere { <.05,-.28,0>, .26, -1 }    //counteract middle palm bulge

  sphere { <.4,.512,-.05>, .26, -1 }  //counteract index knuckle bulge
  sphere { <.4,-.4,0>, .26, -1 }      //counteract index palm bulge

  sphere { <.85,-.68,-.05>, .25, -1 } //counteract thumb knuckle bulge
  sphere { <.41,-.7,0>, .25, -.89 }   //counteract thumb heel bulge


The hand without the swolen joints.

Much better! The negative strength of the spherical components counteracts
approximately half of the field strength at the points where to components
overlap, so the ugly, unrealistic (and painful looking) bulging is cut out
making our hand considerably improved. While we could probably make a yet
more realistic hand with a couple dozen additional components, what we get
this time is a considerable improvement. Any by now, we have enough basic
knowledge of blob mechanics to make a wide array of smooth, flowing organic
shapes!

4.4.3            Height Field Object

A height field is an object that has a surface that is determined by the
color value or palette index number of an image designed for that purpose.
With height fields, realistic mountains and other types of terrain can easily
be made. First, we need an image from which to create the height field. It
just so happens that POV-Ray is ideal for creating such an image.

We make a new file called image.pov and edit it to contain the following:

  #include "colors.inc"

  global_settings {
    assumed_gamma 2.2
    hf_gray_16
  }


The hf_gray_16 keyword causes the output to be in a special 16 bit grayscale
that is perfect for generating height fields. The normal 8 bit output will
lead to less smooth surfaces.

Now we create a camera positioned so that it points directly down the z-axis
at the origin.

  camera {
    location <0, 0, -10>
    look_at 0
  }


We then create a plane positioned like a wall at z=0. This plane will
completely fill the screen. It will be colored with white and gray wrinkles.

  plane { z, 10
    pigment {
      wrinkles
      color_map {
       [0 0.3*White]
       [1 White]
      }
    }
  }


Finally, create a light source.

  light_source { <0, 20, -100> color White }


We render this scene at 640x480 +A0.1 +FT. We will get an image that will
produce an excellent height field. We create a new file called hfdemo.pov and
edit it as follows:

  #include "colors.inc"


We add a camera that is two units above the origin and ten units back ...

  camera{
    location <0, 2, -10>
    look_at 0
    angle 30
  }


... and a light source.

  light_source{ <1000,1000,-1000> White }


Now we add the height field. In the following syntax, a Targa image file is
specified, the height field is smoothed, it is given a simple white pigment,
it is translated to center it around the origin and it is scaled so that it
resembles mountains and fills the screen.

  height_field {
    tga "image.tga"
    smooth
    pigment { White }
    translate <-.5, -.5, -.5>
    scale <17, 1.75, 17>
  }


We save the file and render it at 320x240 -A. Later, when we are satisfied
that the height field is the way we want it, we render it at a higher
resolution with anti-aliasing.

A height field created completely with POV-Ray.


4.4.4            Lathe Object

In the real world, lathe refers to a process of making patterned rounded
shapes by spinning the source material in place and carving pieces out as it
turns. The results can be elaborate, smoothly rounded, elegant looking
artifacts such as table legs, pottery, etc. In POV-Ray, a lathe object is
used for creating much the same kind of items, although we are refering to
the object itself rather than the means of production.

Here is some source for a really basic lathe (called lathdem1.pov).

  #include "colors.inc"

  camera {
    angle 10
    location <1, 9, -50>
    look_at <0, 2, 0>
  }

  light_source {
    <20, 20, -20> color White
  }

  lathe {
    linear_spline
    6,
    <0,0>, <1,1>, <3,2>, <2,3>, <2,4>, <0,4>
    pigment { Blue }
    finish {
      ambient .3
      phong .75
    }
  }


A simple lathe object.

We render this, and what we see is a fairly simply type of lathe, which looks
like a child's top. Let's take a look at how this code produced the effect.

First, a set of six points are declared which the raytracer connects with
lines. We note that there are only two components in the vectors which
describe these points. The lines that are drawn are assumed to be in the
x-y-plane, therefore it is as if all the z-components were assumed to be
zero. The use of a two-dimensional vector is mandatory (Attempting to use a
3D vector would trigger an error... with one exception, which we will explore
later in the discussion of splines).

Once the lines are determined, the ray-tracer rotates this line around the
y-axis, and we can imagine a trail being left through space as it goes, with
the surface of that trail being the surface of our object.

The specified points are connected with straight lines because we used the
linear_spline keyword. There are other types of splines available with the
lathe, which will result in smooth curving lines, and even rounded curving
points of transition, but we will get back to that in a moment.

First, we would like to digress a moment to talk about the difference between
a lathe and a surface of revolution object (SOR). The SOR object, described
in a separate tutorial, may seem terribly similar to the lathe at first
glance. It too declares a series of points and connects them with curving
lines and then rotates them around the y-axis. The lathe has certain
advantages, such as different kinds of splines, linear, quadratic and cubic,
and one more thing:

The simpler mathematics used by a SOR doesn't allow the curve to double back
over the same y-coordinates, thus, if using a SOR, any sudden twist which
cuts back down over the same heights that the curve previously covered will
trigger an error. For example, suppose we wanted a lathe to arc up from <0,0>
to <2,2>, then to dip back down to <4,0>. Rotated around the y-axis, this
would produce something like a gelatin mold - a rounded semi torus, hollow in
the middle. But with the SOR, as soon as the curve doubled back on itself in
the y-direction, it would become an illegal declaration.

Still, the SOR has one powerful strong point: because it uses simpler order
mathematics, it generally tends to render faster than an equivalent lathe. So
in the end, its a matter of: we use a SOR if its limitations will allow, but
when we need a more flexible shape, we go with the lathe instead.

4.4.4.1          Understanding The Concept of Splines

It would be helpful, in order to understand splines, if we had a sort of
Spline Workshop where we could practice manipulating types and points of
splines and see what the effects were like. So let's make one! Now that we
know how to create a basic lathe, it will be easy (see file lathdem2.pov):

  #include "colors.inc"

  camera {
    orthographic
    up <0, 5, 0>
    right <5, 0, 0>
    location <2.5, 2.5, -100>
    look_at <2.5, 2.5, 0>
  }

  /* set the control points to be used */

  #declare Red_Point    = <1.00, 0.00, 0>
  #declare Orange_Point = <1.75, 1.00, 0>
  #declare Yellow_Point = <2.50, 2.00, 0>
  #declare Green_Point  = <2.00, 3.00, 0>
  #declare Blue_Point   = <1.50, 4.00, 0>

  /* make the control points visible */

  cylinder { Red_Point, Red_Point - 20*z, .1
    pigment { Red }
    finish { ambient 1 }
  }

  cylinder { Orange_Point, Orange_Point - 20*z, .1
    pigment { Orange }
    finish { ambient 1 }
  }

  cylinder { Yellow_Point, Yellow_Point - 20*z, .1
    pigment { Yellow }
    finish { ambient 1 }
  }

  cylinder { Green_Point, Green_Point - 20*z, .1
    pigment { Green }
    finish { ambient 1 }
  }

  cylinder { Blue_Point, Blue_Point- 20*z, .1
    pigment { Blue }
    finish { ambient 1 }
  }

  /* something to make the curve show up */

  lathe {
    linear_spline
    5,
    Red_Point,
    Orange_Point,
    Yellow_Point,
    Green_Point,
    Blue_Point

    pigment { White }
    finish { ambient 1 }
  }


A simple "Spline Workshop".

Now, we take a deep breath. We know that all looks a bit weird, but with some
simple explanations, we can easily see what all this does.

First, we are using the orthographic camera. If we haven't read up on that
yet, a quick summary is: it renders the scene flat, eliminating perspective
distortion so that in a side view, the objects look like they were drawn on a
piece of graph paper (like in the side view of a modeller or CAD package).
There are several uses for this practical new type of camera, but here it is
allowing us to see our lathe and cylinders edge on, so that what we see is
almost like a cross section of the curve which makes the lathe, rather than
the lathe itself. To further that effect, we eliminated shadowing with the
ambient 1 finish, which of course also eliminates the need for lighting. We
have also positioned this particular side view so that <0,0> appears at the
lower left of our scene.

Next, we declared a set of points. We note that we used 3D vectors for these
points rather than the 2D vectors we expect in a lathe. That's the exception
we mentioned earlier. When we declare a 3D point, then use it in a lathe, the
lathe only uses the first two components of the vector, and whatever is in
the third component is simply ignored. This is handy here, since it makes
this example possible.

Next we do two things with the declared points. First we use them to place
small diameter cylinders at the locations of the points with the circular
caps facing the camera. Then we re-use those same vectors to determine the
lathe. Since trying to declare a 2D vector can have some odd results, and
isn't really what our cylinder declarations need anyway, we can take
advantage of the lathe's tendancy to ignore the third component by just
setting the z-coordinate in these 3D vectors to zero.

The end result is: when we render this code, we see a white lathe against a
black background showing us how the curve we've declared looks, and the
circular ends of the cylinders show us where along the x-y-plane our control
points are. In this case, it's very simple. The linear spline has been used
so our curve is just straight lines zig-zagging between the points. We change
the declarations of Red_Point and Blue_Point to read as follows (see file
lathdem3.pov).

  #declare Red_Point  = <2.00, 0.00, 0>
  #declare Blue_Point = <0.00, 4.00, 0>


Moving some points of the spline.

We re-render and, as we can see, all that happens is that the straight line
segments just move to accomodate the new position of the red and blue points.
Linear splines are so simple, we could manipulate them in our sleep, no?

Let's try something different. First, we change the points to the following
(see file lathdem4.pov).

  #declare Red_Point    = <1.00, 0.00, 0>
  #declare Orange_Point = <2.00, 1.00, 0>
  #declare Yellow_Point = <3.50, 2.00, 0>
  #declare Green_Point  = <2.00, 3.00, 0>
  #declare Blue_Point   = <1.50, 4.00, 0>



A quadratic spline lathe.

We then go down to the lathe declaration and change linear_spline to
quadratic_spline. We re-render and what do we have? Well, there's a couple of
things worthy of note this time. First, we will see that instead of straight
lines we have smooth arcs connecting the points. These arcs are made from
quadratic curves, so our lathe looks much more interesting this time. Also,
Red_Point is no longer connected to the curve. What happened?

Well, while any two points can determine a straight line, it takes three to
determine a quadratic curve. POV-Ray looks not only to the two points to be
connected, but to the point immediately preceeding them to determine the
formula of the quadratic curve that will be used to connect them. The problem
comes in at the beginning of the curve. Beyond the first point in the curve
there is no previous point. So we need to declare one. Therefore, when using
a quadratic spline, we must remember that the first point we specify is only
there so that POV-Ray can determine what curve to connect the first two
points with. It will not show up as part of the actual curve.

There's just one more thing about this lathe example. Even though our curve
is now put together with smooth curving lines, the transitions between those
lines is... well, kind of choppy, no? This curve looks like the lines between
each individual point have been terribly mismatched. Depending on what we are
trying to make, this could be acceptable, or, we might long for a more
smoothly curving shape. Fortunately, if the latter is true, we have another
option.

The quadratic spline takes longer to render than a linear spline. The math is
more complex. Still longer needs the cubic spline, yet, for a really smoothed
out shape, this is the only way to go. We go back into our example, and
simply replace quadratic_spline with cubic_spline (see file lathdem5.pov). We
render one more time, and take a look at what we have.

A cubic spline lathe.

While a quadratic spline takes three points to determine the curve, a cubic
needs four. So, as we might expect, Blue_Point has now dropped out of the
curve, just as Red_Point did, as the first and last points of our curve are
now only control points for shaping the curves between the remaining points.
But look at the transition from Orange_Point to Yellow_Point and then back to
Green_Point. Now, rather than looking mismatched, our curve segements look
like one smoothly joined curve.

The concept of splines is a handy and necessary one, which will be seen again
in the prism and polygon objects. But with a little tinkering we can quickly
get a feel for working with them.

4.4.5            Mesh Object

Mesh objects are very useful because they allow us to create objects
containing hundreds or thousands of triangles. Compared to a simple union of
triangles the mesh object stores the triangles more efficiently. Copies of
mesh objects need only a little additional memory because the triangles are
stored only once.

Almost every object can be approximated using triangles but we may need a lot
of triangles to create more complex shapes. Thus we will only create a very
simple mesh example. This example will show a very useful feature of the
triangles meshes though: a different texture can be assigned to each triangle
in the mesh.

Now let's begin. We will create a simple box with differently colored sides.
We create an empty file called meshdemo.pov and add the following lines.

  camera {
    location <20, 20, -50>
    look_at <0, 5, 0>
  }

  light_source { <50, 50, -50> color rgb<1, 1, 1> }

  #declare Red = texture {
    pigment { color rgb<0.8, 0.2, 0.2> }
    finish { ambient 0.2 diffuse 0.5 }
  }

  #declare Green = texture {
    pigment { color rgb<0.2, 0.8, 0.2> }
    finish { ambient 0.2 diffuse 0.5 }
  }

  #declare Blue = texture {
    pigment { color rgb<0.2, 0.2, 0.8> }
    finish { ambient 0.2 diffuse 0.5 }
  }


We must declare all textures we want to use inside the mesh before the mesh
is created. Textures cannot be specified inside the mesh due to the poor
memory performance that would result.

Now we add the mesh object. Three sides of the box will use individual
textures while the other will use the global mesh texture.

  mesh {
    /* top side */
    triangle { <-10, 10, -10>, <10, 10, -10>, <10, 10, 10>
      texture { Red }
    }
    triangle { <-10, 10, -10>, <-10, 10, 10>, <10, 10, 10>
      texture { Red }
    }
    /* bottom side */
    triangle { <-10, -10, -10>, <10, -10, -10>, <10, -10, 10> }
    triangle { <-10, -10, -10>, <-10, -10, 10>, <10, -10, 10> }
    /* left side */
    triangle { <-10, -10, -10>, <-10, -10, 10>, <-10, 10, 10> }
    triangle { <-10, -10, -10>, <-10, 10, -10>, <-10, 10, 10> }
    /* right side */
    triangle { <10, -10, -10>, <10, -10, 10>, <10, 10, 10>
      texture { Green }
    }
    triangle { <10, -10, -10>, <10, 10, -10>, <10, 10, 10>
      texture { Green }
    }
    /* front side */
    triangle { <-10, -10, -10>, <10, -10, -10>, <-10, 10, -10>
      texture { Blue }
    }
    triangle { <-10, 10, -10>, <10, 10, -10>, <10, -10, -10>
      texture { Blue }
    }
    /* back side */
    triangle { <-10, -10, 10>, <10, -10, 10>, <-10, 10, 10> }
    triangle { <-10, 10, 10>, <10, 10, 10>, <10, -10, 10> }
    texture {
      pigment { color rgb<0.9, 0.9, 0.9> }
      finish { ambient 0.2 diffuse 0.7 }
    }
  }


Tracing the scene at 320x240 we will see that the top, right and front side
of the box have different textures. Though this is not a very impressive
example it shows what we can do with mesh objects. More complex examples,
also using smooth triangles, can be found under the scene directory as
chesmsh.pov and robotmsh.pov.

4.4.6            Polygon Object

The polygon object can be used to create any planar, n-sided shapes like
squares, rectangles, pentagons, hexagons, octagons, etc.

A polygon is defined by a number of points that describe its shape. Since
polygons have to be closed the first point has to be repeated at the end of
the point sequence.

In the following example we will create the word POV using just one polygon
statement.

We start with thinking about the points we need to describe the desired
shape. We want the letters to lie in the x-y-plane with the letter O being at
the center. The letters extend from y=0 to y=1. Thus we get the following
points for each letter (the z coordinate is automatically set to zero).

Letter P (outer polygon):
    <-0.8, 0.0>, <-0.8, 1.0>,
    <-0.3, 1.0>, <-0.3, 0.5>,
    <-0.7, 0.5>, <-0.7, 0.0>

Letter P (inner polygon):
    <-0.7, 0.6>, <-0.7, 0.9>,
    <-0.4, 0.9>, <-0.4, 0.6>

Letter O (outer polygon):
    <-0.25, 0.0>, <-0.25, 1.0>,
    < 0.25, 1.0>, < 0.25, 0.0>

Letter O (inner polygon):
    <-0.15, 0.1>, <-0.15, 0.9>,
    < 0.15, 0.9>, < 0.15, 0.1>

Letter V:
    <0.45, 0.0>, <0.30, 1.0>,
    <0.40, 1.0>, <0.55, 0.1>,
    <0.70, 1.0>, <0.80, 1.0>,
    <0.65, 0.0>


Both letters P and O have a hole while the letter V consists of only one
polygon. We'll start with the letter V because it is easier to define than
the other two letters.

We create a new file called polygdem.pov and add the following text.

  camera {
    orthographic
    location <0, 0, -10>
    right 1.3 * 4/3 * x
    up 1.3 * y
    look_at <0, 0.5, 0>
  }

  light_source { <25, 25, -100> color rgb 1 }

  polygon {
    8,

    <0.45, 0.0>, <0.30, 1.0>, // Letter "V"
    <0.40, 1.0>, <0.55, 0.1>,
    <0.70, 1.0>, <0.80, 1.0>,
    <0.65, 0.0>,
    <0.45, 0.0>

    pigment { color rgb <1, 0, 0> }
  }


As noted above the polygon has to be closed by appending the first point to
the point sequence. A closed polygon is always defined by a sequence of
points that ends when a point is the same as the first point.

After we have created the letter V we'll continue with the letter P. Since it
has a hole we have to find a way of cutting this hole into the basic shape.
This is quite easy. We just define the outer shape of the letter P, which is
a closed polygon, and add the sequence of points that describes the hole,
which is also a closed polygon. That's all we have to do. There'll be a hole
where both polygons overlap.

In general we will get holes whenever an even number of sub-polygons inside a
single polygon statement overlap. A sub-polygon is defined by a closed
sequence of points.

The letter P consists of two sub-polygons, one for the outer shape and one
for the hole. Since the hole polygon overlaps the outer shape polygon we'll
get a hole.

After we have understood how multiple sub-polygons in a single polygon
statement work, it is quite easy to add the missing O letter.

Finally, we get the complete word POV.

  polygon {
    30,

    <-0.8, 0.0>, <-0.8, 1.0>,    // Letter "P"
    <-0.3, 1.0>, <-0.3, 0.5>,    // outer shape
    <-0.7, 0.5>, <-0.7, 0.0>,
    <-0.8, 0.0>,

    <-0.7, 0.6>, <-0.7, 0.9>,    // whole
    <-0.4, 0.9>, <-0.4, 0.6>,
    <-0.7, 0.6>

    <-0.25, 0.0>, <-0.25, 1.0>,  // Letter "O"
    < 0.25, 1.0>, < 0.25, 0.0>,  // outer shape
    <-0.25, 0.0>,

    <-0.15, 0.1>, <-0.15, 0.9>,  // whole
    < 0.15, 0.9>, < 0.15, 0.1>,
    <-0.15, 0.1>,

    <0.45, 0.0>, <0.30, 1.0>,    // Letter "V"
    <0.40, 1.0>, <0.55, 0.1>,
    <0.70, 1.0>, <0.80, 1.0>,
    <0.65, 0.0>,
    <0.45, 0.0>

    pigment { color rgb <1, 0, 0> }
  }


4.4.7            Prism Object

The prism is essentially a polygon or closed curve which is swept along a
linear path. We can imagine the shape so swept leaving a trail in space, and
the surface of that trail is the surface of our prism. The curve or polygon
making up a prism's face can be a composite of any number of sub-shapes, can
use any kind of three different splines, and can either keep a constant width
as it is swept, or slowly tapering off to a fine point on one end. But before
this gets too confusing, let's start one step at a time with the simplest
form of prism. We enter and render the following POV code (see file
prismdm1.pov).

  #include "colors.inc"

  camera {
    angle 20
    location <2, 10, -30>
    look_at <0, 1, 0>
  }

  light_source { <20, 20, -20> color White }

  prism {
    linear_sweep
    linear_spline
    0, // sweep the following shape from here ...
    1, // ... up through here
    7, // the number of points making up the shape ...

    <3,5>, <-3,5>, <-5,0>, <-3,-5>, <3, -5>, <5,0>, <3,5>

    pigment { Green }
  }


A hexagonal prism shape.

This produces a hexagonal polygon, which is then swept from y=0 through y=1.
In other words, we now have an extruded hexagon. One point to note is that
although this is a six sided figure, we have used a total of seven points.
That is because the polygon is supposed to be a closed shape, which we do
here by making the final point the same as the first. Technically, with
linear polygons, if we didn't do this, POV-Ray would automatically join the
two ends with a line to force it to close, although a warning would be
issued. However, this only works with linear splines, so we mustn't get too
casual about those warning messages!

4.4.7.1          Teaching An Old Spline New Tricks

If we followed the section on splines covered under the lathe tutorial (see
section "Understanding The Concept of Splines"), we know that there are two
additional kinds of splines besides linear: the quadratic and the cubic
spline. Sure enough, we can use these with prisms to make a more free form,
smoothly curving type of prism.

There is just one catch, and we should read this section carefully to keep
from tearing our hair out over mysterious too few points in  prism messages
which keep our prism from rendering. We can probably guess where this is
heading: how to close a non-linear spline. Unlike the linear spline, which
simply draws a line between the last and first points if we forget to make
the last point equal to the first, quadratic and cubic splines are a little
more fussy.

First of all, we remember that quadratic splines determine the equation of
the curve which connects any two points based on those two points and the
previous point, so the first point in any quadratic spline is just a control
point and won't actually be part of the curve. What this means is: when we
make our shape out of a quadratic spline, we must match the second point to
the last, since the first point is not on the curve - it's just a control
point needed for computational purposes.

Likewise, cubic splines need both the first and last points to be control
points, therefore, to close a shape made with a cubic spline, we must match
the second point to the second from last point. If we don't match the correct
points on a quadratic or cubic shape, that's when we will get the too few
points in prism error. POV-Ray is still waiting for us to close the shape,
and when it runs out of points without seeing the closure, an error is
issued.

Confused? Okay, how about an example? We replace the prism in our last bit of
code with this one (see file prismdm2.pov).

  prism {
    cubic_spline
    0, // sweep the following shape from here ...
    1, // ... up through here
    6, // the number of points making up the shape ...

    < 3, -5>, // point#1 (control point... not on curve)
    < 3,  5>, // point#2  ... THIS POINT ...
    <-5,  0>, // point#3
    < 3, -5>, // point#4
    < 3,  5>, // point#5 ... MUST MATCH THIS POINT
    <-5,  0>  // point#6 (control point... not on curve)

    pigment { Green }
  }


A cubic, triangular prism shape.

This simple prism produces what looks like an extruded triangle with its
corners sanded smoothly off. Points two, three and four are the corners of
the triangle and point five closes the shape by returning to the location of
point two. As for points one and six, they are our control points, and aren't
part of the shape - they're just there to help compute what curves to use
between the other points.

4.4.7.2          Smooth Transitions

Now a handy thing to note is that we have made point one equal point four,
and also point six equals point three. Yes, this is important. Although this
prism would still be legally closed if the control points were not what we've
made them, the curve transitions between points would not be as smooth. We
change points one and six to <4,6> and <0,7> respectively and re-render to
see how the back edge of the shape is altered (see file prismdm3.pov).

To put this more generally, if we want a smooth closure on a cubic spline, we
make the first control point equal to the third from last point, and the last
control point equal to the third point. On a quadratic spline, the trick is
similar, but since only the first point is a control point, make that equal
to the second from last point.

4.4.7.3          Multiple Sub-Shapes

Just as with the polygon object (see section "Polygon Object") the prism is
very flexible, and allows us to make one prism out of several sub-prisms. To
do this, all we need to do is keep listing points after we have already
closed the first shape. The second shape can be simply an add on going off in
another direction from the first, but one of the more interesting features is
that if any even number of sub-shapes overlap, that region where they overlap
behaves as though it has been cut away from both sub-shapes. Let's look at
another example. Once again, same basic code as before for camera, light and
so forth, but we substitute this complex prism (see file prismdm4.pov).

  prism {
    linear_sweep
    cubic_spline
    0,  // sweep the following shape from here ...
    1,  // ... up through here
    18, // the number of points making up the shape ...

    <3,-5>, <3,5>, <-5,0>, <3, -5>, <3,5>, <-5,0>, // sub-shape #1
    <2,-4>, <2,4>, <-4,0>, <2,-4>, <2,4>, <-4,0>,  // sub-shape #2
    <1,-3>, <1,3>, <-3,0>, <1, -3>, <1,3>, <-3,0>  // sub-shape #3

    pigment { Green }
  }


Using sub-shapes to create a more complex shape.

For readability purposes, we have started a new line every time we moved on
to a new sub-shape, but the ray-tracer of course tells where each shape ends
based on whether the shape has been closed (as described earlier). We render
this new prism, and look what we've got. It's the same familiar shape, but it
now looks like a smaller version of the shape has been carved out of the
center, then the carved piece was sanded down even smaller and set back in
the hole.

Simply, the outer rim is where only sub-shape one exists, then the carved out
part is where sub-shapes one and two overlap. In the extreme center, the
object reappears because sub-shapes one, two, and three overlap, returning us
to an odd number of overlapping pieces. Using this technique we could make
any number of extremely complex prism shapes!

4.4.7.4          Conic Sweeps And The Tapering Effect

In our original prism, the keyword linear_sweep is actually optional. This is
the default sweep assumed for a prism if no type of sweep is specified. But
there is another, extremely useful kind of sweep: the conic sweep. The basic
idea is like the original prism, except that while we are sweeping the shape
from the first height through the second height, we are constantly expanding
it from a single point until, at the second height, the shape has expanded to
the original points we made it from. To give a small idea of what such
effects are good for, we replace our existing prism with this (see file
prismdm5.pov):

  prism {
    conic_sweep
    linear_spline
    0, // height 1
    1, // height 2
    5, // the number of points making up the shape...

    <4,4>,<-4,4>,<-4,-4>,<4,-4>,<4,4>

    rotate <180, 0, 0>
    translate <0, 1, 0>
    scale <1, 4, 1>
    pigment { gradient y scale .2 }
  }


Creating a pyramid using conic sweeping.

The gradient pigment was selected to give some definition to our object
without having to fix the lights and the camera angle right at this moment,
but when we render it, we what we've created? A horizontally striped pyramid!
By now we can recognize the linear spline connecting the four points of a
square, and the familiar final point which is there to close the spline.

Notice all the transformations in the object declaration. That's going to
take a little explanation. The rotate and translate are easy. Normally, a
conic sweep starts full sized at the top, and tapers to a point at y=0, but
of course that would be upside down if we're making a pyramid. So we flip the
shape around the x-axis to put it rightside up, then since we actually
orbitted around the point, we translate back up to put it in the same
position it was in when we started.

The scale is to put the proportions right for this example. The base is eight
units by eight units, but the height (from y=1 to y=0) is only one unit, so
we've stretched it out a little. At this point, we're probably thinking, "why
not just sweep up from y=0 to y=4 and avoid this whole scaling thing?"

That is a very important gotcha! with conic sweeps. To see what's wrong with
that, let's try and put it into practice (see file prismdm6.pov). We must
make sure to remove the scale statement, and then replace the line which
reads

  1, // height 2
with

  1, // height 2


This sets the second height at y=4, so let's re-render and see if the effect
is the same.

Choosing a second height larger than one for the conic sweep.

Whoa! Our height is correct, but our pyramid's base is now huge! What went
wrong here? Simple. The base, as we described it with the points we used
actually occurs at y=1 no matter what we set the second height for. But if we
do set the second height higher than one, once the sweep passes y=1, it keeps
expanding outward along the same lines as it followed to our original base,
making the actual base bigger and bigger as it goes.

To avoid losing control of a conic sweep prism, it is usually best to let the
second height stay at y=1, and use a scale statement to adjust the height
from its unit size. This way we can always be sure the base's corners remain
where we think they are.

That leads to one more interesting thing about conic sweeps. What if we for
some reason don't want them to taper all the way to a point? What if instead
of a complete pyramid, we want more of a ziggurat step? Easily done. After
putting the second height back to one, and replacing our scale statment, we
change the line which reads

  0, // height 1
to

  0, // height 1


Increasing the first height for the conic sweep.

When we re-render, we see that the sweep stops short of going all the way to
its point, giving us a pyramid without a cap. Exactly how much of the cap is
cut off depends on how close the first height is to the second height.

4.4.8            Superquadric Ellipsoid Object

Sometimes we want to make an object that does not have perfectly sharp edges
like a box does. Then, the superquadric ellipsoid is a useful object. It is
described by the simple syntax:

  superellipsoid { <r, n> }


Where r and n are float values greater than zero and less than or equal to
one. Let's make a superellipsoid and experiment with the values of r and n to
see what kind of shapes we can make.

We create a file called supellps.pov and edit it as follows:

  #include "colors.inc"

  camera {
    location <10, 5, -20>
    look_at 0
    angle 15
  }

  background { color rgb <.5, .5, .5> }

  light_source { <10, 50, -100> White }


The addition of a gray background makes it a little easier to see our object.
We now type:

  superellipsoid { <.25, .25>
    pigment { Red }
  }


We save the file and trace it at 200x150 -A to see the shape. It will look
like a box, but the edges will be rounded off. Now let's experiment with
different values of r and n. For the next trace, try <1, 0.2>. The shape now
looks like a cylinder, but the top edges are rounded. Now try <0.1, 1>. This
shape is an odd one! We don't know exactly what to call it, but it is
interesting. Finally, lets try <1, 1>. Well, this is more familiar... a
sphere!

There are a couple of facts about superellipsoids we should know. First, we
should not use a value of 0 for either r nor n. This will cause POV-Ray to
incorrectly make a black box instead of our desired shape. Second, very small
values of r and n may yield strange results so they should be avoided.
Finally, the Sturmian root solver will not work with superellipsoids.

Superellipsoids are finite objects so they respond to auto-bounding and can
be used in CSG.

Now let's use the superellipsoid to make something that would be useful in a
scene. We will make a tiled floor and place a couple of superellipsoid
objects hovering over it. We can start with the file we have already made.

We rename it to tiles.pov and edit it so that it reads as follows:

  #include "colors.inc"
  #include "textures.inc"

  camera {
    location <10, 5, -20>
    look_at 0
    angle 15
  }
  background { color rgb <.5, .5, .5> }

  light_source{ <10, 50, -100> White }


Note that we have added #include "textures.inc" so we can use pre-defined
textures. Now we want to define the superellipsoid which will be our tile.

  #declare Tile = superellipsoid { <0.5, 0.1>
    scale <1, .05, 1>
  }


Superellipsoids are roughly 2*2*2 units unless we scale them otherwise. If we
wish to lay a bunch of our tiles side by side, they will have to be offset
from each other so they don't overlap. We should select an offset value that
is slightly more than 2 so that we have some space between the tiles to fill
with grout. So we now add this:

  #declare Offset = 2.1


We now want to lay down a row of tiles. Each tile will be offset from the
original by an ever-increasing amount in both the +z and -z directions. We
refer to our offset and multiply by the tile's rank to determine the position
of each tile in the row. We also union these tiles into a single object
called Row like this:

  #declare Row = union {
    object { Tile }
    object { Tile translate z*Offset }
    object { Tile translate z*Offset*2 }
    object { Tile translate z*Offset*3 }
    object { Tile translate z*Offset*4 }
    object { Tile translate z*Offset*5 }
    object { Tile translate z*Offset*6 }
    object { Tile translate z*Offset*7 }
    object { Tile translate z*Offset*8 }
    object { Tile translate z*Offset*9 }
    object { Tile translate z*Offset*10 }
    object { Tile translate -z*Offset }
    object { Tile translate -z*Offset*2 }
    object { Tile translate -z*Offset*3 }
    object { Tile translate -z*Offset*4 }
    object { Tile translate -z*Offset*5 }
    object { Tile translate -z*Offset*6 }
  }


This gives us a single row of 17 tiles, more than enough to fill the screen.
Now we must make copies of the Row and translate them, again by the offset
value, in both the +x and -x directions in ever increasing amounts in the
same manner.

  object { Row }
  object { Row translate x*Offset }
  object { Row translate x*Offset*2 }
  object { Row translate x*Offset*3 }
  object { Row translate x*Offset*4 }
  object { Row translate x*Offset*5 }

  object { Row translate x*Offset*6 }
  object { Row translate x*Offset*7 }
  object { Row translate -x*Offset }
  object { Row translate -x*Offset*2 }
  object { Row translate -x*Offset*3 }
  object { Row translate -x*Offset*4 }
  object { Row translate -x*Offset*5 }
  object { Row translate -x*Offset*6 }
  object { Row translate -x*Offset*7 }


Finally, our tiles are complete. But we need a texture for them. To do this
we union all of the Rows together and apply a White Marble pigment and a
somewhat shiny reflective surface to it:

  union{
    object { Row }
    object { Row translate x*Offset }
    object { Row translate x*Offset*2 }
    object { Row translate x*Offset*3 }
    object { Row translate x*Offset*4 }
    object { Row translate x*Offset*5 }
    object { Row translate x*Offset*6 }
    object { Row translate x*Offset*7 }
    object { Row translate -x*Offset }
    object { Row translate -x*Offset*2 }
    object { Row translate -x*Offset*3 }
    object { Row translate -x*Offset*4 }
    object { Row translate -x*Offset*5 }
    object { Row translate -x*Offset*6 }
    object { Row translate -x*Offset*7 }
    pigment { White_Marble }
    finish { phong 1 phong_size 50 reflection .35 }
  }


We now need to add the grout. This can simply be a white plane. We have
stepped up the ambient here a little so it looks whiter.

  plane { y, 0  //this is the grout
    pigment { color White }
    finish { ambient .4 diffuse .7 }
  }


To complete our scene, let's add five different superellipsoids, each a
different color, so that they hover over our tiles and are reflected in them.


  superellipsoid {
    <0.1, 1>
    pigment { Red }
    translate <5, 3, 0>
    scale .45
  }

  superellipsoid {
    <1, 0.25>
    pigment { Blue }
    translate <-5, 3, 0>
    scale .45
  }

  superellipsoid {
    <0.2, 0.6>
    pigment { Green }
    translate <0, 3, 5>
    scale .45
  }

  superellipsoid {
    <0.25, 0.25>
    pigment { Yellow }
    translate <0, 3, -5>
    scale .45
  }

  superellipsoid {
    <1, 1>
    pigment { Pink }
    translate y*3
    scale .45
  }


Some superellipsoids hovering above a tiled floor.

We trace the scene at 320x200 -A to see the result. If we are happy with
that, we do a final trace at 640x480 +A0.2.

4.4.9            Surface of Revolution Object

Bottles, vases and glasses make nice objects in ray-traced scenes. We want to
create a golden cup using the surface of revolution object (SOR object).

We first start by thinking about the shape of the final object. It is quite
difficult to come up with a set of points that describe a given curve without
the help of a modelling program supporting POV-Eay's surface of revolution
object. If such a program is available we should take advantage of it.

The point configuration of our cup object.

We will use the point configuration shown in the figure above. There are
eight points describing the curve that will be rotated about the y-axis to
get our cup. The curve was calculated using the method described in the
reference section (see "Surface of Revolution").

Now it is time to come up with a scene that uses the above SOR object. We
edit a file called sordemo.pov and enter the following text.

  #include "colors.inc"
  #include "golds.inc"

  global_settings { assumed_gamma 2.2 }

  camera {
    location <10, 15, -20>
    look_at <0, 5, 0>
    angle 45
  }

  background { color rgb<0.2, 0.4, 0.8>  }

  light_source { <100, 100, -100> color rgb 1 }

  plane { y, 0
    pigment { checker color Red, color Green scale 10 }
  }

  sor {
    8,
    <0.0,  -0.5>,
    <3.0,   0.0>,
    <1.0,   0.2>,
    <0.5,   0.4>,
    <0.5,   4.0>,
    <1.0,   5.0>,
    <3.0,  10.0>,
    <4.0,  11.0>
    texture { T_Gold_1B }
  }


The scene contains our cup object resting on a checkered plane. Tracing this
scene at a resolution of 320x200 results in the image below.

A surface of revolution object.

The surface of revolution is described by starting with the number of points
followed by the points with ascending heights. Each point determines the
radius the curve for a given height. E. g. the first point tells POV-Ray that
at height -0.5 the radius is 0. We should take care that each point has a
larger height than its predecessor. If this is not the case the program will
abort with an error message.

4.4.10           Text Object

Creating text objects using POV-Ray always used to mean that the letters had
to be built either from CSG, a painstaking process or by using a black and
white image of the letters as a height field, a method that was only somewhat
satisfactory. Now, for POV-Ray 3.0, a new primitive has been introduced that
can use any TrueType font to create text objects. These objects can be used
in CSG, transformed and textured just like any other POV primitive.

For this tutorial, we will make two uses of the text object. First, let's
just make some block letters sitting on a checkered plane. Any TTF font
should do, but for this tutorial, we will use the ones bundled with POV-Ray
3.0.

We create a file called textdemo.pov and edit it as follows:

  #include "colors.inc"

  camera {
    location <0, 1, -10>
    look_at 0
    angle 35
  }

  light_source { <500,500,-1000> White }

  plane { y,0
    pigment { checker Green White }
  }


Now let's add the text object. We will use the font timrom.ttf and we will
create the string POV-RAY 3.0. For now, we will just make the letters red.
The syntax is very simple. The first string in quotes is the font name, the
second one is the string to be rendered. The two floats are the thickness and
offset values. The thickness float determines how thick the block letters
will be. Values of .5 to 2 are usually best for this. The offset value will
add to the kerning distance of the letters. We will leave this a 0 for now.

  text { ttf "timrom.ttf" "POV-RAY 3.0" 1, 0
    pigment { Red }
  }


Rendering this at 200x150 -A, we notice that the letters are off to the right
of the screen. This is because they are placed so that the lower left front
corner of the first letter is at the origin. To center the string we need to
translate it -x some distance. But how far? In the docs we see that the
letters are all 0.5 to 0.75 units high. If we assume that each one takes
about 0.5 units of space on the x-axis, this means that the string is about 6
units long (12 characters and spaces). Let's translate the string 3 units
along the negative x-axis.

  text { ttf "timrom.ttf" "POV-RAY 3.0" 1, 0
    pigment { Red }
    translate -3*x
  }


That's better. Now let's play around with some of the parameters of the text
object. First, let's raise the thickness float to something outlandish... say
25!

  text { ttf "timrom.ttf" "POV-RAY 3.0" 25, 0
    pigment { Red }
    translate -2.25*x
  }


Actually, that's kind of cool. Now let's return the thickness value to 1 and
try a different offset value. Change the offset float from 0 to 0.1 and
render it again.

Wait a minute?! The letters go wandering off up at an angle! That is not what
the docs describe! It almost looks as if the offset value applies in both the
x- and y-axis instead of just the x axis like we intended. Could it be that a
vector is called for here instead of a float? Let's try it. We replace 0.1
with 0.1*x and render it again.

That works! The letters are still in a straight line along the x-axis, just a
little further apart. Let's verify this and try to offset just in the y-axis.
We replace 0.1*x with 0.1*y. Again, this works as expected with the letters
going up to the right at an angle with no additional distance added along the
x-axis. Now let's try the z-axis. We replace 0.1*y with 0.1*z. Rendering this
yields a disappointment. No offset occurs! The offset value can only be
applied in the x- and y-directions.

Let's finish our scene by giving a fancier texture to the block letters,
using that cool large thickness value, and adding a slight y-offset. For fun,
we will throw in a sky sphere, dandy up our plane a bit, and use a little
more interesting camera viewpoint (we render the following scene at 640x480
+A0.2):

  #include "colors.inc"

  camera {
    location <-5,.15,-2>
    look_at <.3,.2,1>
    angle 35
  }

  light_source { <500,500,-1000> White }

  plane { y,0
    texture {
      pigment { SeaGreen }
      finish { reflection .35 specular 1 }
      normal { ripples .35 turbulence .5 scale .25 }
    }
  }

  text { ttf "timrom.ttf" "POV-RAY 3.0" 25, 0.1*y
    pigment { BrightGold }
    finish { reflection .25 specular 1 }
    translate -3*x
  }

  #include "skies.inc"

  sky_sphere { S_Cloud5 }


Let's try using text in a CSG object. We will attempt to create an inlay in a
stone block using a text object. We create a new file called textcsg.pov and
edit it as follows:

  #include "colors.inc"

  #include "stones.inc"

  background { color rgb 1 }

  camera {
    location <-3, 5, -15>
    look_at 0
    angle 25
  }

  light_source { <500,500,-1000> White }


Now let's create the block. We want it to be about eight units across because
our text string (POV-RAY 3.0) is about six units long. We also want it about
four units high and about one unit deep. But we need to avoid a potential
coincident surface with the text object so we will make the first
z-coordinate 0.1 instead of 0. Finally, we will give this block a nice stone
texture.

  box { <-3.5, -1, 0.1>, <3.5, 1, 1>
    texture { T_Stone10 }
  }


Next, we want to make the text object. We can use the same object we used in
the first tutorial except we will use slightly different thickness and offset
values.

  text { ttf "timrom.ttf" "POV-RAY 3.0" 0.15, 0
    pigment { BrightGold }
    finish { reflection .25 specular 1 }
    translate -3*x
  }


We remember that the text object is placed by default so that its front
surface lies directly on the x-y-plane. If the front of the box begins at
z=0.1 and thickness is set at 0.15, the depth of the inlay will be 0.05
units. We place a difference block around the two objects.

  difference {
    box { <-3.5, -1, 0.1>, <3.5, 1, 1>
      texture { T_Stone10 }
    }
    text { ttf "timrom.ttf" "POV-RAY 3.0" 0.15, 0
      pigment { BrightGold }
      finish { reflection .25 specular 1 }
      translate -3*x
    }
  }


Text carved from stone.

We render this at 200x150 -A. We can see the inlay clearly and that it is
indeed a bright gold color. We re-render at 640x480 +A0.2 to see the results
more clearly, but be forewarned... this trace will take a little time.

4.4.11           Torus Object

A torus can be thought of as a donut or an inner-tube. It is a shape that is
vastly useful in many kinds of CSG so POV-Ray has adopted this 4th order
quartic polynomial as a primitive shape. The syntax for a torus is so simple
that it makes it a very easy shape to work with once we learn what the two
float values mean. Instead of a lecture on the subject, let's create one and
do some experiments with it.

We create a file called tordemo.pov and edit it as follows:

  #include "colors.inc"

  camera {
    location <0, .1, -25>
    look_at 0
    angle 30
  }

  background { color Gray50 } // to make the torus easy to see

  light_source{ <300, 300, -1000> White }

  torus { 4, 1        // major and minor radius
    rotate -90*x      // so we can see it from the top
    pigment { Green }
  }


We trace the scene. Well, it's a donut alright. Let's try changing the major
and minor radius values and see what happens. We change them as follows:

  torus { 5, .25      // major and minor radius


That looks more like a hula-hoop! Let's try this:

  torus { 3.5, 2.5    // major and minor radius


Whoa! A donut with a serious weight problem!

With such a simple syntax, there isn't much else we can do to a torus besides
change its texture... or is there? Let's see...

Torii are very useful objects in CSG. Let's try a little experiment. We make
a difference of a torus and a box:

  difference {
    torus { 4, 1
      rotate x*-90  // so we can see it from the top
    }
    box { <-5, -5, -1>, <5, 0, 1> }
    pigment { Green }
  }


Interesting... a half-torus. Now we add another one flipped the other way.
Only, let's declare the original half-torus and the necessary transformations
so we can use them again:

  #declare Half_Torus = difference {
    torus { 4, 1
      rotate -90*x  // so we can see it from the top
    }
    box { <-5, -5, -1>, <5, 0, 1> }
    pigment { Green }
  }

  #declare Flip_It_Over = 180*x

  #declare Torus_Translate = 8  // twice the major radius


Now we create a union of two Half_Torus objects:

  union {
    object { Half_Torus }
    object { Half_Torus
      rotate Flip_It_Over
      translate Torus_Translate*x
    }
  }


This makes an S-shaped object, but we can't see the whole thing from our
present camera. Let's add a few more links, three in each direction, move the
object along the +z-direction and rotate it about the +y-axis so we can see
more of it. We also notice that there appears to be a small gap where the
half torii meet. This is due to the fact that we are viewing this scene from
directly on the x-z-plane. We will change the camera's y-coordinate from 0 to
0.1 to eliminate this.

  union {
    object { Half_Torus }
    object { Half_Torus
      rotate Flip_It_Over
      translate x*Torus_Translate
    }
    object { Half_Torus
      translate x*Torus_Translate*2
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate x*Torus_Translate*3
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate -x*Torus_Translate
    }
    object { Half_Torus
      translate -x*Torus_Translate*2
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate -x*Torus_Translate*3
    }
    object { Half_Torus
      translate -x*Torus_Translate*4
    }
    rotate y*45
    translate z*20
  }


Rendering this we see a cool, undulating, snake-like something-or-other.
Neato. But we want to model something useful, something that we might see in
real
life. How about a chain?

Thinking about it for a moment, we realize that a single link of a chain can
be easily modeled using two half toruses and two cylinders. We create a new
file. We can use the same camera, background, light source and declared
objects and transformations as we used in tordemo.pov:

  #include "colors.inc"

  camera {
    location <0, .1, -25>
    look_at 0
    angle 30
  }

  background { color Gray50 }

  light_source{ <300, 300, -1000> White }

  #declare Half_Torus = difference {
    torus { 4,1
      sturm
      rotate x*-90  // so we can see it from the top
    }
    box { <-5, -5, -1>, <5, 0, 1> }
    pigment { Green }
  }

  #declare Flip_It_Over = x*180

  #declare Torus_Translate = 8


Now, we make a complete torus of two half toruses:

  union {
    object { Half_Torus }
    object { Half_Torus rotate Flip_It_Over }
  }


This may seem like a wasteful way to make a complete torus, but we are really
going to move each half apart to make room for the cylinders. First, we add
the declared cylinder before the union:

  #declare Chain_Segment = cylinder { <0, 4, 0>, <0, -4, 0>, 1
    pigment { Green }
  }


We then add two chain segments to the union and translate them so that they
line up with the minor radius of the torus on each side:

  union {
    object { Half_Torus }
    object { Half_Torus rotate Flip_It_Over }
    object { Chain_Segment translate  x*Torus_Translate/2 }
    object { Chain_Segment translate -x*Torus_Translate/2 }
  }


Now we translate the two half toruses +y and -y so that the clipped ends meet
the ends of the cylinders. This distance is equal to half of the previously
declared Torus_Translate:

  union {
    object { Half_Torus
      translate y*Torus_Translate/2
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate -y*Torus_Translate/2
    }
    object { Chain_Segment
      translate x*Torus_Translate/2
    }
    object { Chain_Segment
      translate -x*Torus_Translate/2
    }
  }


We render this and viola! A single link of a chain. But we aren't done yet!
Whoever heard of a green chain? We would rather use a nice metallic color
instead. First, we remove any pigment blocks in the declared toruses and
cylinders. Then we add the following before the union:

  #declare Chain_Gold = texture {
    pigment { BrightGold }
    finish {
      ambient .1
      diffuse .4
      reflection .25
      specular 1
      metallic
    }
  }


We then add the texture to the union and declare the union as a single link:

  #declare Link = union {
    object { Half_Torus
      translate y*Torus_Translate/2
    }
    object { Half_Torus
      rotate Flip_It_Over
      translate -y*Torus_Translate/2
    }
    object { Chain_Segment
      translate x*Torus_Translate/2
    }
    object { Chain_Segment
      translate -x*Torus_Translate/2
    }
    texture { Chain_Gold }
  }


Now we make a union of two links. The second one will have to be translated
+y so that its inner wall just meets the inner wall of the other link, just
like the links of a chain. This distance turns out to be double the
previously declared Torus_Translate minus 2 (twice the minor radius). This
can be described by the expression:

  Torus_Translate*2-2*y



We declare this expression as follows:

  #declare Link_Translate = Torus_Translate*2-2*y


In the object block, we will use this declared value so that we can multiply
it to create other links. Now, we rotate the second link 90*y so that it is
perpendicular to the first, just like links of a chain. Finally, we scale the
union by 1/4 so that we can see the whole thing:

  union {
    object { Link }
    object { Link translate y*Link_Translate rotate y*90 }
    scale .25
  }


We render this and we will see a very realistic pair of links. If we want to
make an entire chain, we must declare the above union and then create another
union of this declared object. We must be sure to remove the scaling from the
declared object:

  #declare Link_Pair =
  union {
    object { Link }
    object { Link translate y*Link_Translate rotate y*90 }
  }


Now we declare our chain:

  #declare Chain = union {
    object { Link_Pair}
    object { Link_Pair translate  y*Link_Translate*2 }
    object { Link_Pair translate  y*Link_Translate*4 }
    object { Link_Pair translate  y*Link_Translate*6 }
    object { Link_Pair translate -y*Link_Translate*2 }
    object { Link_Pair translate -y*Link_Translate*4 }
    object { Link_Pair translate -y*Link_Translate*6 }
  }


And finally we create our chain with a couple of transformations to make it
easier to see. These include scaling it down by a factor of 1/10, and
rotating it so that we can clearly see each link:

  object { Chain scale .1 rotate <0, 45, -45> }


The torus object can be used to create chains.

We render this and we should see a very realistic gold chain stretched
diagonally across the screen.

4.5              CSG Objects

Constructive Solid Geometry, CSG, is a powerful tool to combine primitive
objects to create more complex objects as shown in the following sections.

4.5.1            What is CSG?

CSG stands for Constructive Solid Geometry. POV-Ray allows us to construct
complex solids by combining primitive shapes in four different ways. These
are union, where two or more shapes are added together. Intersection, where
two or more shapes are combined to make a new shape that consists of the area
common to both shapes. Difference, where subsequent shapes are subtracted
from the first shape. And last not least merge, which is like a union where
the surfaces inside the union are removed (useful in transparent CSG
objects). We will deal with each of these in detail in the next few sections.


CSG objects can be extremely complex. They can be deeply nested. In other
words there can be unions of differences or intersections of merges or
differences of intersections or even unions of intersections of differences
of merges... ad infinitum. CSG objects are (almost always) finite objects and
thus respond to auto-bounding and can be transformed like any other POV
primitive shape.

4.5.2            CSG Union

Let's try making a simple union. Create a file called csgdemo.pov and edit it
as follows:

  #include "colors.inc"

  camera {
    location <0, 1, -10>
    look_at 0
    angle 36
  }

  light_source { <500, 500, -1000> White }

  plane { y, -1.5
    pigment { checker Green White }
  }


Let's add two spheres each translated 0.5 units along the x-axis in each
direction. We color one blue and the other red.

  sphere { <0, 0, 0>, 1
    pigment { Blue }
    translate -0.5*x
  }
  sphere { <0, 0, 0>, 1
    pigment { Red }
    translate 0.5*x
  }


We trace this file at 200x150 -A. Now we place a union block around the two
spheres. This will create a single CSG union out of the two objects.

  union{
    sphere { <0, 0, 0>, 1
      pigment { Blue }
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      pigment { Red }
      translate 0.5*x
    }
  }


We trace the file again. The union will appear no different from what each
sphere looked like on its own, but now we can give the entire union a single
texture and transform it as a whole. Let's do that now.

  union{
    sphere { <0, 0, 0>, 1
      translate -0.5*x*
    }
    sphere { <0, 0, 0>, 1
      translate 0.5*x
    }
    pigment { Red }
    scale <1, .25, 1>
    rotate <30, 0, 45>
  }


We trace the file again. As we can see, the object has changed dramatically.
We experiment with different values of scale and rotate and try some
different textures.

There are many advantages of assigning only one texture to a CSG object
instead of assigning the texture to each individual component. First, it is
much easier to use one texture if our CSG object has a lot of components
because changing the objects appearance involves changing only one single
texture. Second, the file parses faster because the texture has to be parsed
only once. This may be a great factor when doing large scenes or animations.
Third, using only one texture saves memory because the texture is only stored
once and referenced by all components of the CSG object. Assigning the
texture to all n components means that it is stored n times.

4.5.3            CSG Intersection

Now let's use these same spheres to illustrate the next kind of CSG object,
the intersection. We change the word union to intersection and delete the
scale and rotate statements:

  intersection {
    sphere { <0, 0, 0>, 1
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      translate 0.5*x
    }
    pigment { Red }
  }


We trace the file and will see a lens-shaped object instead of the two
spheres. This is because an intersection consists of the area shared by both
shapes, in this case the lens-shaped area where the two spheres overlap. We
like this lens-shaped object so we will use it to demonstrate differences.

4.5.4            CSG Difference

We rotate the lens-shaped intersection about the y-axis so that the broad
side is facing the camera.

  intersection{
    sphere { <0, 0, 0>, 1
      translate -0.5*x
    }
    sphere { <0, 0, 0>, 1
      translate 0.5*x
    }
    pigment { Red }
    rotate 90*y
  }


Let's create a cylinder and stick it right in the middle of the lens.

  cylinder { <0, 0, -1> <0, 0, 1>, .35
    pigment { Blue }
  }


We render the scene to see the position of the cylinder. We will place a
difference block around both the lens-shaped intersection and the cylinder
like this:

  difference {
    intersection {
      sphere { <0, 0, 0>, 1
        translate -0.5*x
      }
      sphere { <0, 0, 0>, 1
        translate 0.5*x
      }
      pigment { Red }
      rotate 90*y
    }
    cylinder { <0, 0, -1> <0, 0, 1>, .35
      pigment { Blue }
    }
  }


We render the file again and see the lens-shaped intersection with a neat
hole in the middle of it where the cylinder was. The cylinder has been
subtracted from the intersection. Note that the pigment of the cylinder
causes the surface of the hole to be colored blue. If we eliminate this
pigment the surface of the hole will be red.

OK, let's get a little wilder now. Let's declare our perforated lens object
to give it a name. Let's also eliminate all textures in the declared object
because we will want them to be in the final union instead.

  #declare Lens_With_Hole = difference {
    intersection {
      sphere { <0, 0, 0>, 1
        translate -0.5*x
      }
      sphere { <0, 0, 0>, 1
        translate 0.5*x
      }
      rotate 90*y
    }
    cylinder { <0, 0, -1> <0, 0, 1>, .35 }
  }


Let's use a union to build a complex shape composed of copies of this object.


  union {
    object { Lens_With_Hole translate <-.65, .65, 0> }
    object { Lens_With_Hole translate <.65, .65, 0> }
    object { Lens_With_Hole translate <-.65, -.65, 0> }
    object { Lens_With_Hole translate <.65, -.65, 0> }
    pigment { Red }
  }


We render the scene. An interesting object to be sure. But let's try
something more. Let's make it a partially-transparent object by adding some
filter to the pigment block.

  union {
    object { Lens_With_Hole translate <-.65, .65, 0> }
    object { Lens_With_Hole translate <.65, .65, 0> }
    object { Lens_With_Hole translate <-.65, -.65, 0> }
    object { Lens_With_Hole translate <.65, -.65, 0> }
    pigment { Red filter .5 }
  }


We render the file again. This looks pretty good... only... we can see parts
of each of the lens objects inside the union! This is not good.

4.5.5            CSG Merge

This brings us to the fourth kind of CSG object, the merge. Merges are the
same as unions, but the geometry of the objects in the CSG that is inside the
merge is not traced. This should eliminate the problem with our object. Let's
try it.

  merge {
    object { Lens_With_Hole translate <-.65, .65, 0> }
    object { Lens_With_Hole translate <.65, .65, 0> }
    object { Lens_With_Hole translate <-.65, -.65, 0> }
    object { Lens_With_Hole translate <.65, -.65, 0> }
    pigment { Red filter .5 }
  }


4.5.6            CSG Pitfalls


4.5.6.1          Coincidence Surfaces

POV-Ray uses inside/outside tests to determine the points at which a ray
intersects a CSG object. A problem arises when the surfaces of two different
shapes coincide because there is no way (due to numerical problems) to tell
whether a point on the coincident surface belongs to one shape or the other.

Look at the following example where a cylinder is used to cut a hole in a
larger box.

  difference {
    box { -1, 1 pigment { Red } }
    cylinder { -z, z, 0.5 pigment { Green } }
  }


If we trace this object we see red speckles where the hole is supposed to be.
This is caused by the coincident surfaces of the cylinder and the box. One
time the cylinder's surface is hit first by a viewing ray, resulting in the
correct rendering of the hole, and another time the box is hit first, leading
to a wrong result where the hole vanishes and red speckles appear.

This problem can be avoided by increasing the size of the cylinder to get rid
of the coincidence surfaces. This is done by:

  difference {
    box { -1, 1 pigment { Red } }
    cylinder { -1.001*z, 1.001*z, 0.5 pigment { Green } }
  }


In general we have to make the subtracted object a little bit larger in a CSG
difference. We just have to look for coincident surfaces and increase the
subtracted object appropriately to get rid of those surfaces.

The same problem occurs in CSG intersections and is also avoided by scaling
some of the involved objects.

4.6              The Light Source

In any ray-traced scene, the light needed to illuminate our objects and their
surfaces must come from a light source. There are many kinds of light sources
available in POV-Ray and careful use of the correct kind can yield very
impressive results. Let's take a moment to explore some of the different
kinds of light sources and their various parameters.

4.6.1            The Ambient Light Source

The ambient light source is used to simulate the effect of inter-diffuse
reflection. If there wasn't inter-diffuse reflection all areas not directly
lit by a light source would be completely dark. POV-Ray uses the ambient
keyword to determine how much light coming from the ambient light source is
reflected by a surface.

By default the ambient light source, which emits its light everywhere and in
all directions, is pure white (rgb <1,1,1>). Changing its color can be used
to create interesting effects. First of all the overall light level of the
scene can be adjusted easily. Instead of changing all ambient values in every
finish only the ambient light source is modified. By assigning different
colors we can create nice effects like a moody reddish ambient lighting. For
more details about the ambient light source see "Ambient Light".

Below is an example of a red ambient light source.

  global_settings { ambient_light rgb<1, 0, 0> }


4.6.2            The Pointlight Source

Pointlights are exactly what the name indicates. A pointlight has no size, is
invisible and illuminates everything in the scene equally no matter how far
away from the light source it may be (this behavior can be changed). This is
the simplest and most basic light source. There are only two important
parameters, location and color. Let's design a simple scene and place a
pointlight source in it.

We create a new file and name it litedemo.pov. We edit it as follows:

  #include "colors.inc"
  #include "textures.inc"

  camera {
    location  <-4, 3, -9>
    look_at   <0, 0, 0>
    angle 48
  }


We add the following simple objects:

  plane { y, -1
    texture {
      pigment {
        checker
        color rgb<0.5, 0, 0>
        color rgb<0, 0.5, 0.5>
      }
      finish {
        diffuse 0.4
        ambient 0.2
        phong 1
        phong_size 100
        reflection 0.25
      }
    }
  }

  torus { 1.5, 0.5
    texture { Brown_Agate }
    rotate <90, 160, 0>
    translate  <-1, 1, 3>
  }

  box { <-1, -1, -1>, <1, 1, 1>
    texture { DMFLightOak }
    translate  <2, 0, 2.3>
  }

  cone { <0,1,0>, 0, <0,0,0>, 1
    texture { PinkAlabaster }
    scale <1, 3, 1>
    translate  <-2, -1, -1>
  }

  sphere { <0,0,0>,1
    texture { Sapphire_Agate }
    translate  <1.5, 0, -2>
  }


Now we add a pointlight:

  light_source {
    <2, 10, -3>
    color White
  }


We render this at 200x150 -A and see that the objects are clearly visible
with sharp shadows. The sides of curved objects nearest the light source are
brightest in color with the areas that are facing away from the light source
being darkest. We also note that the checkered plane is illuminated evenly
all the way to the horizon. This allows us to see the plane, but it is not
very realistic.

4.6.3            The Spotlight Source

Spotlights are a very useful type of light source. They can be used to add
highlights and illuminate features much as a photographer uses spots to do
the same thing. There are a few more parameters with spotlights than with
pointlights. These are radius, falloff, tightness and point_at. The radius
parameter is the angle of the fully illuminated cone. The falloff parameter
is the angle of the umbra cone where the light falls off to darkness. The
tightness is a parameter that determines the rate of the light falloff. The
point_at parameter is just what it says, the location where the spotlight is
pointing to. Let's change the light in our scene as follows:

  light_source {
    <0, 10, -3>
    color White
    spotlight
    radius 15
    falloff 20
    tightness 10
    point_at <0, 0, 0>
  }


We render this at 200x150 -A and see that only the objects are illuminated.
The rest of the plane and the outer portions of the objects are now unlit.
There is a broad falloff area but the shadows are still razor sharp. Let's
try fiddling with some of these parameters to see what they do. We change the
falloff value to 16 (it must always be larger than the radius value) and
render again. Now the falloff is very narrow and the objects are either
brightly lit or in total darkness. Now we change falloff back to 20 and
change the tightness value to 100 (higher is tighter) and render again. The
spotlight appears to have gotten much smaller but what has really happened is
that the falloff has become so steep that the radius actually appears
smaller.

We decide that a tightness value of 10 (the default) and a falloff value of
18 are best for this spotlight and we now want to put a few spots around the
scene for effect. Let's place a slightly narrower blue and a red one in
addition to the white one we already have:

  light_source {
    <10, 10, -1>
    color Red
    spotlight
    radius 12
    falloff 14
    tightness 10
    point_at <2, 0, 0>
  }

  light_source {
    <-12, 10, -1>
    color Blue
    spotlight
    radius 12
    falloff 14
    tightness 10
    point_at <-2, 0, 0>
  }


Rendering this we see that the scene now has a wonderfully mysterious air to
it. The three spotlights all converge on the objects making them blue on one
side and red on the other with enough white in the middle to provide a
balance.

4.6.4            The Cylindrical Light Source

Spotlights are cone shaped, meaning that their effect will change with
distance. The farther away from the spotlight an object is, the larger the
apparent radius will be. But we may want the radius and falloff to be a
particular size no matter how far away the spotlight is. For this reason,
cylindrical light sources are needed. A cylindrical light source is just like
a spotlight, except that the radius and falloff regions are the same no
matter how far from the light source our object is. The shape is therefore a
cylinder rather than a cone. We can specify a cylindrical light source by
replacing the spotlight keyword with the cylinder keyword. We try this now
with our scene by replacing all three spotlights with cylinder lights and
rendering again. We see that the scene is much dimmer. This is because the
cylindrical constraints do not let the light spread out like in a spotlight.
Larger radius and falloff values are needed to do the job. We try a radius of
20 and a falloff of 30 for all three lights. That's the ticket!

4.6.5            The Area Light Source

So far all of our light sources have one thing in common. They produce sharp
shadows. This is because the actual light source is a point that is
infinitely small. Objects are either in direct sight of the light, in which
case they are fully illuminated, or they are not, in which case they are
fully shaded. In real life, this kind of stark light and shadow situation
exists only in outer space where the direct light of the sun pierces the
total blackness of space. But here on Earth, light bends around objects,
bounces off objects, and usually the source has some dimension, meaning that
it can be partially hidden from sight (shadows are not sharp anymore). They
have what is known as an umbra, or an area of fuzziness where there is
neither total light or shade. In order to simulate these soft shadows, a
ray-tracer must give its light sources dimension. POV-Ray accomplishes this
with a feature known as an area light.

Area lights have dimension in two axis'. These are specified by the first two
vectors in the area light syntax. We must also specify how many lights are to
be in the array. More will give us cleaner soft shadows but will take longer
to render. Usually a 3*3 or a 5*5 array will suffice. We also have the option
of specifying an adaptive value. The adaptive keyword tells the ray-tracer
that it can adapt to the situation and send only the needed rays to determine
the value of the pixel. If adaptive is not used, a separate ray will be sent
for every light in the area light. This can really slow things down. The
higher the adaptive value the cleaner the umbra will be but the longer the
trace will take. Usually an adaptive value of 1 is sufficient. Finally, we
probably should use the jitter keyword. This tells the ray-tracer to slightly
move the position of each light in the area light so that the shadows appear
truly soft instead of giving us an umbra consisting of closely banded
shadows.

OK, let's try one. We comment out the cylinder lights and add the following:

  light_source {
    <2, 10, -3>
    color White
    area_light <5, 0, 0>, <0, 0, 5>, 5, 5
    adaptive 1
    jitter
  }


This is a white area light centered at <2,10,-3>. It is 5 units (along the
x-axis) by 5 units (along the z-axis) in size and has 25 (5*5) lights in it.
We have specified adaptive 1 and jitter. We render this at 200x150 -A.

Right away we notice two things. The trace takes quite a bit longer than it
did with a point or a spotlight and the shadows are no longer sharp! They all
have nice soft umbrae around them. Wait, it gets better.

Spotlights and cylinder lights can be area lights too! Remember those sharp
shadows from the spotlights in our scene? It would not make much sense to use
a 5*5 array for a spotlight, but a smaller array might do a good job of
giving us just the right amount of umbra for a spotlight. Let's try it. We
comment out the area light and change the cylinder lights so that they read
as follows:

  light_source {
    <2, 10, -3>
    color White
    spotlight
    radius 15
    falloff 18
    tightness 10
    area_light <1, 0, 0>, <0, 0, 1>, 2, 2
    adaptive 1
    jitter
    point_at <0, 0, 0>
  }

  light_source {
    <10, 10, -1>
    color Red
    spotlight
    radius 12
    falloff 14
    tightness 10
    area_light <1, 0, 0>, <0, 0, 1>, 2, 2
    adaptive 1
    jitter
    point_at <2, 0, 0>
  }

  light_source {
    <-12, 10, -1>
    color Blue
    spotlight
    radius 12
    falloff 14
    tightness 10
    area_light <1, 0, 0>, <0, 0, 1>, 2, 2
    adaptive 1
    jitter
    point_at <-2, 0, 0>
  }


We now have three area-spotlights, one unit square consisting of an array of
four (2*2) lights, three different colors, all shining on our scene. We
render this at 200x150 -A. It appears to work perfectly. All our shadows have
small, tight umbrae, just the sort we would expect to find on an object under
a real spotlight.

4.6.6            Assigning an Object to a Light Source

Light sources are invisible. They are just a location where the light appears
to be coming from. They have no true size or shape. If we want our light
source to be a visible shape, we can use the looks_like keyword. We can
specify that our light source can look like any object we choose. When we use
looks_like, no_shadow is applied to the object automatically. This is done so
that the object will not block any illumination from the light source. If we
want some blocking to occur (as in a lampshade), it is better to simply use a
union to do the same thing. Let's add such an object to our scene. Here is a
light bulb we have made just for this purpose:

  #declare Lightbulb = union {
    merge {
      sphere { <0,0,0>,1 }
      cylinder { <0,0,1>, <0,0,0>, 1
        scale <0.35, 0.35, 1.0>
        translate  0.5*z
      }
      texture {
        pigment {color rgb <1, 1, 1>}
        finish {ambient .8 diffuse .6}
      }
    }
    cylinder { <0,0,1>, <0,0,0>, 1
      scale <0.4, 0.4, 0.5>
      texture { Brass_Texture }
      translate  1.5*z
    }
    rotate -90*x
    scale .5
  }


Now we add the light source:

  light_source {
    <0, 2, 0>
    color White
    looks_like { Lightbulb }
  }


Rendering this we see that a fairly believable light bulb now illuminates the
scene. However, if we do not specify a high ambient value, the light bulb is
not lit by the light source. On the plus side, all of the shadows fall away
from the light bulb, just as they would in a real situation. The shadows are
sharp, so let's make our bulb an area light:

  light_source {
    <0, 2, 0>
    color White
    area_light <1, 0, 0>, <0, 1, 0>, 2, 2
    adaptive 1
    jitter
    looks_like { Lightbulb }
  }


We note that we have placed this area light in the x-y-plane instead of the
x-z-plane. We also note that the actual appearance of the light bulb is not
affected in any way by the light source. The bulb must be illuminated by some
other light source or by, as in this case, a high ambient value. More
interesting results might therefore be obtained in this case by using halos
(see section "Halos").

4.6.7            Light Source Specials


4.6.7.1          Using Shadowless Lights

Light sources can be assigned the shadowless keyword and no shadows will be
cast due to its presence in a scene. Sometimes, scenes are difficult to
illuminate properly using the lights we have chosen to illuminate our
objects. It is impractical and unrealistic to apply a higher ambient value to
the texture of every object in the scene. So instead, we would place a couple
of fill lights around the scene. Fill lights are simply dimmer lights with
the shadowless keyword that act to boost the illumination of other areas of
the scene that may not be lit well. Let's try using one in our scene.

Remember the three colored area spotlights? We go back and un-comment them
and comment out any other lights we have made. Now we add the following:   li
    <0, 20, 0>
    color Gray50
    shadowless
  }


This is a fairly dim light 20 units over the center of the scene. It will
give a dim illumination to all objects including the plane in the background.
We render it and see.

4.6.7.2          Using Light Fading

If it is realism we want, it is not realistic for the plane to be evenly
illuminated off into the distance. In real life, light gets scattered as it
travels so it diminishes its ability to illuminate objects the farther it
gets from its source. To simulate this, POV-Ray allows us to use two
keywords: fade_distance, which specifies the distance at which full
illumination is achieved, and fade_power, an exponential value which
determines the actual rate of attenuation. Let's apply these keywords to our
fill light.

First, we make the fill light a little brighter by changing Gray50 to Gray75.
Now we change that fill light as follows:

  light_source {
    <0, 20, 0>
    color Gray75
    fade_distance 5
    fade_power 1
    shadowless
  }


This means that the full value of the fill light will be achieved at a
distance of 5 units away from the light source. The fade power of 1 means
that the falloff will be linear (the light falls of at a constant rate). We
render this to see the result.

That definitely worked! Now let's try a fade power of 2 and a fade distance
of 10. Again, this works well. The falloff is much faster with a fade power
of 2 so we had to raise the fade distance to 10.

4.6.7.3          Light Sources and Atmosphere

By definition more than default, light sources are affected by atmosphere,
i.e. their light is scattered by the atmosphere. This can be turned off by
adding atmosphere off to the light source block. The light emitted by a light
source can also be attenuated by the atmosphere (and also fog), that is it
will be diminished as it travels through it, by adding
atmospheric_attenuation on. The falloff is exponential and depends on the
distance parameter of the atmosphere (or fog). We note that this feature only
affects light coming directly from the light source. Reflected and refracted
light is ignored.

Let's experiment with these keywords. First we must add an atmosphere to our
scene:

  #include "atmos.inc"

  atmosphere { Atmosphere2 }


We comment out the three lines that turn each of the three spotlights into
area lights. Otherwise the trace will take to long.

  //area_light <1, 0, 0>, <0, 0, 1>, 2, 2
  //adaptive 1
  //jitter


Tracing the scene at 200x150 -A we see that indeed the spotlights are
visible. We can see where the blue and red spots cross each other and where
the white overhead light shines down through the center of the scene. We also
notice that the spotlights appear to diminish in their intensity as the light
descends from the light source to the objects. The red light is all but gone
in the lower left part of the scene and the blue light all but gone in the
lower right. This is due to the atmospheric attenuation and lends a further
realism to the scene. The atmosphere-light source interaction gives our scene
a smoky, mysterious appearance, but the trace took a long time. Making those
spotlights area lights and it will take even longer. This is an inevitable
trade-off - tracing speed for image quality.

4.7              Simple Texture Options

The pictures rendered so far where somewhat boring regarding the appearance
of the objects. Let's add some fancy features to the texture.

4.7.1            Surface Finishes

One of the main features of a ray-tracer is its ability to do interesting
things with surface finishes such as highlights and reflection. Let's add a
nice little Phong highlight (shiny spot) to the sphere. To do this we need to
add a finish keyword followed by a parameter. We change the definition of the
sphere to this:

  sphere { <0, 1, 2>, 2
    texture {
      pigment { color Yellow } // Yellow is pre-defined in COLORS.INC
      finish { phong 1 }
    }
  }


We render the scene. The phong keyword adds a highlight the same color of the
light shining on the object. It adds a lot of credibility to the picture and
makes the object look smooth and shiny. Lower values of phong will make the
highlight less bright (values should be between 0 and 1).

4.7.2            Adding Bumpiness

The highlight we have added illustrates how much of our perception depends on
the reflective properties of an object. Ray-tracing can exploit this by
playing tricks on our perception to make us see complex details that aren't
really there.

Suppose we wanted a very bumpy surface on the object. It would be very
difficult to mathematically model lots of bumps. We can however simulate the
way bumps look by altering the way light reflects off of the surface.
Reflection calculations depend on a vector called surface normal. This is a
vector which points away from the surface and is perpendicular to it. By
artificially modifying (or perturbing) this normal vector we can simulate
bumps. We change the scene to read as follows and render it:

  sphere { <0, 1, 2>, 2
    texture {
      pigment { color Yellow }
      normal { bumps 0.4 scale 0.2 }
      finish { phong 1}
    }
  }


This tells POV-Ray to use a bump pattern to modify the surface normal. The
value 0.4 controls the apparent depth of the bumps. Usually the bumps are
about 1 unit wide which doesn't work very well with a sphere of radius 2. The
scale makes the bumps 1/5th as wide but does not affect their depth.

4.7.3            Creating Color Patterns

We can do more than assigning a solid color to an object. We can create
complex patterns in the pigment block like in this example:

  sphere { <0, 1, 2>, 2
    texture {
      pigment {
        wood
        color_map {
          [0.0 color DarkTan]
          [0.9 color DarkBrown]
          [1.0 color VeryDarkBrown]
        }
        turbulence 0.05
        scale <0.2, 0.3, 1>
      }
      finish { phong 1 }
    }
  }


The keyword wood specifies a pigment pattern of concentric rings like rings
in wood. The color_map keyword specifies that the color of the wood should
blend from DarkTan to DarkBrown over the first 90% of the vein and from
DarkBrown to VeryDarkBrown over the remaining 10%. The turbulence keyword
slightly stirs up the pattern so the veins aren't perfect circles and the
scale keyword adjusts the size of the pattern.

Most patterns are set up by default to give us one feature across a sphere of
radius 1.0. A feature is very roughly defined as a color transition. For
example, a wood texture would have one band on a sphere of radius 1.0. In
this example we scale the pattern using the scale keyword followed by a
vector. In this case we scaled 0.2 in the x direction, 0.3 in the y direction
and the z direction is scaled by 1, which leaves it unchanged. Scale values
larger than one will stretch an element. Scale values smaller than one will
squish an element. A scale value of one will leave an element unchanged.

4.7.4            Pre-defined Textures

POV-Ray has some very sophisticated textures pre-defined in the standard
include files glass.inc, metals.inc, stones.inc and woods.inc. Some are
entire textures with pigment, normal and/or finish parameters already
defined. Some are just pigments or just finishes. We change the definition of
our sphere to the following and then re-render it:

  sphere { <0, 1, 2>, 2
    texture {
      pigment {
        DMFWood4       // pre-defined in textures.inc
        scale 4        // scale by the same amount in all
                       // directions
      }
      finish { Shiny } // pre-defined in finish.inc
    }
  }


The pigment identifier DMFWood4 has already been scaled down quite small when
it was defined. For this example we want to scale the pattern larger. Because
we want to scale it uniformly we can put a single value after the scale
keyword rather than a vector of x, y, z scale factors.

We look through the file textures.inc to see what pigments and finishes are
defined and try them out. We just insert the name of the new pigment where
DMFWood4 is now or try a different finish in place of Shiny and re-render our
file.

Here is an example of using a complete texture identifier rather than just
the pieces.

  sphere { <0, 1, 2>, 2
    texture { PinkAlabaster }
  }


4.8              Advanced Texture Options

The extremely powerful texturing ability is one thing that really sets
POV-Ray apart from other raytracers. So far we have not really tried anything
too complex but by now we should be comfortable enough with the program's
syntax to try some of the more advanced texture options.

Obviously, we cannot try them all. It would take a tutorial a lot more pages
to use every texturing option available in POV-Ray. For this limited
tutorial, we will content ourselves to just trying a few of them to give an
idea of how textures are created. With a little practice, we will soon be
creating beautiful textures of our own.

4.8.1            Pigment and Normal Patterns

Previous versions of POV-Ray made a distinction between pigment and normal
patterns, i. e. patterns that could be used inside a normal or pigment
statement. With POV-Ray 3.0 this restriction was removed so that all patterns
listed in section "Patterns" can be used as a pigment or normal pattern.

4.8.2            Pigments

Every surface must have a color. In POV-Ray this color is called a pigment.
It does not have to be a single color. It can be a color pattern, a color
list or even an image map. Pigments can also be layered one on top of the
next so long as the uppermost layers are at least partially transparent so
the ones beneath can show through. Let's play around with some of these kinds
of pigments.

We create a file called texdemo.pov and edit it as follows:

  #include "colors.inc"

  camera {
    location <1, 1, -7>
    look_at 0
    angle 36
  }

  light_source { <1000, 1000, -1000> White }

  plane { y, -1.5
    pigment { checker Green, White }
  }

  sphere { <0,0,0>, 1
    pigment { Red }
  }


Giving this file a quick test render at 200x150 -A we see that it is a simple
red sphere against a green and white checkered plane. We will be using the
sphere for our textures.

4.8.2.1          Using Color List Pigments

Before we begin we should note that we have already made one kind of pigment,
the color list pigment. In the previous example we have used a checkered
pattern on our plane. There are two other kinds of color list pigments, brick
and hexagon. Let's quickly try each of these. First, we change the plane's
pigment as follows:

  pigment { hexagon Green, White, Yellow }


Rendering this we see a three-color hexagonal pattern. Note that this pattern
requires three colors. Now we change the pigment to...

  pigment { brick Gray75, Red rotate -90*x scale .25 }


Looking at the resulting image we see that the plane now has a brick pattern.
We note that we had to rotate the pattern to make it appear correctly on the
flat plane. This pattern normally is meant to be used on vertical surfaces.
We also had to scale the pattern down a bit so we could see it more easily.
We can play around with these color list pigments, change the colors, etc.
until we get a floor that we like.

4.8.2.2          Using Pigment and Patterns

Let's begin texturing our sphere by using a pattern and a color map
consisting of three colors. wE replace the pigment block with the following.

  pigment {
    gradient x
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
  }


Rendering this we see that it gives us an interesting pattern of vertical
stripes. We change the gradient direction to y. The stripes are horizontal
now. We change the gradient direction to z. The stripes are now more like
concentric rings. This is because the gradient direction is directly away
from the camera. We change the direction back to x and add the following to
the pigment block.

  pigment {
    gradient x
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
    rotate -45*z          // <- add this line
  }


The vertical bars are now slanted at a 45 degree angle. All patterns can be
rotated, scaled and translated in this manner. Let's now try some different
types of patterns. One at a time, we substitute the following keywords for
gradient x and render to see the result: bozo, marble, agate, granite,
leopard, spotted and wood (if we like we can test all patterns listed in
section "Patterns").

Rendering these we see that each results in a slightly different pattern. But
to get really good results each type of pattern requires the use of some
pattern modifiers.

4.8.2.3          Using Pattern Modifiers

Let's take a look at some pattern modifiers. First, we change the pattern
type to bozo. Then we add the following change.

  pigment {
    bozo
    frequency 3            // <- add this line
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
    rotate -45*z
  }


The frequency modifier determines the number of times the color map repeats
itself per unit of size. This change makes the bozo pattern we saw earlier
have many more bands in it. Now we change the pattern type to marble. When we
rendered this earlier, we saw a banded pattern similar to gradient y that
really did not look much like marble at all. This is because marble really is
a kind of gradient and it needs another pattern modifier to look like marble.
This modifier is called turbulence. We change the line frequency 3 to
turbulence 1 and render again. That's better! Now let's put frequency 3 back
in right after the turbulence and take another look. Even more interesting!

But wait, it get's better! Turbulence itself has some modifiers of its own.
We can adjust the turbulence several ways. First, the float that follows the
turbulence keyword can be any value with higher values giving us more
turbulence. Second, we can use the keywords omega, lambda and octaves to
change the turbulence parameters. Let's try this now:

  pigment {
    marble
    turbulence 0.5
    lambda 1.5
    omega 0.8
    octaves 5
    frequency 3
    color_map {
      [0.00 color Red]
      [0.33 color Blue]
      [0.66 color Yellow]
      [1.00 color Red]
    }
    rotate 45*z
  }


Rendering this we see that the turbulence has changed and the pattern looks
different. We play around with the numerical values of turbulence, lambda,
omega and octaves to see what they do.

4.8.2.4          Using Transparent Pigments and Layered Textures

Pigments are described by numerical values that give the rgb value of the
color to be used (like color rgb <1, 0, 0> giving us a red color). But this
syntax will give us more than just the rgb values. We can specify filtering
transparency by changing it as follows: color rgbf<1, 0, 0, 1>. The f stands
for filter, POV-Ray's word for filtered transparency. A value of one means
that the color is completely transparent, but still filters the light
according to what the pigment is. In this case, the color will be a
transparent red, like red cellophane.

There is another kind of transparency in POV-Ray. It is called transmittance
or non-filtering transparency (the keyword is transmit). It is different from
filter in that it does not filter the light according to the pigment color.
It instead allows all the light to pass through unchanged. It can be
specified like this: rgbt <1, 0, 0, 1>.

Let's use some transparent pigments to create another kind of texture, the
layered texture. Returning to our previous example, declare the following
texture.

  #declare LandArea = texture {
      pigment {
        agate
        turbulence 1
        lambda 1.5
        omega .8
        octaves 8
        color_map {
          [0.00 color rgb <.5, .25, .15>]
          [0.33 color rgb <.1, .5, .4>]
          [0.86 color rgb <.6, .3, .1>]
          [1.00 color rgb <.5, .25, .15>]
        }
      }
    }
  }


This texture will be the land area. Now let's make the oceans by declaring
the following.

  #declare OceanArea = texture {
    pigment {
      bozo
        turbulence .5
        lambda 2
        color_map {
          [0.00, 0.33 color rgb <0, 0, 1>
                      color rgb <0, 0, 1>]
          [0.33, 0.66 color rgbf <1, 1, 1, 1>
                      color rgbf <1, 1, 1, 1>]
          [0.66, 1.00 color rgb <0, 0, 1>
                      color rgb <0, 0, 1>]
        }
      }
    }
  }


Note how the ocean is the opaque blue area and the land is the clear area
which will allow the underlying texture to show through.

Now, let's declare one more texture to simulate an atmosphere with swirling
clouds.

  #declare CloudArea = texture {
    pigment {
      agate
      turbulence 1
      lambda 2
      frequency 2
      color_map {
        [0.0 color rgbf <1, 1, 1, 1>]
        [0.5 color rgbf <1, 1, 1, .35>]
        [1.0 color rgbf <1, 1, 1, 1>]
      }
    }
  }


Now apply all of these to our sphere.

  sphere { <0,0,0>, 1
    texture { LandArea }
    texture { OceanArea }
    texture { CloudArea }
  }


We render this and have a pretty good rendition of a little planetoid. But it
could be better. We don't particularly like the appearance of the clouds.
There is a way they could be done that would be much more realistic.

4.8.2.5          Using Pigment Maps

Pigments may be blended together in the same way as the colors in a color map
using the same pattern keywords that we can use for pigments. Let's just give
it a try.

We add the following declarations, making sure they appear before the other
declarations in the file.

  #declare Clouds1 = pigment {
      bozo
      turbulence 1
      color_map {
        [0.0 color White filter 1]
        [0.5 color White]
        [1.0 color White filter 1]
      }
    }
  #declare Clouds2 = pigment {
    agate
    turbulence 1
    color_map {
      [0.0 color White filter 1]
      [0.5 color White]
      [1.0 color White filter 1]
      }
    }
  #declare Clouds3 = pigment {
    marble
    turbulence 1
    color_map {
      [0.0 color White filter 1]
      [0.5 color White]
      [1.0 color White filter 1]
    }
  }
  #declare Clouds4 = pigment {
    granite
    turbulence 1
    color_map {
      [0.0 color White filter 1]
      [0.5 color White]
      [1.0 color White filter 1]
    }
  }


Now we use these declared pigments in our cloud layer on our planetoid. We
replace the declared cloud layer with.

  #declare CloudArea = texture {
    pigment {
      gradient y
      pigment_map {
        [0.00 Clouds1]
        [0.25 Clouds2]
        [0.50 Clouds3]
        [0.75 Clouds4]
        [1.00 Clouds1]
      }
    }
  }


We render this and see a remarkable pattern that looks very much like weather
patterns on the planet earth. They are separated into bands, simulating the
different weather types found at different latitudes.

4.8.3            Normals

Objects in POV-Ray have very smooth surfaces. This is not very realistic so
there are several ways to disturb the smoothness of an object by perturbing
the surface normal. The surface normal is the vector that is perpendicular to
the angle of the surface. By changing this normal the surface can be made to
appear bumpy, wrinkled or any of the many patterns available. Let's try a
couple of them.

4.8.3.1          Using Basic Normal Modifiers

We comment out the planetoid sphere for now and, at the bottom of the file,
create a new sphere with a simple, single color texture.

  sphere { <0,0,0>, 1
    pigment { Gray75 }
    normal { bumps 1 scale .2 }
  }


Here we have added a normal block in addition to the pigment block (note that
these do not have to be included in a texture block unless they need to be
transformed together or need to be part of a layered texture). We render this
to see what it looks like. Now, one at a time, we substitute for the keyword
bumps the following keywords: dents, wrinkles, ripples and waves (we can also
use any of the patterns listed in "Patterns"). We render each to see what
they look like. We play around with the float value that follows the keyword.
We also experiment with the scale value.

For added interest, we change the plane texture to a single color with a
normal as follows.

  plane { y, -1.5
    pigment { color rgb <.65, .45, .35> }
    normal { dents .75 scale .25 }
  }


4.8.3.2          Blending Normals

Normals can be layered similar to pigments but the results can be unexpected.
Let's try that now by editing the sphere as follows.

  sphere { <0,0,0>, 1
    pigment { Gray75 }
      normal { radial frequency 10 }
      normal { gradient y scale .2 }
  }


As we can see, the resulting pattern is neither a radial nor a gradient. It
is instead the result of first calculating a radial pattern and then
calculating a gradient pattern. The results are simply additive. This can be
difficult to control so POV-Ray gives the user other ways to blend normals.

One way is to use normal maps. A normal map works the same way as the pigment
map we used earlier. Let's change our sphere texture as follows.

  sphere { <0,0,0>, 1
    pigment { Gray75 }
    normal {
      gradient y
      frequency 3
      turbulence .5
      normal_map {
        [0.00 granite]
        [0.25 spotted turbulence .35]
        [0.50 marble turbulence .5]
        [0.75 bozo turbulence .25]
        [1.00 granite]
      }
    }
  }


Rendering this we see that the sphere now has a very irregular bumpy surface.
The gradient pattern type separates the normals into bands but they are
turbulated, giving the surface a chaotic appearance. But this give us an
idea.

Suppose we use the same pattern for a normal map that we used to create the
oceans on our planetoid and applied it to the land areas. Does it follow that
if we use the same pattern and modifiers on a sphere the same size that the
shape of the pattern would be the same? Wouldn't that make the land areas
bumpy while leaving the oceans smooth? Let's try it. First, let's render the
two spheres side-by-side so we can see if the pattern is indeed the same. We
un-comment the planetoid sphere and make the following changes.

  sphere { <0,0,0>, 1
    texture { LandArea }
    texture { OceanArea }
    //texture { CloudArea }  // <-comment this out
    translate -x             // <- add this transformation
  }


Now we change the gray sphere as follows.

  sphere { <0,0,0>, 1
    pigment { Gray75 }
    normal {
      bozo
      turbulence .5
      lambda 2
      normal_map {
        [0.4 dents .15 scale .01]
        [0.6 agate turbulence 1]
        [1.0 dents .15 scale .01]
      }
    }
    translate x // <- add this transformation
  }


We render this to see if the pattern is the same. We see that indeed it is.
So let's comment out the gray sphere and add the normal block it contains to
the land area texture of our planetoid. We remove the transformations so that
the planetoid is centered in the scene again.

  #declare LandArea = texture {
    pigment {
      agate
      turbulence 1
      lambda 1.5
      omega .8
      octaves 8
      color_map {
        [0.00 color rgb <.5, .25, .15>]
        [0.33 color rgb <.1, .5, .4>]
        [0.86 color rgb <.6, .3, .1>]
        [1.00 color rgb <.5, .25, .15>]
      }
    }
    normal {
      bozo
      turbulence .5
      lambda 2
      normal_map {
        [0.4 dents .15 scale .01]
        [0.6 agate turbulence 1]
        [1.0 dents .15 scale .01]
      }
    }
  }


Looking at the resulting image we see that indeed our idea works! The land
areas are bumpy while the oceans are smooth. We add the cloud layer back in
and our planetoid is complete.

There is much more that we did not cover here due to space constraints. On
our own, we should take the time to explore slope maps, average and bump
maps.

4.8.4            Finishes

The final part of a POV-Ray texture is the finish. It controls the properties
of the surface of an object. It can make it shiny and reflective, or dull and
flat. It can also specify what happens to light that passes through
transparent pigments, what happens to light that is scattered by
less-than-perfectly-smooth surfaces and what happens to light that is
reflected by surfaces with thin-film interference properties. There are
twelve different properties available in POV-Ray to specify the finish of a
given object. These are controlled by the following keywords: ambient,
diffuse, brilliance, phong, specular, metallic, reflection, refraction,
caustics, attenuation, crand and iridescence. Let's design a couple of
textures that make use of these parameters.

4.8.4.1          Using Ambient

Since objects in POV-Ray are illuminated by light sources, the portions of
those objects that are in shadow would be completely black were it not for
the first two finish properties, ambient and diffuse. Ambient is used to
simulate the light that is scattered around the scene that does not come
directly from a light source. Diffuse determines how much of the light that
is seen comes directly from a light source. These two keywords work together
to control the simulation of ambient light. Let's use our gray sphere to
demonstrate this. Let's also change our plane back to its original green and
white checkered pattern.

  plane {y,-1.5
    pigment {checker Green, White}
  }

  sphere { <0,0,0>, 1
    pigment {Gray75}
    finish {
      ambient .2
      diffuse .6
  }


In the above example, the default values for ambient and diffuse are used. We
render this to see what the effect is and then make the following change to
the finish.

  ambient 0
  diffuse 0


The sphere is black because we have specified that none of the light coming
from any light source will be reflected by the sphere. Let's change diffuse
back to the default of 0.6.

Now we see the gray surface color where the light from the light source falls
directly on the sphere but the shaded side is still absolutely black. Now
let's change diffuse to 0.3 and ambient to 0.3.

The sphere now looks almost flat. This is because we have specified a fairly
high degree of ambient light and only a low amount of the light coming from
the light source is diffusely reflected towards the camera. The default
values of ambient and diffuse are pretty good averages and a good starting
point. In most cases, an ambient value of 0.1 ... 0.2 is sufficient and a
diffuse value of 0.5 ... 0.7 will usually do the job. There are a couple of
exceptions. If we have a completely transparent surface with high refractive
and/or reflective values, low values of both ambient and diffuse may be best.
Here is an example.

  sphere { <0,0,0>, 1
     pigment { White filter 1 }
       finish {
         ambient 0
         diffuse 0
         reflection .25
         refraction 1
         ior 1.33
         specular 1
         roughness .001
      }
    }
  }


This is glass, obviously. Glass is a material that takes nearly all of its
appearance from its surroundings. Very little of the surface is seen because
it transmits or reflects practically all of the light that shines on it. See
glass.inc for some other examples.

If we ever need an object to be completely illuminated independently of the
lighting situation in a given scene we can do this artificially by specifying
an ambient value of 1 and a diffuse value of 0. This will eliminate all
shading and simply give the object its fullest and brightest color value at
all points. This is good for simulating objects that emit light like
lightbulbs and for skies in scenes where the sky may not be adequately lit by
any other means.

Let's try this with our sphere now.

  sphere { <0,0,0>, 1
    pigment { White }
      finish {
        ambient 1
        diffuse 0
      }
    }
  }


Rendering this we get a blinding white sphere with no visible highlights or
shaded parts. It would make a pretty good streetlight.

4.8.4.2          Using Surface Highlights

In the glass example above, we noticed that there were bright little hotspots
on the surface. This gave the sphere a hard, shiny appearance. POV-Ray gives
us two ways to specify surface specular highlights. The first is called Phong
highlighting. Usually, Phong highlights are described using two keywords:
phong and phong_size. The float that follows phong determines the brightness
of the highlight while the float following phong_size determines its size.
Let's try this.

  sphere { <0,0,0>, 1
    pigment { Gray50 }
    finish {
      ambient .2
      diffuse .6
      phong .75
      phong_size 25
    }
  }


Rendering this we see a fairly broad, soft highlight that gives the sphere a
kind of plastic appearance. Now let's change phong_size to 150. This makes a
much smaller highlight which gives the sphere the appearance of being much
harder and shinier.

There is another kind of highlight that is calculated by a different means
called specular highlighting. It is specified using the keyword specular and
operates in conjunction with another keyword called roughness. These two
keywords work together in much the same way as phong and phong_size to create
highlights that alter the apparent shininess of the surface. Let's try using
specular in our sphere.

  sphere { <0,0,0>, 1
    pigment { Gray50 }
      finish {
        ambient .2
        diffuse .6
        specular .75
        roughness .1
      }
    }
  }


Looking at the result we see a broad, soft highlight similar to what we had
when we used phong_size of 25. Change roughness to .001 and render again. Now
we see a small, tight highlight similar to what we had when we used
phong_size of 150. Generally speaking, specular is slightly more accurate and
therefore slightly more realistic than phong but you should try both methods
when designing a texture. There are even times when both phong and specular
may be used on a finish.

4.8.4.3          Using Reflection and Metallic

There is another surface parameter that goes hand in hand with highlights,
reflection. Surfaces that are very shiny usually have a degree of reflection
to them. Let's take a look at an example.

  sphere { <0,0,0>, 1
    pigment { Gray50 }
      finish {
        ambient .2
        diffuse .6
        specular .75
        roughness .001
        reflection .5
      }
    }
  }


We see that our sphere now reflects the green and white checkered plane and
the black background but the gray color of the sphere seems out of place.
This is another time when a lower diffuse value is needed. Generally, the
higher reflection is the lower diffuse should be. We lower the diffuse value
to 0.3 and the ambient value to 0.1 and render again. That is much better.
Let's make our sphere as shiny as a polished gold ball bearing.

  sphere { <0,0,0>, 1
    pigment { BrightGold }
      finish {
        ambient .1
        diffuse .1
        specular 1
        roughness .001
        reflection .75
      }
    }
  }


That is very close but there is something wrong with the highlight. To make
the surface appear more like metal the keyword metallic is used. We add it
now to see the difference.

  sphere { <0,0,0>, 1
    pigment { BrightGold }
      finish {
        ambient .1
        diffuse .1
        specular 1
        roughness .001
        reflection .75
        metallic
      }
    }
  }


We see that the highlight has taken on the color of the surface rather than
the light source. This gives the surface a more metallic appearance.

4.8.4.4          Using Refraction

Objects that are transparent allow light to pass through them. With some
substances, the light is bent as it travels from one substance into the other
because of the differing optical densities of the objects. This is called
refraction. Water and glass both bend light in this manner. To create water
or glass, POV-Ray gives us a way to specify refraction. This is done with the
keywords refraction and ior. The amount of light that passes through an
object is determined by the value of the filtering and/or transmittance
channel in the pigment. We should use the refraction value only to switch
refraction on or off using values of 1 or 0 respectively (or the boolean
values on and off). See section "Refraction" for a detailed explanation of
the reasons.

The degree of refraction, i. e. the amount of bending that occurs, is given
by the keyword ior, short for index of refraction. If we know the index of
refraction of the substance we are trying to create, we may just use that.
For instance, water is 1.33, glass is around 1.45 and diamond is 1.75. Let's
return to the example of a glass sphere we used earlier.

  sphere { <0,0,0>, 1
    pigment { White filter 1 }
      finish {
        ambient 0
        diffuse 0
        reflection .25
        refraction 1
        ior 1.45
        specular 1
        roughness .001
      }
    }
  }


We render this again and notice how the plane that is visible through the
sphere is distorted and turned upside-down. This is because the light passing
through the sphere is being bent or refracted to the degree specified. We
reduce ior to 1.25 and re-render. We increase it to 1.75 and re-render. We
notice how the distortion changes.

4.8.4.5          Adding Light Attenuation

Transparent objects can be made to cause the intensity of light passing
through them to be reduced. In reality, this is due to impurities in
scattering the light. Two float values determine the effect: fade_distance is
the distance the light has to travel to reach one-half its original intensity
and fade_power is the degree of falloff. Let's try an example of this.

  sphere { <0,0,0>, 1
    pigment { White filter 1 }
      finish {
        ambient .1
        diffuse .1
        reflection .15
        refraction 1
        ior 1.45
        specular 1
        roughness .001
        fade_distance 5
        fade_power 1
    }
  }


The caustics of a translucent sphere.

This gives the sphere a slightly clouded look as if not all of the light was
able to pass through it. For interesting variations of this texture, try
lowering ior to 1.15 and raising reflection to 0.5.

4.8.4.6          Using Faked Caustics


4.8.4.6.1        What are Caustics?

First, let us raid our kitchen cupboard. We are looking for transparent glass
or crystal drinking glasses. If they have a pattern etched in their surface,
so much the better. One by one, we place them under a bright lamp and observe
the shadow they cast on the desk or table beneath. If we look closely we will
make out bright regions within the shadow. These will be places where the
refractive properties of the drinking glass are concentrating light
sufficiently to make the bright spots. If there is a pattern in the surface
of the glass we will see the pattern formed out of the bright areas. Those
bright regions are the caustics caused by refraction, the refractice
caustics. There will also be bright patterns of light on the table that are
caused by light reflected off the glass. These are called reflective
caustics.

Once we know what we are looking for we will be able to spot caustics in many
everyday situations: the shadow cast by a magnifying glass has one, light
streaming through an aquarium might makes them, the light passing through a
piece of crumpled cellophane might cast them on the table top, etc. We will
even see them in the bottom of a swimming pool on a bright sunny day.
Caustics are a subtle lighting effect that can really lend realism to
raytraced images of such items.

POV-Ray uses algorithms that fake refractive caustics (reflective caustices
are not possible).There are inherant limitations on the process of (standard)
ray-tracing in general which make it unsuitable for certain light simulation
applications, such as optical testing and a few very particular architectural
lighting projects. Methods which do the considerably more extensive
calculations needed to do full light simulation including caustics (like
path-tracing, photon-tracing or bi-directional ray-tracing) are very slow and
impractical on average platforms.

This means that we have to tinker with the caustics to get the best possible
look, but with a little experimentation, we will see we can very closely
emulate the real thing. The best way to go is, where ever possible, to study
an example of the thing we are trying to trace. We need to get to know its
pattern of caustics and then adjust our final picture until we are satisfied.

4.8.4.6.2        Applying Caustics to a Scene

Caustics is a new texture property under the area of finishes. We apply it to
the shadows of a transparent, refractive object by adding in the caustics
keyword to the finish. We try the following simple example for a start (see
file caustic1.pov).

  #include "colors.inc"
  #include "textures.inc"

  camera {
    location <0, 15, -40>
    look_at <-2, 0, 1>
    angle 10
  }

  light_source { <10, 20, 10> color White }

  // lay down a boring floor to view the shadow against

  plane { y, 0
    pigment { Grey }
  }

  // here's something to have caustics property applied

  sphere { <0, 3, 0>, 2
    texture {
      Glass3
      finish { caustics .6 }
    }
  }


The caustics in a swimming-pool.

When we render this we will see our sphere in the upper right corner of the
image, floating a little over the plane, and the shadow it casts is sprawled
across the central part of our view. And there in the center is a basic
caustic. That bright area in the center represents the light which normally
refractivity would concentrate in the middle of the shadow.

The only question this leaves is: what is with the floating point value which
follows the caustics keyword? Well, that's where our discussion above on
adjusting the caustic comes in. Remember the drinking glasses? If we had one
that had fairly thin walls and then a thick glass base we will see what we
mean in the shadows it casts. Above, with the thinner walls (with less
refraction) the caustics are less pronounced and more evenly diffused through
the shadow, but when we get to the part of the shadow cast by the thicker,
more refractive base, suddenly the caustic becomes more pronounced and more
tightly focused near the center.

Of course, since this is a simulated caustic, there is no correspondence
between the degree to which the caustic is focused or diffused and the shape,
size and refractivity of the object. But we can manually control it with the
floating point value following the caustic keyword. The closer this value
gets to zero, the more diffused and dimmer the caustic gets, while the nearer
it becomes to 1, the more tightly focused and pronounced the caustic gets. At
1, we have the caustic of a thick, highly refractive piece of lead crystal,
while at 0.1 it is more like a hollow glass sphere. We try this by
re-rendering the above scene, with a range of values from 0.1 to 1.0 and
watching the different caustics we get.

Out of range values work also. Numbers higher than 1 just lead to more and
more tightly focused caustics. Negative numbers are just plain weird, but
interesting. Essentially, the object becomes illuminated in all sorts of
bizzare ways and the shadow becomes like a photographic negative of itself.
Kind of like a 1950's sci-fi raygun effect. It looks strange, and not at all
photo-realistic, but if we like the surreal we may want to try it at least
once and file away the effect in our mind in case we ever want it.

4.8.4.6.3        Caustics And Normals

POV-Ray makes use of surface normal perturbation in a way that is more unique
than people generally stop to think. When we apply a surface normal in a
texture we are actually not altering the surface at all, but rather telling
POV-Ray to treat the surface as if it were altered, for purposes of computing
the illumination falling on each individual spot. In short, it is a trick of
the light and shadow which, supposing only that we don't see it at too sharp
a viewing angle, effectively creates the illusion of distortions in the
surface of an object.

Caustics are also a synthetic trick, as we saw above, and sure enough, they
have been designed to react to texture normal patterns as if those patterns
were genuinely there. Remember the drinking glass experiment? If we found a
glass with patterns etched into the surface we probably noted that the
pattern showed up in the caustics cast by the glass too. When we have a
transparent surface with a normal applied to it, it causes the caustics cast
by that surface to mimick the normal pattern, so that it shows up in the
shadows.

Following is an example of what we mean: it is a simply meant to represent
water in a swimming pool. We have distilled this down to a plane above to
represent the water, one below to represent the floor of the pool, a camera
just below the waterline, looking at the floor, and a light source high above
(see caustic2.pov).

  #include "colors.inc"

  // Our camera is underwater, looking at the bottom of
  // the pool for the best view of the caustics produced

  camera {
    location <0, -5, 0>
    look_at  <0, -10, -5>
  }

  light_source { <0, 100, 49.5> color White }

  // the bottom of the pool...

  plane { y, -10
    texture {
      pigment { color rgb <0.6, 0.7, 0.7> }
      finish { ambient 0.1 diffuse 0.7 }
      scale 0.01
    }
  }

  // and the surface of the water

  plane { y, 0
    texture {
      pigment { rgbf <0.6, 0.67, 0.72, 0.9> }
      normal {
        bumps .6
        scale <.75, .25, .25>
        rotate <0, 45, 0>
      }
      finish { caustics .9 }
    }
  }


The bumps we have given the water plane are meant to represent the small,
random crests and troughs that form on a pool when a light breeze blows over
it. We could have used ripples or waves as well, like something had recently
splashed into it at some point, but the bumps will work well enough for an
example.

We notice that our view of the pool floor shows dozens of tiny caustic light
spots, corresponding approximately to a random bump pattern. If we like we
can try putting in ripples or waves and watch the pattern of the caustics
change. Even though a flat plane itself would cast no caustics (we could try
without the normal), POV-Ray's faked caustic generation knows that if the
surface was really bumped like this normal is indicating, the refraction of
the bumped surface would be just enough to concentrate light in caustics
throughout the bottom of the pool.

We see that just as with a curved surface, such as the sphere previously,
normal patterns also trigger the appearance of caustics cast by an object.
Interestingly enough, this alone would be proof that the caustics really are
faked: our water hasn't even been given any refraction properties in its
finish, yet the caustics are still there just the same!

4.8.4.7          Using Iridescence

Iridescence is what we see on the surface of an oil slick when the sun shines
on it. The rainbow effect is created by something called thin-film
interference (read section "Iridescence" for details). For now let's just try
using it. Iridescence is specified by the irid keyword and three values:
amount, thickness and turbulence. The amount is the contribution to the
overall surface color. Usually 0.1 to 0.5 is sufficient here. The thickness
affects the busyness of the effect. Keep this between 0.25 and 1 for best
results. The turbulence is a little different from pigment or normal
turbulence. We cannot set octaves, lambda or omega but we can specify an
amount which will affect the thickness in a slightly different way from the
thickness value. Values between 0.25 and 1 work best here too. Finally,
iridescence will respond to the surface normal since it depends on the angle
of incidence of the light rays striking the surface. With all of this in
mind, let's add some iridescence to our glass sphere.

  sphere { <0,0,0>, 1
    pigment { White filter 1 }
      finish {
        ambient .1
        diffuse .1
        reflection .2
        refraction 1
        ior 1.5
        specular 1
        roughness .001
        fade_distance 5
        fade_power 1
        caustics 1
        irid {
          0.35
          thickness .5
          turbulence .5
        }
     }
  }


We try to vary the values for amount, thickness and turbulence to see what
changes they make. We also try to add a normal block to see what happens.

4.8.5            Halos

Important notice: The halo feature in POV-Ray 3.0 is somewhat experimental.
There is a high probability that the design and implementation of these
features will be changed in future versions. We cannot guarantee that scenes
using these features in 3.0 will render identically in future releases or
that full backwards compatibility of language syntax can be maintained.

Halos are a powerful feature that can be used to create a lot of different
effects like clouds, fogs, fire, lasers, etc. The name actually comes from
the ability to render halos with it, like the ones seen around the moon or
the sun.

Due to the complexity of the halo feature and the large amount of parameters
provided it is very difficult to get satisfying results. The following
sections will help to create a halo step by step, starting with the basic
things and going to the more subtle stuff.

It is also helpful to read the halo reference sections to get a better
understanding of the halo feature. One should especially read the sections
"Empty and Solid Objects" and "Halo Mapping"  because they are essential for
understanding halos.

4.8.5.1          What are Halos?

Halos are a texture feature allowing us to fill the interior of an object
with particles. The distribution of these particles can be modified using
several density mappings and density functions. The particles can emit light
to give fire- or laser-like effects or they can absorb light to create clouds
or fog.

A halo is attached to an object, the so called container object, just like a
pigment, normal or finish. The container object is completely filled by the
halo but we will not see anything if we do not make sure that the object is
hollow and the surface is translucent. How this is accomplished will be shown
in the next section.

When working with halos we always have to keep in mind that the container
object has to be hollow and translucent.

4.8.5.2          The Emitting Halo

We start with one of the simpler types, the emitting halo. It uses particles
that only emit light. There are no particles that absorb the light coming
from other particles or light sources.

4.8.5.2.1        Starting with a Basic Halo

A clever approach in designing a nice halo effect is to start with a simple,
unit-sized shape that sits on the coordinate system's origin.

In the first example (halo01.pov) we try to create a fiery explosion, which
the sphere is best suited for. We start with a simple scene consisting of a
camera, a light source (we don't care about shadows so we add the shadowless
keyword), a checkered plane and a unit-sized sphere containing the halo.

  camera {
    location <0, 0, -2.5>
    look_at <0, 0, 0>
  }

  light_source { <10, 10, -10> color rgb 1 shadowless }

  plane { z, 2
    pigment { checker color rgb 0, color rgb 1 }
    finish { ambient 1 diffuse 0 }
    scale 0.5
    hollow
  }

  sphere { 0, 1
    pigment { color rgbt <1, 1, 1, 1> }
    halo {
      emitting
      spherical_mapping
      linear
      color_map {
        [ 0 color rgbt <1, 0, 0, 1> ]
        [ 1 color rgbt <1, 1, 0, 0> ]
      }
      samples 10
    }
    hollow
  }


We note that the sphere is set to be hollow and has a translucent surface
(the transmittance channel in the pigment's color is 1), just like it is
required for halos. We also note that the plane has a hollow keyword even
though it has no halo. Why is this necessary?

The reason is quite simple. As described in section "Empty and Solid Objects"
there can be no halo inside any other non-hollow object. Since the camera is
inside the plane object, i. e. it is on the side of the plane that is
considered to be inside, the halo will never be visible unless the plane is
made hollow (or the negative keyword is added to bring the camera on the
outside side of the plane).

What do all those halo keywords and values mean? At the beginning of the halo
the emitting keyword is used to specify what type of halo we want to use. The
emitting halo emits light. That is what is best suited for our fiery
explosion.

The spherical_mapping and linear keywords need a more detailed explanation of
how a halo works (this is also done in chapter "Halo" in more detail).

As noted above the halo is made up of lots of small particles. The
distribution of these particles is described by a density function. In
general, a density function tells us how much particles we'll find at a given
location.

Instead of using an explicitly, mathematical density function, halos rely on
a given set of density mappings and density functions to model a variety of
particle distributions.

The first step in this model is the density mapping function that is used to
map three-dimensional points onto a one-dimensional range of values. In our
example we use a spherical mapping, i.e. we take the distance of a point from
the center of the coordinate system. This is the reason why it is clever to
start with a container object sitting on the coordinate system's center.
Since all density mappings are made relative to this center we won't see
anything if we start with an object sitting somewhere else. Moving the whole
object (including textures and halos) to another location is the correct way
of placing a container object.

Now we have a single value in the range from 0 to 1. This value will be
transformed using a density function to get density values instead of
distance values. Just using this single value won't work because we want to
have particle distributions were the density decreases as we move from the
center of the container object to the outside.

This is done by the density function. There are several alternatives
available as described in the halo reference (see section "Density Function"
). We use the simple linear function that just maps values between 0 and 1
onto a 1 to 0 range. Thus we get a density value of 1 at the center of our
sphere and a value of 0 at its surface.

Now that we have a density function what do we do to see something? This is
where the colour_map keyword comes into play. It is used to describe a color
map that actually tells the program what colors are to be used for what
density. The relation is quite simple: colors at the beginning of the color
map (with small values) will be used for low density values and colors at the
end of the map (high values) will be used for high densities. In our example
the halo will be yellow at the center of the sphere where the density is
greatest and it will blend to red at the surface of the sphere where the
density approaches zero.

The transmittance channel of the colors in the color map is used to model the
translucency of the density field. A value of 0 represents no translucency,
i. e. that areas with the corresponding density will be (almost) opaque,
while a value of 1 means (almost) total translucency.

In our example we use

  color_map {
    [ 0 color rgbt <1, 0, 0, 1> ]
    [ 1 color rgbt <1, 1, 0, 0> ]
  }


which results in a halo with a very translucent, reddish outer area and a
nearly opaque, yellowish inner areas as we can see after tracing the example
image.

The basic halo used in modelling a fiery explosion.

There is one parameter that still needs to be explained: the samples keyword.
This keyword tells POV-Ray how many samples have to be taken along any ray
traveling through the halo to calculate its effect. Using a low value will
result in a high tracing speed while a high value will lead to a low speed.
The sample value has to be increased if the halo looks somewhat noisy, i. e.
if some artifacts of the low sampling rate appear. For more details see
section "Halo Sampling".



4.8.5.2.2        Increasing the Brightness

The colors of the halo in the above image are somewhat dim. There is too much
of the background visible through the halo. That does not look much like
fire, does it? An easy way to fix this is to decrease the transparency of the
particles in the areas of high density. We do this by using use the following
color map instead of the old one (the negative transmittance is correct).

  color_map {
    [ 0 color rgbt <1, 0, 0,  1> ]
    [ 1 color rgbt <1, 1, 0, -1> ]
  }


Looking at the result of halo02.pov we see that the halo is indeed much
brighter.


4.8.5.2.3        Adding Some Turbulence

What we now have does not look like a fiery explosion. It's more a glowing
ball than anything else. Somehow we have to make it look more chaotic, we
have to add some turbulence to it.

This is done by using the turbulence keyword together with the amount of
turbulence we want to add. Just like in the following example.

  sphere { 0, 1
    pigment { color rgbt <1, 1, 1, 1> }
    halo {
      emitting
      spherical_mapping
      linear
      turbulence 1.5
      color_map {
        [ 0 color rgbt <1, 0, 0,  1> ]
        [ 1 color rgbt <1, 1, 0, -1> ]
      }
      samples 10
    }
    hollow
  }


Adding turbulence to the halo moves all points inside the halo container in a
pseudo-random manner. This results in a particle distribution that looks like
there was some kind of flow in the halo (depending on the amount of
turbulence we'll get a laminar or turbulent flow). The high turbulence value
is used because an explosion is highly turbulent.

Looking at the example image (halo03.pov) we'll see that this looks more like
a fiery explosion than the glowing ball we got until now.

Adding some turbulence makes the fiery explosion more realistic.

We notice that the time it took to render the image increased after we added
the turbulence. This is due to the fact that for every sample taken from the
halo the slow turbulence function has to be evaluated.

4.8.5.2.4        Resizing the Halo

There is one strange thing about our fiery explosion though. It still looks
like a sphere. Why does this happen and what can we do to avoid it?

As noted above adding turbulence moves the particles inside the halo
container around. The problem is that some of the particles are actually
moved out of the container object. This leads to high densities at the
surface of the container object revealing the shape of the object (all
particles outside the container are lost and will not visible resulting in a
large, highly visible density change at the surface).

An easy way of avoiding this is to make sure that the particles stay inside
the container object even if we add some turbulence. This is done by scaling
the halo to reduce its size. We do not scale the container object, just the
halo.

This is done by adding the scale keyword inside the halo statement.

  sphere { 0, 1
    pigment { color rgbt <1, 1, 1, 1> }
    halo {
      emitting
      spherical_mapping
      linear
      turbulence 1.5
      color_map {
        [ 0 color rgbt <1, 0, 0,  1> ]
        [ 1 color rgbt <1, 1, 0, -1> ]
      }
      samples 10
      scale 0.5
    }
    hollow
    scale 1.5
  }


The scale 0.5 command tells POV-Ray to scale all points inside the halo by
this amount. This effectively scales the radius we get after the density
mapping to a range of 0 to 0.5 instead of 0 to 1 (without turbulence). If we
now add the turbulence the points are allowed to move half a unit in every
direction without leaving the container object. That is exactly what we want.


To compensate for the smaller halo we would get we scale the sphere (and the
halo inside) by 1.5.

Looking at the new example image (halo04.pov) we will no longer see any signs
of the container sphere. We finally have a nice fiery explosion.

Resizing the halo makes it look much better.

The amount by which to scale the halo depends on the amount of turbulence we
use. The higher the turbulence value the smaller the halo has to be scaled.
That is something to experiment with.

Another way to avoid that points move out of the sphere is to use a larger
sphere, i. e. a sphere with a radius larger than one. It is important to
re-size the sphere before the halo is added because otherwise the halo will
also be scaled.

We note that this only works for spherical and box mapping (and a
non-constant density function). All other mapping types are (partially)
infinite, i. e. the resulting particle distribution covers an infinite space
(see also "Halo Mapping").

4.8.5.2.5        Using Frequency to Improve Realism

Another very good way of improving the realism of our explosion is to use a
frequency value other than one. The way frequency works is explained in
section "Frequency Modifier" in the reference part.

The rather mathematical explanation used there doesn't help much in
understanding how this feature is used. It is quite simple though. The
frequency value just tells the program how many times the color map will be
repeated in the density range from 0 to 1. If a frequency of one (the
default) is specified the color map will be visible once in the density
field, e. g. the color at 0 will be used for density 0, color at 0.5 will be
used for density 0.5 and the color at 1 will be used for density 1. Simple,
isn't it?

If we choose a frequency of two, the color at 0 will be used for density 0,
the color at 0.5 will be used for density 0.25 and the color at 1 will be
used for density 0.5. What about the densities above 0.5? Since there are no
entries in the color map for values above 1 we just start at 0 again. Thus
the color at 0.1 will be used for density 0.55 ((2*0.55) mod 1 = 1.1 mod 1 =
0.1), the color at 0.5 will be used for density 0.75 and the color at 1 will
be used for density 1.

If we are good at mathematics we'll note that the above example is not quite
right because (1 * 2) mod 1 = 0 and not 1. We just think that we used a value
slightly smaller than one and everything will be fine.

We may have noticed that in order to avoid sudden changes in the halo color
for frequencies larger than one we'll have to used a periodic color map, i.e.
a color map whose entries at 0 and 1 are the same.

We'll change our example by using a periodic color map and changing the
frequency value to two.

  sphere { 0, 1
    pigment { color rgbt <1, 1, 1, 1> }
    halo {
      emitting
      spherical_mapping
      linear
      turbulence 1.5
      color_map {
        [ 0.0 color rgbt <1, 0, 0,  1> ]
        [ 0.5 color rgbt <1, 1, 0, -1> ]
        [ 1.0 color rgbt <1, 0, 0,  1> ]
      }
      frequency 2
      samples 20
      scale 0.5
    }
    hollow
    scale 1.5
  }


Using a periodic color map and a frequency of two gives a much nicer
explosion.

Looking at the result of (halo05.pov) we can be quite satisfied with the
explosion we just have created, can't we?

There's one thing left we should be aware of when increasing the frequency
value. It is often necessary to increase the sample rate in (nearly) the same
way as we change the frequency. If we don't do this we'll probably get some
severe aliasing artifacts (like color jumps or strange bands of colors). If
this happens just change the samples value according to the frequency value
(twice sampling rate for a doubled frequency).

4.8.5.2.6        Changing the Halo Color

We have a nice fiery explosion but we want to try to add some science fiction
touch to it by using different colors. How about a nice green, less turbulent
explosion that gets red at its borders?

Nothing easier than that!

  sphere { 0, 1.5
    pigment { color rgbt <1, 1, 1, 1> }
    halo {
      emitting
      spherical_mapping
      linear
      turbulence 0.5
      color_map {
        [ 0 color rgbt <0, 1, 0,  1> ]
        [ 1 color rgbt <1, 0, 0, -1> ]
      }
      samples 10
      scale 0.75
    }
    hollow
    scale 1.5
  }


Using red and green colors gives an unexpected result.

This should do the trick. Looking at the result of halo06.pov we may be
disappointed. Where is the red center of the explosion? The borders are green
as expected but there is a lot of yellow in the center and only a little bit
red. What is happening?

We use an emitting halo in our example. According to the corresponding
section in the halo reference chapter (see "Emitting") this type of halo uses
very small particles that do not attenuate light passing through the halo.
Especially particles near the viewer do not attenuate the light coming from
particles far away from the viewer.

During the calculation of the halo's color near the center of the container
sphere, the ray steps through nearly all possible densities of the particle
distribution. Thus we get red and green colors as we march on, depending on
the current position in the halo. The sum of these colors is used which will
gives as a yellow color (the sum of red and green is yellow). This is what is
happening here.

How can we still get what we want? The answer is to use a glowing halo
instead of the emitting halo. The glowing halo is very similar to the
emitting one except that it attenuates the light passing through. Thus the
light of particles lying behind other particles will be attenuated by the
particles in front.


4.8.5.3          The Glowing Halo

We have mentioned the glowing halo in the section about the emitting halo as
one way to avoid the color mixing that is happening with emitting halos.

The glowing halo is very similar to the emitting halo except that it also
absorbs light. We can view it as a combination of the emitting and the
attenuating halo described in section "The Attenuating Halo".

By just replacing the emitting keyword in the example in section "Changing
the Halo Color" with the glowing keyword we get the desired effect as shown
in the example image (halo11.pov).

Using a glowing halo gives the expected result.

Even though the red color of the high density areas is not very visible
because the green colored, lower density areas lying in front absorb most of
the red light, we don't get yellow color where we would have expected a red
one.

Due to its similarity with the emitting halo we have to make some experiments
with this halo type. We just have to keep all those things we learned in the
previous sections in mind to get some satisfying results.

4.8.5.4          The Attenuating Halo

Another simple halo type is the attenuating halo that only absorbs light. It
doesn't radiate on its own.

A great difference between the attenuating halo and the other halo types is
that the color of the attenuating halo is calculated from the halo's color
map using the total particle density along a given ray. The other types
calculated a (weighted) average of the colors calculated from the density at
each sample.

4.8.5.4.1        Making a Cloud

Attenuating halos are ideal to create clouds and smoke. In the following
examples we will try to make a neat little cloud. We start again by using a
unit-sized sphere that is filled with a basic attenuating halo (halo21.pov).

  camera {
    location <0, 0, -2.5>
    look_at <0, 0, 0>
  }

  light_source { <10, 10, -10> color rgb 1 shadowless }

  plane { z, 2
    pigment { checker color rgb 0, color rgb 1 }
    finish { ambient 1 diffuse 0 }
    scale 0.5
    hollow
  }

  sphere { 0, 1
    pigment { color rgbt <1, 1, 1, 1> }
    halo {
      attenuating
      spherical_mapping
      linear
      color_map {
        [ 0 color rgbt <1, 0, 0, 1> ]
        [ 1 color rgbt <1, 0, 0, 0> ]
      }
      samples 10
    }
    hollow
  }


Even though clouds normally are not red but white or gray, we use the red
color to make it more visible against the black/white checkerboard
background.

The color of an attenuating halo is calculated from the total accumulated
density after a ray has marched through the complete particle field. This has
to be kept in mind when creating the color map. We want the areas of the
cloud with a low density to have a high translucency so we use a color of
rgbt<1,0,0,1> and we want the high density areas to be opaque so we choose a
color of rgbt<1,0,0,0>.


4.8.5.4.2        Scaling the Halo Container

The cloud we have created so far doesn't look very realistic. It's just a
red, partially translucent ball. In order to get a better result we use some
of the methods we have already learned in the sections about emitting halos
above. We add some turbulence to get a more realistic shape, we scale the
halo to avoid the container object's surface to become visible and we
decrease the translucency of the areas with a high particle density.

Another idea is to scale the container object to get an ellipsoid shape that
can be used to model a cloud pretty good. This is done by the scale <1.5,
0.75, 1> command at the end of the sphere. It scales both, the sphere and the
halo inside.

  sphere { 0, 1
    pigment { color rgbt <1, 1, 1, 1> }
    halo {
      attenuating
      spherical_mapping
      linear
      turbulence 1
      color_map {
        [ 0 color rgbt <1, 0, 0,  1> ]
        [ 1 color rgbt <1, 0, 0, -1> ]
      }
      samples 10
      scale 0.75
    }
    hollow
    scale <1.5, 0.75, 1>
  }


Looking at the results of halo22.pov we see that this looks more like a real
cloud (besides the color).


4.8.5.4.3        Adding Additional Halos

Another trick to get some more realism is to use multiple halos. If we look
at cumulus clouds e. g. we notice that they often extend at the top while
they are quite flat at the bottom.

We want to model this appearance by adding two additional halos to our
current container object (see section "Multiple Halos" for more details).
This is done in the following way:

  sphere { 0, 1.5
    pigment { color rgbt <1, 1, 1, 1> }
    halo {
      attenuating
      spherical_mapping
      linear
      turbulence 1
      color_map {
        [ 0 color rgbt <1, 0, 0,  1> ]
        [ 1 color rgbt <1, 0, 0, -1> ]
      }
      samples 10
      scale <0.75, 0.5, 1>
      translate <-0.4, 0, 0>
    }
    halo {
      attenuating
      spherical_mapping
      linear
      turbulence 1
      color_map {
        [ 0 color rgbt <1, 0, 0,  1> ]
        [ 1 color rgbt <1, 0, 0, -1> ]
      }
      samples 10
      scale <0.75, 0.5, 1>
      translate <0.4, 0, 0>
    }
    halo {
      attenuating
      spherical_mapping
      linear
      turbulence 1
      color_map {
        [ 0 color rgbt <1, 0, 0,  1> ]
        [ 1 color rgbt <1, 0, 0, -1> ]
      }
      samples 10
      scale 0.5
      translate <0, 0.2, 0>
    }
    hollow
  }


The three halos used differ only in their location, i. e. in the translation
vector we have used. The first two halos are used to form the base of the
cloud while the last sits on top of the others. The sphere has a different
radius than the previous ones because more space is needed for all three
halos.

The result of halo23.pov somewhat looks like a cloud, even though it may need
some work.


4.8.5.5          The Dust Halo

The dust halo is a very complex halo type. It allows us to see the
interaction of light coming from a light source with the particles in the
halo. These particles absorb light in the same way as the attenuating halo.
In addition they scatter the incoming light. This makes beams of light and
shadows cast by objects onto the halo become visible.

4.8.5.5.1        Starting With an Object Lit by a Spotlight

We start with a box shaped object that is lit by a spotlight. We don't use
any halo at this moment because we want to see if the object is completely
lit by the light (halo31.pov).

  camera {
    location <0, 0, -2.5>
    look_at <0, 0, 0>
  }

  background { color rgb <0.2, 0.4, 0.8> }

  light_source {
    <2.5, 2.5, -2.5>
    colour rgb <1, 1, 1>
    spotlight
    point_at <0, 0, 0>
    radius 12
    falloff 15
    tightness 1
  }

  difference {
    box { -1, 1 }
    box { <-1.1, -0.8, -0.8>, <1.1, 0.8, 0.8> }
    box { <-0.8, -1.1, -0.8>, <0.8, 1.1, 0.8> }
    box { <-0.8, -0.8, -1.1>, <0.8, 0.8, 1.1> }
    pigment { color rgb <1, 0.2, 0.2> }
    scale 0.5
    rotate 45*y
    rotate 45*x
  }


The object we want to use.

As we see the whole object is lit by the light source. Now we can start to
add some dust.

4.8.5.5.2        Adding Some Dust

We use a box to contain the dust halo. Since we use a constant density
function it doesn't matter what kind of density mapping we use. The density
has the value specified by the max_value keyword everywhere inside the halo
(the default value is one). The isotropic scattering is selected with
dust_type .

  box { -1, 1
    pigment { colour rgbt <1, 1, 1, 1> }
    halo {
      dust
      dust_type 1
      box_mapping
      constant
      colour_map {
        [ 0 color rgbt <1, 1, 1, 1> ]
        [ 1 color rgbt <1, 1, 1, 0> ]
      }
      samples 10
    }
    hollow
    scale 5
  }


This dust is too thick.

The result of halo32.pov is too bright. The dust is too thick and we can only
see some parts of the object and no background.

4.8.5.5.3        Decreasing the Dust Density

The density inside the halo has the constant value one. This means that only
the color map entry at position one is used to determine the density and
color of the dust.

We use a transmittance value of 0.7 to get a much thinner dust.

  box { -1, 1
    pigment { colour rgbt <1, 1, 1, 1> }
    halo {
      dust
      dust_type 1
      box_mapping
      constant
      colour_map {
        [ 0 color rgbt <1, 1, 1, 1.0> ]
        [ 1 color rgbt <1, 1, 1, 0.7> ]
      }
      samples 10
    }
    hollow
    scale 5
  }


A thinner dust looks much better.

Beside the ugly aliasing artifacts the image looks much better. We can see
the whole object and even the background is slightly visible (halo33.pov).

4.8.5.5.4        Making the Shadows Look Good

In order to reduce the aliasing artifacts we use three different techniques:
jittering, super-sampling and an increased overall sampling rate.

The jittering is used to add some randomness to the sampling points making
the image look more noisy. This helps because regular aliasing artifacts are
more annoying than noise. A low jitter value is a good choice.

The super-sampling tries to detect fine features by taking additional samples
in areas of high intensity changes. The threshold at which super-sampling is
used and the maximum recursion level can be specified using the aa_threshold
and aa_level keywords.

The approach that always works is to increase the overall sampling rate.
Since this is also the slowest method we should always try to use the other
methods first. If they don't suffice we have to increase the sampling rate.

We use the following halo to reduce the aliasing artifacts (halo34.pov).

  box { -1, 1
    pigment { colour rgbt <1, 1, 1, 1> }
    halo {
      dust
      dust_type 1
      box_mapping
      constant
      colour_map {
        [ 0 color rgbt <1, 1, 1, 1.0> ]
        [ 1 color rgbt <1, 1, 1, 0.7> ]
      }
      samples 50
      aa_level 3
      aa_threshold 0.2
      jitter 0.1
    }
    hollow
    scale 5
  }


Different anti-aliasing methods help to get a satisfying result.

The image looks much better now. There are hardly any aliasing artifacts
left.

The same parameters we have used are discussed in the section about the
atmosphere feature (see "The Atmosphere" for further explanations).

4.8.5.5.5        Adding Turbulence

The major difference between the halo's dust and the atmosphere described in
"The Atmosphere" is the ability to choose a non-uniform particle distribution
for the dust. This includes the fact that the halo is limited to a container
object as well as the different density mappings and functions.

Another interesting way of getting an irregular distribution is to add some
turbulence to the dust. This is done with the turbulence keyword followed by
the amount of turbulence to use, like the following example shows
(halo35.pov).

  box { -1, 1
    pigment { colour rgbt <1, 1, 1, 1> }
    halo {
      dust
      dust_type 1
      box_mapping
      linear
      turbulence 1
      colour_map {
        [ 0 color rgbt <1, 1, 1, 1.0> ]
        [ 1 color rgbt <1, 1, 1, 0.5> ]
      }
      samples 50
      aa_level 3
      aa_threshold 0.2
      jitter 0.1
    }
    hollow
    scale 5
  }


Adding turbulence to the dust makes it much more interesting.

The image we now get looks much more interesting due to the shifts in the
particle density.

We should note that we use a linear density function instead of the previous
constant one. This is necessary because with a constant density function the
density has the same value everywhere. Adding turbulence would have no effect
because wherever the points are moved the density will have this same value.
Only a non-constant density distribution makes sense when turbulence is
added.

The fact that the turbulence value is actually a vector can be used to create
effects like waterfalls by using a large turbulence value in one direction
only (e.g. turbulence <0.2, 1, 0.2> ).

4.8.5.5.6        Using a Coloured Dust

If we want to create a colored dust we can easily do this by using a
non-white color in the halo's color map. In this case we'll also have to set
the filter channels in the color map to non-zero values to specify the amount
of light that will be filtered by the dust's color.

We use the following color map to get a partially filtering, red dust for
example:

  colour_map {
    [ 0 color rgbft <1, 0, 0, 0.5, 1.0> ]
    [ 1 color rgbft <1, 0, 0, 0.5, 0.7> ]
  }


4.8.5.6          Halo Pitfalls

Due to the complexity of the halo feature and the few experiences people have
made so far there are a lot of things still to discover.

Some of the most common problems and pitfalls are described below to help us
avoid the most common problems.

4.8.5.6.1        Where Halos are Allowed

As mentioned above a halo completly fills the interior of an object. Keeping
this in mind it is reasonable that the following example does not make sense.


  sphere { 0, 1
    pigment {
      checker
      texture {
        pigment { color Clear }
        halo { ... }
      }
      texture {
        pigment { color Red }
      }
    }
    hollow
  }


What's wrong with this example? It's simply that a halo is used to describe
the interior of an object and that one cannot describe this interior by
describing how the surface of the object looks like. But that's what was done
in the example above. We cannot imagine what the interior of the sphere will
look like. Will it be filled completey with the halo? Will there be areas
filled by the halo and some filled by air? How will those areas look like?

We won't be able to tell the interior's properties from looking at the
surface. It's just not possible. This should always be kept in mind.

If the above example was meant to create a sphere filled with a halo and
covered with a checker board pattern that partially hid the halo we would
have used the following syntax:

  sphere { 0, 1
    pigment {
      checker
      texture {
        pigment { color Clear }
      }
      texture {
        pigment { color Red }
      }
    }
    halo { ... }
    hollow
  }


A halo is always applied to an object in the following way:

  OBJECT {
    texture {
      pigment { ... }
      normal { ... }
      finish { ... }
      halo { ... }
    }
    hollow
  }


There's no halo allowed inside any pigment statement, color map, pigment map,
texture map, material map, or whatever. We are not hindered to do this but we
will not get what we want.

We can use halos with a layered textures as long as we make sure that the
halos are only attached to the lowest layer (this layer has to be partially
transparent to see the halo of course).

4.8.5.6.2        Overlapping Container Objects

POV-Ray is not able to handle overlapping container objects correctly. If we
create two overlapping spheres that contain a halo we won't get correct
results where the spheres overlap. The halo effect is calculated
independently for each sphere and the results are added.

If we want to add different halos we have to put all halos inside a single
container object to make sure the halo is calculated correctly (see also
"Multiple Halos").

We should also note that non-overlapping, stacked halo containers are handled
correctly. If we put a container object in front of another container object
the halos are rendered correctly.

4.8.5.6.3        Multiple Attenuating Halos

It is currently not possible to use multiple attenuating halos with different
color maps. The color map of the last halo will be used for all halos in the
container object.

4.8.5.6.4        Halos and Hollow Objects

In order to correctly render halo effects we have to make sure that all
objects the camera is inside are hollow. This is done by adding the hollow
keyword.


4.8.5.6.5        Scaling a Halo Container

If we scale a halo container object we should keep in mind that it makes a
great difference where we place the scale keyword.

Scaling the object before the halo statement will only scale the container
object not the halo. This is useful if we want to avoid that the surface of
the container object becomes visible due to the use of turbulence. As we have
learned in the sections above particles may move out of the container object
- where they are invisible - if turbulence is added. This only works for
spherical and box mapping because the density fields described by the other
mapping types don't have finite dimensions.

If the scale keyword is used after the halo statement both, the halo and the
container object, are scaled. This is useful to scale the halo to our needs.

The halo keeps its appearance regardless of the transformations applied to
the container object (after the halo), i.e. the halo's translucency, color
and turbulence characteristics will not change.

4.8.5.6.6        Choosing a Sampling Rate

Normally we will start with a low sampling rate and we willl only increase it
if any aliasing artifacts show up (and don't vanish by using super-sampling
and jittering).

The halo's appearance is independent from the sampling rate as long as there
are enough samples to get a good estimate of what the halo really looks like.
This means that one or two samples are hardly ever enough to determine the
halo's appearance. As we increase the number of samples the halo will quickly
approach its real appearance.

To put it in a nutshell, the halo will not change its appearance with the
sample rate as long as we have a sufficient number of samples and no aliasing
artifacts occur.

4.8.5.6.7        Using Turbulence

As noted in one of the above sections turbulence will have no effect if the
constant density function is used (keyword constant). It doesn't matter how
much or where we move a point if the density is constant and thus does not
depend on the location of the point. We'll get the same density value for all
location.

Whenever we add turbulence to a halo we must not use the constant density
function.

4.9              Working With Special Textures

Many of the pigment patterns we have seen elsewhere in POV-Ray make use of a
color_map statement to blend different colors together. Depending on how we
list the entries of the color map, we can fade gradually from one color to
the next, or have it abruptly make the transition from one to the next. In
fact, the color map is a powerful tool for customizing the various pigment
patterns, which requires a bit of practice to learn to use it correctly. And
all that's fine, when it's just individual colors we want to use. But what if
we could blend entire pigment patterns, normal patterns, or whole other
textures? Starting with POV-Ray 3, we can!

In order to experiment with some of the exciting new texturing options, let
us set up a basic scene file, into which we will be plugging the example
textures to experiment with later. So to begin, we set up the following basic
include files, a camera and a light source.

  #include "colors.inc"
  #include "textures.inc"

  camera {
    orthographic
    up <0, 5, 0>
    right <5, 0, 0>
    location <0, 0, -25>
    look_at <0, 0, 0>
  }

  light_source { <100, 100, -100> color White }


4.9.1            Working With Pigment Maps

Starting with something simple, let's look at the pigment map. We must not
confuse this with a color map, as color maps can only take individual colors
as entries in the map, while pigment maps can use entire other pigment
patterns. To get a feel for these, let's begin by setting up a basic plane
with a simple pigment map. Now, in the following example, we are going to
declare each of the pigments we are going to use before we actually use them.
This isn't strictly necessary (we could put an entire pigment description in
each entry of the map) but it just makes the whole thing more readable.

  // simple Black on White checkboard... it's a classic
  #declare Pigment1 = pigment {
    checker color Black color White
    scale .1
  }

  // kind of a "psychedelic rings" effect
  #declare Pigment2 = pigment {
    wood
    color_map {
      [ 0.0 Red ]
      [ 0.3 Yellow ]
      [ 0.6 Green ]
      [ 1.0 Blue ]
    }
  }

  plane { -z, 0
    pigment {
      gradient x
      pigment_map {
        [ 0.0 Pigment1 ]
        [ 0.5 Pigment2 ]
        [ 1.0 Pigment1 ]
      }
    }
  }


Okay, what we have done here is very simple, and probably quite recognizable
if we have been working with color maps all along anyway. All we have done is
substituted a pigment map where a color map would normally go, and as the
entries in our map, we have referenced our declared pigments. When we render
this example, we see a pattern which fades back and forth between the classic
checkerboard, and those colorful rings. Because we fade from Pigment1 to
Pigment2 and then back again, we see a clear blending of the two patterns at
the transition points. We could just as easily get a sudden transition by
amending the map to read.

  pigment_map {
    [ 0.0 Pigment1 ]
    [ 0.5 Pigment1 ]
    [ 0.5 Pigment2 ]
    [ 1.0 Pigment2 ]
  }


4.9.2            Working With Normal Maps

For our next example, we replace the plane in the scene with this one.

  plane { -z, 0
    pigment { White }
    normal {
      gradient x
      normal_map {
        [ 0.0 bumps 1 scale .1]
        [ 1.0 ripples 1 scale .1]
      }
    }
  }


First of all, we have chosen a solid white color to show off all bumping to
best effect. Secondly, we notice that our map blends smoothly from all bumps
at 0.0 to all ripples at 1.0, but because this is a default gradient, it
falls off abruptly back to bumps at the beginning of the next cycle. We
Render this and see just enough sharp transitions to clearly see where one
normal gives over to another, yet also an example of how two normal patterns
look while they are smoothly blending into one another.

The syntax is the same as we would expect. We just changed the type of map,
moved it into the normal block and supplied appropriate bump types. It is
important to remember that as of POV-Ray 3, all patterns that work with
pigments work as normals as well (and vice versa, of course) so we could just
as easily have blended from wood to granite, or any other pattern we like. We
experiment a bit and get a feel for what the different patterns look like.

After seeing how interesting the various normals look blended, we might like
to see them completely blended all the way through rather than this business
of fading from one to the next. Well, that is possible too, but we would be
getting ahead of ourselves. That is called the average function, and we will
return to it a little bit further down the page.

4.9.3            Working With Texture Maps

We know how to blend colors, pigment patterns, and normals, and we are
probably thinking what about finishes? What about whole textures? Both of
these can be kind of covered under one topic. While there is no finish map
per se, there are texture maps, and we can easily adapt these to serve as
finish maps, simply by putting the same pigment and/or normal in each of the
texture entries of the map. Here is an example. We eliminate the declared
pigments we used before and the previous plane, and add the following.

  #declare Texture1 = texture {
    pigment { Grey }
    finish { reflection 1 }
  }

  #declare Texture2 = texture {
    pigment { Grey }
    finish { reflection 0 }
  }

  cylinder { <-2, 5, -2>, <-2, -5, -2>, 1
    pigment { Blue }
  }

  plane { -z, 0
    rotate y * 30
    texture {
      gradient y
      texture_map {
        [ 0.0 Texture1 ]
        [ 0.4 Texture1 ]
        [ 0.6 Texture2 ]
        [ 1.0 Texture2 ]
      }
      scale 2
    }
  }


Now, what have we done here? The background plane alternates vertically
between two textures, identical except for their finishes. When we render
this, the cylinder has a reflection part of the way down the plane, and then
stops reflecting, then begins and then stops again, in a gradient pattern
down the surface of the plane. With a little adaptation, this could be used
with any pattern, and in any number of creative ways, whether we just wanted
to give various parts of an object different finishes, as we are doing here,
or whole different textures altogether.

One might ask: if there is a texture map, why do we need pigment and normal
maps? Fair question. The answer: speed of calculation. If we use a texture
map, for every in-between point, POV-Ray must make multiple calculations for
each texture element, and then run a weighted average to produce the correct
value for that point. Using just a pigment map (or just a normal map)
decreases the overall number of calculations, and our texture renders a bit
faster in the bargain. As a rule of thumb: we use pigment or normal maps
where we can and only fall back on texture maps if we need the extra
flexibility.

4.9.4            Working With List Textures

If we have followed the corresponding tutorials on simple pigments, we know
that there are three patterns called color list patterns, because rather than
using a color map, these simple but useful patterns take a list of colors
immediately following the pattern keyword. We're talking about checker,
hexagon, and, new to POV-Ray 3, the brick pattern.

Naturally they also work with whole pigments, normals, and entire textures,
just as the other patterns do above. The only difference is that we list
entries in the pattern (as we would do with individual colors) rather than
using a map of entries. Here is an example. We strike the plane and any
declared pigments we had left over in our last example, and add the following
to our basic file.

  #declare Pigment1 = pigment {
    hexagon
    color Yellow color Green color Grey
    scale .1
  }

  #declare Pigment2 = pigment {
    checker
    color Red color Blue
    scale .1
  }

  #declare Pigment3 = pigment {
    brick
    color White color Black
    rotate -90*x
    scale .1
  }

  box { -5, 5
    pigment {
      hexagon
      pigment {Pigment1}
      pigment {Pigment2}
      pigment {Pigment3}
      rotate 90*x
    }
  }


We begin by declaring an example of each of the color list patterns as
individual pigments. Then we use the hexagon pattern as a pigment list
pattern, simply feeding it a list of pigments rather than colors as we did
above. There are two rotate statements throughout this example, because
bricks are aligned along the z-direction, while hexagons align along the
y-direction, and we wanted everything to face toward the camera we originally
declared out in the -z-direction so we can really see the patterns within
patterns effect here.

Of course color list patterns used to be only for pigments, but as of POV-Ray
3, everything that worked for pigments can now also be adapted for normals or
entire textures. A couple of quick examples might look like

  normal {
    brick
    normal { granite .1 }
    normal { bumps 1 scale .1 }
  }


or...

  texture {
    checker
    texture { Gold_Metal }
    texture { Silver_Metal }
  }


4.9.5            What About Tiles?

In earlier versions of POV-Ray, there was a texture pattern called tiles. By
simply using a checker texture pattern (as we just saw above), we can achieve
the same thing as tiles used to do, so it is now obsolete. It is still
supported by POV-Ray 3 for backwards compatibility with old scene files, but
now is a good time to get in the habit of using a checker pattern instead.

4.9.6            Average Function

Now things get interesting. Above, we began to see how pigments and normals
can fade from one to the other when we used them in maps. But how about if we
want a smooth blend of patterns all the way through? That is where a new
feature called average can come in very handy. Average works with pigment,
normal, and texture maps, although the syntax is a little bit different, and
when we are not expecting it, the change can be confusing. Here is a simple
example. We use our standard includes, camera and light source from above,
and enter the following object.

  plane { -z, 0
    pigment { White }
    normal {
      average
      normal_map {
        [ gradient x ]
        [ gradient y ]
      }
    }
  }


What we have done here is pretty self explanatory as soon as we render it. We
have combined a vertical with a horizontal gradient bump pattern, creating
crisscrossing gradients. Actually, the crisscrossing effect is a smooth blend
of gradient x with gradient y all the way across our plane. Now, what about
that syntax difference?

We see how our normal map has changed from earlier examples. The floating
point value to the lefthand side of each map entry has been removed. That
value usually helps in procedurally mapping each entry to the pattern we have
selected, but average is a smooth blend all the way through, not a pattern,
so it cannot use those values. In fact, including them may sometimes lead to
unexpected results, such as entries being lost or misrepresented in some way.
To ensure that we'll get the pattern blend we anticipate, we leave off the
floating point value.

4.9.7            Working With Layered Textures

With the multitudinous colors, patterns, and options for creating complex
textures in POV-Ray, we can easily become deeply engrossed in mixing and
tweaking just the right textures to apply to our latest creations. But as we
go, sooner or later there is going to come that special texture. That texture
that is sort of like wood, only varnished, and with a kind of spotty yellow
streaking, and some vertical gray flecks, that looks like someone started
painting over it all, and then stopped, leaving part of the wood visible
through the paint.

Only... now what? How do we get all that into one texture? No pattern can do
that many things. Before we panic and say image map there is at least one
more option: layered textures.

With layered textures, we only need to specify a series of textures, one
after the other, all associated with the same object. Each texture we list
will be applied one on top of the other, from bottom to top in the order they
appear.

It is very important to note that we must have some degree of transparency
(filter or transmit) in the pigments of our upper textures, or the ones below
will get lost underneath. We won't receive a warning or an error -
technically it is legal to do this: it just doesn't make sense. It is like
spending hours sketching an elaborate image on a bare wall, then slapping a
solid white coat of latex paint over it.

Let's design a very simple object with a layered texture, and look at how it
works. We create a file called LAYTEX.POV and add the following lines.

  #include "colors.inc"
  #include "textures.inc"

  camera {
    location <0, 5, -30>
    look_at <0, 0, 0>
  }

  light_source { <-20, 30, -50> color White }

  plane { y, 0 pigment { checker color Green color Yellow  } }

  background { rgb <.7, .7, 1> }

  box { <-10, 0, -10>, <10, 10, 10>
    texture {
      Silver_Metal // a metal object ...
      normal {     // ... which has suffered a beating
        dents 2
        scale 1.5
      }
    } // (end of base texture)

    texture { // ... has some flecks of rust ...
      pigment {
        granite
        color_map {
          [0.0 rgb <.2, 0, 0> ]
          [0.2 color Brown ]
          [0.2 rgbt <1, 1, 1, 1> ]
          [1.0 rgbt <1, 1, 1, 1> ]
        }
        frequency 16
      }
    } // (end rust fleck texture)

    texture { // ... and some sooty black marks
      pigment {
        bozo
        color_map {
          [0.0 color Black ]
          [0.2 color rgbt <0, 0, 0, .5> ]
          [0.4 color rgbt <.5, .5, .5, .5> ]
          [0.5 color rgbt <1, 1, 1, 1> ]
          [1.0 color rgbt <1, 1, 1, 1> ]
        }
        scale 3
      }
    } // (end of sooty mark texture)

  } // (end of box declaration)


Whew. This gets complicated, so to make it easier to read, we have included
comments showing what we are doing and where various parts of the declaration
end (so we don't get lost in all those closing brackets!). To begin, we
created a simple box over the classic checkerboard floor, and give the
background sky a pale blue color. Now for the fun part...

To begin with we made the box use the Silver_Metal texture as declared in
textures.inc (for bonus points, look up textures.inc and see how this
standard texture was originally created sometime). To give it the start of
its abused state, we added the dents normal pattern, which creates the
illusion of some denting in the surface as if our mysterious metal box had
been knocked around quite a bit.

The flecks of rust are nothing but a fine grain granite pattern fading from
dark red to brown which then abruptly drops to fully transparent for the
majority of the color map. True, we could probably come up with a more
realistic pattern of rust using pigment maps to cluster rusty spots, but
pigment maps are a subject for another tutorial section, so let's skip that
just now.

Lastly, we have added a third texture to the pot. The randomly shifting bozo
texture gradually fades from blackened centers to semi-transparent medium
gray, and then ultimately to fully transparent for the latter half of its
color map. This gives us a look of sooty burn marks further marring the
surface of the metal box. The final result leaves our mysterious metal box
looking truly abused, using multiple texture patterns, one on top of the
other, to produce an effect that no single pattern could generate!

4.9.7.1          Declaring Layered Textures

In the event we want to reuse a layered texture on several objects in our
scene, it is perfectly legal to declare a layered texture. We won't repeat
the whole texture from above, but the general format would be something like
this:

  #declare Abused_Metal =
    texture { /* insert your base texture here... */ }
    texture { /* and your rust flecks here... */ }
    texture { /* and of course, your sooty burn marks here */ }


POV-Ray has no problem spotting where the declaration ends, because the
textures follow one after the other with no objects or directives in between.
The layered texture to be declared will be assumed to continue until it finds
something other than another texture, so any number of layers can be added in
to a declaration in this fashion.

One final word about layered textures: whatever layered texture we create,
whether declared or not, we must not leave off the texture wrapper. In
conventional single textures a common shorthand is to have just a pigment, or
just a pigment and finish, or just a normal, or whatever, and leave them
outside of a texture statement. This shorthand does not extend to layered
textures. As far as POV-Ray is concerned we can layer entire textures, but
not individual pieces of textures. For example

  #declare Bad_Texture =
    texture { /* insert your base texture here... */ }
    pigment { Red filter .5 }
    normal { bumps 1 }


will not work. The pigment and the normal are just floating there without
being part of any particular texture. Inside an object, with just a single
texture, we can do this sort of thing, but with layered textures, we would
just generate an error whether inside the object or in a declaration.

4.9.7.2          Another Layered Textures Example

To further explain how layered textures work another example is described in
detail. A tablecloth is created to be used in a picnic scene. Since a simple
red and white checked cloth looks entirely too new, too flat, and too much
like a tiled floor, layered textures are used to stain the cloth.

We're going to create a scene containing four boxes. The first box has that
plain red and white texture we started with in our picnic scene, the second
adds a layer meant to realistically fade the cloth, the third adds some wine
stains, and the final box adds a few wrinkles (not another layer, but we must
note when and where adding changes to the surface normal have an effect in
layered textures).

We start by placing a camera, some lights, and the first box. At this stage,
the texture is plain tiling, not layered. See file layered1.pov.

  #include "colors.inc"

  camera {
    location <0, 0, -6>
    look_at <0, 0, 0>
  }

  light_source { <-20, 30, -100> color White }
  light_source { <10, 30, -10> color White }
  light_source { <0, 30, 10> color White }

  #declare PLAIN_TEXTURE =
    // red/white check
    texture {
      pigment {
        checker
        color rgb<1.000, 0.000, 0.000>
        color rgb<1.000, 1.000, 1.000>
        scale <0.2500, 0.2500, 0.2500>
      }
    }

  // plain red/white check box

  box { <-1, -1, -1>, <1, 1, 1>
    texture {
      PLAIN_TEXTURE
    }
    translate  <-1.5, 1.2, 0>
  }


We render this scene. It is not particularly interesting, isn't it? That is
why we will use some layered textures to make it more interesting.

First, we add a layer of two different, partially transparent greys. We tile
them as we had tiled the red and white colors, but we add some turbulence to
make the fading more realistic. We add following box to the previous scene
and re-render (see file layered2.pov).

  #declare FADED_TEXTURE =
    // red/white check texture
    texture {
      pigment {
        checker
        color rgb<0.920, 0.000, 0.000>
        color rgb<1.000, 1.000, 1.000>
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // greys to fade red/white
    texture {
      pigment {
        checker
        color rgbf<0.632, 0.612, 0.688, 0.698>
        color rgbf<0.420, 0.459, 0.520, 0.953>
        turbulence 0.500
        scale <0.2500, 0.2500, 0.2500>
      }
    }

  // faded red/white check box

  box { <-1, -1, -1>, <1, 1, 1>
    texture {
      FADED_TEXTURE
    }
    translate  <1.5, 1.2, 0>
  }


Even though it is a subtle difference, the red and white checks no longer
look quite so new.

Since there is a bottle of wine in the picnic scene, we thought it might be a
nice touch to add a stain or two. While this effect can almost be achieved by
placing a flattened blob on the cloth, what we really end up with is a spill
effect, not a stain. Thus it is time to add another layer.

Again, we add another box to the scene we already have scripted and re-render
(see file layered3.pov).

  #declare STAINED_TEXTURE =
    // red/white check
    texture {
      pigment {
        checker
        color rgb<0.920, 0.000, 0.000>
        color rgb<1.000, 1.000, 1.000>
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // greys to fade check
    texture {
      pigment {
        checker
        color rgbf<0.634, 0.612, 0.688, 0.698>
        color rgbf<0.421, 0.463, 0.518, 0.953>
        turbulence 0.500
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // wine stain
    texture {
      pigment {
        spotted
        color_map {
          [ 0.000  color rgb<0.483, 0.165, 0.165> ]
          [ 0.329  color rgbf<1.000, 1.000, 1.000, 1.000> ]
          [ 0.734  color rgbf<1.000, 1.000, 1.000, 1.000> ]

          [ 1.000  color rgb<0.483, 0.165, 0.165> ]
        }
        turbulence 0.500
        frequency 1.500
      }
    }

  // stained box

  box { <-1, -1, -1>, <1, 1, 1>
    texture {
      STAINED_TEXTURE
    }
    translate  <-1.5, -1.2, 0>
  }


Now there's a tablecloth texture with personality.

Another touch we want to add to the cloth are some wrinkles as if the cloth
had been rumpled. This is not another texture layer, but when working with
layered textures, we must keep in mind that changes to the surface normal
must be included in the uppermost layer of the texture. Changes to lower
layers have no effect on the final product (no matter how transparent the
upper layers are).

We add this final box to the script and re-render (see file layered4.pov)

  #declare WRINKLED_TEXTURE =
    // red and white check
    texture {
      pigment {
        checker
        color rgb<0.920, 0.000, 0.000>
        color rgb<1.000, 1.000, 1.000>
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // greys to "fade" checks
    texture {
      pigment {
        checker
        color rgbf<0.632, 0.612, 0.688, 0.698>
        color rgbf<0.420, 0.459, 0.520, 0.953>
        turbulence 0.500
        scale <0.2500, 0.2500, 0.2500>
      }
    }
    // the wine stains
    texture {
      pigment {
        spotted
        color_map {
          [ 0.000  color rgb<0.483, 0.165, 0.165> ]
          [ 0.329  color rgbf<1.000, 1.000, 1.000, 1.000> ]
          [ 0.734  color rgbf<1.000, 1.000, 1.000, 1.000> ]
          [ 1.000  color rgb<0.483, 0.165, 0.165> ]
        }
        turbulence 0.500
        frequency 1.500
      }
      normal {
        wrinkles 5.0000
      }
    }

  // wrinkled box

  box { <-1, -1, -1>, <1, 1, 1>
    texture {
      WRINKLED_TEXTURE
    }
    translate  <1.5, -1.2, 0>
  }


Well, this may not be the tablecloth we want at any picnic we're attending,
but if we compare the final box to the first, we see just how much depth,
dimension, and personality is possible just by the use of creative texturing.


One final note: the comments concerning the surface normal do not hold true
for finishes. If a lower layer contains a specular finish and an upper layer
does not, any place where the upper layer is transparent, the specular will
show through.

4.9.8            When All Else Fails: Material Maps

We have some pretty powerful texturing tools at our disposal, but what if we
want a more free form arrangement of complex textures? Well, just as image
maps do for pigments, and bump maps do for normals, whole textures can be
mapped using a material map, should the need arise.

Just as with image maps and bump maps, we need a source image in bitmapped
format which will be called by POV-Ray to serve as the map of where the
individual textures will go, but this time, we need to specify what texture
will be associated with which palette index. To make such an image, we can
use a paint program which allows us to select colors by their palette index
number (the actual color is irrelevant, since it is only a map to tell
POV-Ray what texture will go at that location). Now, if we have the complete
package that comes with POV-Ray, we have in our include files an image called
povmap.gif which is a bitmapped image that uses only the first four palette
indices to create a bordered square with the words Persistance of Vision in
it. This will do just fine as a sample map for the following example. Using
our same include files, the camera and light source, we enter the follow
object.

  plane { -z, 0
    texture {
      material_map {
        gif "povmap.gif"
        interpolate 2
        once
        texture { PinkAlabaster }          // the inner border
        texture { pigment { DMFDarkOak } } // outer border
        texture { Gold_Metal }             // lettering
        texture { Chrome_Metal }           // the window panel
      }
      translate <-0.5, -0.5, 0>
      scale 5
    }
  }


The position of the light source and the lack of foreground objects to be
reflected do not show these textures off to their best advantage. But at
least we can see how the process works. The textures have simply been placed
according to the location of pixels of a particular palette index. By using
the once keyword (to keep it from tiling), and translating and scaling our
map to match the camera we have been using, we get to see the whole thing
laid out for us.

Of course, that is just with palette mapped image formats, such as GIF and
certain flavors of PNG. Material maps can also use non-paletted formats, such
as the TGA files that POV-Ray itself outputs. That leads to an interesting
consquence: We can use POV-Ray to produce source maps for POV-Ray! Before we
wrap up with some of the limitations of special textures, let's do one more
thing with material maps, to show how POV-Ray can make its own source maps.

To begin with, if using an non-paletted image, POV-Ray looks at the 8 bit red
component of the pixel's color (which will be a value from 0 to 255) to
determine which texture from the list to use. So to create a source map, we
need to control very precisely what the red value of a given pixel will be.
We can do this by

  1.)Using an rgb statement to choose our color such as rgb <x/255, 0, 0>,
  2.)Use no light sources and apply a finish of finish { ambient 1 } to all
     objects, to ensure that highlighting and shadowing will not interfere.


Confused? Alright, here is an example, which will generate a map very much
like povmap.gif which we used earlier, except in TGA file format. We notice
that we have given the pigments blue and green components too. POV-Ray will
ignore that in our final map, so this is really for us humans, whose unaided
eyes cannot tell the difference between red variances of 0 to 4/255ths.
Without those blue and green variances, our map would look to our eyes like a
solid black screen. That may be a great way to send secret messages using
POV-Ray (plug it into a material map to decode) but it is no use if we want
to see what our source map looks like to make sure we have what we expected
to.

We render the following code, and name the resulting file povmap.tga.

  camera {
    orthographic
    up <0, 5, 0>
    right <5, 0, 0>
    location <0, 0, -25>
    look_at <0, 0, 0>
  }

  plane { -z, 0
    pigment { rgb <1/255, 0, 0.5> }
    finish { ambient 1 }
  }

  box { <-2.3, -1.8, -0.2>, <2.3, 1.8, -0.2>
    pigment { rgb <0/255, 0, 1> }
    finish { ambient 1 }
  }

  box { <-1.95, -1.3, -0.4>, <1.95, 1.3, -0.3>
    pigment { rgb <2/255, 0.5, 0.5> }
    finish { ambient 1 }
  }

  text { ttf "crystal.ttf", "The vision", 0.1, 0
    scale <0.7, 1, 1>
    translate <-1.8, 0.25, -0.5>
    pigment { rgb <3/255, 1, 1> }
    finish { ambient 1 }
  }

  text { ttf "crystal.ttf", "Persists!", 0.1, 0
    scale <0.7, 1, 1>
    translate <-1.5, -1, -0.5>
    pigment { rgb <3/255, 1, 1> }
    finish { ambient 1 }
  }


All we have to do is modify our last material map example by changing the
material map from GIF to TGA and modifying the filename. When we render using
the new map, the result is extremely similar to the pallette mapped GIF we
used before, except that we didn't have to use an external paint program to
generate our source: POV-Ray did it all!

4.9.9            Limitations Of Special Textures

There are a couple limitations to all of the special textures we have seen
(from textures, pigment and normal maps through material maps). First, if we
have used the default directive to set the default texture for all items in
our scene, it will not accept any of the special textures discussed here.
This is really quite minor, since we can always declare such a texture and
apply it individually to all objects. It doesn't actually prevent us from
doing anything we couldn't otherwise do.

The other is more limiting, but as we will shortly see, can be worked around
quite easily. If we have worked with layered textures, we have already seen
how we can pile multiple texture patterns on top of one another (as long as
one texture has transparency in it). This very useful technique has a problem
incorporating the special textures we have just seen as a layer. But there is
an answer!

For example, say we have a layered texture called Speckled_Metal, which
produces a silver metallic surface, and then puts tiny specks of rust all
over it. Then we decide, for a really rusty look, we want to create patches
of concentrated rust, randomly over the surface. The obvious approach is to
create a special texture pattern, with transparency to use as the top layer.
But of course, as we have seen, we wouldn't be able to use that texture
pattern as a layer. We would just generate an error message. The solution is
to turn the problem inside out, and make our layered texture part of the
texture pattern instead, like this

  // This part declares a pigment for use
  // in the rust patch texture pattern
  #declare Rusty = pigment {
    granite
    color_map {
      [ 0 rgb <0.2, 0, 0> ]
      [ 1 Brown ]
    }
    frequency 20
  }

  // And this part applies it
  // Notice that our original layered texture
  // "Speckled_Metal" is now part of the map
  #declare Rust_Patches = texture {
    bozo
    texture_map {
      [ 0.0  pigment {Rusty} ]
      [ 0.75 Speckled_Metal ]
      [ 1.0  Speckled_Metal ]
    }
  }


And the ultimate effect is the same as if we had layered the rust patches on
to the speckled metal anyway.

With the full array of patterns, pigments, normals, finishes, layered and
special textures, there is now practically nothing we cannot create in the
way of amazing textures. An almost infinite number of new possibilities are
just waiting to be created!

4.10             Using Atmospheric Effects

POV-Ray offers a variety of atmospheric effects, i. e. features that affect
the background of the scene or the air by which everything is surrounded.

It is easy to assign a simple color or a complex color pattern to a virtual
sky sphere. You can create anything from a cloud free, blue summer sky to a
stormy, heavy clouded sky. Even starfields can easily be created.

You can use different kinds of fog to create foggy scenes. Multiple fog
layers of different colors can add an eerie touch to your scene.

A much more realistic effect can be created by using an atmosphere, a
constant fog that interacts with the light coming from light sources. Beams
of light become visible and objects will cast shadows into the fog.


4.10.1           The Background

The background feature is used to assign a color to all rays that don't hit
any object. This is done in the following way.

  camera {
    location <0, 0, -10>
    look_at <0, 0, 0>
  }

  background { color rgb <0.2, 0.2, 0.3> }

  sphere { 0, 1
    pigment { color rgb <0.8, 0.5, 0.2> }
  }


The background color will be visible if a sky sphere is used and if some
translucency remains after all sky sphere pigment layers are processed.

4.10.2           The Sky Sphere

The sky sphere can be used to easily create a cloud covered sky, a nightly
star sky or whatever sky you have in mind.

In the following examples we'll start with a very simple sky sphere that will
get more and more complex as we add new features to it.

4.10.2.1         Creating a Sky with a Color Gradient

Beside the single color sky sphere that is covered with the background
feature the simplest sky sphere is a color gradient.

You may have noticed that the color of the sky varies with the angle to the
earth's surface normal. If you look straight up the sky normally has a much
deeper blue than it has at the horizon.

We want to model this effect using the sky sphere as shown in the scene below
(skysph1.pov).

  #include "colors.inc"

  camera {
    location <0, 1, -4>
    look_at <0, 2, 0>
    angle 80
  }

  light_source { <10, 10, -10> White }

  sphere { 2*y, 1
    pigment { color rgb <1, 1, 1> }
    finish { ambient 0.2 diffuse 0 reflection 0.6 }
  }

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [0 color Red]
        [1 color Blue]
      }
      scale 2
      translate -1
    }
  }


The interesting part is the sky sphere statement. It contains a pigment that
describe the look of the sky sphere. We want to create a color gradient along
the viewing angle measured against the earth's surface normal. Since the ray
direction vector is used to calculate the pigment colors we have to use the
y-gradient.

The scale and translate transformation are used to map the points derived
from the direction vector to the right range. Without those transformations
the pattern would be repeated twice on the sky sphere. The scale statement is
used to avoid the repetition and the translate -1 statement moves the color
at index zero to the bottom of the sky sphere (that's the point of the sky
sphere you'll see if you look straight down).

After this transformation the color entry at position 0 will be at the bottom
of the sky sphere, i. e. below us, and the color at position 1 will be at the
top, i. e. above us.

The colors for all other positions are interpolated between those two colors
as you can see in the resulting image.

A simple gradient sky sphere.

If you want to start one of the colors at a specific angle you'll first have
to convert the angle to a color map index. This is done by using the formula

  color_map_index = (1 - cos(angle)) / 2


where the angle is measured against the negated earth's surface normal. This
is the surface normal pointing towards the center of the earth. An angle of 0
degrees describes the point below us while an angle of 180 degrees represents
the zenith.

In POV-Ray you first have to convert the degree value to radian values as it
is shown in the following example.

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [(1-cos(radians( 30)))/2 color Red]
        [(1-cos(radians(120)))/2 color Blue]
      }
      scale 2
      translate -1
    }
  }


This scene uses a color gradient that starts with a red color at 30 degrees
and blends into the blue color at 120 degrees. Below 30 degrees everything is
red while above 120 degrees all is blue.

4.10.2.2         Adding the Sun

In the following example we will create a sky with a red sun surrounded by a
red color halo that blends into the dark blue night sky. We'll do this using
only the sky sphere feature.

The sky sphere we use is shown below. A ground plane is also added for
greater realism (skysph2.pov).

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [0.000 0.002 color rgb <1.0, 0.2, 0.0>
                     color rgb <1.0, 0.2, 0.0>]
        [0.002 0.200 color rgb <0.8, 0.1, 0.0>
                     color rgb <0.2, 0.2, 0.3>]
      }
      scale 2
      translate -1
    }
    rotate -135*x
  }

  plane { y, 0
    pigment { color Green }
    finish { ambient .3 diffuse .7 }
  }


The gradient pattern and the transformation inside the pigment are the same
as in the example in the previous section.

The color map consists of three colors. A bright, slightly yellowish red that
is used for the sun, a darker red for the halo and a dark blue for the night
sky. The sun's color covers only a very small portion of the sky sphere
because we don't want the sun to become too big. The color is used at the
color map values 0.000 and 0.002 to get a sharp contrast at value 0.002 (we
don't want the sun to blend into the sky). The darker red color used for the
halo blends into the dark blue sky color from value 0.002 to 0.200. All
values above 0.200 will reveal the dark blue sky.

The rotate -135*x statement is used to rotate the sun and the complete sky
sphere to its final position. Without this rotation the sun would be at 0
degrees, i.e. right below us.

A red sun descends into the night.

Looking at the resulting image you'll see what impressive effects you can
achieve with the sky sphere.

4.10.2.3         Adding Some Clouds

To further improve our image we want to add some clouds by adding a second
pigment. This new pigment uses the bozo pattern to create some nice clouds.
Since it lays on top of the other pigment it needs some translucent colors in
the color map (look at entries 0.5 to 1.0).

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [0.000 0.002 color rgb <1.0, 0.2, 0.0>
                     color rgb <1.0, 0.2, 0.0>]
        [0.002 0.200 color rgb <0.8, 0.1, 0.0>
                     color rgb <0.2, 0.2, 0.3>]
      }
      scale 2
      translate -1
    }
    pigment {
      bozo
      turbulence 0.65
      octaves 6
      omega 0.7
      lambda 2
      color_map {
          [0.0 0.1 color rgb <0.85, 0.85, 0.85>
                   color rgb <0.75, 0.75, 0.75>]
          [0.1 0.5 color rgb <0.75, 0.75, 0.75>
                   color rgbt <1, 1, 1, 1>]
          [0.5 1.0 color rgbt <1, 1, 1, 1>
                   color rgbt <1, 1, 1, 1>]
      }
      scale <0.2, 0.5, 0.2>
    }
    rotate -135*x
  }


A cloudy sky with a setting sun.

The sky sphere has one drawback as you might notice when looking at the final
image (skysph3.pov). The sun doesn't emit any light and the clouds will not
cast any shadows. If you want to have clouds that cast shadows you'll have to
use a real, large sphere with an appropriate texture and a light source
somewhere outside the sphere.

4.10.3           The Fog

You can use the fog feature to add fog of two different types to your scene:
constant fog and ground fog. The constant fog has a constant density
everywhere while the ground fog's density decreases as you move upwards.


4.10.3.1         A Constant Fog

The simplest fog type is the constant fog that has a constant density in all
locations. It is specified by a distance keyword which actually describes the
fog's density and a fog color.

The distance value determines the distance at which 36.8% of the background
are still visible (for a more detailed explanation of how the fog is
calculated read the reference section "Fog").

The fog color can be used to create anything from a pure white to a red,
blood-colored fog. You can also use a black fog to simulate the effect of a
limited range of vision.

The following example will show you how to add fog to a simple scene
(fog1.pov).

  #include "colors.inc"

  camera {
    location  <0, 20, -100>
  }

  background { colour SkyBlue }

  plane { y, -10
    pigment {
      checker colour Yellow colour Green
      scale 20
    }
  }

  sphere { <0, 25, 0>, 40
    pigment { Red }
    finish { phong 1.0 phong_size 20 }
  }

  sphere { <-100, 150, 200>,  20
    pigment { Green }
    finish { phong 1.0 phong_size 20 }
  }

  sphere { <100, 25, 100>, 30
    pigment { Blue }
    finish { phong 1.0 phong_size 20 }
  }

  light_source { <100, 120, 40> colour White}

  fog {
    distance 150
    colour rgb<0.3, 0.5, 0.2>
  }


A foggy scene.

According to their distance the spheres in this scene more or less vanish in
the greenish fog we used, as does the checkerboard plane.

4.10.3.2         Setting a Minimum Translucency

If you want to make sure that the background does not completely vanish in
the fog you can set the transmittance channel of the fog's color to the
amount of background you always want to be visible.

Using as transmittance value of 0.2 as in

  fog {
    distance 150
    colour rgbt<0.3, 0.5, 0.2, 0.2>
  }


the fog's translucency never drops below 20% as you can see in the resulting
image (fog2.pov).

Adding a translucency threshold you make sure that the background does not
vanish.

4.10.3.3         Creating a Filtering Fog

The greenish fog we have used so far doesn't filter the light passing through
it. All it does is to diminish the light's intensity. We can change this by
using a non-zero filter channel in the fog's color (fog3.pov).

  fog {
    distance 150
    colour rgbf<0.3, 0.5, 0.2, 1.0>
  }


The filter value determines the amount of light that is filtered by the fog.
In our example 100% of the light passing through the fog will be filtered by
the fog. If we had used a value of 0.7 only 70% of the light would have been
filtered. The remaining 30% would have passed unfiltered.

A filtering fog.

You'll notice that the intensity of the objects in the fog is not only
diminished due to the fog's color but that the colors are actually influenced
by the fog. The red and especially the blue sphere got a green hue.

4.10.3.4         Adding Some Turbulence to the Fog

In order to make our somewhat boring fog a little bit more interesting we can
add some turbulence, making it look like it had a non-constant density
(fog4.pov).

  fog {
    distance 150
    colour rgbf<0.3, 0.5, 0.2, 1.0>
    turbulence 0.2
    turb_depth 0.3
  }


Adding some turbulence makes the fog more interesting.

The turbulence keyword is used to specify the amount of turbulence used while
the turb_depth value is used to move the point at which the turbulence value
is calculated along the viewing ray. Values near zero move the point to the
viewer while values near one move it to the intersection point (the default
value is 0.5). This parameter can be used to avoid noise that may appear in
the fog due to the turbulence (this normally happens at very far away
intersection points, especially if no intersection occurs, i. e. the
background is hit). If this happens just lower the turb_depth value until the
noise vanishes.

You should keep in mind that the actual density of the fog does not change.
Only the distance-based attenuation value of the fog is modified by the
turbulence value at a point along the viewing ray.

4.10.3.5         Using Ground Fog

The much more interesting and flexible fog type is the ground fog, which is
selected with the fog_type statement. It's appearance is described with the
fog_offset and fog_alt keywords. The fog_offset specifies the height, i. e. y
value, below which the fog has a constant density of one. The fog_alt keyword
determines how fast the density of the fog will approach zero as one moves
along the y axis. At a height of fog_offset+fog_alt the fog will have a
density of 25%.

The following example (fog5.pov) uses a ground fog which has a constant
density below y=25 (the center of the red sphere) and quickly falls off for
increasing altitudes.

  fog {
    distance 150
    colour rgbf<0.3, 0.5, 0.2, 1.0>
    fog_type 2
    fog_offset 25
    fog_alt 1
  }


4.10.3.6         Using Multiple Layers of Fog

It is possible to use several layers of fog by using more than one fog
statement in your scene file. This is quite useful if you want to get nice
effects using turbulent ground fogs. You could add up several, differently
colored fogs to create an eerie scene for example.

Just try the following example (fog6.pov).

  fog {
    distance 150
    colour rgb<0.3, 0.5, 0.2>
    fog_type 2
    fog_offset 25
    fog_alt 1
    turbulence 0.1
    turb_depth 0.2
  }

  fog {
    distance 150
    colour rgb<0.5, 0.1, 0.1>
    fog_type 2
    fog_offset 15
    fog_alt 4
    turbulence 0.2
    turb_depth 0.2
  }

  fog {
    distance 150
    colour rgb<0.1, 0.1, 0.6>
    fog_type 2
    fog_offset 10
    fog_alt 2
  }


Quite nice results can be achieved using multiple layers of fog.

You can combine constant density fogs, ground fogs, filtering fogs,
non-filtering fogs, fogs with a translucency threshold, etc.

4.10.3.7         Fog and Hollow Objects

Whenever you use the fog feature and the camera is inside a non-hollow object
you won't get any fog effects. For a detailed explanation why this happens
see "Empty and Solid Objects".

In order to avoid this problem you have to make all those objects hollow by
either making sure the camera is outside these objects (using the inverse
keyword) or by adding the hollow to them (which is much easier).

4.10.4           The Atmosphere

Important notice: The atmosphere feature in POV-Ray 3.0 are somewhat
experimental. There is a high probability that the design and implementation
of these features will be changed in future versions. We cannot guarantee
that scenes using these features in 3.0 will render identically in future
releases or that full backwards compatibility of language syntax can be
maintained.

The atmosphere feature can be used to model the interaction of light with
particles in the air. Beams of light will become visible and objects will
cast shadows into the fog or dust that's filling the air.

The atmosphere model used in POV-Ray assumes a constant particle density
everywhere except solid objects. If you want to create cloud like fogs or
smoke you'll have to use the halo texturing feature described in section
"Halos".

4.10.4.1         Starting With an Empty Room

We want to create a simple scene to explain how the atmosphere feature works
and how you'll get good results.

Imagine a simple room with a window. Light falls through the window and is
scattered by the dust particles in the air. You'll see beams of light coming
from the window and shining on the floor.

We want to model this scene step by step. The following examples start with
the room, the window and a spotlight somewhere outside the room. Currently
there's no atmosphere to be able to verify if the lighting is correct
(atmos1.pov).

  camera {
    location <-10, 8, -19>
    look_at <0, 5, 0>
    angle 75
  }

  background { color rgb <0.2, 0.4, 0.8> }

  light_source { <0, 19, 0> color rgb 0.5 atmosphere off }

  light_source {
    <40, 25, 0> color rgb <1, 1, 1>
    spotlight
    point_at <0, 5, 0>
    radius 20
    falloff 20
    atmospheric_attenuation on
  }

  union {
    difference {
      box { <-21, -1, -21>, <21, 21, 21> }
      box { <-20, 0, -20>, <20, 20, 20> }
      box { <19.9, 5, -3>, <21.1, 15, 3> }
    }
    box { <20, 5, -0.25>, <21, 15, 0.25> }
    box { <20, 9.775, -3>, <21, 10.25, 3> }
    pigment { color red 1 green 1 blue 1 }
    finish { ambient 0.2 diffuse 0.5 }
  }


The empty room we want to start with.

The point light source is used to illuminate the room from inside without any
interaction with the atmosphere. This is done by adding atmosphere off . We
don't have to care about this light when we add the atmosphere later.

The spotlight is used with the atmospheric_attenuation keyword. This means
that light coming from the spotlight will be diminished by the atmosphere.

The union object is used to model the room and the window. Since we use the
difference between two boxes to model the room (the first two boxes in the
difference statement) there is no need for setting the union hollow. If we
are inside this room we actually will be outside the object (see also "Using
Hollow Objects and Atmosphere").

4.10.4.2         Adding Dust to the Room

The next step is to add an atmosphere to the room. This is done by the
following few lines (atmos2.pov).

  atmosphere {
    type 1
    samples 10
    distance 40
    scattering 0.2
  }


The type keyword selects the type of atmospheric scattering we want to use.
In this case we use the isotropic scattering that equally scatters light in
all directions (see "Atmosphere" for more details about the different
scattering types).

The samples keyword determines the number of samples used in accumulating the
atmospheric effect. For every ray samples are taken along the ray to
determine whether a sample is lit by a light source or not. If the sample is
lit the amount of light scattered into the direction of the viewer is
determined and added to the total intensity.

You can always start with an arbitrary number of samples. If the results do
not fit your ideas you can increase the sampling rate to get better results.
The problem of choosing a good sampling rate is the trade-off between a
satisfying image and a fast rendering. A high sampling rate will almost
always work but the rendering will also take a very long time. That's
something to experiment with.

The distance keyword specifies the density of the atmosphere. It works in the
same way as the distance parameter of the fog feature.

Last but not least will the scattering value determine the amount of light
that is scattered by the particles (the remaining light is absorbed). As
you'll later see this parameter is very useful in adjusting the overall
brightness of the atmosphere.

After adding some dust beams of light become visible.

Looking at the image created from the above scene you'll notice some very
ugly anti-aliasing artifacts known as mach-bands. They are the result of a
low sampling rate.


4.10.4.3         Choosing a Good Sampling Rate

As you've seen a too low sampling rate can cause some ugly results. There are
some ways of reducing or even avoiding those problems.

The brute force approach is to increase the sampling rate until the artifacts
vanish and you get a satisfying image. Though this will always work it is a
bad idea because it is very time consuming. A better approach is to use
jittering and anti-aliasing first. If both features don't help you'll have to
increase the sampling rate.

Jittering moves each sample point by a small, random amount along the
sampling direction. This helps to reduce regular features resulting from
aliasing. There is (hardly) nothing more annoying to the human visual system
than the regular features resulting from a low sampling rate. It's much
better to add some extra noise to the image by jittering the sample
positions. The human eye is much more forgiving to that.

Use the jitter keyword followed by the amount of jittering you want to use.
Good jittering values are up to 0.5, higher values result in too much noise.

You should be aware that jittering can not fix the artifacts introduced by a
too low sampling rate. It can only make them less visible.

An additional and better way of reducing aliasing artifacts is to use
(adaptive) super-sampling. This method casts additional samples where it is
likely that they are needed. If the intensity between two adjacent samples
differs too much additional samples are taken in-between. This step is done
recursively until a specified recursion level is reached or the sample get
close to each other.

The aa_level and aa_threshold keywords give full control over the
super-sampling process. The aa_level keyword determines the maximum recursion
level while aa_threshold specifies the maximum allowed difference between two
sample before the super-sampling is done.

After all this theory we get back to our sample scene and add the appropriate
keywords to use both jittering and super-sampling (atmos3.pov).

  atmosphere {
    type 1
    samples 50
    distance 40
    scattering 0.2
    aa_level 4
    aa_threshold 0.1
    jitter 0.2
  }


A very low threshold value was chosen to super-sample even between adjacent
points with a very similar intensity. The maximum recursion level of 4 will
lead to a maximum of fifteen super-samples.

If you are looking at the results that you get after adding jittering and
super-sampling you won't be satisfied. The only way of reducing the still
visible artifacts is to increase the sampling rate by choosing a higher
number of samples.

A high sampling rate leads to a satisfying image.

Doing this you'll get a good result showing (almost) no artifacts. BTW, the
amount of dust floating around in this room may be a little bit exaggerated
but it's just an example. And examples tend to be exaggerated.

4.10.4.4         Using a Coloured Atmosphere

You can assign a color to the atmosphere that gives you more control over the
atmosphere's appearance. First of all the color is used to filter all light
passing through it, whether it comes from light sources, reflected and
refracted rays, or the background. The amount by which the passing light is
filtered by the atmosphere's color is determined by the color's filter value.
A value of 0 means that the light is not influenced by the atmosphere's color
while a value of 1 means that all light will be filtered by the color.

If you want to create a reddish atmosphere for example, you can add the
following line to the atmosphere statement used in the above example.

  color rgbf <1, 0, 0, 0.25>


Just using rgb <1,0,0> does not work because the color's filter value will be
zero and thus no light will be filtered by the color, i. e. no light will be
multiplied with the color's RGB components.

The filter value of 0.25 means that 25% of the light passing through the
atmosphere will be filtered by the red color and 75% will pass unfiltered.

The transmittance channel of the atmosphere's color is used to specify a
minimum translucency. By default the transmittance channel is zero and thus
there is no such minimum translucency. Using a positive value lets you
determine the amount of background light that will always pass through the
atmosphere, regardless of its thickness set by the distance keyword.

If you use e.g. a color of rgbt <0,0,0,0.3> with our room example you can
make the blue background become visible. Until now it was hidden by the
atmosphere.

4.10.4.5         Atmosphere Tips

It is very difficult to get satisfying results when using the atmosphere
feature. Some of the more common problems will be discussed in the next
sections to help you to solve them (see also the FAQ section about the
atmosphere in "Atmosphere Questions").

4.10.4.5.1       Choosing the Distance and Scattering Parameters

The first difficult step is to choose a good distance and scattering value.
You need to be able to control the visibility of the objects in the scene and
the atmospheric effects.

The best approach is to choose the distance value first. This value
determines the visibility of the objects in the scene regardless of
atmospheric light scattering. It works in the same way as the distance value
of the fog feature.

Since fog is very similar to the unlit atmosphere you can use a fog instead
of an atmosphere to quickly choose a working distance value. If you do this
with room scene we used earlier you would use the following fog statement
instead of the atmosphere (atmos4.pov).

  fog {
    distance 40
    color rgb <0, 0, 0>
  }


A black fog can be used to get a working distance value for the atmosphere.

The black color is used to simulate the attenuation you'll get in those parts
of the atmosphere scene lying in shadow.

If you want to use a colored atmosphere you'll have to use the same color for
the fog as you want to use for the atmosphere, including the filter and
transmittance channel values (see "Using a Coloured Atmosphere" and
"Atmosphere" for an explanation of the atmosphere's color).

If you (roughly) want to simulate the appearance of those parts lit by a
light source you can use the color of the atmosphere inside the fog statement
instead.

After you are satisfied with the distance value you'll have to choose a
scattering value. This value lets you fit the atmosphere's intensity to your
needs. Starting with a value of one you have to increase the value if the
atmosphere effects are hardly visible. If you don't see anything in the lit
parts of the atmosphere you'll have to decrease the value.

You should be aware that you may have to use very small or very large values
to get the desired results.

4.10.4.5.2       Atmosphere and Light Sources

The best results are generated with spotlights and cylindrical light sources.
They create nice beams of light and are fast to render because the
atmospheric sampling takes only place inside the light cone of the spotlight
or light cylinder of the cylindrical light.

If you want to add a light source that does not interact with the atmosphere
you can use the atmosphere keyword inside the light source statement (see
"Atmosphere Interaction"). Just add atmosphere off.

By default the light coming from any light source will not be diminished by
the atmosphere. Thus the highlights in your scene will normally be too
bright. This can be changed with atmospheric_attenuation on.

4.10.4.5.3       Atmosphere Scattering Types

The different scattering types listed in "Atmosphere" can be used to model
different types of particles. This is something for you to experiment with.

The Rayleigh scattering is used for small particles like dust and smoke while
the Mie scattering is used for fog.

If you ever saw the lighthouse scene in the movie Casper you'll know what
effect the scattering type has. In this scene the beam of light coming from
the lighthouse becomes visible while it points nearly towards the viewer. As
it starts to point away from the viewer it vanishes. This behaviour is
typical for minuscule water droplets as modeled by the Mie scattering.

4.10.4.5.4       Increasing the Image Resolution

You have to be aware that you may have to increase the atmosphere sampling
rate if you increase the resolution of the image. Otherwise some aliasing
artifacts that were no visible at the lower resolution may become visible.

4.10.4.5.5       Using Hollow Objects and Atmosphere

Whenever you use the atmosphere feature you have to make sure that all
objects that ought to be filled with atmosphere are set to hollow using the
hollow keyword.

Even though this is not obvious this holds for infinite and patch objects
like quadrics, quartics, triangles, polygons, etc. Whenever you add one of
those objects you should add the hollow keyword as long as you are not
absolutely sure you don't need it. You also have to make sure that all
objects the camera is inside are set to be hollow.

Whenever you get unexpected results you should check for solid objects and
set them to be hollow.

4.10.5           The Rainbow

The rainbow feature can be used to create rainbows and maybe other more
strange effects. The rainbow is a fog like effect that is restricted to a
cone-like volume.

4.10.5.1         Starting With a Simple Rainbow

The rainbow is specified with a lot of parameters: the angle under which it
is visible, the width of the color band, the direction of the incoming light,
the fog-like distance based particle density and last not least the color map
to be used.

The size and shape of the rainbow are determined by the angle and width
keywords. The direction keyword is used to set the direction of the incoming
light, thus setting the rainbow's position. The rainbow is visible when the
angle between the direction vector and the incident light direction is larger
than angle-width/2 and smaller than angle+width/2.

The incoming light is the virtual light source that is responsible for the
rainbow. There needn't be a real light source to create the rainbow effect.

The rainbow is a fog-like effect, i.e. the rainbow's color is mixed with the
background color based on the distance to the intersection point. If you
choose small distance values the rainbow will be visible on objects, not just
in the background. You can avoid this by using a very large distance value.

The color map is the crucial part of the rainbow since it contains all the
colors that normally can be seen in a rainbow. The color of the innermost
color band is taken from the color map entry 0 while the outermost band is
take from entry 1. You should note that due to the limited color range any
monitor can display it is impossible to create a real rainbow. There are just
some colors that you cannot display.

The filter channel of the rainbow's color map is used in the same way as with
fogs. It determines how much of the light passing through the rainbow is
filtered by the color.

The following example shows a simple scene with a ground plane, three spheres
and a somewhat exaggerated rainbow (rainbow1.pov).

  #include "colors.inc"

  camera {
    location <0, 20, -100>
    look_at <0, 25, 0>
    angle 80
  }

  background { color SkyBlue }

  plane { y, -10 pigment { colour Green } }

  light_source {<100, 120, 40> colour White}

  // declare rainbow's colours

  #declare r_violet1 = colour rgbf<1.0, 0.5, 1.0, 1.0>
  #declare r_violet2 = colour rgbf<1.0, 0.5, 1.0, 0.8>
  #declare r_indigo  = colour rgbf<0.5, 0.5, 1.0, 0.8>
  #declare r_blue    = colour rgbf<0.2, 0.2, 1.0, 0.8>
  #declare r_cyan    = colour rgbf<0.2, 1.0, 1.0, 0.8>
  #declare r_green   = colour rgbf<0.2, 1.0, 0.2, 0.8>
  #declare r_yellow  = colour rgbf<1.0, 1.0, 0.2, 0.8>
  #declare r_orange  = colour rgbf<1.0, 0.5, 0.2, 0.8>
  #declare r_red1    = colour rgbf<1.0, 0.2, 0.2, 0.8>
  #declare r_red2    = colour rgbf<1.0, 0.2, 0.2, 1.0>

  // create the rainbow

  rainbow {
    angle 42.5
    width 5
    distance 1.0e7
    direction <-0.2, -0.2, 1>
    jitter 0.01
    colour_map {
      [0.000  colour r_violet1]
      [0.100  colour r_violet2]
      [0.214  colour r_indigo]
      [0.328  colour r_blue]
      [0.442  colour r_cyan]
      [0.556  colour r_green]
      [0.670  colour r_yellow]
      [0.784  colour r_orange]
      [0.900  colour r_red1]
    }
  }


Some irregularity is added to the color bands using the jitter keyword.

A colorful rainbow.

The rainbow in our sample is much too bright. You'll never see a rainbow like
this in reality. You can decrease the rainbow's colors by decreasing the RGB
values in the color map.

4.10.5.2         Increasing the Rainbow's Translucency

The result we have so far looks much too bright. Just reducing the rainbow's
color helps but it's much better to increase the translucency of the rainbow
because it is more realistic if the background is visible through the
rainbow.

We can use the transmittance channel of the colors in the color map to
specify a minimum translucency, just like we did with the fog. To get
realistic results we have to use very large transmittance values as you can
see in the following example (rainbow2.pov).

  rainbow {
    angle 42.5
    width 5
    distance 1.0e7
    direction <-0.2, -0.2, 1>
    jitter 0.01
    colour_map {
      [0.000  colour r_violet1 transmit 0.98]
      [0.100  colour r_violet2 transmit 0.96]
      [0.214  colour r_indigo  transmit 0.94]
      [0.328  colour r_blue    transmit 0.92]
      [0.442  colour r_cyan    transmit 0.90]
      [0.556  colour r_green   transmit 0.92]
      [0.670  colour r_yellow  transmit 0.94]
      [0.784  colour r_orange  transmit 0.96]
      [0.900  colour r_red1    transmit 0.98]
    }
  }


The transmittance values increase at the outer bands of the rainbow to make
it softly blend into the background.

A much more realistic rainbow.


4.10.5.3         Using a Rainbow Arc

Currently our rainbow has a circular shape, even though most of it is hidden
below the ground plane. You can easily create a rainbow arc by using the
arc_angle keyword with an angle below 360 degrees.

If you use arc_angle 120 for example you'll get a rainbow arc that abruptly
vanishes at the arc's ends. This does not look good. To avoid this the
falloff_angle keyword can be used to specify a region where the arc smoothly
blends into the background.

As explained in the rainbow's reference section (see "Rainbow") the arc
extends from -arc_angle/2 to arc_angle/2 while the blending takes place from
-arc_angle/2 to -falloff_angle/2 and falloff_angle/2 to arc_angle/2. This is
the reason why the falloff_angle has to be smaller or equal to the arc_angle.


In the following examples we use an 120 degrees arc with a 45 degree falloff
region on both sides of the arc (rainbow3.pov).

  rainbow {
    angle 42.5
    width 5
    arc_angle 120
    falloff_angle 30
    distance 1.0e7
    direction <-0.2, -0.2, 1>
    jitter 0.01
    colour_map {
      [0.000  colour r_violet1 transmit 0.98]
      [0.100  colour r_violet2 transmit 0.96]
      [0.214  colour r_indigo  transmit 0.94]
      [0.328  colour r_blue    transmit 0.92]
      [0.442  colour r_cyan    transmit 0.90]
      [0.556  colour r_green   transmit 0.92]
      [0.670  colour r_yellow  transmit 0.94]
      [0.784  colour r_orange  transmit 0.96]
      [0.900  colour r_red1    transmit 0.98]
    }
  }


The arc angles are measured against the rainbows up direction which can be
specified using the up keyword. By default the up direction is the y-axis.

A rainbow arc.


4.10.6           Animation

There are a number of programs available that will take a series of still TGA
files (such as POV-Ray outputs) and assemble them into animations. Such
programs can produce AVI, MPEG, FLI/FLC, or even animated GIF files (for use
on the World Wide Web). The trick, therefore, is how to produce the frames.
That, of course, is where POV-Ray comes in. In earlier versions producing an
animation series was no joy, as everything had to be done manually. We had to
set the clock variable, and handle producing unique file names for each
individual frame by hand. We could achieve some degree of automation by using
batch files or similar scripting devices, but still, We had to set it all up
by hand, and that was a lot of work (not to mention frustration... imagine
forgetting to set the individual file names and coming back 24 hours later to
find each frame had overwritten the last).

Now, at last, with POV-Ray 3, there is a better way. We no longer need a
separate batch script or external sequencing programs, because a few simple
settings in our INI file (or on the command line) will activate an internal
animation sequence which will cause POV-Ray to automatically handle the
animation loop details for us.

Actually, there are two halves to animation support: those settings we put in
the INI file (or on the command line), and those code modifications we work
into our scene description file. If we've already worked with animation in
previous versions of POV-Ray, we can probably skip ahead to the section "INI
File Settings" below. Otherwise, let's start with basics. Before we get to
how to activate the internal animation loop, let's look at a couple examples
of how a couple of keywords can set up our code to describe the motions of
objects over time.

4.10.6.1         The Clock Variable: Key To It All

POV-Ray supports an automatically declared floating point variable identified
as clock (all lower case). This is the key to making image files that can be
automated. In command line operations, the clock variable is set using the +k
switch. For example, \Clo{+k3.4} from the command line would set the value of
clock to 3.4. The same could be accomplished from the INI file
using\IFKINDEX{Clock}

  Clock = 3.4


If we don't set clock for anything, and the animation loop is not used (as
will be described a little later) the clock variable is still there - it's
just set for the default value of 0.0, so it is possible to set up some POV
code for the purpose of animation, and still render it as a still picture
during the object/world creation stage of our project.

The simplest example of using this to our advantage would be having an object
which is travelling at a constant rate, say, along the x-axis. We would have
the statement

  translate <clock, 0, 0>


in our object's declaration, and then have the animation loop assign
progressively higher values to clock. And that's fine, as long as only one
element or aspect of our scene is changing, but what happens when we want to
control multiple changes in the same scene simulatneously?

The secret here is to use normalized clock values, and then make other
variables in your scene proportional to clock. That is, when we set up our
clock, (we're getting to that, patience!) have it run from 0.0 to 1.0, and
then use that as a multiplier to some other values. That way, the other
values can be whatever we need them to be, and clock can be the same 0 to 1
value for every application. Let's look at a (relatively) simple example

  #include "colors.inc"

  camera {
    location <0, 3, -6>
    look_at <0, 0, 0>
  }

  light_source { <20, 20, -20> color White }

  plane { y, 0
    pigment { checker color White color Black }
  }

  sphere { <0, 0, 0> , 1
    pigment {
      gradient x
      color_map {
        [0.0 Blue  ]
        [0.5 Blue  ]
        [0.5 White ]
        [1.0 White ]
      }
      scale .25
    }
    rotate <0, 0, -clock*360>
    translate <-pi, 1, 0>
    translate <2*pi*clock, 0, 0>
  }


Assuming that a series of frames is run with the clock progressively going
from 0.0 to 1.0, the above code will produce a striped ball which rolls from
left to right across the screen. We have two goals here:

  2.Rotate the ball in exactly the right proportion to its linear movement to
    imply that it is rolling -- not gliding -- to its final position.


Taking the second goal first, we start with the sphere at the origin, because
anywhere else and rotation will cause it to orbit the origin instead of
rotating. Throughout the course of the animation, the ball will turn one
complete 360 degree turn. Therefore, we used the formula, 360*clock to
determine the rotation in each frame. Since clock runs 0 to 1, the rotation
of the sphere runs from 0 degrees through 360.

Then we used the first translation to put the sphere at its initial starting
point. Remember, we couldn't have just declared it there, or it would have
orbited the origin, so before we can meet our other goal (translation), we
have to compensate by putting the sphere back where it would have been at the
start. After that, we re-translate the sphere by a clock relative distance,
causing it to move relative to the starting point. We've chosen the formula
of 2*pi* r*clock (the widest circumference of the sphere times current clock
value) so that it will appear to move a distance equal to the circumference
of the sphere in the same time that it rotates a complete 360 degrees. In
this way, we've synchronized the rotation of the sphere to its translation,
making it appear to be smoothly rolling along the plane.

Besides allowing us to coordinate multiple aspects of change over time more
cleanly, mathematically speaking, the other good reason for using normalized
clock values is that it will not matter whether we are doing a ten frame
animated GIF, or a three hundred frame AVI. Values of the clock are
proportioned to the number of frames, so that same POV code will work without
regard to how long the frame sequence is. Our rolling ball will still travel
the exact same amount no matter how many frames our animation ends up with.

4.10.6.2         Clock Dependant Variables And Multi-Stage Animations

Okay, what if we wanted the ball to roll left to right for the first half of
the animation, then change direction 135 degrees and roll right to left, and
toward the back of the scene. We would need to make use of POV's new
conditional rendering directives, and test the clock value to determine when
we reach the halfway point, then start rendering a different clock dependant
sequence. But our goal, as above, it to be working in each stage with a
variable in the range of 0 to 1 (normalized) because this makes the math so
much cleaner to work with when we have to control multiple aspects during
animation. So let's assume we keep the same camera, light, and plane, and let
the clock run from 0 to 2! Now, replace the single sphere declaration with
the following...

  #if ( clock <= 1 )
    sphere { <0, 0, 0> , 1
      pigment {
        gradient x
        color_map {
          [0.0 Blue  ]
          [0.5 Blue  ]
          [0.5 White ]
          [1.0 White ]
        }
        scale .25
      }
      rotate <0, 0, -clock*360>
      translate <-pi, 1, 0>
      translate <2*pi*clock, 0, 0>
    }
  #else
    // (if clock is > 1, we're on the second phase)

    // we still want to work with  a value from 0 - 1

    #declare ElseClock = clock - 1

    sphere { <0, 0, 0> , 1
      pigment {
        gradient x
        color_map {
          [0.0 Blue  ]
          [0.5 Blue  ]
          [0.5 White ]
          [1.0 White ]
        }
        scale .25
      }
      rotate <0, 0, ElseClock*360>
      translate <-2*pi*ElseClock, 0, 0>
      rotate <0, 45, 0>
      translate <pi, 1, 0>
    }
  #end


If we spotted the fact that this will cause the ball to do an unrealistic
snap turn when changing direction, bonus points for us - we're a born
animator. However, for the simplicity of the example, let's ignore that for
now. It will be easy enough to fix in the real world, once we examine how the
existing code works.

All we did differently was assume that the clock would run 0 to 2, and that
we wanted to be working with a normalized value instead. So when the clock
goes over 1.0, POV assumes the second phase of the journey has begun, and we
declare a new variable Elseclock which we make relative to the original built
in clock, in such a way that while clock is going 1 to 2, Elseclock is going
0 to 1. So, even though there is only one clock, there can be as many
additional variables as we care to declare (and have memory for), so even in
fairly complex scenes, the single clock variable can be made the common
coordinating factor which orchestrates all other motions.

4.10.6.3         The Phase Keyword

There is another keyword we should know for purposes of animations: the phase
keyword. The phase keyword can be used on many texture elements, especially
those that can take a color, pigment, normal or texture map. Remember the
form that these maps take. For example:

  color_map {
    [0.00 White ]
    [0.25 Blue ]
    [0.76 Green ]
    [1.00 Red ]
  }


The floating point value to the left inside each set of brackets helps
POV-Ray to map the color values to various areas of the object being
textured. Notice that the map runs cleanly from 0.0 to 1.0?

Phase causes the color values to become shifted along the map by a floating
point value which follows the keyword phase. Now, if we are using a
normalized clock value already anyhow, we can make the variable clock the
floating point value associated with phase, and the pattern will smoothly
shift over the course of the animation. Let's look at a common example using
a gradient normal pattern

  #include "colors.inc"
  #include "textures.inc"

  #background { rgb<0.8, 0.8, 0.8> }

  camera {
    location <1.5, 1, -30>
    look_at <0, 1, 0>
    angle 10
  }

  light_source { <-100, 20, -100> color White }

  // flag

  polygon { 5, <0, 0>, <0, 1>, <1, 1>, <1, 0>, <0, 0>
    pigment { Blue }
    normal {
      gradient x
      phase clock
      scale <0.2, 1, 1>
      sine_wave
    }
    scale <3, 2, 1>
    translate <-1.5, 0, 0>
  }

  // flagpole

  cylinder { <-1.5, -4, 0>, <-1.5, 2.25, 0>, 0.05
    texture { Silver_Metal }
  }

  // polecap

  sphere { <-1.5, 2.25, 0>, 0.1
    texture { Silver_Metal }
  }


Now, here we've created a simple blue flag with a gradient normal pattern on
it. We've forced the gradient to use a sine-wave type wave so that it looks
like the flag is rolling back and forth as though flapping in a breeze. But
the real magic here is that phase keyword. It's been set to take the clock
variable as a floating point value which, as the clock increments slowly
toward 1.0, will cause the crests and troughs of the flag's wave to shift
along the x-axis. Effectively, when we animate the frames created by this
code, it will look like the flag is actually rippling in the wind.

This is only one, simple example of how a clock dependant phase shift can
create interesting animation effects. Trying phase will all sorts of texture
patterns, and it is amazing the range of animation effects we can create
simply by phase alone, without ever actually moving the object.

4.10.6.4         Do Not Use Jitter Or Crand

One last piece of basic information to save frustration. Because jitter is an
element of anti-aliasing, we could just as easily have mentioned this under
the INI file settings section, but there are also forms of anti-aliasing used
in area lights, and the new atmospheric effects of POV-Ray, so now is as good
a time as any.

Jitter is a very small amount of random ray perturbation designed to diffuse
tiny aliasing errors that might not otherwise totally disappear, even with
intense anti-aliasing. By randomizing the placement of erroneous pixels, the
error becomes less noticable to the human eye, because the eye and mind are
naturally inclined to look for regular patterns rather than random
distortions.

This concept, which works fantasticly for still pictures, can become a
nightmare in animations. Because it is random in nature, it will be different
for each frame we render, and this becomes even more severe if we dither the
final results down to, say 256 color animations (such as FLC's). The result
is jumping pixels all over the scene, but especially concentrated any place
where aliasing would normally be a problem (e.g., where an infinite plane
disappears into the distance).

For this reason, we should always set jitter to off in area lights and
anti-aliasing options when preparing a scene for an animation. The
(relatively) small extra measure quality due to the use of jitter will be
offset by the ocean of jumpies that results. This general rule also applies
to any truly random texture elements, such as crand.

4.10.6.5         INI File Settings

Okay, so we have a grasp of how to code our file for animation. We know about
the clock variable, user declared clock-relative variables, and the phase
keyword. We know not to jitter or crand when we render a scene, and we're all
set build some animations. Alright, let's have at it.

The first concept we'll need to know is the INI file settings, Initial_Frame
and Final_Frame. These are very handy settings that will allow us to render a
particular number of frames and each with its own unique frame number, in a
completely hands free way. It is of course, so blindingly simple that it
barely needs explanation, but here's an example anyway. We just add the
following lines to our favorite INI file settings

  Initial_Frame = 1
  Final_Frame = 20


and we'll initiate an automated loop that will generate 20 unique frames. The
settings themselves will automatically append a frame number onto the end of
whatever we have set the output file name for, thus giving each frame an
unique file number without having to think about it. Secondly, by default, it
will cycle the clock variable up from 0 to 1 in increments proportional to
the number of frames. This is very convenient, since, no matter whether we
are making a five frame animated GIF or a 300 frame MPEG sequence, we will
have a clock value which smoothly cylces from exactly the same start to
exactly the same finish.

Next, about that clock. In our example with the rolling ball code, we saw
that sometimes we want the clock to cycle through values other than the
default of 0.0 to 1.0. Well, when that's the case, there are setting for that
too. The format is also quite simple. To make the clock run, as in our
example, from 0.0 to 2.0, we would just add to your INI file the lines

  Initial_Clock = 0.0
  Final_Clock = 2.0


Now, suppose we were developing a sequence of 100 frames, and we detected a
visual glitch somewhere in frames, say 51 to 75. We go back over our code and
we think we've fixed it. We'd like to render just those 25 frames instead of
redoing the whole sequence from the beginning. What do we change?

If we said make Initial_Frame = 51, and Final_Frame = 75, we're wrong. Even
though this would re-render files named with numbers 51 through 75, they will
not properly fit into our sequence, because the clock will begin at its
initial value starting with frame 51, and cycle to final value ending with
frame 75. The only time Initial_Frame and Final_Frame should change is if we
are doing an essentially new sequence that will be appended onto existing
material.

If we wanted to look at just 51 through 75 of the original animation, we need
two new INI settings

  Subset_Start_Frame = 51
  Subset_End_Frame = 75


Added to settings from before, the clock will still cycle through its values
proportioned from frames 1 to 100, but we will only be rendering that part of
the sequence from the 51st to the 75th frames.

This should give us a basic idea of how to use animation. Although, this
introductory tutorial doesn't cover all the angles. For example, the last two
settings we just saw, subset animation, can take fractional values, like 0.5
to 0.75, so that the number of actual frames will not change what portion of
the animation is being rendered. There is also support for efficient odd-even
field rendering as would be useful for animations prepared for display in
interlaced playback such as television (see the reference section for full
details).

With POV-Ray 3 now fully supporting a complete host of animation options, a
whole fourth dimension is added to the raytracing experience. Whether we are
making a FLIC, AVI, MPEG, or simply an animated GIF for our web site,
animation support takes a lot of the tedium out of the process. And don't
forget that phase and clock can be used to explore the range of numerous
texture elements, as well as some of the more difficult to master objects
(hint: the julia fractal for example). So even if we are completely content
with making still scenes, adding animation to our repetoire can greatly
enhance our understanding of what POV-Ray is capable of. Adventure awaits!

5                POV-Ray Reference

The reference section describes all command line switches and INI file
keywords that are used to set the options of POV-Ray, the scene description
language and all other features that are part of POV-Ray. It is supposed to
be used as a reference for looking up things. It does not contain detailed
explanations on how scenes are written or how POV-Ray is used. It just
explains all features, their syntax, applications, limits, drawbacks, etc.

6                POV-Ray Options

POV-Ray was originally created as a command-line program for operating
systems without graphical interfaces, dialog boxes and pull-down menus. Most
versions of POV-Ray still use command-line switches to tell it what to do.
This documentation assumes you are using the command-line version. If you are
using Macintosh, MS-Windows or other GUI versions, there will be dialog boxes
or menus which do the same thing. There is system-specific documentation for
each system describing the specific commands.

6.1              Setting POV-Ray Options

There are two distinct ways of setting POV-Ray options: command line switches
and INI file keywords. Both are explained in detail in the following
sections.

6.1.1            Command Line Switches

Command line switches consist of a + (plus) or - (minus) sign, followed by
one or more alphabetic characters and possibly a numeric value. Here is a
typical command line with switches.

  POVRAY +Isimple.pov +V +W80 +H60


povray is the name of the program and it is followed by several switches.
Each switch begins with a plus or minus sign. The +I switch with the filename
tells POV-Ray what scene file it should use as input and +V tells the program
to output its status to the text screen as it's working. The +W and +H
switches set the width and height of the image in pixels. This image will be
80 pixels wide by 60 pixels high.

In switches which toggle a feature, the plus turns it on and minus turns it
off. For example +P turns on the pause for keypress  when finished option
while -P turns it off. Other switches are used to specify values and do not
toggle a feature. Either plus or minus may be used in that instance. For
example +W320 sets the width to 320 pixels. You could also use -W320 and get
the same results.

Switches may be specified in upper or lower case. They are read left to right
but in general may be specified in any order. If you specify a switch more
than once, the previous value is generally overwritten with the last
specification. The only exception is the +L switch for setting library paths.
Up to ten unique paths may be specified.

Almost all +/- switches have an equivalent option which can be used in an INI
file which is described in the next section. A detailed description of each
switch is given in the option reference section.

6.1.2            Using INI Files

Because it is difficult to set more than a few options on a command line, you
have the ability to put multiple options in one or more text files. These
initialization files or INI files have .ini as their default extension.
Previous versions of POV-Ray called them default files or DEF files. You may
still use existing DEF files with this version of POV-Ray.

The majority of options you use will be stored in INI files. The command line
switches are recommended for options which you will turn off or on frequently
as you perform test renderings of a scene you are developing. The file
povray.ini is automatically read if present. You may specify additional INI
files on the command-line by simply typing the file name on the command line.
For example:

  POVRAY MYOPTS.INI


If no extension is given, then .ini is assumed. POV-Ray knows this is not a
switch because it is not preceded by a plus or minus. In fact a common error
among new users is that they forget to put the +I switch before the input
file name. Without the switch, POV-Ray thinks that the scene file simple.pov
is an INI file. Don't forget! If no plus or minus precedes a command line
switch, it is assumed to be an INI file name.

You may have multiple INI files on the command line along with switches. For
example:

  POVRAY MYOPTS +V OTHER


This reads options from myopts.ini, then sets the +V switch, then reads
options from other.ini.

An INI file is a plain ASCII text file with options of the form...

  Option_keyword=VALUE ; Text after semicolon is a comment


For example the INI equivalent of the switch +Isimple.pov is...

  Input_File_Name=simple.pov


Options are read top to bottom in the file but in general may be specified in
any order. If you specify an option more than once, the previous values are
generally overwritten with the last specification. The only exception is the
Library_Path=path options. Up to ten unique paths may be specified.

Almost all INI-style options have equivalent +/- switches. The option
reference section gives a detailed description of all POV-Ray options. It
includes both the INI-style settings and the +/- switches.

The INI keywords are not case sensitive. Only one INI option is permitted per
line of text. You may also include switches in your INI file if they are
easier for you. You may have multiple switches per line but you should not
mix switches and INI options on the same line. You may nest INI files by
simply putting the file name on a line by itself with no equals sign after
it. Nesting may occur up to ten levels deep.

For example:

  ; This is a sample INI file. This entire line is a comment.
  ; Blank lines are permitted.

  Input_File_Name=simple.pov ;This sets the input file name

  +W80 +H60 ; Traditional +/- switches are permitted too

  MOREOPT   ; Read MOREOPT.INI and continue with next line

  +V        ; Another switch

  ; That's all folks!


INI files may have labeled sections so that more than one set of options may
be stored in a single file. Each section begins with a label in [] brackets.
For example:

  ; RES.INI
  ; This sample INI file is used to set resolution.

  +W120 +H100  ; This section has no label.
               ; Select it with "RES"

  [Low]
  +W80 +H60    ; This section has a label.
               ; Select it with "RES[Low]"

  [Med]
  +W320 +H200  ; This section has a label.
               ; Select it with "RES[Med]"

  [High]
  +W640 +H480  ; Labels are not case sensitive.
               ; "RES[high]" works

  [Really High]
  +W800 +H600  ; Labels may contain blanks


When you specify the INI file you should follow it with the section label in
brackets. For example...

  POVRAY RES[Med] +Imyfile.pov


POV-Ray reads res.ini and skips all options until it finds the label Med. It
processes options after that label until it finds another label and then it
skips. If no label is specified on the command line then only the unlabeled
area at the top of the file is read. If a label is specified, the unlabeled
area is ignored.

6.1.3            Using the POVINI Environment Variable

The environment variable POVINI is used to specify the location and name of a
default INI file that is read every time POV-Ray is executed. If POVINI is
not specified a default INI file may be read depending on the platform used.
If the specified file does not exist a warning message is printed.

To set the environment variable under MS-DOS you might put the following line
in your autoexec.bat file...

  set POVINI=c:\povray3\default.ini


On most operating systems the sequence of reading options is as follows:

  1.Read options from default INI file specified by the POVINI environment
  2.Read switches from command line (this includes reading any specified
    INI/DEF files).


The POVRAYOPT environment variable supported by previous POV-Ray versions is
no longer available.

6.2              Options Reference

As explained in the previous section, options may be specified by switches or
INI-style options. Almost all INI-style options have equivalent +/- switches
and most switches have equivalent INI-style option. The following sections
give a detailed description of each POV-Ray option. It includes both the
INI-style settings and the +/- switches.

The notation and terminology used is described in the tables below.

  Keyword=bool turn Keyword on if bool equals true, yes, on or 1 and turn it
  Keyword=fileeany valid file name. Note: some options prohibit the use of
               any of the above true or false values as a file name. They are
               noted in later sections.


  path yany directory name, drive optional, no final path separator ("\" or
        "/", depending on the operating system)


Unless otherwise specifically noted, you may assume that either a plus or
minus sign before a switch will produce the same results.

6.2.1            Animation Options

POV-Ray 3.0 greatly improved its animation capability with the addition of an
internal animation loop, automatic output file name numbering and the ability
to shell out to the operating system to external utilities which can assemble
individual frames into an animation. The internal animation loop is simple
yet flexible. You may still use external programs or batch files to create
animations without the internal loop as you may have done in POV-Ray 2.

6.2.1.1          External Animation Loop

  +Kn.n=n.nSame as Clock=n.nt identifier to n.n


The Clock=n.n option or the +Kn.n switch may be used to pass a single float
value to the program for basic animation. The value is stored in the float
identifier clock. If an object had a rotate <0,clock,0> attached then you
could rotate the object by different amounts over different frames by setting
+K10.0, +K20.0... etc. on successive renderings. It is up to the user to
repeatedly invoke POV-Ray with a different Clock value and a different
Output_File_Name for each frame.

6.2.1.2          Internal Animation Loop

  +KFn.nClock=n.n.nSame as Final_Clock=n.n.n to n


The internal animation loop new to POV-Ray 3.0 relieves the user of the task
of generating complicated sets of batch files to invoke POV-Ray multiple
times with different settings. While the multitude of options may look
intimidating, the clever set of default values means that you will probably
only need to specify the Final_Frame=n or the +KFFn option to specify the
number of frames. All other values may remain at their defaults.

Any Final_Frame setting other than -1 will trigger POV-Ray's internal
animation loop. For example Final_Frame=10 or +KFF10 causes POV-Ray to render
your scene 10 times. If you specified Output_File_Name=file.tga then each
frame would be output as file01.tga, file02.tga, file03.tga etc. The number
of zero-padded digits in the file name depends upon the final frame number.
For example +KFF100 would generate file001.tga through file100.tga. The frame
number may encroach upon the file name. On MS-DOS with an eight character
limit, myscene.pov would render to mysce001.tga through mysce100.tga.

The default Initial_Frame=1 will probably never have to be changed. You would
only change it if you were assembling a long animation sequence in pieces.
One scene might run from frame 1 to 50 and the next from 51 to 100. The
Initial_Frame=n or +KFIn option is for this purpose.

Note that if you wish to render a subset of frames such as 30 through 40 out
of a 1 to 100 animation, you should not change Frame_Initial or Frame_Final.
Instead you should use the subset commands described in section "Subsets of
Animation Frames".

Unlike some animation packages, the action in POV-Ray animated scenes does
not depend upon the integer frame numbers. Rather you should design your
scenes based upon the float identifier clock. By default, the clock value is
0.0 for the initial frame and 1.0 for the final frame. All other frames are
interpolated between these values. For example if your object is supposed to
rotate one full turn over the course of the animation, you could specify
rotate  360*clock*y. Then as clock runs from 0.0 to 1.0, the object rotates
about the y-axis from 0 to 360 degrees.

The major advantage of this system is that you can render a 10 frame
animation or a 100 frame or 500 frame or 329 frame animation yet you still
get one full 360 degree rotation. Test renders of a few frames work exactly
like final renders of many frames.

In effect you define the motion over a continuous float valued parameter (the
clock) and you take discrete samples at some fixed intervals (the frames). If
you take a movie or video tape of a real scene it works the same way. An
object's actual motion depends only on time. It does not depend on the frame
rate of your camera.

Many users have already created scenes for POV-Ray 2 that expect clock values
over a range other than the default 0.0 to 1.0. For this reason we provide
the Initial_Clock=n.n or +KIn.n and Final_Clock=n.n or +KFn.n options. For
example to run the clock from 25.0 to 75.0 you would specify
Initial_Clock=25.0 and Final_Clock=75.0. Then the clock would be set to 25.0
for the initial frame and 75.0 for the final frame. In-between frames would
have clock values interpolated from 25.0 through 75.0 proportionally.

Users who are accustomed to using frame numbers rather than clock values
could specify Initial_Clock=1.0 and Final_Clock=10.0 and Frame_Final=10 for a
10 frame animation.

For new scenes, we recommend you do not change the Initial_Clock or
Final_Clock from their default 0.0 to 1.0 values. If you want the clock to
vary over a different range than the default 0.0 to 1.0, we recommend you
handle this inside your scene file as follows...

  #declare Start    = 25.0
  #declare End      = 75.0
  #declare My_Clock = Start+(End-Start)*clock


Then use My_Clock in the scene description. This keeps the critical values
25.0 and 75.0 in your .pov file.

Note that more details concerning the inner workings of the animation loop
are in the section on shell-out operating system commands in section
"Shell-out to Operating System".

6.2.1.3          Subsets of Animation Frames

  +EFn or +EF0.nme=0.n.nSame as Subset_End_Frameme n percentnt


When creating a long animation, it may be handy to render only a portion of
the animation to see what it looks like. Suppose you have 100 frames but only
want to render frames 30 through 40. If you set Initial_Frame=30 and
Final_Frame=40 then the clock would vary from 0.0 to 1.0 from frames 30
through 40 rather than 0.30 through 0.40 as it should. Therefore you should
leave Initial_Frame=1 and Final_Frame=100 and use Subset_Start_Frame=30 and
Subset_End_Frame=40 to selectively render part of the scene. POV-Ray will
then properly compute the clock values.

Usually you will specify the subset using the actual integer frame numbers
however an alternate form of the subset commands takes a float value in the
range 0.0 <=n.nnn <=1.0 which is interpreted as a fraction of the whole
animation. For example, Subset_Start_Frame=0.333 and Subset_End_Frame=0.667
would render the middle 1/3rd of a sequence regardless of the number of
frames.

6.2.1.4          Cyclic Animation

  -KClic_Animation=boolTurn cyclic animation offoff


Many computer animation sequences are designed to be run in a continuous
loop. Suppose you have an object that rotates exactly 360 degrees over the
course of your animation and you did rotate  360*clock*y to do so. Both the
first and last frames would be identical. Upon playback there would be a
brief one frame jerkiness. To eliminate this problem you need to adjust the
clock so that the last frame does not match the first. For example a ten
frame cyclic animation should not use clock 0.0 to 1.0. It should run from
0.0 to 0.9 in 0.1 increments. However if you change to 20 frames it should
run from 0.0 to 0.95 in 0.05 increments. This complicates things because you
would have to change the final clock value every time you changed
Final_Frame. Setting Cyclic_Animation=on or using +KC will cause POV-Ray to
automatically adjust the final clock value for cyclic animation regardless of
how many total frames. The default value for this setting is off.

6.2.1.5          Field Rendering

  -UO_Field=booloolSet odd field flag offffoff


Field rendering is sometimes used for animations when the animation is being
output for television. TVs only display alternate scan lines on each vertical
refresh. When each frame is being displayed the fields are interlaced to give
the impression of a higher resolution image. The even scan lines make up the
even field, and are drawn first (i. e. scan lines 0, 2, 4, etc.), followed by
the odd field, made up of the odd numbered scan lines are drawn afterwards.
If objects in an animation are moving quickly, their position can change
noticeably from one field to the next. As a result, it may be desirable in
these cases to have POV-Ray render alternate fields at the actual field rate
(which is twice the frame rate), rather than rendering full frames at the
normal frame rate. This would save a great deal of time compared to rendering
the entire animation at twice the frame rate, and then only using half of
each frame.

By default, field rendering is not used. Setting Field_Render=on or using +UF
will cause alternate frames in an animation to be only the even or odd fields
of an animation. By default, the first frame is the even field, followed by
the odd field. You can have POV-Ray render the odd field first by specifying
Odd_Field=on, or by using the +UO switch.

6.2.2            Output Options


6.2.2.1          General Output Options


6.2.2.1.1        Height and Width of Output

  +Wnth=nnSame as Width=nn (when n > 8)


These switches set the height and width of the image in pixels. This
specifies the image size for file output. The preview display, if on, will
generally attempt to pick a video mode to accommodate this size but the
display settings do not in any way affect the resulting file output.

6.2.2.1.2        Partial Output Options

  +ER0.n or +E0.nnSame as End_Row=0.nercent of heightthh


When doing test rendering it is often convenient to define a small,
rectangular sub-section of the whole screen so you can quickly check out one
area of the image. The Start_Row, End_Row, Start_Column and End_Column
options allow you to define the subset area to be rendered. The default
values are the full size of the image from (1,1) which is the upper left to
(w,h) on the lower right where w and h are the Width=n and Height=n values
you have set.

Note if the number specified is greater than 1 then it is interpreted as an
absolute row or column number in pixels. If it is a decimal value between 0.0
and 1.0 then it is interpreted as a percent of the total width or height of
the image. For example: Start_Row=0.75 and Start_Column=0.75 starts on a row
75% down from the top at a column 75% from the left. Thus it renders only the
lower-right 25% of the image regardless of the specified width and height.

The +SR, +ER, +SC and +EC switches work in the same way as the corresponding
INI-style settings for both absolute settings or percentages. Early versions
of POV-Ray allowed only start and end rows to be specified with +Sn and +En
so they are still supported in addition to +SR and +ER.

6.2.2.1.3        Interrupting Options

  -Xnt_Abort_Count=nSet to test for abort off (in future test every n pixels)



On some operating systems once you start a rendering you must let it finish.
The Test_Abort=on option or +X switch causes POV-Ray to test the keyboard for
keypress. If you have pressed a key, it will generate a controlled user
abort. Files will be flushed and closed but only data through the last full
row of pixels is saved. POV-Ray exits with an error code 2 (normally POV-Ray
returns 0 for a successful run or 1 for a fatal error).

When this option is on, the keyboard is polled on every line while parsing
the scene file and on every pixel while rendering. Because polling the
keyboard can slow down a rendering, the Test_Abort_Count=n option or +Xn
switch causes the test to be performed only every n pixels rendered or scene
lines parsed.

6.2.2.1.4        Resuming Options

  +GIsss_Ini=falseoolSame as Create_Ini=sss previously set file.ini


If you abort a render while it's in progress or if you used the End_Row
option to end the render prematurely, you can use Continue_Trace=on or +C
option to continue the render later at the point where you left off. This
option reads in the previously generated output file, displays the partial
image rendered so far, then proceeds with the ray-tracing. This option cannot
be used if file output is disabled with Output_to_file=off or -F.

The Continue_Trace option may not work if the Start_Row option has been set
to anything but the top of the file, depending on the output format being
used.

POV-Ray tries to figure out where to resume an interrupted trace by reading
any previously generated data in the specified output file. All file formats
contain the image size, so this will override any image size settings
specified. Some file formats (namely TGA and PNG) also store information
about where the file started (i. e. +SCn and +SRn options), alpha output +UA,
and bit-depth +FNn, which will override these settings. It is up to the user
to make sure that all other options are set the same as the original render.

The Create_Ini option or +GI switch provides an easy way to create an INI
file with all of the rendering options, so you can re-run files with the same
options, or ensure you have all the same options when resuming. This option
creates an INI file with every option set at the value used for that
rendering. This includes default values which you have not specified. For
example if you run POV-Ray with...

  POVRAY +Isimple.pov MYOPTS +GIrerun.ini MOREOPTS


POV-Ray will create a file called rerun.ini with all of the options used to
generate this scene. The file is not written until all options have been
processed. This means that in the above example, the file will include
options from both myopts.ini and moreopts.ini despite the fact that the +GI
switch is specified between them. You may now re-run the scene with...

  POVRAY RERUN


or resume an interrupted trace with

  POVRAY RERUN +C


If you add other switches with the rerun.ini reference, they will be included
in future re-runs because the file is re-written every time you use it.

The Create_Ini option is also useful for documenting how a scene was
rendered. If you render waycool.pov with Create_Ini=on then it will create a
file waycool.ini that you could distribute along with your scene file so
other users can exactly re-create your image.

6.2.2.2          Display Output Options


6.2.2.2.1        Display Hardware Settings

  Display_Gamma=n.nSets the display gamma to n.n, palette 'y' in future


The Display=on or +D switch will turn on the graphics display of the image
while it is being rendered. Even on some non-graphics systems, POV-Ray may
display an 80 by 24 character ASCII-Art version of your image. Where
available, the display may be full, 24-bit true color. Setting Display=off or
using the -D switch will turn off the graphics display which is the default.

The Video_Mode=x option sets the display mode or hardware type chosen where x
is a single digit or letter that is machine dependent (see section "Display
Types" for a description of the modes supported by the MS-DOS version).
Generally Video_Mode=0 means the default or an auto-detected setting should
be used. When using switches, this character immediately follows the switch.
For example the +D0 switch will turn on the graphics display in the default
mode.

The Palette=y option selects the palette to be used. Typically the single
character parameter y is a digit which selects one of several fixed palettes
or a letter such G for gray scale, H for 15-bit or 16-bit high color or T for
24-bit true color. When using switches, this character is the 2nd character
after the switch. For example the +D0T switch will turn on the graphics
display in the default mode with a true color palette.

The Display_Gamma=n.n setting is new with POV-Ray 3.0, and is not available
as a command-line switch. The Display_Gamma setting overcomes the problem of
images (whether ray-traced or not) having different brightness when being
displayed on different monitors, different video cards, and under different
operating systems. Note that the Display_Gamma is a setting based on your
computer's display hardware, and should be set correctly once and not
changed. The Display_Gamma INI setting works in conjunction with the new
assumed_gamma global setting to ensure that POV scenes and the images they
create look the same on all systems. See section "Assumed_Gamma" which
describes the assumed_gamma global setting and describes gamma more
thoroughly.

While the Display_Gamma can be different for each system, there are a few
general rules that can be used for setting Display_Gamma if you don't know it
exactly. If the Display_Gamma keyword does not appear in the INI file,
POV-Ray assumes that the display gamma is 2.2. This is because most PC
monitors have a gamma value in the range 1.6 to 2.6 (newer models seem to
have a lower gamma value). MacOS has the ability to do gamma correction
inside the system software (based on a user setting in the gamma control
panel). If the gamma control panel is turned off, or is not available, the
default Macintosh system gamma is 1.8. Some high-end PC graphics cards can do
hardware gamma correction and should use the current Display_Gamma setting,
usually 1.0. A gamma test image is also available to help users to set their
Display_Gamma accurately.

For scene files that do not contain an assumed_gamma global setting the INI
file option Display_Gamma will not have any affect on the preview output of
POV-Ray or for most output file formats. However, the Display_Gamma value is
used when creating PNG format output files, and also when rendering the
POV-Ray example files (because they have an assumed_gamma), so it should
still be correctly set for your system to ensure proper results.

6.2.2.2.2        Display Related Settings

  -UDw_Vistas=boolboolTurn draw vistas offofffoff


On some systems, when the image is complete, the graphics display is cleared
and POV-Ray switches back into text mode to print the final statistics and to
exit. Normally when the graphics display is on, you want to look at the image
awhile before continuing. Using Pause_When_Done=on or +P causes POV-Ray to
pause in graphics mode until you to press a key to continue. The default is
not to pause (-P).

When the graphics display is not used, it is often desirable to monitor
progress of the rendering. Using Verbose=on or +V turns on verbose reporting
of your rendering progress. This reports the number of the line currently
being rendered, the elapsed time for the current frame and other information.
On some systems, this textual information can conflict with the graphics
display. You may need to turn this off when the display is on. The default
setting is off (-V).

The option Draw_Vistas=on or +UD was originally a debugging help for
POV-Ray's vista buffer feature but it was such fun we decided to keep it.
Vista buffering is a spatial sub-division method that projects the 2-D
extents of bounding boxes onto the viewing window. POV-Ray tests the 2-D x, y
pixel location against these rectangular areas to determine quickly which
objects, if any, the viewing ray will hit. This option shows you the 2-D
rectangles used. The default setting is off (-UD) because the drawing of the
rectangles can take considerable time on complex scenes and it serves no
critical purpose. See section "Automatic Bounding Control" for more details.

6.2.2.2.3        Mosaic Preview

  +EPniew_End_Size=n=nSame as Preview_End_Size=ne to n n


Typically, while you are developing a scene, you will do many low resolution
test renders to see if objects are placed properly. Often this low resolution
version doesn't give you sufficient detail and you have to render the scene
again at a higher resolution. A feature called mosaic preview solves this
problem by automatically rendering your image in several passes.

The early passes paint a rough overview of the entire image using large
blocks of pixels that look like mosaic tiles. The image is then refined using
higher resolutions on subsequent passes. This display method very quickly
displays the entire image at a low resolution, letting you look for any major
problems with the scene. As it refines the image, you can concentrate on more
details, like shadows and textures. You don't have to wait for a full
resolution render to find problems, since you can interrupt the rendering
early and fix the scene, or if things look good, you can let it continue and
render the scene at high quality and resolution.

To use this feature you should first select a width and height value that is
the highest resolution you will need. Mosaic preview is enabled by specifying
how big the mosaic blocks will be on the first pass using
Preview_Start_Size=n or +SPn. The value n should be a number greater than
zero that is a power of two (1, 2, 4, 8, 16, 32, etc.) If it is not a power
of two, the nearest power of two less than n is substituted. This sets the
size of the squares, measured in pixels. A value of 16 will draw every 16th
pixel as a 16*16 pixel square on the first pass. Subsequent passes will use
half the previous value (such as 8*8, 4*4 and so on.)

The process continues until it reaches 1*1 pixels or until it reaches the
size you set with Preview_End_Size=n or +EPn. Again the value n should be a
number greater than zero that is a power of two and less than or equal to
Preview_Start_Size. If it is not a power of two, the nearest power of two
less than n is substituted. The default ending value is 1. If you set
Preview_End_Size to a value greater than 1 the mosaic passes will end before
reaching 1*1, but POV-Ray will always finish with a 1*1. For example, if you
want a single 8*8 mosaic pass before rendering the final image, set
Preview_Start_Size=8 and Preview_End_Size=8.

No file output is performed until the final 1*1 pass is reached. Although the
preliminary passes render only as many pixels as needed, the 1*1 pass
re-renders every pixel so that anti-aliasing and file output streams work
properly. This makes the scene take up to 25% longer than the regular 1*1
pass to render, so it is suggested that mosaic preview not be used for final
rendering. Also, the lack of file output until the final pass means that
renderings which are interrupted before the 1*1 pass can not be resumed
without starting over from the beginning.

Future versions of POV-Ray will include some system of temporary files or
buffers which will eliminate these inefficiencies and limitations. Mosaic
preview is still a very useful feature for test renderings.

6.2.2.3          File Output Options

  -Ftput_to_File=boolSets file output off(use default type)


By default, POV-Ray writes an image file to disk. When you are developing a
scene and doing test renders, the graphic preview may be sufficient. To save
time and disk activity you may turn file output off with Output_to_File=off
or -F.

6.2.2.3.1        Output File Type

  -Fxnut_File_Type=xSets file output off; but in future use format 'x', depth
  Bits_Per_Color=nl Sets file output bits/color to 'n'


The default type of image file depends on which platform you are using.
MS-DOS and most others default to 24-bit uncompressed Targa. See your
platform-specific documentation to see what your default file type is. You
may select one of several different file types using Output_File_Type=x or
+Fx where x is one of the following...

  +FTUncompressed Targa-24 formatPict or Windows BMPoded)


Note that the obsolete +FD dump format and +FR raw format have been dropped
from POV-Ray 3.0 because they were rarely used and no longer necessary. PPM,
PNG, and system specific formats have been added. PPM format images are
uncompressed, and have a simple text header, which makes it a widely portable
image format. PNG is a new image format designed not only to replace GIF, but
to improve on its shortcomings. PNG offers the highest compression available
without loss for high quality applications, such as ray-tracing. The system
specific format depends on the platform used and is covered in the
appropriate system specific documentation.

Most of these formats output 24 bits per pixel with 8 bits for each of red,
green and blue data. PNG allows you to optionally specify the output bit
depth from 5 to 16 bits for each of the red, green, and blue colors, giving
from 15 to 48 bits of color information per pixel. The default output depth
for all formats is 8 bits/color (16 million possible colors), but this may be
changed for PNG format files by setting Bits_Per_Color=n or by specifying
+FNn, where n is the desired bit depth.

Specifying a smaller color depth like 5 bits/color (32768 colors) may be
enough for people with 8- or 16-bit (256 or 65536 color) displays, and will
improve compression of the PNG file. Higher bit depths like 10 or 12 may be
useful for video or publishing applications, and 16 bits/color is good for
grayscale height field output (See section "Height Field" for details on
height fields).

Targa format also allows 8 bits of alpha transparency data to be output,
while PNG format allows 5 to 16 bits of alpha transparency data, depending on
the color bit depth as specified above. You may turn this option on with
Output_Alpha=on or +UA. The default is off or -UA. See section "Using the
Alpha Channel" for further details on transparency.

In addition to support for variable bit-depths, alpha channel, and grayscale
formats, PNG files also store the Display_Gamma value so the image displays
properly on all systems (see section "Display Hardware Settings"). The
hf_gray_16 global setting, as described in section "HF_Gray_16" will also
affect the type of data written to the output file.

6.2.2.3.2        Output File Name

  +Ofile_File_Name=fileSame as Output_File_Name=file


The default output filename is created from the scene name and need not be
specified. The scene name is the input name with all drive, path, and
extension information stripped. For example if the input file name is
c:\povray3\mystuff\myfile.pov the scene name is myfile. The proper extension
is appended to the scene name based on the file type. For example myfile.tga
or myfile.png might be used.

You may override the default output name using Output_File_Name=file or
+Ofile. For example:

  Input_File_Name=myinput.pov
  Output_File_Name=myoutput.tga


If an output file name of "-" is specified (a single minus sign), then the
image will be written to standard output, usually the screen. The output can
then be piped into another program or to a GUI if desired.

6.2.2.3.3        Output File Buffer

  Buffer_Size=n=boolSet output buffer size to 'n' kilobytes. If n is zero, no
                    buffering. If n < system default, the system default is
  -Bn               Turn buffer off, but for future set size n


The Buffer_Output and Buffer_Size options and the +B switch allows you to
assign large buffers to the output file. This reduces the amount of time
spent writing to the disk. If this parameter is not specified, then as each
row of pixels is finished, the line is written to the file and the file is
flushed. On most systems, this operation ensures that the file is written to
the disk so that in the event of a system crash or other catastrophic event,
at least a part of the picture has been stored properly and retrievable on
disk. The default is not to use any buffer.

6.2.2.4          CPU Utilization Histogram

The CPU utilization histogram is a way of finding out where POV-Ray is
spending its rendering time, as well as an interesting way of generating
heightfields. The histogram splits up the screen into a rectangular grid of
blocks. As POV-Ray renders the image, it calculates the amount of time it
spends rendering each pixel and then adds this time to the total rendering
time for each grid block. When the rendering is complete, the histogram is a
file which represents how much time was spent computing the pixels in each
grid block.

Not all versions of POV-Ray allow the creation of histograms. The histogram
output is dependent on the file type and the system that POV-Ray is being run
on.

6.2.2.4.1        File Type

  +HTxogram_Type=xSame as Histogram_Type=x(turn off if type is 'X')


The histogram output file type is nearly the same as that used for the image
output file types in "Output File Type". The available histogram file types
are as follows.

  +HTXNo histogram file output is generatedindows BMPscaleets


Note that +HTC does not generate a compressed Targa-24 format output file but
rather a text file with a comma-separated list of the time spent in each grid
block, in left-to-right and top-to bottom order. The units of time output to
the CSV file are system dependent. See the system specific documentation for
further details on the time units in CSV files.

The Targa and PPM format files are in the POV heightfield format (see "Height
Field"), so the histogram information is stored in both the red and green
parts of the image, which makes it unsuitable for viewing. When used as a
height field, lower values indicate less time spent calculating the pixels in
that block, while higher indicate more time spent in that block.

PNG format images are stored as grayscale images and are useful for both
viewing the histogram data as well as for use as a heightfield. In PNG files,
the darker (lower) areas indicate less time spent in that grid block, while
the brighter (higher) areas indicate more time spent in that grid block.

6.2.2.4.2        File Name

  +HNfileam_Name=fileSame as Histogram_Name=file


The histogram file name is the name of the file in which to write the
histogram data. If the file name is not specified it will default to
histgram.ext, where ext is based on the file type specified previously. Note
that if the histogram name is specified the file name extension should match
the file type.

6.2.2.4.3        Grid Size

  +HSxx.yym_Grid_Size=xx.yySame as Histogram_Grid_Size=xx.yy


The histogram grid size gives the number of times the image is split up in
both the horizontal and vertical directions. For example

  povray +Isample +W640 +H480 +HTN +HS160.120 +HNhistogrm.png


will split the image into 160*120 grid blocks, each of size 4*4 pixels, and
output a PNG file, suitable for viewing or for use as a heightfield. Smaller
numbers for the grid size mean more pixels are put into the same grid block.
With CSV output, the number of values output is the same as the number of
grid blocks specified. For the other formats the image size is identical to
the rendered image rather than the specified grid size, to allow easy
comparison between the histogram and the rendered image. If the histogram
grid size is not specified, it will default to the same size as the image, so
there will be one grid block per pixel.

Note that on systems that do task-switching or multi-tasking the histogram
may not exactly represent the amount of time POV-Ray spent in a given grid
block since the histogram is based on real time rather than CPU time. As a
result, time may be spent for operating system overhead or on other tasks
running at the same time. This will cause the histogram to have speckling,
noise or large spikes. This can be reduced by decreasing the grid size so
that more pixels are averaged into a given grid block.

6.2.3            Scene Parsing Options

POV-Ray reads in your scene file and processes it to create an internal model
of your scene. The process is called parsing. As your file is parsed other
files may be read along the way. This section covers options concerning what
to parse, where to find it and what version specific assumptions it should
make while parsing it.

6.2.3.1          Input File Name

  +IfileFile_Name=fileSame as Input_File_Name=file


You will probably always set this option but if you do not the default input
filename is object.pov. If you do not have an extension then .pov is assumed.
On case-sensitive operating systems both .pov and .POV are tried. A full path
specification may be used (on MS-DOS systems +Ic:\povray3\mystuff\myfile.pov
is allowed for example). In addition to specifying the input file name this
also establishes the scene name.

The scene name is the input name with drive, path and extension stripped. In
the above example the scene name is myfile. This name is used to create a
default output file name and it is referenced other places.

If you use "-" as the input file name the input will be read from standard
input. Thus you can pipe a scene created by a program to POV-Ray and render
it without having a scene file.

Under MS-DOS you can try this feature by typing.

  type ANYSCENE.POV | povray +I-


6.2.3.2          Library Paths

  +Lpathy_Path=pathSame as Library_Path=pathry paths


POV-Ray looks for files in the current directory. If it does not find a file
it needs it looks in various other library directories which you specify.
POV-Ray does not search your operating system path. It only searches the
current directory and directories which you specify with this option. For
example the standard include files are usually kept in one special directory.
You tell POV-Ray to look there with...

  Library_Path=c:\povray3\include


You must not specify any final path separators ("\" or "/") at the end.

Multiple uses of this option switch do not override previous settings. Up to
ten unique paths may be specified. If you specify the exact same path twice
it is only counts once. The current directory will be searched first followed
by the indicated library directories in the order in which you specified
them.

6.2.3.3          Language Version

  +MVn.nn=n.nSame as Version=n.ne compatibility to version n.n


While many language changes have been made for POV-Ray 3.0, all of version
2.0 syntax and most of version 1.0 syntax still works. Whenever possible we
try to maintain backwards compatibility. One feature introduced in 2.0 that
was incompatible with any 1.0 scene files is the parsing of float
expressions. Setting Version=1.0 or using +MV1.0 turns off expression parsing
as well as many warning messages so that nearly all 1.0 files will still
work. The changes between 2.0 and 3.0 are not as extensive. Setting
Version=2.0 is only necessary to eliminate some warning messages. Naturally
the default setting for this option is Version=3.0.

The #version language directive can also be used to change modes several
times within scene files. The above options affect only the initial setting.
See section "Version Directive" for more details about the language version
directive.

6.2.3.4          Removing User Bounding

  -SUit_Unions=boollTurn split bounded unions offoffoffoff


Early versions of POV-Ray had no system of automatic bounding or spatial
sub-division to speed up ray-object intersection tests. Users had to manually
create bounding boxes to speed up the rendering. POV-Ray 3.0 has more
sophisticated automatic bounding than any previous version. In many cases the
manual bounding on older scenes is slower than the new automatic systems.
Therefore POV-Ray removes manual bounding when it knows it will help. In rare
instances you may want to keep manual bounding. Some older scenes incorrectly
used bounding when they should have used clipping. If POV-Ray removes the
bounds in these scenes the image will not look right. To turn off the
automatic removal of manual bounds you should specify Remove_Bounds=off or
use -UR. The default is Remove_Bounds=on.

One area where the jury is still out is the splitting of manually bounded
unions. Unbounded unions are always split into their component parts so that
automatic bounding works better. Most users do not bound unions because they
know that doing so is usually slower. If you do manually bound a union we
presume you really want it bound. For safety sake we do not presume to remove
such bounds. If you want to remove manual bounds from unions you should
specify Split_Unions=on or use +SU. The default is Split_Unions=off.

6.2.4            Shell-out to Operating System

  Fatal_Error_Command=sSet command when POV-Ray has fatal error


Note that no +/- switches are available for these options. They cannot be
used from the command line. They may only be used from INI files.

POV-Ray offers you the opportunity to shell-out to the operating system at
several key points to execute another program or batch file. Usually this is
used to manage files created by the internal animation loop however the shell
commands are available for any scene. The CMD is a single line of text which
is passed to the operating system to execute a program. For example

  Post_Scene_Command=tga2gif -d -m myfile


would use the utility tga2gif with the -D and -M parameters to convert
myfile.tga to myfile.gif after the scene had finished rendering.

6.2.4.1          String Substitution in Shell Commands

It could get cumbersome to change the Post_Scene_Command every time you
changed scene names. POV-Ray can substitute various values into a CMD string
for you. For example:

  Post_Scene_Command=tga2gif -d -m %s


POV-Ray will substitute the %s with the scene name in the command. The scene
name is the Input_File_Name or +I setting with any drive, directory or
extension removed. For example:

  Input_File_Name=c:\povray3\scenes\waycool.pov


is stripped down to the scene name waycool which results in...

  Post_Scene_Command=tga2gif -d -m waycool


In an animation it may be necessary to have the exact output file name with
the frame number included. The string %o will substitute the output file
name. Suppose you want to save your output files in a zip archive using
pkzip. You could do...

  Post_Frame_Command=pkzip -m %s %o


After rendering frame 12 of myscene.pov POV-Ray would shell to the operating
system with "pkzip -m myscene mysce012.tga". The -M switch in pkzip moves
mysce012.tga to myscene.zip and removes it from the directory. Note that %o
includes frame numbers only when in an animation loop. During the
Pre_Scene_Command and Post_Scene_Command there is no frame number so the
original, unnumbered Output_File_Name is used. Any User_Abort_Command or
Fatal_Error_Command not inside the loop will similarly give an unnumbered %o
substitution.

Here is the complete list of substitutions available for a common string.


6.2.4.2          Shell Command Sequencing

Here is the sequence of events in an animation loop. Non-animated scenes work
the exact same way except there is no loop.

  1)  Process all INI file keywords and command line switches just once.
  2)  Open any text output streams and do Create_INI if any.
  3)  Execute Pre_Scene_Command if any.
  4)  Loop through frames (or just do once on non-animation).
      a)  Execute Pre_Frame_Command if any.
      b)  Parse entire scene file, open output file and read settings,
          turn on display, render the frame, destroy all objects,
          textures etc., close output file, close display.
      c)  Execute Post_Frame_Command if any.
      d)  Go back to 4 a until all frames are done.
  5)  Execute Post_Scene_Command if any.
  6)  Exit POV-Ray.


If the user interrupts processing the User_Abort_Command, if any, is
executed. User aborts can only occur during the parsing and rendering parts
of step 4 a above.

If a fatal error occurs that POV-Ray notices the Fatal_Error_Command, if any,
is executed. Sometimes an unforeseen bug or memory error could cause a total
crash of the program in which case there is no chance to shell out. Fatal
errors can occur just about anywhere including during the processing of
switches or INI files. If a fatal error occurs before POV-Ray has read the
Fatal_Error_Command string then obviously no shell can occur.

Note that the entire scene is re-parsed for every frame. Future versions of
POV-Ray may allow you to hold over parts of a scene from one frame to the
next but for now it starts from scratch every time. Note also that the
Pre_Frame_Command occurs before the scene is parsed. You might use this to
call some custom scene generation utility before each frame. This utility
could rewrite your .pov or .inc files if needed. Perhaps you will want to
generate new .gif or .tga files for image maps or height fields on each
frame.

6.2.4.3          Shell Command Return Actions

  Fatal_Error_Return=sSet fatal return actionstions


Note that no +/- switches are available for these options. They cannot be
used from the command line. They may only be used from INI files.

Most operating systems allow application programs to return an error code if
something goes wrong. When POV-Ray executes a shell command it can make use
of this error code returned from the shell process and take some appropriate
action if the code is zero or non-zero. POV-Ray itself returns such codes. It
returns 0 for success, 1 for fatal error and 2 for user abort.

The actions are designated by a single letter in the different ..._Return=s
options. The possible actions are:

  F generate a fatal error in POV-Ray


For example if your Pre_Frame_Command calls a program which generates your
height field data and that utility fails then it will return a non-zero code.
We would probably want POV-Ray to abort as well. The option
Pre_Frame_Return=F will cause POV-Ray to do a fatal abort if the
Pre_Frame_Command returns a non-zero code.

Sometimes a non-zero code from the external process is a good thing. Suppose
you want to test if a frame has already been rendered. You could use the S
action to skip this frame if the file is already rendered. Most utilities
report an error if the file is not found. For example the command pkzip -V
myscene mysce012.tga tells pkzip you want to view the catalog of myscene.zip
for the file mysce012.tga. If the file isn't in the archive pkzip returns a
non-zero code.

However we want to skip if the file is found. Therefore we need to reverse
the action so it skips on zero and doesn't skip on non-zero. To reverse the
zero vs. non-zero triggering of an action precede it with a "-" sign (note a
"!" will also work since it is used in many programming languages as a negate
operator).

Pre_Frame_Return=S will skip if the code shows error (non-zero) and will
proceed normally on no error (zero). Pre_Frame_Return=-S will skip if there
is no error (zero) and will proceed normally if there is an error (non-zero).


The default for all shells is I which means that the return action is ignored
no matter what. POV-Ray simply proceeds with whatever it was doing before the
shell command. The other actions depend upon the context. You may want to
refer back to the animation loop sequence chart in the previous section. The
action for each shell is as follows.

On return from any User_Abort_Command if there is an action triggered and you
have specified...

  F            then turn this user abort into a fatal error. Do the
  S, A, Q, or Uthen proceed with the user abort. Exit POV-Ray with error code
2.


On return from any Fatal_Error_Command proceed with the fatal error no matter
what. Exit POV-Ray with error code 1. On return from any Pre_Scene_Command,
Pre_Frame_Command, Post_Frame_Command or Post_Scene_Commands if there is an
action triggered and you have specified...

  F then generate a fatal error. Do the Fatal_Error_Command, if any. Exit
  U then generate a user abort. Do the User_Abort_Command, if any. Exit
  Q then quit POV-Ray immediately. Acts as though POV-Ray never really ran.
    Do no further shells, (not even Post_Scene_Command) and exit POV-Ray with
    an error code 0.


On return from a Pre_Scene_Command if there is an action triggered and you
have specified...

  S then skip rendering all frames. Acts as though the scene completed all
    frames normally. Do not do any Pre_Frame_Command or Post_Frame_Commands.
    Do the Post_Scene_Command, if any. Exit POV-Ray with error code 0. On the
  A then skip all scene activity. Works exactly like Q quit. On the earlier
    chart this means skip to step #6.


On return from a Pre_Frame_Command if there is an action triggered and you
have specified...

  S then skip only this frame. Acts as though this frame never existed. Do
    not do the Post_Frame_Command. Proceed with the next frame. On the
    earlier chart this means skip steps #4b and #4c but loop back as needed
  A then skip rendering this frame and all remaining frames. Acts as though
    the scene completed all frames normally. Do not do any further
    Post_Frame_Commands. Do the Post_Scene_Command, if any. Exit POV-Ray with
    error code 0. On the earlier chart this means skip the rest of step #4
    and proceed at step #5.


On return from a Post_Frame_Command if there is an action triggered and you
have specified...

  S then skip rendering all remaining frames. Acts as though the scene
    completed all frames normally. Do the Post_Scene_Command, if any. Exit
    POV-Ray with error code 0. On the earlier chart this means skip the rest
  A same as S for this shell command..


On return from any Post_Scene_Command if there is an action triggered and you
have specified...


6.2.5            Text Output

Text output is an important way that POV-Ray keeps you informed about what it
is going to do, what it is doing and what it did. New to POV-Ray 3.0, the
program splits its text messages into 7 separate streams. Some versions of
POV-Ray color codes the various types of text. Some versions allow you to
scroll back several pages of messages. All versions allow you to turn some of
these text streams off/on or to direct a copy of the text output to one or
several files. This section details the options which give you control over
text output.

6.2.5.1          Text Streams

There are seven distinct text streams that POV-Ray uses for output. On some
versions each stream is designated by a particular color. Text from these
streams are displayed whenever it is appropriate so there is often an
intermixing of the text. The distinction is only important if you choose to
turn some of the streams off or to direct some of the streams to text files.
On some systems you may be able to review the streams separately in their own
scroll-back buffer.

Here is a description of each stream.

BANNER: This stream displays the program's sign-on banner, copyright,
contributor's list, and some help screens. It cannot be turned off or
directed to a file because most of this text is displayed before any options
or switches are read. Therefore you cannot use an option or switch to control
it. There are switches which display the help screens. They are covered in
section "Help Screen Switches".

DEBUG: This stream displays debugging messages. It was primarily designed for
developers but this and other streams may also be used by the user to display
messages from within their scene files. See section "Text Message Streams"
for details on this feature. This stream may be turned off and/or directed to
a text file.

FATAL: This stream displays fatal error messages. After displaying this text,
POV-Ray will terminate. When the error is a scene parsing error, you may be
shown several lines of scene text that leads up to the error. This stream may
be turned off and/or directed to a text file.

RENDER: This stream displays information about what options you have
specified to render the scene. It includes feedback on all of the major
options such as scene name, resolution, animation settings, anti-aliasing and
others. This stream may be turned off and/or directed to a text file.

STATISTICS: This stream displays statistics after a frame is rendered. It
includes information about the number of rays traced, the length of time of
the processing and other information. This stream may be turned off and/or
directed to a text file.

STATUS: This stream displays one-line status messages that explain what
POV-Ray is doing at the moment. On some systems this stream is displayed on a
status line at the bottom of the screen. This stream cannot be directed to a
file because there is generally no need to. The text displayed by the Verbose
option or +V switch is output to this stream so that part of the status
stream may be turned off.

WARNING: This stream displays warning messages during the parsing of scene
files and other warnings. Despite the warning, POV-Ray can continue to render
the scene. You will be informed if POV-Ray has made any assumptions about
your scene so that it can proceed. In general any time you see a warning, you
should also assume that this means that future versions of POV-Ray will not
allow the warned action. Therefore you should attempt to eliminate warning
messages so your scene will be able to run in future versions of POV-Ray.
This stream may be turned off and/or directed to a text file.

6.2.5.2          Console Text Output

  All_Console=boolboololTurn on/off all debug, fatal, render, statistic and
  -GA                   Same as All_Console=Off.


You may suppress the output to the console of the Debug, Fatal, Render,
Statistic or Warning text streams. For example the Statistic_Console=off
option or the -GS switch can turn off the Statistic stream. Using on or +GS
you may turn it on again. You may also turn all five of these streams on or
off at once using the All_Console option or +GA switch.

Note that these options take effect immediately when specified. Obviously any
Error or Warning messages that might occur before the option is read are not
be affected.

6.2.5.3          Directing Text Streams to Files

  All_File=truefileeeeEcho all debug, fatal, render, statistic and warning
  All_File=false      Turn off file output of all debug, fatal, render,
  All_File=file       Echo all debug, fatal, render, statistic and warning
  -GAfile             Both All_Console=Off, All_File=file


You may direct a copy of the text streams to a text file for the Debug,
Fatal, Render, Statistic or Warning text streams. For example the
Statistic_File=s option or the +GSs switch. If the string s is true or any of
the other valid true strings then that stream is redirected to a file with a
default name. Valid true values are true, yes, on or 1. If the value is false
the direction to a text file is turned off. Valid false values are false, no,
off or 0. Any other string specified turns on file output and the string is
interpreted as the output file name.

Similarly you may specify such a true, false or file name string after a
switch such as +GSfile. You may also direct all five streams to the same file
using the All_File option or +GA switch. You may not specify the same file
for two or more streams because POV-Ray will fail when it tries to open or
close the same file twice.

Note that these options take effect immediately when specified. Obviously any
Error or Warning messages that might occur before the option is read will not
be affected.

6.2.5.4          Help Screen Switches

  +?0 to +?8Same as +H0 to +H8 to 8 if this is the only switch


Note that there are no INI style equivalents to these options.

Graphical interface versions of POV-Ray such as Mac or Windows have extensive
online help. Other versions of POV-Ray have only a few quick-reference help
screens. The +? switch, optionally followed by a single digit from 0 to 8,
will display these help screens to the Banner text stream. After displaying
the help screens, POV-Ray terminates. Because some operating systems do not
permit a question mark as a command line switch you may also use the +H
switch. Note however that this switch is also used to specify the height of
the image in pixels. Therefore the +H switch is only interpreted as a help
switch if it is the only switch on the command line and if the value after
the switch is less than or equal to 8.

6.2.6            Tracing Options

There is more than one way to trace a ray. Sometimes there is a trade-off
between quality and speed. Sometimes options designed to make tracing faster
can slow things down. This section covers options that tell POV-Ray how to
trace rays with the appropriate speed and quality settings.

6.2.6.1          Quality Settings

  +Qnlity=nSame as Quality=n to n (0 <= n <= 11)


The Quality=n option or +Qn switch allows you to specify the image rendering
quality. You may choose to lower the quality for test rendering and raise it
for final renders. The quality adjustments are made by eliminating some of
the calculations that are normally performed. For example settings below 4 do
not render shadows. Settings below 8 do not use reflection or refraction. The
values correspond to the following quality levels:

  0,1Just show quick colors. Use full ambient lighting only. Quick colors are
  4,3Render shadows, but no extended lights. 5 Render shadows, including
  9,7Compute halos.ted, refracted, and transmitted rays.


6.2.6.2          Radiosity Setting

  +QRTurns radiosity on -QR Turns radiosity on


Radiosity is an additional calculation which computes diffuse
inter-reflection. It is an extremely slow calculation that is somewhat
experimental. The parameters which control how radiosity calculations are
performed are specified in the radiosity section of the global_settings
statement. See section "Radiosity" for further details.

6.2.6.3          Automatic Bounding Control

  -UVta_Buffer=boold=nTurn vista buffer offoffuture threshold to n


POV-Ray uses a variety of spatial sub-division systems to speed up ray-object
intersection tests. The primary system uses a hierarchy of nested bounding
boxes. This system compartmentalizes all finite objects in a scene into
invisible rectangular boxes that are arranged in a tree-like hierarchy.
Before testing the objects within the bounding boxes the tree is descended
and only those objects are tested whose bounds are hit by a ray. This can
greatly improve rendering speed. However for scenes with only a few objects
the overhead of using a bounding system is not worth the effort. The
Bounding=off option or -MB switch allows you to force bounding off. The
default value is on.

The Bounding_Threshold=n or +MBn switch allows you to set the minimum number
of objects necessary before bounding is used. The default is +MB25 which
means that if your scene has fewer than 25 objects POV-Ray will automatically
turn bounding off because the overhead isn't worth it. Generally it's a good
idea to use a much lower threshold like +MB5.

Additionally POV-Ray uses systems known as vista buffers and light buffers to
further speed things up. These systems only work when bounding is on and when
there are a sufficient number of objects to meet the bounding threshold. The
vista buffer is created by projecting the bounding box hierarchy onto the
screen and determining the rectangular areas that are covered by each of the
elements in the hierarchy. Only those objects whose rectangles enclose a
given pixel are tested by the primary viewing ray. The vista buffer can only
be used with perspective and orthographic cameras because they rely on a
fixed viewpoint and a reasonable projection (i. e. straight lines have to
stay straight lines after the projection).

The light buffer is created by enclosing each light source in an imaginary
box and projecting the bounding box hierarchy onto each of its six sides.
Since this relies on a fixed light source, light buffers will not be used for
area lights.

Reflected and transmitted rays do not take advantage of the light and vista
buffer.

The default settings are Vista_Buffer=on or +UV and Light_Buffer=on or +UL.
The option to turn these features off is available to demonstrate their
usefulness and as protection against unforeseen bugs which might exist in any
of these bounding systems.

In general, any finite object and many types of CSG of finite objects will
properly respond to this bounding system. In addition blobs and meshes use an
additional internal bounding system. These systems are not affected by the
above switch. They can be switched off using the appropriate syntax in the
scene file (see "Blob" and "Mesh" for details). Text objects are split into
individual letters that are bounded using the bounding box hierarchy. Some
CSG combinations of finite and infinite objects are also automatically bound.
The end result is that you will rarely need to add manual bounding objects as
was necessary in earlier versions of POV-Ray unless you use many infinite
objects.

6.2.6.4          Anti-Aliasing Options

  Jitter_Amount=n.nld=n.nSets aa-jitter amount to n.n. If n.n <= 0 aa-jitter
  +Jn.n                  Sets aa-jitter on; jitter amount to n.n. If n.n <= 0
  +Rnialias_Depth=n      Same as Antialias_Depth=n9)amount n.n in future)


The ray-tracing process is in effect a discrete, digital sampling of the
image with typically one sample per pixel. Such sampling can introduce a
variety of errors. This includes a jagged, stair-step appearance in sloping
or curved lines, a broken look for thin lines, moire patterns of interference
and lost detail or missing objects, which are so small they reside between
adjacent pixels. The effect that is responsible for those errors is called
aliasing.

Anti-aliasing is any technique used to help eliminate such errors or to
reduce the negative impact they have on the image. In general, anti-aliasing
makes the ray-traced image look smoother. The Antialias=on option or +A
switch turns on POV-Ray's anti-aliasing system.

When anti-aliasing is turned on, POV-Ray attempts to reduce the errors by
shooting more than one viewing ray into each pixel and averaging the results
to determine the pixel's apparent color. This technique is called
super-sampling and can improve the appearance of the final image but it
drastically increases the time required to render a scene since many more
calculations have to be done.

POV-Ray gives you the option to use one of two alternate super-sampling
methods. The Sampling_Method=n option or +AMn switch selects non-adaptive
super-sampling (method 1) or adaptive super-sampling (method 2). Selecting
one of those methods does not turn anti-aliasing on. This has to be done by
using the +A command line switch or Antialias=on option.

In the default, non-adaptive method (+AM1), POV-Ray initially traces one ray
per pixel. If the color of a pixel differs from its neighbors (to the left or
above) by more than a threshold value then the pixel is super-sampled by
shooting a given, fixed number of additional rays. The default threshold is
0.3 but it may be changed using the Antialias_Threshold=n.n option. When the
switches are used, the threshold may optionally follow the +A. For example
+A0.1 turns anti-aliasing on and sets the threshold to 0.1.

The threshold comparison is computed as follows. If r_1, g_1, b_1 and r_2,
g_2, b_2 are the rgb components of two pixels then the difference between
pixels is computed by

  diff = abs(r1-r2) + abs(g1-g2) + abs(b1-b2).


If this difference is greater than the threshold both pixels are
super-sampled. The rgb values are in the range from 0.0 to 1.0 thus the most
two pixels can differ is 3.0. If the anti-aliasing threshold is 0.0 then
every pixel is super-sampled. If the threshold is 3.0 then no anti-aliasing
is done. Lower threshold means more anti-aliasing and less speed. Use
anti-aliasing for your final version of a picture, not the rough draft. The
lower the contrast, the lower the threshold should be. Higher contrast
pictures can get away with higher tolerance values. Good values seem to be
around 0.2 to 0.4.

When using the non-adaptive method, the default number of super-samples is
nine per pixel, located on a 3*3 grid. The Antialias_Depth=n option or +Rn
switch controls the number of rows and columns of samples taken for a
super-sampled pixel. For example +R4 would give 4*4=16 samples per pixel.

The second, adaptive super-sampling method starts by tracing four rays at the
corners of each pixel. If the resulting colors differ more than the threshold
amount additional samples will be taken. This is done recursively, i. e. the
pixel is divided into four sub-pixels that are separately traced and tested
for further subdivision. The advantage of this method is the reduced number
of rays that have to be traced. Samples that are common among adjacent pixels
and sub-pixels are stored and reused to avoid re-tracing of rays. The
recursive character of this method makes it adaptive, i. e. the
super-sampling concentrates on those parts of the pixel that are more likely
to need super-sampling (see figure below).

Example of how the adapative super-sampling works.

The maximum number of subdivisions is specified by the Antialias_Depth=n
option or +Rn switch. This is different from the non-adaptive method were the
total number of super-samples is specified. A maximum number of n
subdivisions results in a maximum number of samples per pixel that is given
by the following table.

      Number of samples per    Maximum number of samples
      super-sampled pixel for  per super-sampled pixel for
 +Rn  the non-adaptive method  the adaptive method
  1                1                       9
  2                4                      25
  3                9                      81
  4               16                     289
  5               25                    1089
  6               36                    4225
  7               49                   16641
  8               64                   66049
  9               81                  263169


You should note that the maximum number of samples in the adaptive case is
hardly ever reached for a given pixel. If the adaptive method is used with no
anti-aliasing each pixel will be the average of the rays traced at its
corners. In most cases a recursion level of three is sufficient.

Another way to reduce aliasing artifacts is to introduce noise into the
sampling process. This is called jittering and works because the human visual
system is much more forgiving to noise than it is to regular patterns. The
location of the super-samples is jittered or wiggled a tiny amount when
anti-aliasing is used. Jittering is used by default but it may be turned off
with the Jitter=off option or -J switch. The amount of jittering can be set
with the Jitter_Amount=n.n option. When using switches the jitter scale may
be specified after the +J switch. For example +J0.5 uses half the normal
jitter. The default amount of 1.0 is the maximum jitter which will insure
that all super-samples remain inside the original pixel. Note that the
jittering noise is random and non-repeatable so you should avoid using jitter
in animation sequences as the anti-aliased pixels will vary and flicker
annoyingly from frame to frame.

If anti-aliasing is not used one sample per pixel is taken regardless of the
super-sampling method specified.

7                Scene Description Language

The Scene Description Language allows you to describe the world in a readable
and convenient way. Files are created in plain ASCII text using an editor of
your choice. The input file name is specified using the Input_File_Name=file
option or +Ifile switch. By default the files have the extension .pov.
POV-Ray reads the file, processes it by creating an internal model of the
scene and then renders the scene.

The overall syntax of a scene is a file that contains any number of the
following items in any order.

   LANGUAGE_DIRECTIVES
   camera { CAMERA_ITEMS }
   OBJECT_STATEMENTS
   ATMOSPHERE_STATEMENTS
   global_settings { GLOBAL_ITEMS }


See section "Language Directives", section "Objects", section "Camera",
section "Atmospheric Effects" and section "Global Settings" for details.

7.1              Language Basics

The POV-Ray language consists of identifiers, reserved keywords, floating
point expressions, strings, special symbols and comments. The text of a
POV-Ray scene file is free format. You may put statements on separate lines
or on the same line as you desire. You may add blank lines, spaces or
indentations as long as you do not split any keywords or identifiers.

7.1.1            Identifiers and Keywords

POV-Ray allows you to define identifiers for later use in the scene file. An
identifier may be 1 to 40 characters long. It may consist of upper or lower
case letters, the digits 0 through 9 or an underscore character ("_"). The
first character must be an alphabetic character. The declaration of
identifiers is covered later.

POV-Ray has a number of reserved keywords which are listed below.


aa_level                 fog_offset           reciprocal
aa_threshold             fog_type             recursion_limit
abs                      frequency            red
acos                     gif                  reflection
acosh                    global_settings      refraction
adaptive                 glowing              render
adc_bailout              gradient             repeat
agate                    granite              rgb
agate_turb               gray_threshold       rgbf
all                      green                rgbft
alpha                    halo                 rgbt
ambient                  height_field         right
ambient_light            hexagon              ripples
angle                    hf_gray_16           rotate
aperture                 hierarchy            roughness
arc_angle                hollow               samples
area_light               hypercomplex         scale
asc                      if                   scallop_wave
asin                     ifdef                scattering
asinh                    iff                  seed
assumed_gamma            image_map            shadowless
atan                     incidence            sin
atan2                    include              sine_wave
atanh                    int                  sinh
atmosphere               interpolate          sky
atmospheric_attenuation  intersection         sky_sphere
attenuating              inverse              slice
average                  ior                  slope_map
background               irid                 smooth
bicubic_patch            irid_wavelength      smooth_triangle
black_hole               jitter               sor
blob                     julia_fractal        specular
blue                     lambda               sphere
blur_samples             lathe                spherical_mapping
bounded_by               leopard              spiral
box                      light_source         spiral1
box_mapping              linear               spiral2
bozo                     linear_spline        spotlight
break                    linear_sweep         spotted
brick                    location             sqr
brick_size               log                  sqrt
brightness               looks_like           statistics
brilliance               look_at              str
bumps                    low_error_factor     strcmp
bumpy1                   mandel               strength
bumpy2                   map_type             strlen
bumpy3                   marble               strlwr
bump_map                 material_map         strupr
bump_size                matrix               sturm
camera                   max                  substr
case                     max_intersections    superellipsoid
caustics                 max_iteration        switch
ceil                     max_trace_level      sys
checker                  max_value            t
chr                      merge                tan
clipped_by               mesh                 tanh
clock                    metallic             test_camera_1
color                    min                  test_camera_2
color_map                minimum_reuse        test_camera_3
colour                   mod                  test_camera_4
colour_map               mortar               text
component                nearest_count        texture
composite                no                   texture_map
concat                   normal               tga
cone                     normal_map           thickness
confidence               no_shadow            threshold
conic_sweep              number_of_waves      tightness
constant                 object               tile2
control0                 octaves              tiles
control1                 off                  torus
cos                      offset               track
cosh                     omega                transform
count                    omnimax              translate
crackle                  on                   transmit
crand                    once                 triangle
cube                     onion                triangle_wave
cubic                    open                 true
cubic_spline             orthographic         ttf
cylinder                 panoramic            turbulence
cylindrical_mapping      pattern1             turb_depth
debug                    pattern2             type
declare                  pattern3             u
default                  perspective          ultra_wide_angle
degrees                  pgm                  union
dents                    phase                up
difference               phong                use_color
diffuse                  phong_size           use_colour
direction                pi                   use_index
disc                     pigment              u_steps
distance                 pigment_map          v
distance_maximum         planar_mapping       val
div                      plane                variance
dust                     png                  vaxis_rotate
dust_type                point_at             vcross
eccentricity             poly                 vdot
else                     polygon              version
emitting                 pot                  vlength
end                      pow                  vnormalize
error                    ppm                  volume_object
error_bound              precision            volume_rendered
exp                      prism                vol_with_light
exponent                 pwr                  vrotate
fade_distance            quadratic_spline     v_steps
fade_power               quadric              warning
falloff                  quartic              warp
falloff_angle            quaternion           water_level
false                    quick_color          waves
file_exists              quick_colour         while
filter                   quilted              width
finish                   radial               wood
fisheye                  radians              wrinkles
flatness                 radiosity            x
flip                     radius               y
floor                    rainbow              yes
focal_point              ramp_wave            z
fog                      rand

fog_alt                  range


All reserved words are fully lower case. Therefore it is recommended
that your identifiers contain at least one upper case character so it
is sure to avoid conflict with reserved words.

The following keywords are in the above list of reserved keywords but
are not currently used by POV-Ray however they remain reserved.

  bumpy1               test_camera_1
  bumpy2               test_camera_2
  bumpy3               test_camera_3
  incidence            test_camera_4
  pattern1             track
  pattern2             volume_object
  pattern3             volume_rendered
  spiral               vol_with_light


7.1.2            Comments

Comments are text in the scene file included to make the scene file easier to
read or understand. They are ignored by the ray-tracer and are there for your
information. There are two types of comments in POV-Ray.

Two slashes are used for single line comments. Anything on a line after a
double slash (//) is ignored by the ray-tracer. For example:

  // This line is ignored


You can have scene file information on the line in front of the comment as
in:

  object { FooBar }  // this is an object


The other type of comment is used for multiple lines. It starts with "/*" and
ends with "*/". Everything in-between is ignored. For example:

  /* These lines
     are ignored
     by the
     ray-tracer */


This can be useful if you want to temporarily remove elements from a scene
file. /* ... */ comments can comment out lines containing other // comments
and thus can be used to temporarily or permanently comment out parts of a
scene. /* ... */ comments can be nested, the following is legal:

  /* This is a comment
  // This too
  /* This also */
  */


Use comments liberally and generously. Well used, they really improve the
readability of scene files.

7.1.3            Float Expressions

Many parts of the POV-Ray language require you to specify one or more
floating point numbers. A floating point number is a number with a decimal
point. Floats may be specified using literals, identifiers or functions which
return float values. You may also create very complex float expressions from
combinations of any of these using various familiar operators.

Where POV-Ray needs an integer value it allows you to specify a float value
and it truncates it to an integer. When POV-Ray needs a logical or boolean
value it interprets any non-zero float as true and zero as false. Because
float comparisons are subject to rounding errors POV-Ray accepts values
extremely close to zero as being false when doing boolean functions.
Typically values whose absolute values are less than a preset value epsilon
are considered false for logical expressions. The value of epsilon is system
dependent but is generally about 1.0e-10. Two floats a and b are considered
to be equal if abs(a-b) < epsilon.

7.1.3.1          Float Literals

Float literals are represented by an optional sign ("+" or "-") digits, an
optional decimal point and more digits. If the number is an integer you may
omit the decimal point and trailing zero. If it is all fractional you may
omit the leading zero. POV-Ray supports scientific notation for very large or
very small numbers. The following are all valid float literals:

  -2.0    -4    34    3.4e6    2e-5    .3    0.6


7.1.3.2          Float Identifiers

Float identifiers may be declared to make scene files more readable and to
parameterize scenes so that changing a single declaration changes many
values. An identifier is declared as follows.

  #declare IDENTIFIER = EXPRESSION


Where IDENTIFIER is the name of the identifier up to 40 characters long and
EXPRESSION is any valid expression which evaluates to a float value. Here are
some examples.

  #declare Count = 0
  #declare Rows = 5.3
  #declare Cols = 6.15
  #declare Number = Rows*Cols
  #declare Count = Count+1


As the last example shows, you can re-declare a float identifier and may use
previously declared values in that re-declaration. There are several built-in
identifiers which POV-Ray declares for you. See "Built-in Identifiers" for
details.

7.1.3.3          Float Operators

Arithmetic float expressions can be created from float literals, identifiers
or functions using the following operators in this order of precedence...

  ()             expressions in parentheses first
  +A   -A   !A   unary minus, unary plus and logical "not"
  A*B  A/B       multiplication and division
  A+B  A-B       addition and subtraction


Relational, logical and conditional expressions may also be created. However
there is a restriction that these types of expressions must be enclosed in
parentheses first. This restriction, which is not imposed by most computer
languages, is necessary because POV-Ray allows mixing of float and vector
expressions. Without the parentheses there is an ambiguity problem.
Parentheses are not required for the unary logical not operator "!" as shown
above. The operators and their precedence are shown here.

Relational expressions: The operands are arithmetic expressions and the
result is always boolean with 1 for true and 0 for false. All relational
operators have the same precedence.

  (A > B))A is greater than Br equal to Bbs(A-B)>=EPSILON)


Logical expressions: The operands are converted to boolean values of 0 for
false and 1 for true. The result is always boolean. All logical operators
have the same precedence. Note that these are not bit-wise operations, they
are logical.

  (A | B)true if either A or B or both are truelse otherwise


Conditional expressions: The operand C is boolean while operands A and B are
any expressions. The result is of the same type as A and B.

  (C ? A : B)if C then A else B


Assuming the various identifiers have been declared, the following are
examples of valid expressions...

  1+2+3       2*5         1/3         Row*3       Col*5
  (Offset-5)/2            This/That+Other*Thing
  ((This<That) & (Other>=Thing)?Foo:Bar)


Expressions are evaluated left to right with innermost parentheses evaluated
first, then unary +, - or !, then multiply or divide, then add or subtract,
then relational, then logical, then conditional.

7.1.4            Vector Expressions

POV-Ray often requires you to specify a vector. A vector is a set of related
float values. Vectors may be specified using literals, identifiers or
functions which return vector values. You may also create very complex vector
expressions from combinations of any of these using various familiar
operators.

POV-Ray vectors may have from two to five components but the vast majority of
vectors have three components. Unless specified otherwise, you should assume
that the word vector means a three component vector. POV-Ray operates in a 3D
x, y, z coordinate system and you will use three component vectors to specify
x, y and z values. In some places POV-Ray needs only two coordinates. These
are often specified by a 2D vector called an UV vector. Fractal objects use
4D vectors. Color expressions use 5D vectors but allow you to specify 3, 4 or
5 components and use default values for the unspecified components. Unless
otherwise noted, all 2, 4 or 5 component vectors work just like 3D vectors
but they have a different number of components.

7.1.4.1          Vector Literals

Vectors consist of two to five float expressions that are bracketed by angle
brackets < and >. The terms are separated by commas. For example here is a
typical three component vector:

  < 1.0, 3.2, -5.4578 >


The commas between components are necessary to keep the program from thinking
that the 2nd term is the single float expression 3.2-5.4578 and that there is
no 3rd term. If you see an error message such as Float expected but '>' found
instead you probably have missed a comma.

Sometimes POV-Ray requires you to specify floats and vectors side-by-side.
The rules for vector expressions allow for mixing of vectors with vectors or
vectors with floats so commas are required separators whenever an ambiguity
might arise. For example < 1,2,3>-4 evaluates as a mixed float and vector
expression where 4 is subtracted from each component resulting in <
-3,-2,-1>. However the comma in <1,2,3>,-4 means this is a vector followed by
a float.

Each component may be a full float expression. For example <
This+3,That/3,5*Other_Thing> is a valid vector.

7.1.4.2          Vector Identifiers

Vector identifiers may be declared to make scene files more readable and to
parameterize scenes so that changing a single declaration changes many
values. An identifier is declared as follows...

  #declare IDENTIFIER = EXPRESSION


Where IDENTIFIER is the name of the identifier up to 40 characters long and
EXPRESSION is any valid expression which evaluates to a vector value. Here
are some examples...

  #declare Here = <1,2,3>
  #declare There = <3,4,5>
  #declare Jump = <Foo*2,Bar-1,Bob/3>
  #declare Route = There-Here
  #declare Jump = Jump+<1,2,3>


Note that you invoke a vector identifier by using its name without any angle
brackets. As the last example shows, you can re-declare a vector identifier
and may use previously declared values in that re-declaration. There are
several built-in identifiers which POV-Ray declares for you. See section
"Built-in Identifiers" for details.

7.1.4.3          Vector Operators

Vector literals, identifiers and functions may also be combined in
expressions the same as float values. Operations are performed on a
component-by-component basis. For example <1,2,3> + <4,5,6> evaluates the
same as < 1+4,2+5,3+6> or <5,7,9>. Other operations are done on a similar
component-by-component basis. For example (< 1,2,3> = <3,2,1>) evaluates to <
0,1,0> because the middle components are equal but the others are not.
Admittedly this isn't very useful but its consistent with other vector
operations.

Conditional expressions such as (C ? A : B) require that C is a float
expression but A and B may be vector expressions. The result is that the
entire conditional evaluates as a valid vector. For example if Foo and Bar
are floats then

  Foo < Bar ? <1,2,3> : <5,6,7>
evaluates as the vector <1,2,3> if Foo is less than Bar and evaluates as
<5,6,7> otherwise.

You may use the dot operator to extract a single component from a vector.
Suppose the identifier Spot was previously defined as a vector. Then Spot.x
is a float value that is the first component of this x, y, z vector.
Similarly Spot.y and Spot.z reference the 2nd and 3rd components. If Spot was
a two component UV vector you could use Spot.u and Spot.v to extract the
first and second component. For a 4D vector use .x, .y, .z and .t to extract
each float component. The dot operator is also used in color expressions
which are covered later.

7.1.4.4          Operator Promotion

You may use a lone float expression to define a vector whose components are
all the same. POV-Ray knows when it needs a vector of a particular type and
will promote a float into a vector if need be. For example the POV-Ray scale
statement requires a three component vector. If you specify scale 5 then
POV-Ray interprets this as scale <5,5,5> which means you want to scale by 5
in every direction.

Versions of POV-Ray prior to 3.0 only allowed such use of a float as a vector
in various limited places such as scale and turbulence. However you may now
use this trick anywhere. For example...

  box{0,1}    // Same as box{<0,0,0>,<1,1,1>}
  sphere{0,1} // Same as sphere{<0,0,0>,1}


When promoting a float into a vector of 2, 3, 4 or 5 components, all
components are set to the float value, however when promoting a vector of a
lower number of components into a higher order vector, all remaining
components are set to zero. For example if POV-Ray expects a 4D vector and
you specify 9 the result is <9,9,9,9> but if you specify <7,6> the result is
< 7,6,0,0>.

7.1.5            Specifying Colors

POV-Ray often requires you to specify a color. Colors consist of five values
or color components. The first three are called red, green and blue. They
specify the intensity of the primary colors red, green and blue using an
additive color system like the one used by the red, green and blue color
phosphors on a color monitor.

The 4th component, called filter, specifies the amount of filtered
transparency of a substance. Some real-world examples of filtered
transparency are stained glass windows or tinted cellophane. The light
passing through such objects is tinted by the appropriate color as the
material selectively absorbs some frequencies of light while allowing others
to pass through. The color of the object is subtracted from the light passing
through so this is called subtractive transparency.

The 5th component, called transmit, specifies the amount of non-filtered
light that is transmitted through a surface. Some real-world examples of
non-filtered transparency are thin see-through cloth, fine mesh netting and
dust on a surface. In these examples, all frequencies of light are allowed to
pass through tiny holes in the surface. Although the amount of light passing
through is diminished, the color of the light passing through is unchanged.
The color of the object is added to the light passing through so this is
called additive transparency.

Note that early versions of POV-Ray used the keyword alpha to specify
filtered transparency. However that word is often used to describe
non-filtered transparency. For this reason alpha is no longer used.

Each of the five components of a color are float values which are normally in
the range between 0.0 and 1.0. However any values, even negatives may be
used.

Colors may be specified using vectors, keywords with floats or identifiers.
You may also create very complex color expressions from combinations of any
of these using various familiar operators. The syntax for specifying a color
has evolved since POV-Ray was first released. We have maintained the original
keyword-based syntax and added a short-cut vector notation. Either the old or
new syntax is acceptable however the vector syntax is easier to use when
creating color expressions.

7.1.5.1          Color Vectors

The syntax for a color vector is any of the following...

  color rgb VECTOR3
  color rgbf VECTOR4
  color rgbt VECTOR4
  color rgbft VECTOR5


where VECTOR3, VECTOR4 or VECTOR5 are any valid vector expressions of 3, 4 or
5 components. For example

  color rgb <1.0, 0.5, 0.2>


This specifies a color whose red component is 1.0 or 100% of full intensity.
The green component is 0.5 or 50% of full intensity and the blue component is
0.2 or 20% of full intensity. Although the filter and transmit components are
not explicitly specified, they exist and are set to their default values of 0
or no transparency.

The rgbf keyword requires a four component vector. The 4th component is the
filter component and the transmit component defaults to zero. Similarly the
rgbt keyword requires four components where the 4th value is moved to the 5th
component which is transmit and then the filter component is set to zero.

The rgbft keyword allows you to specify all five components. Internally in
expressions all five are always used.

Under most circumstances the keyword color is optional and may be omitted. We
also support the British or Canadian spelling colour. Under some
circumstances, if the vector expression is a 5 component expression or there
is a color identifier in the expression then the rgbtf keyword is optional.

7.1.5.2          Color Keywords

The older keyword method of specifying a color is still useful and many users
prefer it. Like a color vector, you begin with the optional keyword color.
This is followed by any of five additional keywords red, green, blue, filter
or transmit. Each of these component keywords is followed by a float
expression. For example

  color red 1.0 green 0.5


This specifies a color whose red component is 1.0 or 100% of full intensity
and the green component is 0.5 or 50% of full intensity. Although the blue,
filter and transmit components are not explicitly specified, they exist and
are set to their default values of 0. The component keywords may be given in
any order and if any component is unspecified its value defaults to zero.

7.1.5.3          Color Identifiers

Color identifiers may be declared to make scene files more readable and to
parameterize scenes so that changing a single declaration changes many
values. A color identifier is declared as either of the following...

  #declare IDENTIFIER = COLOR_VECTOR
  #declare IDENTIFIER = COLOR_KEYWORDS...


Where IDENTIFIER is the name of the identifier up to 40 characters long and
COLOR_VECTOR or COLOR_KEYWORDS are any valid color specifications as
described in the two previous sections of this document. Here are some
examples...

  #declare White = rgb <1,1,1>
  #declare Cyan = color blue 1.0  green 1.0
  #declare Weird = rgb <Foo*2,Bar-1,Bob/3>
  #declare LightGray = White*0.8
  #declare LightCyan = Cyan red 0.6


As the LightGray example shows you do not need any color keywords when
creating color expressions based on previously declared colors. The last
example shows you may use a color identifier with the keyword style syntax.
Make sure that the identifier comes first before any other component
keywords.

Like floats and vectors, you may re-define colors throughout a scene but the
need to do so is rare.

7.1.5.4          Color Operators

Color vectors may be combined in expressions the same as float or vector
values. Operations are performed on a component-by-component basis. For
example rgb <1.0, 0.5 0.2> * 0.9 evaluates the same as rgb <1.0, 0.5 0.2> *
<0.9, 0.9, 0.9> or rgb <0.9, 0.45,  0.18>. Other operations are done on a
similar component-by-component basis.

You may use the dot operator to extract a single component from a color.
Suppose the identifier Shade was previously defined as a color. Then
Shade.red is the float value of the red component of Shade. Similarly
Shade.green, Shade.blue, Shade.filter and Shade.transmit extract the float
value of the other color components.

7.1.5.5          Common Color Pitfalls

The variety and complexity of color specification methods can lead to some
common mistakes. Here are some things to consider when specifying a color.

When using filter transparency, the colors which come through are multiplied
by the primary color components. For example if gray light such as rgb
<0.9,0.9,0.9> passes through a filter such as rgbf <1.0,0.5,0.0,1.0> the
result is rgb <0.9,0.45,0.0> with the red let through 100%, the green cut in
half from 0.9 to 0.45 and the blue totally blocked. Often users mistakenly
specify a clear object by

  color filter 1.0


but this has implied red, green and blue values of zero. You've just
specified a totally black filter so no light passes through. The correct way
is either

  color red 1.0   green 1.0   blue 1.0   filter 1.0


or

  color transmit 1.0


In the 2nd example it doesn't matter what the rgb values are. All of the
light passes through untouched.

Another pitfall is the use of color identifiers and expressions with color
keywords. For example...

  color My_Color red 0.5


this substitutes whatever was the red component of My_Color with a red
component of 0.5 however...

  color My_Color + red 0.5


adds 0.5 to the red component of My_Color and even less obvious...

  color My_Color * red 0.5


that cuts the red component in half as you would expect but it also
multiplies the green, blue, filter and transmit components by zero! The part
of the expression after the multiply operator evaluates to rgbft
<0.5,0,0,0,0> as a full 5 component color.

The following example results in no change to My_Color.

  color red 0.5 My_Color


This is because the identifier fully overwrites the previous value. When
using identifiers with color keywords, the identifier should be first.

One final issue, some POV-Ray syntax allows full color specifications but
only uses the rgb part. In these cases it is legal to use a float where a
color is needed. For example:

  finish { ambient 1 }


The ambient keyword expects a color so the value 1 is promoted to <1,1,1,1,1>
which is no problem. However

  pigment { color 0.4 }


is legal but it may or may not be what you intended. The 0.4 is promoted to
<0.4,0.4,0.4,0.4,0.> with the filter and transmit set to 0.4 as well. It is
more likely you wanted...

  pigment { color rgb 0.4 }


in which case a 3 component vector is expected. Therefore the 0.4 is promoted
to <0.4,0.4,0.4,0.0,0.0> with default zero for filter and transmit.

7.1.6            Strings

The POV-Ray language requires you to specify a string of characters to be
used as a file name, text for messages or text for a text object. Strings may
be specified using literals, identifiers or functions which return string
values. Although you cannot build string expressions from symbolic operators
such as are used with floats, vectors or colors, you may perform various
string operations using string functions. Some applications of strings in
POV-Ray allow for non-printing formatting characters such as newline or
form-feed.

7.1.6.1          String Literals

String literals begin with a double quote mark '"' which is followed by up to
256 printable ASCII characters and are terminated by another double quote
mark. The following are all valid string literals:

  "Here"   "There"    "myfile.gif"    "textures.inc"


Note if you need to specify a quote mark in a string literal you must preceed
it with a backslash. For example

  "Joe said \"Hello\" as he walked in."


is converted to

  Joe said "Hello" as he walked in.


If you need to specify a backslash, most of the time you need do nothing
special. However if the string ends in a backslash, you will have to specify
two. For example:

  "This is a backslash  and so is this"


Is converted to:

  This is a backslash  and so is this\


The

regardless usage however other formating codes such as \n for new line are
supported in user message streams. See "Text Formatting" for details.

7.1.6.2          String Identifiers

String identifiers may be declared to make scene files more readable and to
parameterize scenes so that changing a single declaration changes many
values. An identifier is declared as follows...

  #declare IDENTIFIER = STRING


Where IDENTIFIER is the name of the identifier up to 40 characters long and
STRING is a string literal, string identifier or function which returns a
string value. Here are some examples...

  #declare Font_Name = "ariel.ttf"
  #declare Inc_File = "myfile.inc"
  #declare Name = "John"
  #declare Name = concat(Name," Doe")


As the last example shows, you can re-declare a string identifier and may use
previously declared values in that re-declaration.

7.1.7            Built-in Identifiers

There are several built-in float and vector identifiers. You can use them to
specify values or to create expressions but you cannot re-declare them to
change their values.

7.1.7.1          Constant Built-in Identifiers

Most built-in identifiers never change value. They are defined as though the
following lines were at the start of every scene.

  #declare pi = 3.1415926535897932384626
  #declare true = 1
  #declare yes = 1
  #declare on = 1
  #declare false = 0
  #declare no = 0
  #declare off = 0
  #declare u = <1,0>
  #declare v = <0,1>
  #declare x = <1,0,0>
  #declare y = <0,1,0>
  #declare z = <0,0,1>
  #declare t = <0,0,0,1>


The built-in float identifier pi is obviously useful in math expressions
involving circles.

The built-in float identifiers on,off, yes, no, true and false are designed
for use as boolean constants.

The built-in vector identifiers x, y and z provide much greater readability
for your scene files when used in vector expressions. For example....

  plane { y, 1}        // The normal vector is obviously "y".
  plane { <0,1,0>, 1}  // This is harder to read.

  translate 5*x        // Move 5 units in the "x" direction.
  translate <5,0,0>    // This is less obvious.


An expression like 5*x evaluates to 5 <1,0,0> or <5,0,0>.

Similarly u and v may be used in 2D vectors. When using 4D vectors you should
use x, y, z, and t and POV-Ray will promote x, y and z to 4D when used where
4D is required.

7.1.7.2          Built-in Identifier 'clock'

The built-in float identifier clock is used to control animations in POV-Ray.
Unlike some animation packages, the action in POV-Ray animated scenes does
not depend upon the integer frame numbers. Rather you should design your
scenes based upon the float identifier clock. For non-animated scenes its
default value is 0 but you can set it to any float value using the INI file
option Clock=n.n or the command-line switch +Kn.n to pass a single float
value your scene file.

Other INI options and switches may be used to animate scenes by automatically
looping through the rendering of frames using various values for clock. By
default, the clock value is 0 for the initial frame and 1 for the final
frame. All other frames are interpolated between these values. For example if
your object is supposed to rotate one full turn over the course of the
animation you could specify rotate 360*clock*y. Then as clock runs from 0 to
1, the object rotates about the y-axis from 0 to 360 degrees.

Although the value of clock will change from frame-to-frame, it will never
change throughout the parsing of a scene.


7.1.7.3          Built-in Identifier 'version'

The built-in float identifier version contains the current setting of the
version compatibility option. Although this value defaults to 3 which is the
current POV-Ray version number, the initial value of version may be set by
the INI file option Version=n.n or by the +MVn.n command-line switch. This
tells POV-Ray to parse the scene file using syntax from an earlier version of
POV-Ray.

The INI option or switch only affects the initial setting. Unlike other
built-in identifiers, you may change the value of version throughout a scene
file. You do not use #declare to change it though. The #version language
directive is used to change modes. Such changes may occur several times
within scene files.

Together with the built-in version identifier the #version directive allows
you to save and restore the previous values of this compatibility setting.
For example suppose mystuff.inc is in version 1 format. At the top of the
file you could put:

  #declare Temp_Vers = version    // Save previous value
  #version 1.0                    // Change to 1.0 mode

  ... // Version 1.0 stuff goes here...

  #version Temp_Vers              // Restore previous version


7.1.8            Functions

POV-Ray defines a variety of built-in functions for manipulating floats,
vectors and strings. The functions are listed grouped according to their
usage and not by the type of value they return. For example vdot computes the
dot product of two vectors and is listed as a vector function even though it
returns a single float value.

Function calls consist of a keyword which specifies the name of the function
followed by a parameter list enclosed in parentheses. Parameters are
separated by commas. For example:

  keyword(param1,param2)


Functions evaluate to values that are floats, vectors or strings and may be
used in expressions or statements anywhere that literals or identifiers of
that type may be used.

7.1.8.1          Float Functions

The following are the functions which take one or more float parameters and
return float values. Assume that A and B are any valid expression that
evaluates to a float. See section "Vector Functions" and section "String
Functions" for other functions which return float values but whose primary
purpose is more closely related to vectors and strings.

abs(A): Absolute value of A. If A is negative, returns -A otherwise returns
A.

acos(A): Arc-cosine of A. Returns the angle, measured in radians, whose
cosine is A.

asin(A): Arc-sine of A. Returns the angle, measured in radians, whose sine is
A.

atan2(A,B): Arc-tangent of (A/B). Returns the angle, measured in radians,
whose tangent is (A/B). Returns appropriate value even if B is zero. Use
atan2(A,1) to compute usual atan(A) function.

ceil(A): Ceiling of A. Returns the smallest integer greater than A. Rounds up
to the next higher integer.

cos(A): Cosine of A. Returns the cosine of the angle A, where A is measured
in radians.

degrees(A): Convert radians to degrees. Returns the angle measured in degrees
whose value in radians is A. Formula is degrees=A/pi*180.0.

div(A,B): Integer division. The integer part of (A/B).

exp(A): Exponential of A. Returns the value of e raised to the power A where
e is the base of the natural logarithm, i.e. the non-repeating value
approximately equal to 2.71828182846.

floor(A): Floor of A. Returns the largest integer less than A. Rounds down to
the next lower integer.

int(A): Integer part of A. Returns the truncated integer part of A. Rounds
towards zero.

log(A): Natural logarithm of A. Returns the natural logarithm base e of the
value A.

max(A,B): Maximum of A and B. Returns A if A larger than B. Otherwise returns
B.

min(A,B): Minimum of A and B. Returns A if A smaller than B. Otherwise
returns B.

mod(A,B): Value of A modulo B. Returns the remainder after the integer
division of A/B. Formula is mod=((A/B)-int(A/B))*B.

pow(A,B): Exponentiation. Returns the value of A raised to the power B.

radians(A): Convert degrees to radians. Returns the angle measured in radians
whose value in degrees is A. Formula is radians=A*pi/180.0.

rand(A): Returns the next pseudo-random number from the stream specified by
the positive integer A. You must call seed() to initialize a random stream
before calling rand(). The numbers are uniformly distributed, and have values
between 0.0 and 1.0, inclusively. The numbers generated by separate streams
are independent random variables.

seed(A): Initializes a new pseudo-random stream with the initial seed value
A. The number corresponding to this random stream is returned. Any number of
pseudo-random streams may be used as shown in the example below:

  #declare R1 = seed(0)
  #declare R2 = seed(12345)

  #sphere { <rand(R1), rand(R1), rand(R1)>, rand(R2) }


Multiple random generators are very useful in situations where you use rand()
to place a group of objects, and then decide to use rand() in another
location earlier in the file to set some colors or place another group of
objects. Without separate rand() streams, all of your objects would move when
you added more calls to rand(). This is very annoying.

sin(A): Sine of A. Returns the sine of the angle A, where A is measured in
radians.

sqrt(A): Square root of A. Returns the value whose square is A.

tan(A): Tangent of A. Returns the tangent of the angle A, where A is measured
in radians.

7.1.8.2          Vector Functions

The following are the functions which take one or more vector and float
parameters and return vector or float values. All of these functions support
only three component vectors. Assume that A and B are any valid expression
that evaluates to a three component vector and that F is any valid expression
that evaluates to a float.

vaxis_rotate(A,B,F): Rotate A about B by F. Given the x,y,z coordinates of a
point in space designated by the vector A, rotate that point about an
arbitrary axis defined by the vector B. Rotate it through an angle specified
in degrees by the float value F. The result is a vector containing the new
x,y,z coordinates of the point.

vcross(A,B): Cross product of A and B. Returns a vector that is the vector
cross product of the two vectors. The resulting vector is perpendicular to
the two original vectors and its length is proportional to the angle between
them. See the animated demo scene VECT2.POV for an illustration.

vdot(A,B): Dot product of A and B. Returns a float value that is the dot
product (sometimes called scaler product of A with B. Formula is vdot=A.x*B.x
+ A.y*B.y + A.z*B.z. See the animated demo scene VECT2.POV for an
illustration.

vlength(A): Length of A. Returns a float value that is the length of vector
A. Can be used to compute the distance between two points. Dist=vlength(B-A).
Formula is vlength=sqrt(vdot(A,A)).

vnormalize(A): Normalize vector A. Returns a unit length vector that is the
same direction as A. Formula is vnormalize=A/vlength(A).

vrotate(A,B): Rotate A about origin by B. Given the x,y,z coordinates of a
point in space designated by the vector A, rotate that point about the origin
by an amount specified by the vector B. Rotate it about the x-axis by an
angle specified in degrees by the float value B.x. Similarly B.y and B.z
specify the amount to rotate in degrees about the y-axis and z-axis. The
result is a vector containing the new x,y,z coordinates of the point.

7.1.8.3          String Functions

The following are the functions which take one or more string and float
parameters and return string or float values. Assume that S1 and S2 are any
valid strings and that A, L and P are any valid expressions that evaluate to
floats.

asc(S1): ASCII value of S1. Returns an integer value in the range 0 to 255
that is the ASCII value of the first character of S1. For example asc("ABC")
is 65 because that is the value of the character "A".

chr(A): Character whose ASCII value is A. Returns a single character string.
The ASCII value of the character is specified by an integer A which must be
in the range 0 to 255. For example chr(70) is the string "F". When rendering
text objects you should be aware that the characters rendered for values of A
> 127 are dependent on the (TTF) font being used. Many (TTF) fonts use the
Latin-1 (ISO 8859-1) character set, but not all do.

concat(S1,S2,[S3...]): Concatenate strings S1 and S2. Returns a string that
is the concatenation of all parameter strings. Must have at least 2
parameters but may have more. For example:

  concat("Value is ", str(A,3,1), " inches")


If the float value A was 12.34 the result is "Value is 12.3 inches" which is
a string.

file_exists(S1): Search for file specified by S1. Attempts to open the file
whose name is specified by the string S1. The current directory and all
directories specified in any Library_Path INI options or +L command line
switches are searched. File is immediately closed. Returns a boolean value 1
on success and 0 on failure.

str(A,L,P): Convert float A to a formatted string. Returns a formatted string
representation of float value A. The float parameter L specifies the minimum
length of the string and the type of left padding used if the string's
representation is shorter than the minimum. If L is positive then the padding
is with blanks. If L is negative then the padding is with zeros. The overall
minimum length of the formatted string is abs(L). If the string needs to be
longer, it will be made as long as necessary to represent the value.

The float parameter P specifies the number of digits after the decimal point.
If P is negative then a compiler-specific default precision is use. Here are
some examples:

  str(123.456,0,3)   "123.456"
  str(123.456,4,3)   "123.456"
  str(123.456,9,3)   "  123.456"
  str(123.456,-9,3)  "00123.456"
  str(123.456,0,2)   "123.46"
  str(123.456,0,0)   "123"
  str(123.456,5,0)   "  123"
  str(123.000,7,2)   " 123.00"
  str(123.456,0,-1)  "123.456000" (platform specific)


strcmp(S1,S2): Compare string S1 to S2. Returns a float value zero if the
strings are equal, a positive number if S1 comes after S2 in the ASCII
collating sequence, else a negative number.

strlen(S1): Length of S1. Returns an integer value that is the number of
characters in the string S1.

strlwr(S1): Lower case of S1. Returns a new string in which all upper case
letters in the string S1 are converted to lower case. The original string is
not affected. For example strlwr("Hello There!") results in "hello there!".

substr(S1,P,L): Sub-string from S1. Returns a string that is a subset of the
characters in parameter S1 starting at the position specified by the integer
value P for a length specified by the integer value L. For example
substr("ABCDEFGHI",4,2) evaluates to the string "EF". If P+L>strlen(S1) an
error occurs.

strupr(S1): Upper case of S1. Returns a new string in which all lower case
letters in the string S1 are converted to upper case. The original string is
not affected. For example strupr("Hello There!") results in "HELLO THERE!".

val(S1): Convert string S1 to float. Returns a float value that is
represented by the text in S1. For example val("123.45") is 123.45 as a
float.

7.2              Language Directives

The POV Scene Language contains several statements called language
directives which tell the file parser how to do its job. These directives can
appear in almost any place in the scene file - even in the middle of some
other statements. They are used to include other text files in the stream of
commands, to declare identifiers, to define conditional or looped parsing and
to control other important aspects of scene file processing.

Each directive begins with the hash character # (often called a number sign
or pound sign). It is followed by a keyword and optionally other parameters.

In versions of POV-Ray prior to 3.0, the use of this # character was
optional. Language directives could only be used between objects, camera or
light_source statements and could not appear within those statements. The
exception was the #include which could appear anywhere. Now that all language
directives can be used almost anywhere, the # character is mandatory.

The following keywords introduce language directives.


#break              #default            #statistics
#case               #else               #switch
#debug              #end                #version
#declare            #render             #warning


Earlier versions of POV-Ray considered the keyword
#max_intersections and the keyword #max_trace_level to
be language directives but they have been moved to the
global_settings statement. Their use as a directive still works
but it generates a warning and may be discontinued in the future.


7.2.1            Include Files

The language allows include files to be specified by placing the line

  #include "filename.inc"


at any point in the input file. The filename may be specified by any valid
string expression but it usually is a literal string enclosed in double
quotes. It may be up to 40 characters long (or your computer's limit),
including the two double-quote characters.

The include file is read in as if it were inserted at that point in the file.
Using include is the same as actually cutting and pasting the entire contents
of this file into your scene.

Include files may be nested. You may have at most 10 nested include files.
There is no limit on un-nested include files.

Generally, include files have data for scenes but are not scenes in
themselves. By convention scene files end in .pov and include files end with
.inc.

It is legal to specify drive and directory information in the file
specification however it is discouraged because it makes scene files less
portable between various platforms.

It is typical to put standard include files in a special sub-directory.
POV-Ray can only read files in the current directory or one referenced by the
Library_Path option (See section "Library Paths").

7.2.2            Declare

Identifiers may be declared and later referenced to make scene files more
readable and to parametrize scenes so that changing a single declaration
changes many values. There are several built-in identifiers which POV-Ray
declares for you. See section "Built-in Identifiers"  for details.

7.2.2.1          Declaring identifiers

An identifier is declared as follows.

  #declare IDENTIFIER = ITEM


Where IDENTIFIER is the name of the identifier up to 40 characters long and
ITEM is any of the following

  float, vector, color or string expressions
  objects (all kinds)
  texture, pigment, normal, finish or halo
  color_map, pigment_map, slope_map, normal_map
  camera, light_source
  atmosphere
  fog
  rainbow
  sky_sphere
  transform


Here are some examples.

  #declare Rows = 5
  #declare Count = Count+1
  #declare Here = <1,2,3>
  #declare White = rgb <1,1,1>
  #declare Cyan = color blue 1.0  green 1.0
  #declare Font_Name = "ariel.ttf"
  #declare Ring = torus {5,1}
  #declare Checks = pigment { checker White, Cyan }

  object{ Rod scale y*5 }         // not "cylinder { Rod }"
  object {
    Ring
    pigment { Checks scale 0.5 }
    transform Skew
  }


Declarations, like most language directives, can appear anywhere in the file
- even within other statements. For example:

  #declare Here=<1,2,3>
  #declare Count=0                   // initialize Count

  union {
    object { Rod translate Here*Count }
    #declare Count=Count+1           // re-declare inside union
    object { Rod translate Here*Count }
    #declare Count=Count+1           // re-declare inside union
    object { Rod translate Here*Count }
  }


As this example shows, you can re-declare an identifier and may use
previously declared values in that re-declaration. However if you attempt to
re-declare an identifier as anything other than its original type, it will
generate a warning message.

Declarations may be nested inside each other within limits. In the example in
the previous section you could declare the entire union as a object. However
for technical reasons you may not use any language directive inside the
declaration of floats, vectors or color expressions.

7.2.3            Default Directive

POV-Ray creates a default texture when it begins processing. You may change
those defaults as described below. Every time you specify a texture
statement, POV-Ray creates a copy of the default texture. Anything you put in
the texture statement overrides the default settings. If you attach a
pigment, normal or finish to an object without any texture statement then
POV-Ray checks to see if a texture has already been attached. If it has a
texture then the pigment, normal or finish will modify the existing texture.
If no texture has yet been attached to the object then the default texture is
copied and the pigment, normal or finish will modify that texture.

You may change the default texture, pigment, normal or finish using the
language directive #default as follows:

  #default {
    texture {
      pigment {...}
      normal  {...}
      finish  {...}
    }
  }


Or you may change just part of it like this:

  #default {
    pigment {...}
  }


This still changes the pigment of the default texture. At any time there is
only one default texture made from the default pigment, normal and finish.
The example above does not make a separate default for pigments alone. Note
that the special textures tiles and material_map or a texture with a
texture_map may not be used as defaults.

You may change the defaults several times throughout a scene as you wish.
Subsequent #default statements begin with the defaults that were in effect at
the time. If you wish to reset to the original POV-Ray defaults then you
should first save them as follows:

  //At top of file
  #declare Original_Default = texture {}


later after changing defaults you may restore it with...

  #default {texture {Original_Default}}


If you do not specify a texture for an object then the default texture is
attached when the object appears in the scene. It is not attached when an
object is declared. For example:

  #declare My_Object =
    sphere{ <0,0,0>, 1 }  // Default texture not applied
  object { My_Object }    // Default texture added here


You may force a default texture to be added by using an empty texture
statement as follows:

  #declare My_Thing =
    sphere { <0,0,0>, 1 texture {} }  // Default texture applied


The original POV-Ray defaults for all items are given throughout the
documentation under each appropriate section.

7.2.4            Version Directive

While many language changes have been made for POV-Ray 3.0, all of version
2.0 syntax and most of version 1.0 syntax still works. Whenever possible we
try to maintain backwards compatibility. One feature introduced in 2.0 that
was incompatible with any 1.0 scene files is the parsing of float
expressions. Setting +MV1.0 command line switch or the Version=1.0 INI option
turns off expression parsing as well as many warning messages so that nearly
all 1.0 files will still work. The changes between 2.0 and 3.0 are not as
extensive. Setting Version=2.0 is only necessary to eliminate some warning
messages. Naturally the default setting for this option is Version=3.0.

The #version language directive is used to change modes within scene files.
This switch or INI options only affects the initial setting.

Together with the built-in version identifier the #version directive allows
you to save and restore the previous values of this compatibility setting.
For example suppose mystuff.inc is in version 1.0 format. At the top of the
file you could put:

  #declare Temp_Vers = version // Save previous value
  #version 1.0                    // Change to 1.0 mode

  ... // Version 1.0 stuff goes here ...

  #version Temp_Vers              // Restore previous version


Previous versions of POV-Ray would not allow you to change versions inside an
object or declaration but that restriction has been lifted for POV-Ray 3.0.

Future versions of POV-Ray may not continue to maintain full backward
compatibility even with the #version directive. We strongly encourage you to
phase in 3.0 syntax as much as possible.

7.2.5            Conditional Directives

POV-Ray 3.0 allows a variety of new language directives to implement
conditional parsing of various sections of your scene file. This is
especially useful in describing the motion for animations but it has other
uses as well. Also available is a #while loop directive. You may nest
conditional directives 200 levels deep.

7.2.5.1          IF ELSE Directives

The simplest conditional directive is a traditional #if directive. It is of
the form...

  #if (COND)
    // This section is
    //  parsed if COND is true
  #else
    // This section is
    // parsed if COND is false
  #end // End of conditional part


where (COND) is a float expression that evaluates to a boolean value. A value
of 0.0 is false and any non-zero value is true. Note that extremely small
values of about 1e-10 are considered zero in case of round off errors. The
parentheses around the condition are required. The #else directive is
optional. The #end directive is required.

7.2.5.2          IFDEF Directives

The #ifdef directive is similar to the #if directive however it is used to
determine if an identifier has been previously declared. After the #ifdef
directive instead of a boolean expression you put a lone identifier enclosed
in parentheses. For example:

 #ifdef (User_Thing)
   // This section is parsed if the
   // identifier "User_Thing" was
   // previously declared
   object{User_Thing} // invoke identifier
 #else
   // This section is parsed if the
   // identifier "User_Thing" was not
   // previously declared
   box{<0,0,0>,<1,1,1>} // use a default
 #end
   // End of conditional part


7.2.5.3          IFNDEF Directives

The #ifndef directive is similar to the #ifdef directive however it is used
to determine if the given identifier isn't declared yet. For example:

 #ifndef (User_Thing)
   // This section is parsed if the
   // identifier "User_Thing" was not
   // previously declared
   box{<0,0,0>,<1,1,1>} // use a default
 #else
   // This section is parsed if the
   // identifier "User_Thing" was
   // previously declared
   object{User_Thing} // invoke identifier
 #end
   // End of conditional part


7.2.5.4          SWITCH CASE and RANGE Directives

A more powerful conditional is the #switch directive. The syntax is as
follows...

  #switch (VALUE)
    #case (TEST_1)
      // This section is parsed if VALUE=TEST_1
    #break  //First case ends

    #case (TEST_2)
      // This section is parsed if VALUE=TEST_2
    #break  //Second case ends

    #range (LOW_1,HIGH_1)
      // This section is parsed if (VALUE>=LOW_1)&(VALUE<=HIGH_1)
    #break  //Third case ends

    #range (LOW_2,HIGH_2)
      // This section is parsed if (VALUE>=LOW_2)&(VALUE<=HIGH_2)
    #break  //Fourth case ends

    #else
      // This section is parsed if no other case or
      // range is true.
  #end // End of conditional part


The float expression VALUE following the #switch directive is evaluated and
compared to the values in the #case or #range directives. When using #case,
it is followed by a float expression TEST_1 in parentheses. It is compared to
the VALUE. As usual in POV-Ray, float comparisons are considered equal if
their difference is under 1e-10. If the values are equal, parsing continues
normally until a #break, #else or #end directive is reached. If the
comparison fails POV-Ray skips until another #case or #range is found.

If you use the #range directive it is followed by two float expressions LOW_1
and HIGH_1 which are enclosed in parentheses and separated by a comma. If the
switch VALUE is in the range specified then parsing continues normally until
a #break, #else or #end directive is reached. If the VALUE is outside the
range the comparison fails and POV-Ray skips until another #case or #range is
found.

If no #case or #range succeeds the #else section is parsed. The #else
directive is optional. If no #else is specified and no match succeeds then
parsing resumes after the #end directive.

There may be any number of #case or #range directives in any order you want.
If a segment evaluates true but no #break is specified, the parsing will fall
through to the next #case or #range and will continue until a #break, #else
or #end. Hitting a #break while parsing a successful section causes an
immediate jump to the #end without processing subsequent sections, even if a
subsequent condition would also have been satisfied.

7.2.5.5          WHILE Directive

The #while directive is a looping feature that makes it easy to place
multiple objects in a pattern or other uses. The #while directive is followed
by a float expression that evaluates to a boolean value. A value of 0.0 is
false and any non-zero value is true. Note that extremely small values of
about 1e-10 are considered zero in case of round off errors. The parentheses
around the expression are required. If the condition is true parsing
continues normally until an #end directive is reached. At the end, POV-Ray
loops back to the #while directive and the condition is re-evaluated. Looping
continues until the condition fails. When it fails, parsing continues after
the #end directive. For example:

  #declare Count=0
  #while (Count < 5)
    object{MyObject translate x*3*Count}
    #declare Count=Count+1
  #end


This example places five copies of MyObject in a row spaced three units apart
in the x-direction.

7.2.6            User Message Directives

With the addition of conditional and loop directives, the POV-Ray language
has the potential to be more like an actual programming language. This means
that it will be necessary to have some way to see what is going on when
trying to debug loops and conditionals. To fulfill this need we have added
the ability to print text messages to the screen. You have a choice of five
different text streams to use including the ability to generate a fatal error
if you find it necessary. Limited formatting is available for strings output
by this method.

7.2.6.1          Text Message Streams

The syntax for a text message is any of the following:

  #debug      STRING
  #error      STRING
  #render     STRING
  #statistics STRING
  #warning    STRING


Where STRING is any valid string of text including string identifiers or
functions which return strings. For example:

  #switch (clock*360)
    #range (0,180)
      #render "Clock in 0 to 180 range\n"
    #break

    #range (180,360)
      #render "Clock in 180 to 360 range\n"
    #break

    #else
      #warning "Clock outside expected range\n"
      #warning concat("Value is:",str(clock*360,5,0),"\n")
  #end


There are seven distinct text streams that POV-Ray uses for output. You may
output only to five of them. On some versions of POV-Ray, each stream is
designated by a particular color. Text from these streams are displayed
whenever it is appropriate so there is often an intermixing of the text. The
distinction is only important if you choose to turn some of the streams off
or to direct some of the streams to text files. On some systems you may be
able to review the streams separately in their own scroll-back buffer. See
"Console Text Output" for details on re-directing the streams to a text file.


Here is a description of how POV-Ray uses each stream. You may use them for
whatever purpose you want except note that use of the #error stream causes a
fatal error after the text is displayed.

DEBUG: This stream displays debugging messages. It was primarily designed for
developers but this and other streams may also be used by the user to display
messages from within their scene files.

FATAL: This stream displays fatal error messages. After displaying this text,
POV-Ray will terminate. When the error is a scene parsing error, you may be
shown several lines of scene text that leads up to the error.

RENDER: This stream displays information about what options you have
specified to render the scene. It includes feedback on all of the major
options such as scene name, resolution, animation settings, anti-aliasing and
others.

STATISTICS: This stream displays statistics after a frame is rendered. It
includes information about the number of rays traced, the length of time of
the processing and other information.

WARNING: This stream displays warning messages during the parsing of scene
files and other warnings. Despite the warning, POV-Ray can continue to render
the scene.


7.2.6.2          Text Formatting

Some escape sequences are available to include non-printing control
characters in your text. These sequences are similar to those used in string
literals in the C programming language. The sequences are:

  "\""Double quote 0x2209D 0x0A


For example:

  #debug "This is one line.\nBut this is another"


Depending on what platform you are using, they may not be fully supported for
console output. However they will appear in any text file if you re-direct a
stream to a file.

Note that most of these control characters only apply in text message
directives. They are not implemented for other string usage in POV-Ray such
as text objects or file names.

The exceptions are the


7.3              POV-Ray Coordinate System

Objects, lights and the camera are positioned using a typical 3D coordinate
system. The usual coordinate system for POV-Ray has the positive y-axis
pointing up, the positive x-axis pointing to the right and the positive
z-axis pointing into the screen. The negative values of the axes point the
other direction as shown in the images in section "Understanding POV-Ray's
Coordinate System".

Locations within that coordinate system are usually specified by a three
component vector. The three values correspond to the x, y and z directions
respectively. For example, the vector < 1,2,3> means the point that's one
unit to the right, two units up and three units in front of the center of the
universe at <0,0,0>.

Vectors are not always points though. They can also refer to an amount to
size, move or rotate a scene element or to modify the texture pattern applied
to an object.

The supported transformations are rotate, scale and translate. They are used
to turn, size and translate an object or texture. A transformation matrix may
also be used to specify complex transformations directly.

7.3.1            Transformations

The supported transformations are rotate, scale and translate. They are used
to turn, size and translate an object or texture.

  rotate <VECTOR>
  scale <VECTOR>
  translate <VECTOR>


7.3.1.1          Translate

An object or texture pattern may be moved by adding a translate parameter. It
consists of the keyword translate followed by a vector expression. The terms
of the vector specify the number of units to move in each of the x, y and z
directions. Translate moves the element relative to it's current position.
For example

  sphere { <10, 10, 10>, 1
    pigment { Green }
    translate <-5, 2, 1>
  }


will move the sphere from <10,10,10> to < 5,12,11>. It does not move it to
the absolute location <-5,2,1>. Translating by zero will leave the element
unchanged on that axis. For example:

  sphere { <10, 10, 10>, 1
    pigment { Green }
    translate 3*x // evaluates to <3,0,0> so move 3 units
                  // in the x direction and none along y or z
  }


7.3.1.2          Scale

You may change the size of an object or texture pattern by adding a scale
parameter. It consists of the keyword scale followed by a vector expression.
The 3 terms of the vector specify the amount of scaling in each of the x, y
and z directions.

Scale is used to stretch or squish an element. Values larger than one stretch
the element on that axis while values smaller than one are used to squish it.
Scale is relative to the current element size. If the element has been
previously re-sized using scale then scale will size relative to the new
size. Multiple scale values may used.

For example

  sphere { <0,0,0>, 1
    scale <2,1,0.5>
  }


will stretch and smash the sphere into an ellipsoid shape that is twice the
original size along the x-direction, remains the same size in the y-direction
and is half the original size in the z-direction.

If a lone float expression is specified it is promoted to a three component
vector whose terms are all the same. Thus the item is uniformly scaled by the
same amount in all directions. For example:

  object {
    MyObject
    scale 5 // Evaluates as <5,5,5> so uniformly scale
            // by 5 in every direction.
  }


7.3.1.3          Rotate

You may change the orientation of an object or texture pattern by adding a
rotate parameter. It consists of the keyword rotate followed by a vector
expression. The three terms of the vector specify the number of degrees to
rotate about each of the x-, y- and z-axes.

Note that the order of the rotations does matter. Rotations occur about the
x-axis first, then the y-axis, then the z-axis. If you are not sure if this
is what you want then you should only rotate on one axis at a time using
multiple rotation statements to get a correct rotation. As in

  rotate <0, 30, 0>  // 30 degrees around Y axis then,
  rotate <-20, 0, 0> // -20 degrees around X axis then,
  rotate <0, 0, 10>  // 10 degrees around Z axis.


Rotation is always performed relative to the axis. Thus if an object is some
distance from the axis of rotation it will not only rotate but it will orbit
about the axis as though it was swinging around on an invisible string.

To work out the rotation directions you must perform the famous Computer
Graphics Aerobics exercise as explained in the section "Understanding
POV-Ray's Coordinate System".

7.3.1.4          Matrix Keyword

The matrix keyword can be used to explicitly specify the transformation
matrix to be used for objects or textures. Its syntax is:

  matrix < m00, m01, m02,
           m10, m11, m12,
           m20, m21, m22,
           m30, m31, m32 >


Where m00 through m32 are float expressions that specify the elements of a
4*4 matrix with the fourth column implicitly set to <0,0,0,1>. A point P,
P=<px, py, pz>, is transformed into Q, Q=<qx, qy, qz> by

  qx = M00 * px + M10 * py + M20 * pz + M30
  qy = M01 * px + M11 * py + M21 * pz + M31
  qz = M02 * px + M12 * py + M22 * pz + M32


Normally you won't use the matrix keyword because it's less descriptive than
the transformation commands and harder to visualize. There is an intersecting
aspect of the matrix command though. It allows more general transformation
like shearing. The following matrix causes an object to be sheared along the
y-axis.

  object {
    MyObject
    matrix < 1, 1, 0,
             0, 1, 0,
             0, 0, 1,
             0, 0, 0 >
  }


7.3.2            Transformation Order

Because rotations are always relative to the axis and scaling is relative to
the origin, you will generally want to create an object at the origin and
scale and rotate it first. Then you may translate it into its proper
position. It is a common mistake to carefully position an object and then to
decide to rotate it because a rotation of an object causes it to orbit about
the axis, the position of the object may change so much that it orbits out of
the field of view of the camera!

Similarly scaling after translation also moves an object unexpectedly. If you
scale after you translate the scale will multiply the translate amount. For
example

  translate <5, 6, 7>
  scale 4


will translate to <20,24,28> instead of < 5,6,7>. Be careful when
transforming to get the order correct for your purposes.

7.3.3            Transform Identifiers

At times it is useful to combine together several transformations and apply
them in multiple places. A transform identifier may be used for this purpose.
Transform identifiers are declared as follows:

  #declare IDENT = transform { TRANSFORMATION... }


Where IDENT is the identifier to be declared and TRANSFORMATION is one or
more translate, rotate, scale or matrix specifications or a previously
declared transform identifier. A transform identifier is invoked by the
transform keyword without any brackets as shown here:

  object {
    MyObject           // Get a copy of MyObject
    transform MyTrans  // Apply the transformation
    translate -x*5     // Then move it 5 units left
  }
  object {
    MyObject           // Get another copy of MyObject
    transform MyTrans  // Apply the same transformation
    translate -x*5     // Then move this one 5 units right
  }


On extremely complex CSG objects with lots of components it may speed up
parsing if you apply a declared transformation rather than the individual
translate, rotate, scale or matrix specifications. The transform is attached
just once to each component. Applying each individual translate, rotate,
scale or matrix specifications takes long. This only affects parsing -
rendering works the same either way.

7.3.4            Transforming Textures and Objects

When an object is transformed all textures attached to the object at that
time are transformed as well. This means that if you have a translate,
rotate, scale or matrix in an object before a texture the texture will not be
transformed. If the transformation is after the texture then the texture will
be transformed with the object. If the transformation is inside the texture
statement then only the texture is affected. The shape remains the same. For
example:

  sphere { 0, 1
    texture { Jade }  // texture identifier from TEXTURES.INC
    scale 3           // this scale affects both the
                      // shape and texture
  }

  sphere { 0, 1
    scale 3           // this scale affects the shape only
    texture { Jade }
  }

  sphere { 0, 1
    texture {
      Jade
      scale 3         // this scale affects the texture only
    }
  }


Transformations may also be independently applied to pigment patterns and
surface normal patterns. Note that scaling a normal pattern affects only the
width and spacing. It does not affect the apparent height or depth of the
bumps. For example:

  box { <0, 0, 0>, <1, 1, 1>
    texture {
      pigment {
        checker Red, White
        scale 0.25 // This affects only the color pattern
      }
      normal {
        bumps 0.3  // This specifies apparent height of bumps
        scale 0.2  // Scales diameter and space between bumps
                   // but not the height. Has no effect on
                   // color pattern.
      }
      rotate y*45  // This affects the entire texture but
    }              // not the object.
  }


7.4              Camera

The camera definition describes the position, projection type and properties
of the camera viewing the scene. Its syntax is:

  camera {
    [ perspective | orthographic | fisheye |
      ultra_wide_angle | omnimax | panoramic |
      cylinder FLOAT ]
    location <VECTOR>
    look_at <VECTOR>
    right <VECTOR>
    up <VECTOR>
    direction <VECTOR>
    sky <VECTOR>
    right <VECTOR>
    angle FLOAT
    blur_samples FLOAT
    aperture FLOAT
    focal_point <VECTOR>
    normal { NORMAL }
  }


Depending on the projection type some of the parameters are required, some
are optional and some aren't used. If no projection type is given the
perspective camera will be used (pinhole camera). If no camera is specified a
default camera is used.

Regardless of the projection type all cameras use the location, look_at,
right, up, direction and sky keywords to determine the location and
orientation of the camera. Their meaning differs with the projection type
used. A more detailed explanation of the camera placement follows later.

7.4.1            Type of Projection

The following list explains the different projection types that can be used
with the camera. The most common types are the perspective and orthographic
projections.

Perspective projection: This projection represents the classic pinhole
camera. The (horizontal) viewing angle is either determined by the ratio
between the length of the direction vector and the length of the right vector
or by the optional keyword angle, which is the preferred way. The viewing
angle has to be larger than 0 degrees and smaller than 180 degrees. See the
figure below for the geometry of the perspective camera.

The perspective camera.

Orthographic projection: This projection uses parallel camera rays to create
an image of the scene. The size of the image is determined by the lengths of
the right and up vectors.

If you add the orthographic keyword after all other parameters of a
perspective camera you'll get an orthographic view with the same image area,
i.e. the size of the image is the same. In this case you needn't specify the
lengths of the right and up vector because they'll be calculated
automatically. You should be aware though that the visible parts of the scene
change when switching from perspective to orthographic view. As long as all
objects of interest are near the look_at location they'll be still visible if
the orthographic camera is used. Objects farther away may get out of view
while nearer objects will stay in view.

Fisheye projection: This is a spherical projection. The viewing angle is
specified by the angle keyword. An angle of 180 degrees creates the
"standard" fisheye while an angle of 360 degrees creates a super-fisheye
("I-see-everything-view"). If you use this projection you should get a
circular image. If this isn't the case, i.e. you get an elliptical image, you
should read "Aspect Ratio".

Ultra wide angle projection: This projection is somewhat similar to the
fisheye but it projects the image onto a rectangle instead of a circle. The
viewing angle can be specified using the angle keyword.

Omnimax projection: The omnimax projection is a 180 degrees fisheye that has
a reduced viewing angle in the vertical direction. In reality this projection
is used to make movies that can be viewed in the dome-like Omnimax theaters.
The image will look somewhat elliptical. The angle keyword isn't used with
this projection.

Panoramic projection: This projection is called "cylindrical equirectangular
projection". It overcomes the degeneration problem of the perspective
projection if the viewing angle approaches 180 degrees. It uses a type of
cylindrical projection to be able to use viewing angles larger than 180
degrees with a tolerable lateral-stretching distortion. The angle keyword is
used to determine the viewing angle.

Cylindrical projection: Using this projection the scene is projected onto a
cylinder. There are four different types of cylindrical projections depending
on the orientation of the cylinder and the position of the viewpoint. The
viewing angle and the length of the up or right vector determine the
dimensions of the camera and the visible image. The camera to use is
specified by a number. The types are:

  4 horizontal cylinder, viewpoint moves along the cylinder's axis


If the perspective camera is used the angle keyword overrides the viewing
angle specified by the direction keyword and vice versa. Each time angle is
used the length of the direction vector is adjusted to fit the new viewing
angle.

There is no limitation to the viewing angle except for the perspective
projection. If you choose viewing angles larger than 360 degrees you'll see
repeated images of the scene (the way the repetition takes place depends on
the camera). This might be useful for special effects.

You should note that the vista buffer can only be used with the perspective
and orthographic camera.

7.4.2            Focal Blur

Simulates focal depth-of-field by shooting a number of sample rays from
jittered points within each pixel and averaging the results.

The aperture keyword determines the depth of the sharpness zone. Large
apertures give a lot of blurring, while narrow apertures will give a wide
zone of sharpness. Note that, while this behaves as a real camera does, the
values for aperture are purely arbitrary and are not related to f-stops.

The center of the zone of sharpness is the focal_point vector (the default
focal_point is <0,0,0>).

The blur_samples value controls the maximum number of rays to use for each
pixel. More rays give a smoother appearance but is slower, although this is
controlled somewhat by an adaptive mechanism that stops shooting rays when a
certain degree of confidence has been reached that shooting more rays would
not result in a significant change.

The confidence and variance keywords control the adaptive function. The
confidence value is used to determine when the samples seem to be close
enough to the correct color. The variance value specifies an acceptable
tolerance on the variance of the samples taken so far. In other words, the
process of shooting sample rays is terminated when the estimated color value
is very likely (as controlled by the confidence probability) near the real
color value.

Since the confidence is a probability its values can range from 0 to 1 (the
default is 0.9, i. e. 90%). The value for the variance should be in the range
of the smallest displayable color difference (the default is 1/128).

Larger confidence values will lead to more samples, slower traces and better
images. The same holds for smaller variance thresholds.

By default no focal blur is used, i. e. the default aperture is 0 and the
default number of samples is 0.

7.4.3            Camera Ray Perturbation

The optional keyword normal may be used to assign a normal pattern to the
camera. All camera rays will be perturbed using this pattern. This lets you
create special effects. See the animated scene camera2.pov for an example.

7.4.4            Placing the Camera

In the following sections the placing of the camera will be further
explained.

7.4.4.1          Location and Look_At

Under many circumstances just two vectors in the camera statement are all you
need to position the camera: location and look_at. For example:

  camera {
    location <3,5,-10>
    look_at  <0,2,1>
  }


The location is simply the x, y, z coordinates of the camera. The camera can
be located anywhere in the ray-tracing universe. The default location is <0,
0, 0>. The look_at vector tells POV-Ray to pan and tilt the camera until it
is looking at the specified x, y, z coordinates. By default the camera looks
at a point one unit in the z-direction from the location.

The look_at specification should almost always be the last item in the camera
statement. If other camera items are placed after the look_at vector then the
camera may not continue to look at the specified point.

7.4.4.2          The Sky Vector

Normally POV-Ray pans left or right by rotating about the y-axis until it
lines up with the look_at point and then tilts straight up or down until the
point is met exactly. However you may want to slant the camera sideways like
an airplane making a banked turn. You may change the tilt of the camera using
the sky vector. For example:

  camera {
    location <3,5,-10>
    sky      <1,1,0>
    look_at  <0,2,1>
  }


This tells POV-Ray to roll the camera until the top of the camera is in line
with the sky vector. Imagine that the sky vector is an antenna pointing out
of the top of the camera. Then it uses the sky vector as the axis of rotation
left or right and then to tilt up or down in line with the sky vector. In
effect you're telling POV-Ray to assume that the sky isn't straight up. Note
that the sky vector must appear before the look_at vector.

The sky vector does nothing on its own. It only modifies the way the look_at
vector turns the camera. The default value for sky is <0, 1, 0>.

7.4.4.3          The Direction Vector

The direction vector tells POV-Ray the initial direction to point the camera
before moving it with look_at or rotate vectors (the default is direction <0,
0, 1>). It may also be used to control the (horizontal) field of view with
some types of projection. This should be done using the easier to use angle
keyword though.

If you are using the ultra wide angle, panoramic or cylindrical projection
you should use a unit length direction vector to avoid strange results.

The length of the direction vector doesn't matter if one of the following
projection types is used: orthographic, fisheye or omnimax.

7.4.4.4          Angle

The angle keyword specifies the (horizontal) viewing angle in degrees of the
camera used. Even though it is possible to use the direction vector to
determine the viewing angle for the perspective camera it is much easier to
use the angle keyword.

The necessary calculations to convert from one method to the other are
described below. These calculations are used to determine the length of the
direction vector whenever the angle keyword is encountered.

The viewing angle is converted to a direction vector length and vice versa
using the formula The viewing angle is given by the formula

  angle = 2 * arctan(0.5 * right_length / direction_length)


where right_length and direction_length are the lengths of the right and
direction vector respectively and arctan is the inverse tangens function.

From this the length of the direction vector can be calculated for a given
viewing angle and right vector.

From this the length of the direction vector can be calculated for a given
viewing angle and right vector.

  direction_length = 0.5 * right_length / tan(angle / 2)


7.4.4.5          Up and Right Vectors

The direction of the up and right vectors (together with the direction
vector) determine the orientation of the camera in the scene. They are set
implicitly by their default values of

  right 4/3*x
  up y


or the look_at parameter (in combination with location). The directions of an
explicitly specified right and up vector will be overridden by any following
look_at parameter.

While some camera types ignore the length of these vectors others use it to
extract valuable information about the camera settings. The following list
will explain the meaning of the right and up vector for each camera type.
Since the direction the vectors is always used to describe the orientation of
the camera it will not be explained again.

Perspective projection: The lengths of the up and right vectors are used to
set the size of the viewing window and the aspect ratio as described in
detail in section "Aspect Ratio". Since the field of view depends on the
length of the direction vector (implicitly set by the angle keyword or
explicitly set by the direction keyword) and the lengths of the right and up
vectors you should carefully choose them in order to get the desired results.


Orthographic projection: The lengths of the right and up vector set the size
of the viewing window regardless of the direction vector length, which is not
used by the orthographic camera. Again the relation of the lengths is used to
set the aspect ratio.

Fisheye projection: The right and up vectors are used to set the aspect
ratio.

Ultra wide angle projection: The up and right vectors work in a similar way
as for the perspective camera.

Omnimax projection: The omnimax projection is a 180 degrees fisheye that has
a reduced viewing angle in the vertical direction. In reality this projection
is used to make movies that can be viewed in the dome-like Omnimax theaters.
The image will look somewhat elliptical. The angle keyword isn't used with
this projection.

Panoramic projection: The up and right vectors work in a similar way as for
the perspective camera.

Cylindrical projection: In cylinder type 1 and 3 the axis of the cylinder
lies along the up vector and the width is determined by the length of right
vector or it may be overridden with the angle vector. In type 3 the up vector
determines how many units high the image is. For example if you have up 4*y
on a camera at the origin. Only points from y=2 to y=-2 are visible. All
viewing rays are perpendicular to the y-axis. For type 2 and 4, the cylinder
lies along the right vector. Viewing rays for type 4 are perpendicular to the
right vector.

Note that the up, right and direction vectors should always remain
perpendicular to each other or the image will be distorted. If this is not
the case a warning message will be printed. The vista buffer will not work
for non-perpendicular camera vectors.

7.4.4.5.1        Aspect Ratio

Together the right and up vectors define the aspect ratio (height to width
ratio) of the resulting image. The default values up  <0, 1, 0> and right
<1.33, 0,  0> result in an aspect ratio of 4 to 3. This is the aspect ratio
of a typical computer monitor. If you wanted a tall skinny image or a short
wide panoramic image or a perfectly square image you should adjust the up and
right vectors to the appropriate proportions.

Most computer video modes and graphics printers use perfectly square pixels.
For example Macintosh displays and IBM SVGA modes 640x480, 800x600 and
1024x768 all use square pixels. When your intended viewing method uses square
pixels then the width and height you set with the +W and +H switches should
also have the same ratio as the right and up vectors. Note that 640/480 = 4/3
so the ratio is proper for this square pixel mode.

Not all display modes use square pixels however. For example IBM VGA mode
320x200 and Amiga 320x400 modes do not use square pixels. These two modes
still produce a 4/3 aspect ratio image. Therefore images intended to be
viewed on such hardware should still use 4/3 ratio on their up and right
vectors but the +W and +H settings will not be 4/3.

For example:

  camera {
    location <3,5,-10>
    up       <0,1,0>
    right    <1,0,0>
    look_at  <0,2,1>
  }


This specifies a perfectly square image. On a square pixel display like SVGA
you would use +W and +H settings such as +W480 +H480 or +W600 +H600. However
on the non-square pixel Amiga 320x400 mode you would want to use values of
+W240 +H400 to render a square image.

7.4.4.5.2        Handedness

The right vector also describes the direction to the right of the camera. It
tells POV-Ray where the right side of your screen is. The sign of the right
vector can be used to determine the handedness of the coordinate system in
use. The default right statement is:

  right <1.33, 0, 0>


This means that the +x-direction is to the right. It is called a left-handed
system because you can use your left hand to keep track of the axes. Hold out
your left hand with your palm facing to your right. Stick your thumb up.
Point straight ahead with your index finger. Point your other fingers to the
right. Your bent fingers are pointing to the +x-direction. Your thumb now
points into +y-direction. Your index finger points into the +z-direction.

To use a right-handed coordinate system, as is popular in some CAD programs
and other ray-tracers, make the same shape using your right hand. Your thumb
still points up in the +y-direction and your index finger still points
forward in the +z-direction but your other fingers now say the +x-direction
is to the left. That means that the right side of your screen is now in the
-x-direction. To tell POV-Ray to act like this you can use a negative x value
in the right vector like this:

  right <-1.33, 0, 0>


Since x increasing to the left doesn't make much sense on a 2D screen you now
rotate the whole thing 180 degrees around by using a positive z value in your
camera's location. You end up with something like this.

  camera {
    location <0,0,10>
    up       <0,1,0>
    right    <-1.33,0,0>
    look_at  <0,0,0>
  }


Now when you do your ray-tracer's aerobics, as explained in the section
"Understanding POV-Ray's Coordinate System", you use your right hand to
determine the direction of rotations.

In a two dimensional grid, x is always to the right and y is up. The two
versions of handedness arise from the question of whether z points into the
screen or out of it and which axis in your computer model relates to up in
the real world.

Architectural CAD systems, like AutoCAD, tend to use the God's  Eye
orientation that the z-axis is the elevation and is the model's up direction.
This approach makes sense if you're an architect looking at a building
blueprint on a computer screen. z means up, and it increases towards you,
with x and y still across and up the screen. This is the basic right handed
system.

Stand alone rendering systems, like POV-Ray, tend to consider you as a
participant. You're looking at the screen as if you were a photographer
standing in the scene. Up in the model is now y, the same as up in the real
world and x is still to the right, so z must be depth, which increases away
from you into the screen. This is the basic left handed system.

7.4.4.6          Transforming the Camera

The translate and rotate commands can re-position the camera once you've
defined it. For example:

  camera {
    location  < 0,  0,  0>
    direction < 0,  0,  1>
    up        < 0,  1,  0>
    right     < 1,  0,  0>
    rotate    <30, 60, 30>
    translate < 5,  3,  4>
  }


In this example, the camera is created, then rotated by 30 degrees about the
x-axis, 60 degrees about the y-axis and 30 degrees about the z-axis, then
translated to another point in space.

7.4.5            Camera Identifiers

You may declare several camera identifiers if you wish. This makes it easy to
quickly change cameras. For example:

  #declare Long_Lens =
    camera {
      location -z*100
      angle 3
    }

  #declare Short_Lens =
    camera {
      location -z*50
      angle 15
    }

  camera {
    Long_Lens    // edit this line to change lenses
    look_at Here
  }


7.5              Objects

Objects are the building blocks of your scene. There are a lot of different
types of objects supported by POV-Ray: finite solid primitives, finite patch
primitives, infinite solid polynomial primitives and light sources.
Constructive Solid Geometry (CSG) is also supported.

The basic syntax of an object is a keyword describing its type, some floats,
vectors or other parameters which further define its location and/or shape
and some optional object modifiers such as texture, pigment, normal, finish,
bounding, clipping or transformations.

The texture describes what the object looks like, i. e. its material.
Textures are combinations of pigments, normals, finishes and halos. Pigment
is the color or pattern of colors inherent in the material. Normal is a
method of simulating various patterns of bumps, dents, ripples or waves by
modifying the surface normal vector. Finish describes the reflective and
refractive properties of a material. The halo is used to describe the
interior of the object.

Bounding shapes are finite, invisible shapes which wrap around complex, slow
rendering shapes in order to speed up rendering time. Clipping shapes are
used to cut away parts of shapes to expose a hollow interior. Transformations
tell the ray-tracer how to move, size or rotate the shape and/or the texture
in the scene.

7.5.1            Empty and Solid Objects

It is very important that you know the basic concept behind empty and solid
objects in POV-Ray to fully understand how features like halos and
translucency are used.

Objects in POV-Ray can either be solid, empty or filled with (small)
particles.

A solid object is made from the material specified by its pigment and finish
statements (and to some degree its normal statement). By default all objects
are assumed to be solid. If you assign a stone texture to a sphere you'll get
a ball made completely of stone. It's like you had cut this ball from a block
of stone. A glass ball is a massive sphere made of glass.

You should be aware that solid objects are conceptual things. If you e. g.
clip away parts of the sphere you'll see that the sphere is empty, i. e.
you'll clearly see that the interior is empty and it just has a very thin
surface.

This is not contrary to the concept of a solid object used in POV-Ray. It is
assumed that all space inside the sphere is covered by the sphere's material.
Thus there is no room for any other particles like those used by fog or
halos.

Empty objects are created by adding the hollow keyword (see "Hollow") to the
object statement. An empty (or hollow) object is assumed to be made of a very
thin surface which is of the material specified by the pigment, finish and
normal statements. The object's interior is empty, i. e. it normally contains
air molecules.

An empty object can be filled with particles by adding fog or atmosphere to
the scene or by adding a halo to the object. It is very important to
understand that in order to fill an object with any kind of particles it
first has to be made hollow.

7.5.1.1          Halo Pitfall

There is a pitfall in the current empty/solid object implementation that you
have to be aware of.

In order to be able to put solid objects inside a halo (this also holds for
fog and atmosphere) a test has to be made for every ray that passes through
the halo. If this ray travels through a solid object the halo will not be
calculated. This is what anyone will expect.

The problem arises when the camera ray is inside any non-hollow object. In
this case the ray is already traveling through a solid object and even if the
halo's container object is hit and it is hollow, the halo will not be
calculated. There is no way of telling between these two cases.

POV-Ray has to determine whether the camera is inside any object prior to
tracing a camera ray in order to be able to correctly render halos when the
camera is inside the container object. There's no way around doing this.

The solution to this problem (that will often happen with infinite objects
like planes) is to make those objects hollow too. Thus the ray will travel
through a hollow object, will hit the container object and the halo will be
calculated.


7.5.1.2          Refraction Pitfall

There is a pitfall in the way refractive (and non-refractive translucent)
objects are handled.

Imagine you want to create an object that's partially made of glass and
stone. You'd use something like the following merge because you don't want to
see any inside surfaces.

  merge {
    sphere { <-1,0,0>, 2 texture { Stone } }
    sphere { <+1,0,0>, 2 texture { Glass } }
  }


What's wrong with this, you may ask? The problem is that there is no way of
telling what the interior of the actual object will look like. This is not a
problem of POV-Ray, it's a general problem. You can't define the interior of
any object in a surface based model. You would have to create some (complex)
rules to decide what the interior will look like. Is it made of stone? Is it
made of glass? Is it made of some bizarre mixture between glass and stone? Is
it half stone and half glass? Where is the boundary between the two materials
and what does it look like?

You will not be able to answer any of the above questions by just looking at
the above object. You need more information.

If you wanted to create an object made half of stone and half of glass you
would have used the following statements.

  union {
    intersection {
      sphere { <-1,0,0>, 2 }
      plane { x, 0 }
      texture { Stone }
    }
    intersection {
      sphere { <+1,0,0>, 2 }
      plane { x, 0 inverse }
      texture { Glass }
    }
  }


This example is correct because there is one object made only of stone and
one made only of glass.

You should never use objects whose interior is not well defined, i. e. there
must not be different textures for the object having different refractive
(and translucent) properties. You should be aware that this holds only for
the lowest layer if you use layered textures.


7.5.2            Finite Solid Primitives

There are twelve different solid finite primitive shapes: blob, box, cone,
cylinder, fractal, height field, lathe, sphere, superellipsoid, surface of
revolution, text object and torus. These have a well-defined inside and can
be used in CSG (see section "Constructive Solid Geometry"). They are finite
and respond to automatic bounding. As with all shapes they can be translated,
rotated and scaled.

7.5.2.1          Blob

Blobs are an interesting and flexible object type. Mathematically they are
iso-surfaces of scalar fields, i. e. their surface is defined by the strength
of the field in each point. If this strength is equal to a threshold value
you're on the surface otherwise you're not.

Picture each blob component as an object floating in space. This object is
filled with a field that has its maximum at the center of the object and
drops off to zero at the object's surface. The field strength of all those
components are added together to form the field of the blob. Now POV-Ray
looks for points where this field has a given value, the threshold value. All
these points form the surface of the blob object. Points with a greater field
value than the threshold value are considered to be inside while points with
a smaller field value are outside.

There's another, simpler way of looking at blobs. They can be seen as a union
of flexible components that attract or repel each other to form a blobby
organic looking shape. The components' surfaces actually stretch out smoothly
and connect as if they were made of honey or something like that.

A blob is made up of spherical and cylindrical components and is defined as
follows:

  blob {
    threshold THRESHOLD_VALUE
    cylinder { <END1>, <END2>, RADIUS, [ strength ] STRENGTH }
    sphere { <CENTER>, RADIUS, [ strength ] STRENGTH }
    [ component STRENGTH, RADIUS, <CENTER> ]
    [ hierarchy FLAG ]
    [ sturm ]
  }


The threshold keyword determines the total field strength value that POV-Ray
is looking for. By following the ray out into space and looking at how each
blob component affects the ray, POV-Ray will find the points in space where
the field strength is equal to the threshold value. The following list shows
some things you should know about the threshold value.

  2)A component disappears if the threshold value is greater than its
  3)As the threshold value gets larger the surface you see gets closer to the
  4)As the threshold value gets smaller, the surface you see gets closer to
    the surface of the components.


Cylindrical components are specified by the keyword cylinder giving a
cylinder formed by the base <END1>, the apex <END2> and the radius. The
cylinder has hemispherical caps at the base and apex. Spherical components
are specified by the keyword sphere forming a sphere at <CENTER> with the
given radius. Each component can be individually translated, rotated, scaled
and textured. The complete syntax for the cylindrical and spherical
components is:

  sphere { <CENTER>, RADIUS, [strength] STRENGTH
    [ translate <VECTOR> ]
    [ rotate <VECTOR> ]
    [ scale <VECTOR> ]
    TEXTURE_MODIFIERS
  }

  cylinder { <END1>, <END2>, RADIUS, [strength] STRENGTH
    [ translate <VECTOR> ]
    [ rotate <VECTOR> ]
    [ scale <VECTOR> ]
    TEXTURE_MODIFIERS
  }


By unevenly scaling a spherical component you can create ellipsoidal
components. The component keyword gives a spherical component and is only
used for compatibility with earlier POV-Ray versions.

The strength parameter is a float value specifying the field strength at the
center of the object. The strength may be positive or negative. A positive
value will make that component attract other components while a negative
value will make it repel other components. Components in different, separate
blob shapes do not affect each other.

You should keep the following things in mind.

  1)The strength value may be positive or negative. Zero is a bad value, as
    the net result is that no field was added --- you might just as well have
  2)If strength is positive, then POV-Ray will add the component's field to
    the space around the center of the component. If this adds enough field
  3)If the strength value is negative, then POV-Ray will subtract thesurface.
    component's field from the space around the center of the component. This
    will only do something if there happen to be positive components nearby.
    What happens is that the surface around any nearby positive components
    will be dented away from the center of the negative component.


The components of each blob object are internally bounded by a spherical
bounding hierarchy to speed up blob intersection tests and other operations.
By using the optional keyword hierarchy you can switch this hierarchy off.

An example of a three component blob is:

  blob {
    threshold 0.6
    sphere { <.75, 0, 0>, 1, 1 }
    sphere { <-.375, .64952, 0>, 1, 1 }
    sphere { <-.375, -.64952, 0>, 1, 1 }
    scale 2
  }


If you have a single blob component then the surface you see will just look
like the object used, i. e. a sphere or a cylinder, with the surface being
somewhere inside the surface specified for the component. The exact surface
location can be determined from the blob equation listed below (you will
probably never need to know this, blobs are more for visual appeal than for
exact modeling).

For the more mathematically minded, here's the formula used internally by
POV-Ray to create blobs. You don't need to understand this to use blobs. The
formula used for a single blob component is:

  density = strength * (1 - radius^2)^2


This formula has the nice property that it is exactly equal to the strength
parameter at the center of the component and drops off to exactly 0 at a
distance from the center of the component that is equal to the radius value.
The density formula for more than one blob component is just the sum of the
individual component densities:


  density = density1 + density2 + ...


The calculations for blobs must be very accurate. If this shape renders
improperly you may add the keyword sturm after the last component to use
POV-Ray's slower-yet-more-accurate Sturmian root solver.

7.5.2.2          Box

A simple box can be defined by listing two corners of the box like this:

  box { <CORNER1>, <CORNER2> }


The geometry of a box.

Where <CORNER1> and <CORNER2> are vectors defining the x, y, z coordinates of
the opposite corners of the box.

Note that all boxes are defined with their faces parallel to the coordinate
axes. They may later be rotated to any orientation using the rotate keyword.

Each element of <CORNER1> should always be less than the corresponding
element in <CORNER2>. If any elements of <CORNER1> are larger than <CORNER2>
the box will not appear in the scene.

Boxes are calculated efficiently and make good bounding shapes (if manually
bounding seems to be necessary).

7.5.2.3          Cone

A finite length cone or a frustum (a cone with the point cut off) may be
defined by.

  cone {
    <BASE_POINT>, BASE_RADIUS, <CAP_POINT>, CAP_RADIUS
    [ open ]
  }


The geometry of a cone.

Where <BASE_POINT> and < CAP_POINT> are vectors defining the x, y, z
coordinates of the center of the cone's base and cap and BASE_RADIUS and
CAP_RADIUS are float values for the corresponding radii.

Normally the ends of a cone are closed by flat planes which are parallel to
each other and perpendicular to the length of the cone. Adding the optional
keyword open after CAP_RADIUS will remove the end caps and results in a
tapered hollow tube like a megaphone or funnel.

7.5.2.4          Cylinder

A finite length cylinder with parallel end caps may be defined by.

  cylinder {
    <BASE_POINT>, <CAP_POINT>, RADIUS
    [ open ]
  }


The geometry of a cylinder.

Where <BASE_POINT> and < CAP_POINT> are vectors defining the x, y, z
coordinates of the cylinder's base and cap and RADIUS is a float value for
the radius.

Normally the ends of a cylinder are closed by flat planes which are parallel
to each other and perpendicular to the length of the cylinder. Adding the
optional keyword open after the radius will remove the end caps and results
in a hollow tube.

7.5.2.5          Height Field

Height fields are fast, efficient objects that are generally used to create
mountains or other raised surfaces out of hundreds of triangles in a mesh.
The height field syntax is:

  height_field {
    FILE_TYPE "FILENAME"
    [ hierarchy BOOL ]
    [ smooth BOOL ]
    [ water_level FLOAT ]
  }


A height field is essentially a one unit wide by one unit long square with a
mountainous surface on top. The height of the mountain at each point is taken
from the color number or palette index of the pixels in a graphic image file.
The maximum height is one, which corresponds to the maximum possible color or
palette index value in the image file.

        ________  <---- image index 255 (or 65535 for 16-bit images)
      /        /|
+1y  ---------- |
     |        | |
     |        | |+1z <- Image upper-right
     |        | /
0,0,0---------- +1x
     ^
     |____ Image lower-left
The size and orientation of an un-scaled height field.

The mesh of triangles corresponds directly to the pixels in the image file.
Each square formed by four neighboring pixels is divided into two triangles.
An image with a resolution of N*M pixels has (N-1)*(M-1) squares that are
divided into 2*(N-1)*(M-1) triangles.

Four pixels of an image and the resulting heights and triangles in the height
field.

The resolution of the height field is influenced by two factors: the
resolution of the image and the resolution of the color/index values. The
size of the image determines the resolution in the x- and z-direction. A
larger image uses more triangles and looks smoother. The resolution of the
color/index value determines the resolution along the y-axis. A height field
made from an 8 bit image can have 256 different height levels while one made
from a 16 bit image can have up to 65536 different height levels. Thus the
second height field will look much smoother in the y-direction if the height
field is created appropriately.

The size/resolution of the image does not affect the size of the height
field. The un-scaled height field size will always be 1* 1. Higher resolution
image files will create smaller triangles, not larger height fields.

There are six or possibly seven types of files which can define a
heightfield, as follows:

  height_field { gif "filename.gif" }
  height_field { pgm "filename.pgm" }
  height_field { png "filename.png" }
  height_field { pot "filename.pot" }
  height_field { ppm "filename.ppm" }
  height_field { sys "filename.???" }
  height_field { tga "filename.tga" }


The image file used to create a height field can be a GIF, TGA, POT, PNG,
PGM, PPM and possibly a system specific (e. g. Windows BMP or Macintosh Pict)
format file. The GIF, PNG, PGM and possibly system format files are the only
ones that can be created using a standard paint program. Though there are
paint programs for creating TGA image files they won't be of much use for
creating the special 16 bit TGA files used by POV-Ray (see below and
"HF_Gray_16" for more details).

In an image file like GIF that uses a color palette the color number is the
palette index at a given pixel. Use a paint program to look at the palette of
a GIF image. The first color is palette index zero, the second is index one,
the third is index two and so on. The last palette entry is index 255.
Portions of the image that use low palette entries will result in lower parts
of the height field. Portions of the image that use higher palette entries
will result in higher parts of the height field.

Height fields created from GIF files can only have 256 different height
levels because the maximum number of colors in a GIF file is 256.

The color of the palette entry does not affect the height of the pixel. Color
entry 0 could be red, blue, black or orange but the height of any pixel that
uses color entry 0 will always be 0. Color entry 255 could be indigo, hot
pink, white or sky blue but the height of any pixel that uses color entry 255
will always be 1.

You can create height field GIF images with a paint program or a fractal
program like Fractint. You can usually get Fractint from most of the same
sources as POV-Ray.

A POT file is essentially a GIF file with a 16 bit palette. The maximum
number of colors in a POT file is 65536. This means a POT height field can
have up to 65536 possible height values. This makes it possible to have much
smoother height fields. Note that the maximum height of the field is still 1
even though more intermediate values are possible.

At the time of this writing the only program that created POT files was a
freeware IBM-PC program called Fractint. POT files generated with this
fractal program create fantastic landscapes.

The TGA and PPM file formats may be used as a storage device for 16 bit
numbers rather than an image file. These formats use the red and green bytes
of each pixel to store the high and low bytes of a height value. These files
are as smooth as POT files but they must be generated with special
custom-made programs. Several programs can create TGA heightfields in the
format POV uses, such as gforge and Terrain Maker.

PNG format heightfields are usually stored in the form of a grayscale image
with black corresponding to lower and white to higher parts of the height
field. Because PNG files can store up to 16 bits in grayscale images they
will be as smooth as TGA and PPM images. Since they are grayscale images you
will be able to view them with a regular image viewer. gforge can create
16-bit heightfields in PNG format. Color PNG images will be used in the same
way as TGA and PPM images.

SYS format is a platform specific file format. See your platform specific
documentation for details.

An optional water_level parameter may be added after the file name. It
consists of the keyword water_level followed by a float value telling the
program to ignore parts of the height field below that value. The default
value is zero and legal values are between zero and one. For example
water_level .5 tells POV-Ray to only render the top half of the height field.
The
other half is below the water and couldn't be seen anyway. This term comes
from the popular use of height fields to render landscapes. A height field
would be used to create islands and another shape would be used to simulate
water around the islands. A large portion of the height field would be
obscured by the water so the water_level parameter was introduced to allow
the ray-tracer to ignore the unseen parts of the height field. water_level is
also used to cut away unwanted lower values in a height field. For example if
you have an image of a fractal on a solid colored background, where the
background color is palette entry 0, you can remove the background in the
height field by specifying, water_level .001.

Normally height fields have a rough, jagged look because they are made of
lots of flat triangles. Adding the keyword smooth causes POV-Ray to modify
the surface normal vectors of the triangles in such a way that the lighting
and shading of the triangles will give a smooth look. This may allow you to
use a lower resolution file for your height field than would otherwise be
needed. However, smooth triangles will take longer to render.

In order to speed up the intersection tests an one-level bounding hierarchy
is available. By default it is always used but it can be switched off to
eventually improve the rendering speed for small height fields (i. e. low
resolution images).

7.5.2.6          Julia Fractal

A julia fractal object is a 3-D slice of a 4-D object created by generalizing
the process used to create the classic Julia sets. You can make a wide
variety of strange objects using julia_fractal, including some that look like
bizarre blobs of twisted taffy.

The julia_fractal syntax (with default values listed in comments) is:

  julia_fractal {
    4DJULIA_PARAMETER                 // default is <1,0,0,0>
    [ quaternion | hypercomplex ]     // default is quaternion
    [ sqr | cube | exp |
      reciprocal | sin | asin |
      sinh | asinh | cos | acos |
      cosh | acosh | tan | atan |
      tanh | atanh | log | pwr(X,Y) ] // default is sqr
    [ max_iteration MAX_ITERATION ]   // default value 20
    [ precision PRECISION ]           // default value 20
    [ slice 4DNORMAL, DISTANCE ]      // default <0,0,0,1>,0
  }


The 4-D vector 4DJULIA_PARAMETER is the classic Julia parameter p in the
iterated formula f(h) + p.

The julia fractal object is calculated by using an algorithm that determines
whether an arbitrary point h(0) in 4-D space is inside or outside the object.
The algorithm requires generating the sequence of vectors h(0), h(1), ... by
iterating the formula

  h(n+1) = f(h(n)) + p (n = 0, 1, ..., max_iteration-1)


where p is the fixed 4-D vector parameter of the julia fractal and f() is one
of the functions sqr, cube, ... specified by the presence of the
corresponding keyword. The point h(0) that begins the sequence is considered
inside the julia fractal object if none of the vectors in the sequence
escapes a hypersphere of radius 4 about the origin before the iteration
number reaches the max_iteration value. As you increase max_iteration, some
points escape that did not previously escape, forming the julia fractal.
Depending on the JULIA_PARAMETER, the julia fractal object is not necessarily
connected; it may be scattered fractal dust. Using a low max_iteration can
fuse together the dust to make a solid object. A high max_iteration is more
accurate but slows rendering. Even though it is not accurate, the solid
shapes you get with a low_maximum iteration value can be quite interesting.

Since the mathematical object described by this algorithm is four-dimensional
and POV-Ray renders three dimensional objects, there must be a way to reduce
the number of dimensions of the object from four dimensions to three. This is
accomplished by intersecting the 4-D fractal with a 3-D plane defined by the
slice field and then projecting the intersection to 3-D space. The slice
plane is the 3-D space that is perpendicular to NORMAL4D and is DISTANCE
units from the origin. Zero length NORMAL4D vectors or a NORMAL4D vector with
a zero fourth component are illegal.

You can get a good feel for the four dimensional nature of a julia fractal by
using POV-Ray's animation feature to vary a slice's DISTANCE parameter. You
can make the julia fractal appear from nothing, grow, then shrink to nothing
as DISTANCE changes, much as the cross section of a 3-D object changes as it
passes through a plane.

The precision parameter is a tolerance used in the determination of whether
points are inside or outside the fractal object. Larger values give more
accurate results but slower rendering. Use as low a value as you can without
visibly degrading the fractal object's appearance.

The presence of the keywords quaternion or hypercomplex determine which 4-D
algebra is used to calculate the fractal. Both are 4-D generalizations of the
complex numbers but neither satisfies all the field properties (all the
properties of real and complex numbers that many of us slept through in high
school). Quaternions have non-commutative multiplication and hypercomplex
numbers can fail to have a multiplicative inverse for some non-zero elements
(it has been proved that you cannot successfully generalize complex numbers
to four dimensions with all the field properties intact, so something has to
break). Both of these algebras were discovered in the 19th century. Of the
two, the quaternions are much better known, but one can argue that
hypercomplex numbers are more useful for our purposes, since complex valued
functions such as sin, cos, etc. can be generalized to work for hypercomplex
numbers in a uniform way.

For the mathematically curious, the algebraic properties of these two
algebras can be derived from the multiplication properties of the unit basis
vectors 1 = <1,0,0,0>, i=< 0,1,0,0>, j=<0,0,1,0> and k=< 0,0,0,1>. In both
algebras 1 x = x 1 = x for any x (1 is the multiplicative identity). The
basis vectors 1 and i behave exactly like the familiar complex numbers 1 and
i in both algebras.

Quaternion basis vector multiplication rules:

  ij = k;            jk  = i;   ki = j
  ji = -k;           kj  = -i;  ik = -j
  ii = jj = kk = -1; ijk = -1;


Hypercomplex basis vector multiplication rules:

  ij = k;            jk = -i;   ki = -j
  ji = k;            kj = -i;   ik = -j
  ii = jj = kk = -1; ijk = 1;


A distance estimation calculation is used with the quaternion calculations to
speed them up. The proof that this distance estimation formula works does not
generalize from two to four dimensions but the formula seems to work well
anyway, the absence of proof notwithstanding!

The presence of one of the function keywords sqr, cube, etc. determines which
function is used for f(h) in the iteration formula h(n+1) = f(h(n)) + p. Most
of the function keywords work only if the hypercomplex keyword is present.
Only sqr and cube work with quaternions. The functions are all familiar
complex functions generalized to four dimensions.

  Function Keyword    Maps 4-D value h to:
================================================
  sqr                 h*h
  cube                h*h*h
  exp                 e raised to the power h
  reciprocal          1/h
  sin                 sine of h
  asin                arcsine of h
  sinh                hyperbolic sine of h
  asinh               inverse hyperbolic sine of h
  cos                 cosine of h
  acos                arccosine of h
  cosh                hyperbolic cos of h
  acosh               inverse hyperbolic cosine of h

  tan                 tangent of h
  atan                arctangent of h
  tanh                hyperbolic tangent of h
  atanh               inverse hyperbolic tangent of h
  log                 natural logarithm of h
  pwr(x,y)            h raised to the complex power x+iy


A simple example of a julia fractal object is:

  julia_fractal {
    <-0.083,0.0,-0.83,-0.025>
    quaternion
    sqr
    max_iteration 8
    precision 15
  }


The first renderings of julia fractals using quaternions were done by Alan
Norton and later by John Hart in the '80's. This new POV-Ray implementation
follows Fractint in pushing beyond what is known in the literature by using
hypercomplex numbers and by generalizing the iterating formula to use a
variety of transcendental functions instead of just the classic Mandelbrot
z^2 + c formula. With an extra two dimensions and eighteen functions to work
with, intrepid explorers should be able to locate some new fractal beasties
in hyperspace, so have at it!

7.5.2.7          Lathe

The lathe is an object generated from rotating a two-dimensional curve about
an axis. This curve is defined by a set of points which are connected by
linear, quadratic or cubic spline curves. The syntax is:

  lathe {
    [ linear_spline | quadratic_spline | cubic_spline ]
    NUMBER_OF_POINTS,
    <POINT_1>, <POINT_2>, ..., <POINT_n>
    [ sturm ]
  }


The parameter NUMBER_OF_POINTS determines how many two-dimensional points are
forming the curve. These points are connected by linear, quadratic or cubic
splines as specified by an optional keyword (the default is linear_spline).
Since the curve is not automatically closed, i. e. the first and last points
are not automatically connected, you'll have to do this by your own if you
want a closed curve. The curve thus defined is rotated about the y-axis to
form the lathe object which is centered at the origin.

The following examples creates a simple lathe object that looks like a thick
cylinder, i. e. a cylinder with a thick wall:

  lathe {
    linear_spline
    5,
    <2, 0>, <3, 0>, <3, 5>, <2, 5>, <2, 0>
    pigment {Red}
  }


The cylinder has an inner radius of 2 and an outer radius of 3, giving a wall
width of 1. It's height is 5 and it's located at the origin pointing up, i.
e. the rotation axis is the y-axis. Note that the first and last point are
equal to get a closed curve.

The splines that are used by the lathe and prism objects are a little bit
difficult to understand. The basic concept of splines is to draw a curve
through a given set of points in a determined way. The linear spline is the
simplest spline because it's nothing more than connecting consecutive points
with a line. This means that the curve that is drawn between two points only
depends on those two points. No additional information is taken into account.
Quadratic and cubic splines are different in that they do not only take other
points into account when connecting two points but they also look smoother
and - in the case of the cubic spline - produce smoother transitions at each
point.

Quadratic splines are made of quadratic curves. Each of them connects two
consecutive points. Since those two points (call them second and third point)
are not sufficient to describe a quadratic curve the predecessor of the
second point is taken into account when the curve is drawn. Mathematically
the relationship (their location on the 2-D plane) between the first and
second point determines the slope of the curve at the second point. The slope
of the curve at the third point is out of control. Thus quadratic splines
look much smoother than linear splines but the transitions at each point are
generally not smooth because the slopes on both sides of the point are
different.

Cubic splines overcome the transition problem of quadratic splines because
they also take the fourth point into account when drawing the curve between
the second and third point. The slope at the fourth point is under control
now and allows a smooth transition at each point. Thus cubic splines produce
the most flexible and smooth curves.

You should note that the number of spline segments, i. e. curves between two
points, depends on the spline type used. For linear splines you get n-1
segments connecting the points P[i], i=1,...,n. A quadratic spline gives you
n-2 segments because the last point is only used for determining the slope as
explained above (thus you'll need at least three points to define a quadratic
spline). The same holds for cubic splines where you get n-3 segments with the
first and last point used only for slope calculations (thus needing at least
four points).

If you want to get a closed quadratic and cubic spline with smooth
transitions at the end points you have to make sure that in the cubic case
P[n-1] = P[2] (to get a closed curve), P[n] = P[3] and P[n-2] = P[1] (to
smooth the transition). In the quadratic case P[n-1] = P[1] (to close the
curve) and P[n] = P[2].

The slower but more accurate Sturmian root solver may be used with the
quadratic spline lathe if the shape does not render properly. Since a
quadratic polynomial has to be solved for the linear spline lathe the
Sturmian root solver is not needed. In case of cubic splines the Sturmian
root solver is always used because a 6th order polynomial has to be solved.

7.5.2.8          Prism

The prism is an object generated from sweeping one or more two-dimensional,
closed curves along an axis. These curves are defined by a set of points
which are connected by linear, quadratic or cubic splines.

The syntax for the prism is:

  prism {
    [ linear_sweep | conic_sweep ]
    [ linear_spline | quadratic_spline | cubic_spline ]
    HEIGHT1,
    HEIGHT2,
    TOTAL_NUMBER_OF_POINTS,
    <POINT_1>, <POINT_2>, ..., <POINT_n>
    [ open ]
    [ sturm ]
  }


The prism object allows you to use any number of sub-prisms inside one prism
statement (they are of the same spline and sweep type). Wherever an even
number of sub-prisms overlaps a hole appears.

The syntax of the prism object depends on the type of spline curve used.
Below the syntax of the linear spline prism is given.

  prism {
    linear_spline
    HEIGHT1,
    HEIGHT2,
    TOTAL_NUMBER_OF_POINTS,
    <A_1>, <A_2>, ..., <A_na>, <A_1>,
    <B_1>, <B_2>, ..., <B_nb>, <B_1>,
    <C_1>, <C_2>, ..., <C_nc>, <C_1>,
    ...
  }


Each of the sub-prisms has to be closed by repeating the first point of a
sub-prism at the end of the sub-prism's point sequence. If this is not the
case a warning is issued and the prism is ignored (with linear splines
automatic closing is used). This implies that all points of a prism are
different (except the first and last of course). This applies to all spline
types though the control points of the quadratic and cubic splines can be
arbitrarily chosen.

The last sub-prism of a linear spline prism is automatically closed - just
like the last sub-polygon in the polygon statement - if the first and last
point of the sub-polygon's point sequence are not the same. This make it very
easy to convert between polygons and prisms. Quadratic and cubic splines are
never automatically closed.

The syntax for quadratic spline prisms is:

  prism {
    quadratic_spline
    HEIGHT1,
    HEIGHT2,
    TOTAL_NUMBER_OF_POINTS,
    <CL_A>, <A_1>, <A_2>, ..., <A_na>, <A_1>,
    <CL_B>, <B_1>, <B_2>, ..., <B_nb>, <B_1>,
    <CL_C>, <C_1>, <C_2>, ..., <C_nc>, <C_1>,
    ...
  }


Quadratic spline sub-prisms need an additional control point at the beginning
of each sub-prisms' point sequence to determine the slope at the start of the
curve.

Last but not least the syntax for the cubic spline prism.

  prism {
    cubic_spline
    HEIGHT1,
    HEIGHT2,
    TOTAL_NUMBER_OF_POINTS,
    <CL_A1>, <A_1>, <A_2>, ..., <A_na>, <A_1>, <CL_A2>,
    <CL_B1>, <B_1>, <B_2>, ..., <B_nb>, <B_1>, <CL_B2>,
    <CL_C1>, <C_1>, <C_2>, ..., <C_nc>, <C_1>, <CL_C2>,
    ...
  }


In addition to the closed point sequence each cubic spline sub-prism needs
two control points to determine the slopes at the start and end of the curve.


The parameter TOTAL_NUMBER_OF_POINTS determines how many two-dimensional
points (lying in the x-z-plane) form the curves (this includes all control
points needed for quadratic and cubic splines). The curves are swept along
the y-axis from HEIGHT1 to HEIGHT2 to form the prism object. By default
linear sweeping is used to create the prism, i. e. the prism's walls are
perpendicular to the x-z-plane (the size of the curve does not change during
the sweep). You can also use conic sweeping (conic_sweep) that leads to a
prism with cone-like walls by scaling the curve down during the sweep.

Like cylinders the prism is normally closed. You can remove the caps on the
prism by using the open keyword. If you do so you shouldn't use it with CSG
because the results may get wrong.

The following example creates a simple prism object that looks like a piece
of cake:

  prism {
    linear_sweep
    linear_spline
    0, 1,
    4,
    <-1, 0>, <1, 0>, <0, 5>, <-1, 0>
    pigment {Red}
  }


For an explanation of the spline concept read the description of the lathe
object.

The slower but more accurate Sturmian root solver may be used with the cubic
spline prisms if the shape does not render properly. The linear and quadratic
spline prisms do not need the Sturmian root solver.

7.5.2.9          Sphere

The syntax of the sphere object is:

  sphere {
    <CENTER>, RADIUS
  }


The geometry of a sphere.

Where <CENTER> is a vector specifying the x, y, z coordinates of the center
of the sphere and RADIUS is a float value specifying the radius. Spheres may
be scaled unevenly giving an ellipsoid shape.

Because spheres are highly optimized they make good bounding shapes (if
manual bounding seems to be necessary).

7.5.2.10         Superquadric Ellipsoid

The superquadric ellipsoid is an extension of the quadric ellipsoid. It can
be used to create boxes and cylinders with round edges and other interesting
shapes. Mathematically it is given by the equation:

  f(x, y, z) = (|x|^(2/e) + |y|^(2/e)) ^ (e/n) + |z|^(2/n) - 1 = 0


The values of e and n, called the east-west and north-south exponent,
determine the shape of the superquadric ellipsoid. Both have to be greater
than zero. The sphere is e. g. given by e = 1 and n = 1.

The syntax of the superquadric ellipsoid, which is located at the origin, is:


  superellipsoid { <e, n> }


Two useful objects are the rounded box and the rounded cylinder. These are
declared in the following way.

  #declare Rounded_Box = superellipsoid { <r, r> }
  #declare Rounded_Cylinder = superellipsoid { <1, r> }


The roundedness r determines the roundedness of the edges and has to be
greater than zero and smaller than one. The smaller you choose the values of
r the smaller and sharper the edges will get.

Very small values of e and n might cause problems with the root solver (the
Sturmian root solver cannot be used).

7.5.2.11         Surface of Revolution

The surface of revolution (SOR) object is generated by rotating the graph of
a function about an axis. This function describes the dependence of the
radius from the position on the rotation axis. The syntax of the SOR object
is:

  sor {
    NUMBER_OF_POINTS,
    <POINT0>, <POINT1>, ..., <POINTn-1>
    [ open ]
    [ sturm ]
  }


The points <POINT0> through <POINTn-1> are two-dimensional vectors consisting
of the radius and the corresponding height, i. e. the position on the
rotation axis. These points are smoothly connected (the curve is passing
through the specified points) and rotated about the y-axis to form the SOR
object. The first and last points are only used to determine the slopes of
the function at the start and end point. The function used for the SOR object
is similar to the splines used for the lathe object. The difference is that
the SOR object is less flexible because it underlies the restrictions of any
mathematical function, i. e. to any given point y on the rotation axis
belongs at most one function value, i. e. one radius value. You can't rotate
closed curves with the SOR object.

The optional keyword open allows you to remove the caps on the SOR object. If
you do this you shouldn't use it with CSG anymore because the results may be
wrong.

The SOR object is useful for creating bottles, vases, and things like that. A
simple vase could look like this:

  #declare Vase = sor {
    7,
    <0.000000, 0.000000>
    <0.118143, 0.000000>
    <0.620253, 0.540084>
    <0.210970, 0.827004>
    <0.194093, 0.962025>
    <0.286920, 1.000000>
    <0.468354, 1.033755>
    open
  }


One might ask why there is any need for a SOR object if there is already a
lathe object which is much more flexible. The reason is quite simple. The
intersection test with a SOR object involves solving a cubic polynomial while
the test with a lathe object requires to solve of a 6th order polynomial (you
need a cubic spline for the same smoothness). Since most SOR and lathe
objects will have several segments this will make a great difference in
speed. The roots of the 3rd order polynomial will also be more accurate and
easier to find.

The slower but more accurate Sturmian root solver may be used with the
surface of revolution object if the shape does not render properly.

The following explanations are for the mathematically interested reader who
wants to know how the surface of revolution is calculated. Though it is not
necessary to read on it might help in understanding the SOR object.

The function that is rotated about the y-axis to get the final SOR object is
given by

  r^2 = f(h) = A*h^3 + B*h^2 + C*h + D


with radius r and height h. Since this is a cubic function in h it has enough
flexibility to allow smooth curves.

The curve itself is defined by a set of n points P(i), i=0...n-1, which are
interpolated using one function for every segment of the curve. A segment j,
j=1...n-3, goes from point P(j) to point P(j+1) and uses points P(j-1) and
P(j+2) to determine the slopes at the endpoints. If there are n points we
will have n-3 segments. This means that we need at least four points to get a
proper curve.

The coefficients A(j), B(j), C(j) and D(j) are calculated for every segment
using the equation

  b = M * x, with

      /                                        \
      | r(j)^2                                 |
      |                                        |
      | r(j+1)^2                               |
  b = |                                        |
      | 2*r(j)*(r(j+1)-r(j-1))/(h(j+1)-h(j-1)) |
      |                                        |
      | 2*r(j+1)*(r(j+2)-r(j))/(h(j+2)-h(j))   |
                                              /

      /                                 \
      |   h(j)^3    h(j)^2    h(j)    1 |
      |                                 |
      |   h(j+1)^3  h(j+1)^2  h(j+1)  1 |
  M = |                                 |
      | 3*h(j)^2    2*h(j)    1       0 |
      |                                 |
      | 3*h(j+1)^2  2*h(j+1)  1       0 |
                                       /

      /      \
      | A(j) |
      |      |
      | B(j) |
  x = |      |
      | C(j) |
      |      |
      | D(j) |
            /


where r(j) is the radius and h(j) is the height of point P(j).

The figure below shows the configuration of the points P(i), the location of
segment j, and the curve that is defined by this segment.

Segment j of n-3 segments in a point configuration of n points. The points
describe the curve of a surface of revolution.

7.5.2.12         Text

A text object creates 3-D text as an extruded block letter. Currently only
TrueType fonts are supported but the syntax allows for other font types to be
added in the future. The syntax is:

  text {
    ttf "FONTNAME.TTF",
    "STRING_OF_TEXT",
    THICKNESS_FLOAT, OFFSET_VECTOR
  }


Where fontname.ttf is the name of the TrueType font file. It is a quoted
string literal or string expression. The string expression which follows is
the actual text of the string object. It too may be a quoted string literal
or string expression. See section "Strings" for more on string expressions.

The text will start with the origin at the lower left, front of the first
character and will extend in the +x-direction. The baseline of the text
follows the x-axis and decenders drop into the -y-direction. The front of the
character sits in the x-y-plane and the text is extruded in the +z-direction.
The front-to-back thickness is specified by the required value
THICKNESS_FLOAT.

Characters are generally sized so that 1 unit of vertical spacing is correct.
The characters are about 0.5 to 0.75 units tall.

The horizontal spacing is handled by POV-Ray internally including any kerning
information stored in the font. The required vector OFFSET_VECTOR defines any
extra translation between each character. Normally you should specify a zero
for this value. Specifing 0.1*x would put additional 0.1 units of space
between each character.

Only printable characters are allowed in text objects. Characters such as
return, line feed, tabs, backspace etc. are not supported.

7.5.2.13         Torus

A torus is a 4th order quartic polynomial shape that looks like a donut or
inner tube. Because this shape is so useful and quartics are difficult to
define, POV-Ray lets you take a short-cut and define a torus by:

  torus {
    MAJOR, MINOR
    [ sturm ]
  }


where MAJOR is a float value giving the major radius and MINOR is a float
specifying the minor radius. The major radius extends from the center of the
hole to the mid-line of the rim while the minor radius is the radius of the
cross-section of the rim. The torus is centered at the origin and lies in the
x-z-plane with the y-axis sticking through the hole.

|---------------------------------------------------------------|
|                                                               |
|    ----------- - - - - - - - ----------              +Y       |
|   /                        /                        |       |
|  /                        /                         |       |
| |              |          |       |<-B-->|       -X---|---+X  |
|              /                        /             |       |
|   __________/_ _ _ _ _ _ _ __________/              |       |
|                     |<-----A----->|                  -Y       |
|                                                               |
|  A = Major Radius                                             |
|  B = Minor Radius                                             |
|                                                               |
|---------------------------------------------------------------|
Major and minor radius of a torus.

The torus is internally bounded by two cylinders and two rings forming a
thick cylinder. With this bounding cylinder the performance of the torus
intersection test is vastly increased. The test for a valid torus
intersection, i. e. solving a 4th order polynomial, is only performed if the
bounding cylinder is hit. Thus a lot of slow root solving calculations are
avoided.

Calculations for all higher order polynomials must be very accurate. If the
torus renders improperly you may add the keyword sturm after the MINOR value
to use POV-Ray's slower-yet-more-accurate Sturmian root solver.

7.5.3            Finite Patch Primitives

There are six totally thin, finite objects which have no well-defined inside.
They are bicubic patch, disc, smooth triangle, triangle, polygon and mesh.
They may be combined in CSG union but cannot be use in other types of CSG (or
inside a clipped_by statement). Because these types are finite POV-Ray can
use automatic bounding on them to speed up rendering time. As with all shapes
they can be translated, rotated and scaled.

7.5.3.1          Bicubic Patch

A bicubic patch is a 3D curved surface created from a mesh of triangles.
POV-Ray supports a type of bicubic patch called a Bezier patch. A bicubic
patch is defined as follows:

  bicubic_patch {
    type PATCH_TYPE
    flatness FLATNESS_VALUE
    u_steps NUM_U_STEPS
    v_steps NUM_V_STEPS
    <CP1>,  <CP2>,   <CP3>,   <CP4>,
    <CP5>,  <CP6>,   <CP7>,   <CP8>,
    <CP9>,  <CP10>,  <CP11>,  <CP12>,
    <CP13>, <CP14>,  <CP15>,  <CP16>
  }


The keyword type is followed by a float PATCH_TYPE which currently must be
either 0 or 1. For type 0 only the control points are retained within
POV-Ray. This means that a minimal amount of memory is needed but POV-Ray
will need to perform many extra calculations when trying to render the patch.
Type 1 preprocesses the patch into many subpatches. This results in a
significant speedup in rendering at the cost of memory.

The four parameters type, flatness, u_steps and v_steps may appear in any
order. They are followed by 16 vectors that define the x, y, z coordinates of
the 16 control points which define the patch. The patch touches the four
corner points <CP1>, <CP4>, < CP13> and <CP16> while the other 12 points pull
and stretch the patch into shape. The Bezier surface is enclosed by the
convex hull formed by the 16 control points, this is known as the convex hull
property.

The keywords u_steps and v_steps are each followed by float values which tell
how many rows and columns of triangles are the minimum to use to create the
surface. The maximum number of individual pieces of the patch that are tested
by POV-Ray can be calculated from the following:

  sub-pieces = 2^u_steps * 2^v_steps


This means that you really should keep u_steps and v_steps under 4. Most
patches look just fine with u_steps  3 and v_steps 3, which translates to 64
subpatches (128 smooth triangles).

As POV-Ray processes the Bezier patch it makes a test of the current piece of
the patch to see if it is flat enough to just pretend it is a rectangle. The
statement that controls this test is flatness. Typical flatness values range
from 0 to 1 (the lower the slower).

If the value for flatness is 0 POV-Ray will always subdivide the patch to the
extend specified by u_steps and v_steps. If flatness is greater than 0 then
every time the patch is split, POV-Ray will check to see if there is any need
to split further.

There are both advantages and disadvantages to using a non-zero flatness. The
advantages include:

  - If the patch isn't very curved, then this will be detected and POV-Ray
  - If the patch is only highly curved in a couple of places, POV-Ray will
    keep subdividing there and concentrate it's efforts on the hard part.


The biggest disadvantage is that if POV-Ray stops subdividing at a particular
level on one part of the patch and at a different level on an adjacent part
of the patch there is the potential for cracking. This is typically visible
as spots within the patch where you can see through. How bad this appears
depends very highly on the angle at which you are viewing the patch.

Like triangles, the bicubic patch is not meant to be generated by hand. These
shapes should be created by a special utility. You may be able to acquire
utilities to generate these shapes from the same source from which you
obtained POV-Ray.

  bicubic_patch {
    type 1
    flatness 0.01
    u_steps 4
    v_steps 4
    <0, 0, 2>, <1, 0, 0>, <2, 0, 0>, <3, 0,-2>,
    <0, 1  0>, <1, 1, 0>, <2, 1, 0>, <3, 1, 0>,
    <0, 2, 0>, <1, 2, 0>, <2, 2, 0>, <3, 2, 0>,
    <0, 3, 2>, <1, 3, 0>, <2, 3, 0>, <3, 3, -2>
  }


The triangles in a POV-Ray bicubic_patch are automatically smoothed using
normal interpolation but it is up to the user (or the user's utility program)
to create control points which smoothly stitch together groups of patches.

7.5.3.2          Disc

One other flat, finite object available with POV-Ray is the disc. The disc is
infinitely thin, it has no thickness. If you want a disc with true thickness
you should use a very short cylinder. A disc shape may be defined by:

  disc {
    <CENTER>, <NORMAL>, RADIUS [, HOLE_RADIUS ]
  }


The vector <CENTER> defines the x, y, z coordinates of the center of the
disc. The < NORMAL> vector describes its orientation by describing its
surface normal vector. This is followed by a float specifying the RADIUS.
This may be optionally followed by another float specifying the radius of a
hole to be cut from the center of the disc.

7.5.3.3          Mesh

The mesh object can be used to efficiently store large numbers of triangles.
Its syntax is:

  mesh {
    triangle {
      <CORNER1>, <CORNER2>, <CORNER3>
      [ texture { STRING } ]
    }
    smooth_triangle {
      <CORNER1>, <NORMAL1>,
      <CORNER2>, <NORMAL2>,
      <CORNER3>, <NORMAL3>
      [ texture { STRING } ]
    }
    [ hierarchy FLAG ]
  }


Any number of triangles and/or smooth triangles can be used and each of those
triangles can be individually textured by assigning a texture name to it. The
texture has to be declared before the mesh is parsed. It is not possible to
use texture definitions inside the triangle or smooth triangle statements.
This is a restriction that is necessary for an efficient storage of the
assigned textures.

The mesh's components are internally bounded by a bounding box hierarchy to
speed up intersection testing. The bounding hierarchy can be turned off with
the hierarchy keyword. This should only be done if memory is short or the
mesh consists of only a few triangles.

Copies of a mesh object refer to the same triangle data and thus consume very
little memory. You can easily trace hundred copies of an 10000 triangle mesh
without running out of memory (assuming the first mesh fits into memory).

The mesh object has two advantages over a union of triangles: it needs less
memory and it is transformed faster. The memory requirements are reduced by
efficiently storing the triangles vertices and normals. The parsing time for
transformed meshes is reduced because only the mesh object has to be
transformed and not every single triangle as it is necessary for unions.

The mesh object can currently only include triangle and smooth triangle
components. That restriction is liable to change, allowing polygonal
components, at some point in the future.

7.5.3.4          Polygon

Polygons are useful for creating rectangles, squares and other planar shapes
with more than three edges. Their syntax is:

  polygon {
    TOTAL_NUMBER_OF_POINTS,
    <A_1>, <A_2>, ..., <A_na>, <A_1>,
    <B_1>, <B_2>, ..., <B_nb>, <B_1>,
    <C_1>, <C_2>, ..., <C_nc>, <C_1>,
    ...
  }


The points <A_1> through <A_na> describe the first sub-polygon, the points
<B_1> through <B_nb> describe the second sub-polygon, and so on. A polygon
can contain any number of sub-polygons, either overlapping or not. In places
where an even number of polygons overlaps a hole appears. You only have to be
sure that each of these polygons is closed. This is insured by repeating the
first point of a sub-polygon at the end of the sub-polygon's point sequence.
This implies that all points of a sub-polygon are different.

If the (last) sub-polygon is not closed a warning is issued and the program
automatically closes the polygon. This is useful because polygons imported
from other programs may not be closed, i. e. their first and last point are
not the same.

All points of a polygon are three-dimensional vectors that have to lay on one
plane. If this is not the case an error occurs. You can also use
two-dimensional vectors to describe the polygon. POV-Ray assumes that the z
value is zero in this case.

A square polygon that matches the default planar imagemap is simply:

  polygon {
    4,
    <0, 0>, <0, 1>, <1, 1>, <1, 0>
    texture {
      finish { ambient 1 diffuse 0 }
      pigment { image_map { gif "test.gif"  } }
    }
    //scale and rotate as needed here
  }


The sub-polygon feature can be used to generate complex shapes like the
letter "P", where a hole is cut into another polygon:

  #declare P = polygon {
    12,
    <0, 0>, <0, 6>, <4, 6>, <4, 3>, <1, 3>, <1, 0>, <0, 0>,
    <1, 4>, <1, 5>, <3, 5>, <3, 4>, <1, 4>
  }


The first sub-polygon (on the first line) describes the outer shape of the
letter "P". The second sub-polygon (on the second line) describes the
rectangular hole that is cut in the top of the letter "P". Both rectangles
are closed, i. e. their first and last points are the same.

The feature of cutting holes into a polygon is based on the polygon
inside/outside test used. A point is considered to be inside a polygon if a
straight line drawn from this point in an arbitrary direction crosses an odd
number of edges (this is known as Jordan's curve  theorem).

Another very complex example showing one large triangle with three small
holes and three separate, small triangles is given below:

  polygon {
    28,
    <0, 0> <1, 0> <0, 1> <0, 0>          // large outer triangle
    <.3, .7> <.4, .7> <.3, .8> <.3, .7>  // small outer triangle #1
    <.5, .5> <.6, .5> <.5, .6> <.5, .5>  // small outer triangle #2
    <.7, .3> <.8, .3> <.7, .4> <.7, .3>  // small outer triangle #3
    <.5, .2> <.6, .2> <.5, .3> <.5, .2>  // inner triangle #1
    <.2, .5> <.3, .5> <.2, .6> <.2, .5>  // inner triangle #2
    <.1, .1> <.2, .1> <.1, .2> <.1, .1>  // inner triangle #3
  }


7.5.3.5          Triangle and Smooth Triangle

The triangle primitive is available in order to make more complex objects
than the built-in shapes will permit. Triangles are usually not created by
hand but are converted from other files or generated by utilities. A triangle
is defined by

  triangle {
    <CORNER1>, <CORNER2>, <CORNER3>
  }


where <CORNERn> is a vector defining the x, y, z coordinates of each corner
of the triangle.

Because triangles are perfectly flat surfaces it would require extremely
large numbers of very small triangles to approximate a smooth, curved
surface. However much of our perception of smooth surfaces is dependent upon
the way light and shading is done. By artificially modifying the surface
normals we can simulate as smooth surface and hide the sharp-edged seams
between individual triangles.

The smooth triangle primitive is used for just such purposes. The smooth
triangles use a formula called Phong normal interpolation to calculate the
surface normal for any point on the triangle based on normal vectors which
you define for the three corners. This makes the triangle appear to be a
smooth curved surface. A smooth triangle is defined by

  smooth_triangle {
    <CORNER1>, <NORMAL1>,
    <CORNER2>, <NORMAL2>,
    <CORNER3>, <NORMAL3>
  }


where the corners are defined as in regular triangles and < NORMALn> is a
vector describing the direction of the surface normal at each corner.

These normal vectors are prohibitively difficult to compute by hand.
Therefore smooth triangles are almost always generated by utility programs.
To achieve smooth results, any triangles which share a common vertex should
have the same normal vector at that vertex. Generally the smoothed normal
should be the average of all the actual normals of the triangles which share
that point.

7.5.4            Infinite Solid Primitives

There are five polynomial primitive shapes that are possibly infinite and do
not respond to automatic bounding. They are plane, cubic, poly, quadric and
quartic. They do have a well defined inside and may be used in CSG and inside
a clipped_by statement. As with all shapes they can be translated, rotated
and scaled..

7.5.4.1          Plane

The plane primitive is a simple way to define an infinite flat surface. The
plane is specified as follows:

  plane { <NORMAL>, DISTANCE }


The <NORMAL> vector defines the surface normal of the plane. A surface normal
is a vector which points up from the surface at a 90 degree angle. This is
followed by a float value that gives the distance along the normal that the
plane is from the origin (that is only true if the normal vector has unit
length; see below). For example:

  plane { <0, 1, 0>, 4 }


This is a plane where straight up is defined in the positive y-direction. The
plane is 4 units in that direction away from the origin. Because most planes
are defined with surface normals in the direction of an axis you will often
see planes defined using the x, y or z built-in vector identifiers. The
example above could be specified as:

  plane { y, 4 }


The plane extends infinitely in the x- and z-directions. It effectively
divides the world into two pieces. By definition the normal vector points to
the outside of the plane while any points away from the vector are defined as
inside. This inside/outside distinction is only important when using planes
in CSG and clipped_by.

A plane is called a polynomial shape because it is defined by a first order
polynomial equation. Given a plane:

  plane { <A, B, C>, D }


it can be represented by the equation

  A*x + B*y + C*z - D*sqrt(A^2 + B^2 + C^2) = 0.


Therefore our example plane { y,4 } is actually the polynomial equation y=4.
You can think of this as a set of all x, y, z points where all have y values
equal to 4, regardless of the x or z values.

This equation is a first order polynomial because each term contains only
single powers of x, y or z. A second order equation has terms like x^2, y^2,
z^2, xy, xz and yz. Another name for a 2nd order equation is a quadric
equation. Third order polys are called cubics. A 4th order equation is a
quartic. Such shapes are described in the sections below.

7.5.4.2          Poly, Cubic and Quartic

Higher order polynomial surfaces may be defined by the use of a poly shape.
The syntax is

  poly { ORDER, <T1, T2, T3, .... Tm> }


where ORDER is an integer number from 2 to 7 inclusively that specifies the
order of the equation. T1, T2, ... Tm are float values for the coefficients
of the equation. There are m such terms where

  m = ((ORDER+1)*(ORDER+2)*(ORDER+3))/6.


An alternate way to specify 3rd order polys is:

  cubic { <T1, T2,... T20> }


Also 4th order equations may be specified with:

  quartic { <T1, T2,... T35> }


Here's a more mathematical description of quartics for those who are
interested. Quartic surfaces are 4th order surfaces and can be used to
describe a large class of shapes including the torus, the lemniscate, etc.
The general equation for a quartic equation in three variables is (hold onto
your hat):

  a00 x^4 + a01 x^3 y + a02 x^3 z+ a03 x^3 + a04 x^2 y^2+
  a05 x^2 y z+ a06 x^2 y + a07 x^2 z^2+a08 x^2 z+a09 x^2+
  a10 x y^3+a11 x y^2 z+ a12 x y^2+a13 x y z^2+a14 x y z+
  a15 x y + a16 x z^3 + a17 x z^2 + a18 x z + a19 x+
  a20 y^4 + a21 y^3 z + a22 y^3+ a23 y^2 z^2 +a24 y^2 z+
  a25 y^2 + a26 y z^3 + a27 y z^2 + a28 y z + a29 y+
  a30 z^4 + a31 z^3 + a32 z^2 + a33 z + a34 = 0


To declare a quartic surface requires that each of the coefficients (a0 ...
a34) be placed in order into a single long vector of 35 terms.

As an example let's define a torus the hard way. A Torus can be represented
by the equation:

 x^4 + y^4 + z^4 + 2 x^2 y^2 + 2 x^2 z^2 + 2 y^2 z^2 -
 2 (r_0^2 + r_1^2) x^2 + 2 (r_0^2 - r_1^2) y^2 -
 2 (r_0^2 + r_1^2) z^2 + (r_0^2 - r_1^2)^2 = 0


Where r_0 is the major radius of the torus, the distance from the hole of the
donut to the middle of the ring of the donut, and r_1 is the minor radius of
the torus, the distance from the middle of the ring of the donut to the outer
surface. The following object declaration is for a torus having major radius
6.3 minor radius 3.5 (Making the maximum width just under 20).

  // Torus having major radius sqrt(40), minor radius sqrt(12)

  quartic {
    < 1,   0,   0,   0,   2,   0,   0,   2,   0,
   -104,   0,   0,   0,   0,   0,   0,   0,   0,
      0,   0,   1,   0,   0,   2,   0,  56,   0,
      0,   0,   0,   1,   0, -104,  0, 784 >
    sturm
    bounded_by { // bounded_by speeds up the render,
                 // see bounded_by
                 // explanation later
                 // in docs for more info.
     sphere { <0, 0, 0>, 10 }
    }
  }


Poly, cubic and quartics are just like quadrics in that you don't have to
understand what one is to use one. The file shapesq.inc has plenty of
pre-defined quartics for you to play with. The syntax for using a pre-defined
quartic is:

  object { Quartic_Name }


Polys use highly complex computations and will not always render perfectly.
If the surface is not smooth, has dropouts, or extra random pixels, try using
the optional keyword sturm in the definition. This will cause a slower but
more accurate calculation method to be used. Usually, but not always, this
will solve the problem. If sturm doesn't work, try rotating or translating
the shape by some small amount. See the sub-directory math in the scene files
directory for examples of polys in scenes.

There are really so many different quartic shapes, we can't even begin to
list or describe them all. If you are interested and mathematically inclined,
an excellent reference book for curves and surfaces where you'll find more
quartic shape formulas is:

  "The CRC Handbook of Mathematical Curves and Surfaces"
  David von Seggern
  CRC Press, 1990


7.5.4.3          Quadric

Quadric surfaces can produce shapes like ellipsoids, spheres, cones,
cylinders, paraboloids (dish shapes) and hyperboloids (saddle or hourglass
shapes). Note that you do not confuse quaDRic with quaRTic. A quadric is a
2nd order polynomial while a quartic is 4th order. Quadrics render much
faster and are less error-prone.

A quadric is defined in POV-Ray by

  quadric { <A,B,C>, <D,E,F>, <G,H,I>, J }


where A through J are float expressions that define a surface of x, y, z
points which satisfy the equation

  A x^2   + B y^2   + C z^2 +
  D xy    + E xz    + F yz +
  G x     + H y     + I z    + J = 0


Different values of A, B, C, ... J will give different shapes. If you take
any three dimensional point and use its x, y and z coordinates in the above
equation the answer will be 0 if the point is on the surface of the object.
The answer will be negative if the point is inside the object and positive if
the point is outside the object. Here are some examples:

  X^2 + Y^2 + Z^2 - 1 = 0  Sphere
  X^2 + Y^2 - 1 = 0        Infinite cylinder along the Z axis
  X^2 + Y^2 - Z^2 = 0      Infinite cone along the Z axis


The easiest way to use these shapes is to include the standard file
shapes.inc into your program. It contains several pre-defined quadrics and
you can transform these pre-defined shapes (using translate, rotate and
scale) into the ones you want. You can invoke them by using the syntax:

  object { Quadric_Name }


The pre-defined quadrics are centered about the origin < 0,0,0> and have a
radius of 1. Don't confuse radius with width. The radius is half the diameter
or width making the standard quadrics 2 units wide.

Some of the pre-defined quadrics are,

  Ellipsoid
  Cylinder_X, Cylinder_Y, Cylinder_Z
  QCone_X, QCone_Y, QCone_Z
  Paraboloid_X, Paraboloid_Y, Paraboloid_Z


7.5.5            Constructive Solid Geometry

POV-Ray supports Constructive Solid Geometry (CSG) with five different
operations: difference, intersection, merge, union and negation (inversion).
While the first four operations represent binary operators, i. e. they need
two arguments, the negation is a unary operator, it takes only one argument.

7.5.5.1          About CSG

Constructive Solid Geometry is a technique for combining two or more objects
to create a new object using the three boolean set operators union,
intersection, and negation. It only works with solid objects, i. e. objects
that have a well-defined interior. This is the case for all objects described
in the sections "Finite Solid Primitives" and "Infinite Solid Primitives".

CSG shapes may be used anywhere a standard shape can be used, even inside
other CSG shapes. They can be translated, rotated or scaled in the same way
as any other shape. The shapes making up the CSG shape may be individually
translated, rotated and scaled as well.

7.5.5.2          Inside and Outside

Most shape primitives, like spheres, boxes and blobs divide the world into
two regions. One region is inside the object and one is outside.

Given any point in space you can say it's either inside or outside any
particular primitive object. Well, it could be exactly on the surface but
this case is rather hard to determine due to numerical problems.

Even planes have an inside and an outside. By definition, the surface normal
of the plane points towards the outside of the plane. You should note that
triangles and triangle-based shapes cannot be used as solid objects in CSG
since they have no well defined inside and outside.

CSG uses the concepts of inside and outside to combine shapes together as
explained in the following sections.

Imagine you have to objects that partially overlap like shown in the figure
below. Four different areas of points can be distinguished: points that are
neither in object A nor in object B, points that are in object A but not in
object B, points that are not in object A but in object B and last not least
points that are in object A and object B.

* = Object A
% = Object B

         *
        * *    %
       *   *  % %
      *     *%   %
     *      %*    %
    *      %  *    %
   *      %    *    %
  *******%*******    %
        %             %
       %%%%%%%%%%%%%%%%%
Two overlapping objects.

Keeping this in mind it will be quite easy to understand how the CSG
operations work.

7.5.5.3          Inverse

When using CSG it is often useful to invert an object so that it'll be
inside-out. The appearance of the object is not changed, just the way that
POV-Ray perceives it. When the inverse keyword is used the inside of the
shape is flipped to become the outside and vice versa.

Note that the difference operation is performed by intersecting the first
object with the negation of the second object.

7.5.5.4          Union

         *
        * *    %
       *   *  % %
      *     *%   %
     *      %*    %
    *      %  *    %
   *      %    *    %
  *******%*******    %
        %             %
       %%%%%%%%%%%%%%%%%
The union of two objects.

Unions are simply glue used to bind two or more shapes into a single entity
that can be manipulated as a single object. The image above shows the union
of A and B. The new object created by the union operation can be scaled,
translated and rotated as a single shape. The entire union can share a single
texture but each object contained in the union may also have its own texture,
which will override any matching texture statements in the parent object.

You should be aware that the surfaces inside the union will not be removed.
As you can see from the figure this may be a problem for transparent unions.
If you want those surfaces to be removed you'll have to use the merge
operations explained in a later section.

The following union will contain a box and a sphere.

  union {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }


Earlier versions of POV-Ray placed restrictions on unions so you often had to
combine objects with composite statements. Those earlier restrictions have
been lifted so composite is no longer needed. Composite is still supported
for backwards compatibility but it is recommended that union is now used in
it's place since future support for the composite keyword is not guaranteed.

7.5.5.5          Intersection

A point is inside an intersection if it is inside both objects, A and B, as
show in the figure below.

          %*
         %  *
        %    *
       %*******
The intersection of two objects.

For example:

  intersection {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }


7.5.5.6          Difference

The CSG difference operation takes the intersection between the first object
and the negation of the second object. Thus only points inside object A and
outside object B belong to the difference of both objects.

The results is a subtraction of the 2nd shape from the first shape as shown
in the figure below.

       *
      * *
     *   *
    *     *
   *  1   %
  *      %
 *      %
*******%
The difference between two objects.

For example:

  difference {
    box { <-1.5, -1, -1>, <0.5, 1, 1> }
    cylinder { <0.5, 0, -1>, <0.5, 0, 1>, 1 }
  }


7.5.5.7          Merge

The union operation just glues objects together, it does not remove the
objects' surfaces inside the union. If a transparent union is used those
surface will get visible.

The merge operations can be used to avoid this problem. It works just like
union but it eliminates the inner surfaces like shown in the figure below.

         *
        * *    %
       *   *  % %
      *     *%   %
     *            %
    *              %
   *                %
  *******%           %
        %             %
       %%%%%%%%%%%%%%%%%
Merge removes inner surfaces.

7.5.6            Light Sources

The last object covered is the light source. Light sources have no visible
shape of their own. They are just points or areas which emit light. Their
full syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    [ spotlight ]
    [ point_at <POINT_AT> ]
    [ radius RADIUS ]
    [ falloff FALLOFF ]
    [ tightness TIGHTNESS ]
    [ area_light <AXIS1>, <AXIS2>, SIZE1, SIZE2 ]
    [ adaptive ADAPTIVE ]
    [ jitter JITTER ]
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmospheric_attenuation BOOL ]
  }


The different types of light sources and the optional modifiers are described
in the following sections.

7.5.6.1          Point Lights

A point light source sends light of the specified color uniformly in all
directions. Its location is described by the location keyword and its color
is given by the color keyword. The complete syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmospheric_attenuation BOOL ]
  }


7.5.6.2          Spotlights

A spotlight is a point light source where the rays of light are constrained
by a cone. The light is bright in the center of this cone and falls off or
darkens at the edges of the cone. The syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    spotlight
    point_at <POINT_AT>
    radius RADIUS
    falloff FALLOFF
    tightness TIGHTNESS
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmospheric_attenuation BOOL ]
  }


The spotlight is identified by the spotlight keyword. It is located at
LOCATION and points at POINT_AT. The following illustration will be helpful
in understanding how these values relate to each other.

     (+) location
     / \
    /   \
   /     \
  /       \
 /         \
/           \
+-----*-----+
      ^ point_at
The geometry of a spotlight.

The spotlight's other parameters are radius, falloff and tightness.

Think of a spotlight as two nested cones as shown in the figure. The inner
cone is specified by the radius parameter and is fully lit. The outer cone is
the falloff cone beyond which there is no light. The values for these two
parameters are half the opening angles of the corresponding cones, both
angles have to be smaller than 90 degrees. The light smoothly falls off
between the radius and the falloff angle like shown in the figures below (as
long as the radius angle is not negative).

Intensity multiplier curve with a fixed falloff angle of 45 degrees.

Intensity multiplier curve with a fixed radius angle of 45 degrees.

The tightness value specifies how quickly the light dims, or falls off, from
the spotlight's center line to the falloff cone (full darkness outside). The
default value for tightness is 10. Lower tightness values will make the
spotlight brighter, making the spot wider and the edges sharper. Higher
values will dim the spotlight, making the spot tighter and the edges softer.
Values from 1 to 100 are acceptable.

Intensity multiplier curve with fixed angle and falloff angles of 30 and 60
degrees respectively and different tightness values.

You should note from the figures that the radius and falloff angles interact
with the tightness parameter. Only negative radius angles will give the
tightness value full control over the spotlight's appearance as you can see
from the figure below. In that case the falloff angle has no effect and the
lit area is only determined by the tightness parameter.

Intensity multiplier curve with a negative radius angle and different
tightness values.

Spotlights may be used anyplace that a normal light source is used. Like any
light sources, they are invisible. They are treated as shapes and may be
included in CSG shapes. They may also be used in conjunction with area
lights.

7.5.6.3          Cylindrical Lights

Cylindrical light sources work pretty much like spotlights except that the
light rays are constraint by a cylinder and not a cone. The syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    cylinder
    point_at <POINT_AT>
    radius RADIUS
    falloff FALLOFF
    tightness TIGHTNESS
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmospheric_attenuation BOOL ]
  }


The radius, falloff and tightness keywords control the same features as with
the spotlight.

You should keep in mind that the cylindrical light source is still a point
light source. The rays are emitted from one point and are only constraint by
a cylinder. The light rays are not parallel.

7.5.6.4          Area Lights

Area light sources occupy a finite, one- or two-dimensional area of space.
They can cast soft shadows because they can partially block light.

The area lights used in POV-Ray are rectangular in shape, sort of like a flat
panel light. Rather than performing the complex calculations that would be
required to model a true area light, it is approximated as an array of point
light sources spread out over the area occupied by the light. The intensity
of each individual point light in the array is dimmed so that the total
amount of light emitted by the light is equal to the light color specified in
the declaration. The syntax is:

  light_source {
    <LOCATION>
    color <COLOUR>
    area_light <AXIS1>, <AXIS2>, SIZE1, SIZE2
    adaptive ADAPTIVE
    jitter JITTER
    [ spotlight ]
    [ point_at <POINT_AT> ]
    [ radius RADIUS ]
    [ falloff FALLOFF ]
    [ tightness TIGHTNESS ]
    [ looks_like { OBJECT } ]
    [ fade_distance FADE_DISTANCE ]
    [ fade_power FADE_POWER ]
    [ atmosphere BOOL ]
    [ atmospheric_attenuation BOOL ]
  }


The light's location and color are specified in the same way as a for a
regular light source.

The area_light command defines the size and orientation of the area light as
well as the number of lights in the light source array. The vectors AXIS1 and
AXIS2 specify the lengths and directions of the edges of the light. Since the
area lights are rectangular in shape these vectors should be perpendicular to
each other. The larger the size of the light the thicker the soft part of
shadows will be. The numbers SIZE1 and SIZE2 specify the dimensions of the
array of point lights. The more lights you use the smoother your shadows will
be but the longer they will take to render.

The jitter command is optional. When used it causes the positions of the
point lights in the array to be randomly jittered to eliminate any shadow
banding that may occur. The jittering is completely random from render to
render and should not be used when generating animations.

Note that it is possible to specify spotlight parameters along with the area
light parameters to create area spotlights. Using area spotlights is a good
way to speed up scenes that use area lights since you can confine the lengthy
soft shadow calculations to only the parts of your scene that need them.

An interesting effect can be created using a linear light source. Rather than
having a rectangular shape, a linear light stretches along a line sort of
like a thin fluorescent tube. To create a linear light just create an area
light with one of the array dimensions set to 1.

The adaptive command is used to enable adaptive sampling of the light source.
By default POV-Ray calculates the amount of light that reaches a surface from
an area light by shooting a test ray at every point light within the array.
As you can imagine this is very slow. Adaptive sampling on the other hand
attempts to approximate the same calculation by using a minimum number of
test rays. The number specified after the keyword controls how much adaptive
sampling is used. The higher the number the more accurate your shadows will
be but the longer they will take to render. If you're not sure what value to
use a good starting point is adaptive 1. The adaptive keyword only accepts
integer values and cannot be set lower than 0.

When performing adaptive sampling POV-Ray starts by shooting a test ray at
each of the four corners of the area light. If the amount of light received
from all four corners is approximately the same then the area light is
assumed to be either fully in view or fully blocked. The light intensity is
then calculated as the average intensity of the light received from the four
corners. However, if the light intensity from the four corners differs
significantly then the area light is partially blocked. The area light is
split into four quarters and each section is sampled as described above. This
allows POV-Ray to rapidly approximate how much of the area light is in view
without having to shoot a test ray at every light in the array. Visually the
sampling goes like shown below.

 level       0            1           2         3
 rays        4            9           25        81
         * . . . *    x . * . x   x * x * x
         . . . . .    . . . . .   * * * * *
         . . . . .    * . * . *   x * x * x    etc...
         . . . . .    . . . . .   * * * * *
         * . . . *    x . * . x   x * x * x

 * new samples
 x reused samples from previous level
Area light adaptive samples.

While the adaptive sampling method is fast (relatively speaking) it can
sometimes produces inaccurate shadows. The solution is to reduce the amount
of adaptive sampling without completely turning it off. The number after the
adaptive keyword adjusts the number of times that the area light will be
split before the adaptive phase begins. For example if you use adaptive 0 a
minimum of 4 rays will be shot at the light. If you use adaptive 1 a minimum
of 9 rays will be shot (adaptive 2 gives 25 rays, adaptive 3 gives 81 rays,
etc). Obviously the more shadow rays you shoot the slower the rendering will
be so you should use the lowest value that gives acceptable results.

The number of rays never exceeds the values you specify for rows and columns
of points. For example area_light x,y,4,4 specifies a 4 by 4 array of lights.
If you specify adaptive 3 it would mean that you should start with a 9 by 9
array. In this case no adaptive sampling is done. The 4 by 4 array is used.

7.5.6.5          Shadowless Lights

Using the shadowless keyword you can stop a light source from casting
shadows.

7.5.6.6          Looks_like

Normally the light source itself has no visible shape. The light simply
radiates from an invisible point or area. You may give a light source any
shape by adding a looks_like { OBJECT } statement.

There is an implied no_shadow attached to the looks_like object so that light
is not blocked by the object. Without the automatic no_shadow the light
inside the object would not escape. The object would, in effect, cast a
shadow over everything.

If you want the attached object to block light then you should attach it with
a union and not a looks_like as follows:

  union {
    light_source { <100, 200, -300> color White }
    object { My_Lamp_Shape }
  }


7.5.6.7          Light Fading

By default POV-Ray does not diminish light from any light source as it
travels through space. In order to get a more realistic effect fade_distance
and fade_power can be used to model the distance based falloff in light
intensity.

The fade_distance keyword is used to specify the distance at which the full
light intensity arrives, i. e. the intensity which was given by the color
keyword. The actual attenuation is described by the fade_power keyword, which
determines the falloff rate. E. g. linear or quadratic falloff can be used by
setting FADE_POWER to 1 or 2 respectively. The complete formula to calculate
the factor by which the light is attenuated is

                                 2
  attenuation = --------------------------------------
                 1 + (d / FADE_DISTANCE) ^ FADE_POWER


with d being the distance the light has traveled.

Light fading functions for different fading powers.

You should note two important facts: First, for FADE_DISTANCEs larger than
one the light intensity at distances smaller than FADE_DISTANCE actually
increases. This is necessary to get the light source color if the distance
traveled equals the FADE_DISTANCE. Second, only light coming directly from
light sources is attenuated. Reflected or refracted light is not attenuated
by distance.

7.5.6.8          Atmosphere Interaction

By default light sources will interact with an atmosphere added to the scene.
This behaviour can be switched off by using the atmosphere keyword inside the
light source statement.

  light_source {
    ...
    atmosphere off
  }


7.5.6.9          Atmospheric Attenuation

Normally light coming from light sources is not influenced by fog or
atmosphere. This can be changed by turning the atmospheric attenuation for a
given light source on. All light coming from this light source will now be
diminished as it travels through the fog or atmosphere. This results in an
distance-based, exponential intensity falloff ruled by the used fog or
atmosphere. If there is no fog or atmosphere no change will be seen.

7.5.7            Object Modifiers

A variety of modifiers may be attached to objects. Transformations such as
translate, rotate and scale have already been discussed. Textures are in a
section of their own below. Here are three other important modifiers:
clipped_by, bounded_by and no_shadow. Although the examples below use object
statements and object identifiers, these modifiers may be used on any type of
object such as sphere, box etc.

7.5.7.1          Clipped_By

The clipped_by statement is technically an object modifier but it provides a
type of CSG similar to CSG intersection. You attach a clipping object like
this:

  object {
    My_Thing
    clipped_by{plane{y,0}}
  }


Every part of the object My_Thing that is inside the plane is retained while
the remaining part is clipped off and discarded. In an intersection object
the hole is closed off. With clipped_by it leaves an opening. For example the
following figure shows object A being clipped by object B.

   *       *
  *         *
 *           *
***************
An object clipped by another object.

clipped_by may be used to slice off portions of any shape. In many cases it
will also result in faster rendering times than other methods of altering a
shape.

Often you will want to use the clipped_by and bounded_by options with the
same object. The following shortcut saves typing and uses less memory.

  object {
    My_Thing
    bounded_by { box { <0,0,0>, <1,1,1> } }
    clipped_by { bounded_by }
  }


7.5.7.2          Bounded_By

The calculations necessary to test if a ray hits an object can be quite time
consuming. Each ray has to be tested against every object in the scene.
POV-Ray attempts so speed up the process by building a set of invisible
boxes, called bounding boxes, which cluster the objects together. This way a
ray that travels in one part of the scene doesn't have to be tested against
objects in another, far away part of the scene. When large a number of
objects are present the boxes are nested inside each other. POV-Ray can use
bounding boxes on any finite object and even some clipped or bounded
quadrics. However infinite objects (such as a planes, quartic, cubic and
poly) cannot be automatically bound. CSG objects are automatically bound if
they contain finite (and in some cases even infinite) objects. This works by
applying the CSG set operations to the bounding boxes of all objects used
inside the CSG object. For difference and intersection operations this will
hardly ever lead to an optimal bounding box. It's sometimes better (depending
on the complexity of the CSG object) to use a bounded_by statement with such
shapes.

Normally bounding shapes are not necessary but there are cases where they can
be used to speed up the rendering of complex objects. Bounding shapes tell
the ray-tracer that the object is totally enclosed by a simple shape. When
tracing rays, the ray is first tested against the simple bounding shape. If
it strikes the bounding shape the ray is further tested against the more
complicated object inside. Otherwise the entire complex shape is skipped,
which greatly speeds rendering.

To use bounding shapes, simply include the following lines in the declaration
of your object:

  bounded_by {
    object { ... }
  }


An example of a bounding shape:

  intersection {
    sphere { <0,0,0>, 2 }
    plane  { <0,1,0>, 0 }
    plane  { <1,0,0>, 0 }
    bounded_by { sphere { <0,0,0>, 2 } }
  }


The best bounding shape is a sphere or a box since these shapes are highly
optimized, although, any shape may be used. If the bounding shape is itself a
finite shape which responds to bounding slabs then the object which it
encloses will also be used in the slab system.

CSG shapes can benefit from bounding slabs without a bounded_by statement
however they may do so inefficiently in intersection, difference and merge.
In these three CSG types the automatic bound used covers all of the component
objects in their entirety. However the result of these intersections may
result in a smaller object. Compare the sizes of the illustrations for union
and intersection in the CSG section above. It is possible to draw a much
smaller box around the intersection of A and B than the union of A and B yet
the automatic bounds are the size of the union of A and B regardless of the
kind of CSG specified.

While it is almost always a good idea to manually add a bounded_by to
intersection, difference and merge, it is often best to not bound a union. If
a union has no bounded_by and no clipped_by POV-Ray can internally split
apart the components of a union and apply automatic bounding slabs to any of
its finite parts. Note that some utilities such as raw2pov may be able to
generate bounds more efficiently than POV-Ray's current system. However most
unions you create yourself can be easily bounded by the automatic system. For
technical reasons POV-Ray cannot split a merge object. It is probably best to
hand bound a merge, especially if it is very complex.

Note that if bounding shape is too small or positioned incorrectly it may
clip the object in undefined ways or the object may not appear at all. To do
true clipping, use clipped_by as explained above. Often you will want to use
the clipped_by and bounded_by options with the same object. The following
shortcut saves typing and uses less memory.

  object {
    My_Thing
    clipped_by{ box { <0,0,0>,<1,1,1 > }}
    bounded_by{ clipped_by }
  }


7.5.7.3          Hollow

POV-Ray by default assumes that objects are made of a solid material that
completely fills the interior of an object. By adding the hollow keyword to
the object you can make it hollow. That is very useful if you want
atmospheric effects to exist inside an object. It is even required for
objects containing a halo (see "Halo" for details).

In order to get a hollow CSG object you just have to make the top level
object hollow. All children will assume the same hollow state except their
state is explicitly set. The following example will set both spheres inside
the union hollow

  union {
    sphere { -0.5*x, 1 }
    sphere {  0.5*x, 1 }
    hollow
  }


while the next example will only set the second sphere hollow because the
first sphere was explicitly set to be not hollow.

  union {
    sphere { -0.5*x, 1 hollow off }
    sphere {  0.5*x, 1 }
    hollow
  }


7.5.7.4          No_Shadow

You may specify the no_shadow keyword in an object to make that object cast
no shadow. This is useful for special effects and for creating the illusion
that a light source actually is visible. This keyword was necessary in
earlier versions of POV-Ray which did not have the looks_like statement. Now
it is useful for creating things like laser beams or other unreal effects.

Simply attach the keyword as follows:

  object {
    My_Thing
    no_shadow
  }


7.5.7.5          Sturm

Some of POV-Ray's objects allow you to choose between a fast but sometimes
inaccurate root solver and a slower but more accurate one. This is the case
for all objects that involve the solution of a cubic or quartic polynomial.
There are analytic mathematical solutions for those polynomials that can be
used.

Lower order polynomials are trivial to solve while higher order polynomials
require iterative algorithms to solve them. One of those algorithms is the
Sturmian root solver.

The following list shows all objects for which the Sturmian root solver can
be used.

  blob
  cubic
  lathe    (only with quadratic splines)
  poly
  prism    (only with cubic splines)
  quartic
  sor


7.6              Textures

The texture describes what the object looks like, i. e. its material.
Textures are combinations of pigments, normals, finishes and halos. Pigment
is the color or pattern of colors inherent in the material. Normal is a
method of simulating various patterns of bumps, dents, ripples or waves by
modifying the surface normal vector. Finish describes the reflective and
refractive properties of a material. Halo simulates effects like clouds, fog,
fire etc. by using a density field defined inside the object.

A plain texture consists of a single pigment, an optional normal, a single
finish and optionally one or more halos. A special  texture combines two or
more textures using a pattern or blending function. Special textures may be
made quite complex by nesting patterns within patterns. At the innermost
levels however, they are made up from plain textures. Note that although we
call a plain texture plain it may be a very complex texture. The term plain
only means that it has a single pigment, normal, finish and halo.

The most complete form for defining a plain texture is as follows:

  texture {
    TEXTURE_IDENTIFIER
    pigment {...}
    normal {...}
    finish {...}
    halo {...}
    TRANSFORMATIONS
  }


Each of the items in a texture are optional but if they are present the
identifier must be first and the transformations must be last. The pigment,
normal and finish parameters modify any pigment, normal and finish already
specified in the TEXTURE_IDENTIFIER. Any halos are added to the already
existing halos. If no texture identifier is specified the pigment, normal and
finish statements modify the current default values and any halo is added to
the default halo, if any. TRANSFORMATIONs are translate, rotate, scale and
matrix statements. They should be specified last.

The sections below describe all of the options available in pigments,
normals, finishes and halos. Special textures are covered later.

7.6.1            Pigment

The color or pattern of colors for an object is defined by a pigment
statement. All plain textures must have a pigment. If you do not specify one
the default pigment is used. A pigment statement is part of a texture
specification. However it can be tedious to use a texture statement just to
add a color to an object. Therefore you may attach a pigment directly to an
object without explicitly specifying that it as part of a texture. For
example:

  //this...                //can be shortened to this...

  object {                 object {
    My_Object                My_Object
    texture {                pigment {color Red}
      pigment {color Red}  }
    }
  }


The color you define is the way you want the object to look if fully
illuminated. You pick the basic color inherent in the object and POV-Ray
brightens or darkens it depending on the lighting in the scene. The parameter
is called pigment because we are defining the basic color the object actually
is rather than how it looks.

The most complete form for defining a pigment is as follows:

  pigment {
    PIGMENT_IDENTIFIER
    PATTERN_TYPE
    PIGMENT_MODIFIERS...
  }


Each of the items in a pigment are optional but if they are present, they
should be in the order shown above to insure that the results are as
expected. Any items after the PIGMENT_IDENTIFIER modify or override settings
given in the identifier. If no identifier is specified then the items modify
the pigment values in the current default texture. Valid PIGMENT_MODIFIERS
are color_map, pigment_map, image_map and quick_color statements as well as
any of the generic PATTERN_MODIFIERS such as translate, rotate, scale,
turbulence, wave shape and warp statements. Such modifiers apply only to the
pigment and not to other parts of the texture. Modifiers should be specified
last.

The various pattern types fall into roughly four categories. Each category is
discussed below. They are solid color, color list patterns, color mapped
patterns and image maps.

7.6.1.1          Solid Color Pigments

The simplest type of pigment is a solid color. To specify a solid color you
simply put a color specification inside a pigment. For example:

  pigment {color Orange}


A color specification consists of the option keyword color followed by a
color identifier or by a specification of the amount of red, green, blue,
filtered and unfiltered transparency in the surface. See section "Specifying
Colors" for more details about colors. Any pattern modifiers used with a
solid color are ignored because there is no pattern to modify.

7.6.1.2          Color List Pigments

There are three color list patterns: checker, hexagon and brick. The result
is a pattern of solid colors with distinct edges rather than a blending of
colors as with color mapped patterns. Each of these patterns is covered in
more detail in a later section. The syntax for each is:

  pigment { brick COLOR1, COLOR2 MODIFIERS ... }
  pigment { checker COLOR1, COLOR2 MODIFIERS ... }
  pigment { hexagon COLOR1, COLOR2, COLOR3 MODIFIERS ... }


Each COLORn is any valid color specification. There should be a comma between
each color or the color keyword should be used as a separator so that POV-Ray
can determine where each color specification starts and ends.

7.6.1.3          Color Maps

Most of the color patterns do not use abrupt color changes of just two or
three colors like those in the brick, checker or hexagon patterns. They
instead use smooth transitions of many colors that gradually change from one
point to the next. The colors are defined in a pigment modifier called a
color map that describes how the pattern blends from one color to the next.

Each of the various pattern types available is in fact a mathematical
function that takes any x, y, z location and turns it into a number between
0.0 and 1.0 inclusive. That number is used to specify what mix of colors to
use from the color map.

A color map is specified by...

  pigment{
    PATTERN_TYPE
    color_map {
      [ NUM_1 COLOR_1]
      [ NUM_2 COLOR_2]
      [ NUM_3 COLOR_3]
       ...
    }
    PIGMENT_MODIFIERS...
  }


Where NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive.
COLOR_1, COLOR_2, ... are color specifications. Note that the [] brackets are
part of the actual statement. They are not notational symbols denoting
optional parts. The brackets surround each entry in the color map. There may
be from 2 to 256 entries in the map. The alternate spelling colour_map may be
used.

For example

  sphere {
    <0,1,2>, 2
    pigment {
      gradient x       //this is the PATTERN_TYPE
      color_map {
        [0.1  color Red]
        [0.3  color Yellow]
        [0.6  color Blue]
        [0.6  color Green]
        [0.8  color Cyan]
      }
    }
  }


The pattern function is evaluated and the result is a value from 0.0 to 1.0.
If the value is less than the first entry (in this case 0.1) then the first
color (red) is used. Values from 0.1 to 0.3 use a blend of red and yellow
using linear interpolation of the two colors. Similarly values from 0.3 to
0.6 blend from yellow to blue. Note that the 3rd and 4th entries both have
values of 0.6. This causes an immediate abrupt shift of color from blue to
green. Specifically a value that is less than 0.6 will be blue but exactly
equal to 0.6 will be green. Moving along, values from 0.6 to 0.8 will be a
blend of green and cyan. Finally any value greater than or equal to 0.8 will
be cyan.

If you want areas of unchanging color you simply specify the same color for
two adjacent entries. For example:

  color_map {
    [0.1  color Red]
    [0.3  color Yellow]
    [0.6  color Yellow]
    [0.8  color Green]
  }


In this case any value from 0.3 to 0.6 will be pure yellow.

The color_map keyword may be used with any pattern except brick, checker,
hexagon and image_map. You may declare and use color_map identifiers. For
example:

  #declare Rainbow_Colors=
    color_map {
      [0.0   color Magenta]
      [0.33  color Yellow]
      [0.67  color Cyan]
      [1.0   color Magenta]
    }

  object{My_Object
    pigment{
      gradient x
      color_map{Rainbow_Colors}
    }
  }


7.6.1.4          Pigment Maps

In addition to specifying blended colors with a color map you may create a
blend of pigments using a pigment map. The syntax for a pigment map is
identical to a color map except you specify a pigment in each map entry (and
not a color).

A pigment map is specified by...

  pigment{
    PATTERN_TYPE
    pigment_map {
      [ NUM_1 PIGMENT_BODY_1]
      [ NUM_2 PIGMENT_BODY_2]
      [ NUM_3 PIGMENT_BODY_3]
       ...
    }
    PIGMENT_MODIFIERS...
  }


Where NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive. A
PIGMENT_BODY is anything that would normally appear inside a pigment
statement but the pigment keyword and {} braces are not needed. Note that the
[] brackets are part of the actual statement. They are not notational symbols
denoting optional parts. The brackets surround each entry in the map. There
may be from 2 to 256 entries in the map.

For example

  sphere {
    <0,1,2>, 2
    pigment {
      gradient x       //this is the PATTERN_TYPE
      pigment_map {
        [0.3 wood scale 0.2]
        [0.3 Jade]    //this is a pigment identifier
        [0.6 Jade]
        [0.9 marble turbulence 1]
      }
    }
  }


When the gradient x function returns values from 0.0 to 0.3 the scaled wood
pigment is used. From 0.3 to 0.6 the pigment identifier Jade is used. From
0.6 up to 0.9 a blend of Jade and a turbulent marble is used. From 0.9 on up
only the turbulent marble is used.

Pigment maps may be nested to any level of complexity you desire. The
pigments in a map may have color maps or pigment maps or any type of pigment
you want. Any entry of a pigment map may be a solid color however if all
entries are solid colors you should use a color map which will render
slightly faster.

Entire pigments may also be used with the block patterns such as checker,
hexagon and brick. For example...

  pigment {
    checker
    pigment { Jade scale .8 }
    pigment { White_Marble scale .5 }
  }


Note that in the case of block patterns the pigment wrapping is required
around the pigment information.

A pigment map is also used with the average pigment type. See "Average" for
details.

You may not use pigment_map or individual pigments with an image_map. See
section "Texture Maps" for an alternative way to do this.

7.6.1.5          Image Maps

When all else fails and none of the above pigment pattern types meets your
needs you can use an image map to wrap a 2-D bit-mapped image around your 3-D
objects.

7.6.1.5.1        Specifying an Image Map

The syntax for an image map is...

  pigment {
    image_map {
      FILE_TYPE "filename"
      MODIFIERS...
    }
  }


Where FILE_TYPE is one of the following keywords gif, tga, iff, ppm, pgm, png
or sys. This is followed by the name of the file in quotes. Several optional
modifiers may follow the file specification. The modifiers are described
below. Note that earlier versions of POV-Ray allowed some modifiers before
the FILE_TYPE but that syntax is being phased out in favor of the syntax
described here.

Filenames specified in the image_map statements will be searched for in the
home (current) directory first and, if not found, will then be searched for
in directories specified by any -L (library path) options active. This would
facilitate keeping all your image maps files in a separate subdirectory and
giving an -L option on the command line to where your library of image maps
are.

By default, the image is mapped onto the x-y-plane. The image is projected
onto the object as though there were a slide projector somewhere in the
-z-direction. The image exactly fills the square area from (x,y) coordinates
(0,0) to (1,1) regardless of the image's original size in pixels. If you
would like to change this default you may translate, rotate or scale the
pigment or texture to map it onto the object's surface as desired.

In section "Checker" the checker pigment pattern is explained. The checks are
described as solid cubes of colored clay from which objects are carved. With
image maps you should imagine that each pixel is a long, thin, square,
colored rod that extends parallel to the z-axis. The image is made from rows
and columns of these rods bundled together and the object is then carved from
the bundle.

If you would like to change this default orientation you may translate,
rotate or scale the pigment or texture to map it onto the object's surface as
desired.

7.6.1.5.2        The map_type Option

The default projection of the image onto the x-y-plane is called a planar map
type. This option may be changed by adding the map_type keyword followed by a
number specifying the way to wrap the image around the object.

A map_type 0 gives the default planar mapping already described.

A map_type 1 gives a spherical mapping. It assumes that the object is a
sphere of any size sitting at the origin. The y-axis is the north/south pole
of the spherical mapping. The top and bottom edges of the image just touch
the pole regardless of any scaling. The left edge of the image begins at the
positive x-axis and wraps the image around the sphere from west to east in a
-y-rotation. The image covers the sphere exactly once. The once keyword has
no meaning for this mapping type.

With map_type 2 you get a cylindrical mapping. It assumes that a cylinder of
any diameter lies along the y-axis. The image wraps around the cylinder just
like the spherical map but the image remains one unit tall from y=0 to y=1.
This band of color is repeated at all heights unless the once keyword is
applied.

Finally map_type 5 is a torus or donut shaped mapping. It assumes that a
torus of major radius one sits at the origin in the x-z-plane. The image is
wrapped around similar to spherical or cylindrical maps. However the top and
bottom edges of the map wrap over and under the torus where they meet each
other on the inner rim.

Types 3 and 4 are still under development.

Note that the map_type option may also be applied to bump_map and
material_map statements.

7.6.1.5.3        The Filter and Transmit Bitmap Modifiers

To make all or part of an image map transparent you can specify filter and/or
transmit values for the color palette/registers of PNG, GIF or IFF pictures
(at least for the modes that use palettes). You can do this by adding the
keyword filter or transmit following the filename. The keyword is followed by
two numbers. The first number is the palette number value and the second is
the amount of transparency. The values should be separated by a comma. For
example:

  image_map {
    gif "mypic.gif"
    filter   0, 0.5 // Make color 0 50% filtered transparent
    filter   5, 1.0 // Make color 5 100% filtered transparent
    transmit 8, 0.3 // Make color 8 30% non-filtered transparent
  }


You can give the entire image a filter or transmit value using filter all
VALUE or transmit all VALUE. For example:

  image_map {
    gif "stnglass.gif"
    filter all 0.9
  }


Note that early versions of POV-Ray used the keyword alpha to specify
filtered transparency however that word is often used to describe
non-filtered transparency. For this reason alpha is no longer used.

See section "Specifying Colors" for details on the differences between
filtered and non-filtered transparency.

7.6.1.5.4        Using the Alpha Channel

Another way to specify non-filtered transmit transparency in an image map is
by using the alpha channel.

PNG allows you to store a different transparency for each color index in the
PNG file, if desired. If your paint programs support this feature of PNG you
can do the transparency editing within your paint program rather than
specifying transmit values for each color in the POV file. Since PNG and TGA
image formats can also store full alpha channel (transparency) information
you can generate image maps that have transparency which isn't dependent on
the color of a pixel but rather its location in the image.

Although POV uses transmit 0.0 to specify no transparency and 1.0 to specify
full transparency, the alpha data ranges from 0 to 255 in the opposite
direction. Alpha data 0 means the same as transmit 1.0 and alpha data 255
produces transmit 0.0.

7.6.1.6          Quick Color

When developing POV-Ray scenes its often useful to do low quality test runs
that render faster. The +Q command line switch can be used to turn off some
time consuming color pattern and lighting calculations to speed things up.
However all settings of +Q5 or lower turns off pigment calculations and
creates gray objects.

By adding a quick_color to a pigment you tell POV-Ray what solid color to use
for quick renders instead of a patterned pigment. For example:

  pigment {
    gradient x
    color_map{
      [0.0 color Yellow]
      [0.3 color Cyan]
      [0.6 color Magenta]
      [1.0 color Cyan]
    }
    turbulence 0.5
    lambda 1.5
    omega 0.75
    octaves 8
    quick_color Neon_Pink
  }


This tells POV-Ray to use solid Neon_Pink for test runs at quality +Q5 or
lower but to use the turbulent gradient pattern for rendering at +Q6 and
higher.

Note that solid color pigments such as

  pigment {color Magenta}


automatically set the quick_color to that value. You may override this if you
want. Suppose you have 10 spheres on the screen and all are yellow. If you
want to identify them individually you could give each a different
quick_color like this:

  sphere {
    <1,2,3>,4
    pigment { color Yellow  quick_color Red }
  }

  sphere {
    <-1,-2,-3>,4
    pigment { color Yellow  quick_color Blue }
  }


and so on. At +Q6 or higher they will all be yellow but at +Q5 or lower each
would be different colors so you could identify them.

7.6.2            Normal

Ray-tracing is known for the dramatic way it depicts reflection, refraction
and lighting effects. Much of our perception depends on the reflective
properties of an object. Ray tracing can exploit this by playing tricks on
our perception to make us see complex details that aren't really there.

Suppose you wanted a very bumpy surface on the object. It would be very
difficult to mathematically model lots of bumps. We can however simulate the
way bumps look by altering the way light reflects off of the surface.
Reflection calculations depend on a vector called a surface normal vector.
This is a vector which points away from the surface and is perpendicular to
it. By artificially modifying (or perturbing) this normal vector you can
simulate bumps.

The normal statement is the part of a texture which defines the pattern of
normal perturbations to be applied to an object. Like the pigment statement,
you can omit the surrounding texture block to save typing. Do not forget
however that there is a texture implied. For example...

  //this...                    //can be shortened to this...

  object {                     object {
    My_Object                    My_Object
    texture {                    pigment {color Purple}
      pigment {color Purple}     normal {bumps 0.3}
      normal {bumps 0.3}       }
    }
  }


Note that attaching a normal pattern does not really modify the surface. It
only affects the way light reflects or refracts at the surface so that it
looks bumpy.

The most complete form for defining a normal is as follows:

  normal {
    NORMAL_IDENTIFIER
    PATTERN_TYPE FloatValue
    NORMAL_MODIFIERS
    TRANSFORMATIONS...
  }


Each of the items in a normal are optional but if they are present they
should be in the order shown above to insure that the results are as
expected. Any items after the NORMAL_IDENTIFIER modify or override settings
given in the identifier. If no identifier is specified then the items modify
the normal values in the current default texture. The PATTERN_TYPE may
optionally be followed by a float value that controls the apparent depth of
the bumps. Typical values range from 0.0 to 1.0 but any value may be used.
Negative values invert the pattern. The default value if none is specified is
0.5.

Valid NORMAL_MODIFIERS are slope_map, normal_map, bump_map and bump_size
statements as well as any of the generic PATTERN_MODIFIERS such as translate,
rotate, scale, turbulence, wave shape and warp statements. Such modifiers
apply only to the normal and not to other parts of the texture. Modifiers
should be specified last.

There are three basic types of NORMAL_PATTERN_TYPEs. They are pattern
normals, specialized normals and bump maps. They differ in the types of
modifiers you may use with them. Originally POV-Ray had some patterns which
were exclusively used for pigments while others were exclusively used for
normals. Since POV-Ray 3.0 you can use any pattern for either pigments or
normals. For example it is now valid to use ripples as a pigment or wood as a
normal type. The patterns bumps, dents, ripples, waves, wrinkles and bump_map
were once exclusively normal patterns which could not be used as pigments.
Because these six types use specialized normal modification calculations they
cannot have slope_map, normal_map or wave shape modifiers. All other normal
pattern types may use them.

7.6.2.1          Slope Maps

A slope map is a normal pattern modifier which gives the user a great deal of
control over the exact shape of the bumpy features. It is best illustrated
with a gradient normal pattern. Suppose you have...

  plane{ z, 0
    pigment{ White }
    normal { gradient x }
  }


This gives a ramp wave pattern that looks like small linear ramps that climb
from the points at x=0 to x=1 and then abruptly drops to 0 again to repeat
the ramp from x=1 to x=2. A slope map turns this simple linear ramp into
almost any wave shape you want. The syntax is as follows...

  normal{
    PATTERN_TYPE Value
    slope_map {
      [ NUM_1 POINT_SLOPE_1]
      [ NUM_2 POINT_SLOPE_2]
      [ NUM_3 POINT_SLOPE_3]
       ...
    }
    NORMAL_MODIFIERS...
  }


Note that the [] brackets are part of the actual statement. They are not
notational symbols denoting optional parts. The brackets surround each entry
in the slope map. There may be from 2 to 256 entries in the map.

The NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive.
POINT_SLOPE_1, POINT_SLOPE_2, ... are 2 component vectors such as <0,1> where
the first value represents the apparent height of the wave and the second
value represents the slope of the wave at that point. The height should range
between 0.0 and 1.0 but any value could be used.

The slope value is the change in height per unit of distance. For example a
slope of zero means flat, a slope of 1.0 means slope upwards at a 45 degree
angle and a slope of -1 means slope down at 45 degrees. Theoretically a slope
straight up would have infinite slope. In practice, slope values should be
kept in the range -3.0 to +3.0. Keep in mind that this is only the visually
apparent slope. A normal does not actually change the surface.

For example here is how to make the ramp slope up for the first half and back
down on the second half creating a triangle wave with a sharp peak in the
center.

  normal {
    gradient x       // this is the PATTERN_TYPE
    slope_map {
      [0   <0, 1>]   // start at bottom and slope up
      [0.5 <1, 1>]   // halfway through reach top still climbing
      [0.5 <1,-1>]   // abruptly slope down
      [1   <0,-1>]   // finish on down slope at bottom
    }
  }


The pattern function is evaluated and the result is a value from 0.0 to 1.0.
The first entry says that at x=0 the apparent height is 0 and the slope is 1.
At x=0.5 we are at height 1 and slope is still up at 1. The third entry also
specifies that at x=0.5 (actually at some tiny fraction above 0.5) we have
height 1 but slope -1 which is downwards. Finally at x=1 we are at height 0
again and still sloping down with slope -1.

Although this example connects the points using straight lines the shape is
actually a cubic spline. This example creates a smooth sine wave.

  normal {
    gradient x          // this is the PATTERN_TYPE
    slope_map {
      [0    <0.5, 1>]   // start in middle and slope up
      [0.25 <1.0, 0>]   // flat slope at top of wave
      [0.5  <0.5,-1>]   // slope down at mid point
      [0.75 <0.0, 0>]   // flat slope at bottom
      [1    <0.5, 1>]   // finish in middle and slope up
    }
  }


This example starts at height 0.5 sloping up at slope 1. At a fourth of the
way through we are at the top of the curve at height 1 with slope 0 which is
flat. The space between these two is a gentle curve because the start and end
slopes are different. At half way we are at half height sloping down to
bottom out at 3/4ths. By the end we are climbing at slope 1 again to complete
the cycle. There are more examples in slopemap.pov in the sample scenes.

A slope_map may be used with any pattern except brick, checker, hexagon,
bumps, dents, ripples, waves, wrinkles and bump_map.

You may declare and use slope map identifiers. For example:

  #declare Fancy_Wave =
    slope_map {       // Now let's get fancy
      [0.0  <0, 1>]   // Do tiny triangle here
      [0.2  <1, 1>]   //  down
      [0.2  <1,-1>]   //     to
      [0.4  <0,-1>]   //       here.
      [0.4  <0, 0>]   // Flat area
      [0.5  <0, 0>]   //   through here.
      [0.5  <1, 0>]   // Square wave leading edge
      [0.6  <1, 0>]   //   trailing edge
      [0.6  <0, 0>]   // Flat again
      [0.7  <0, 0>]   //   through here.
      [0.7  <0, 3>]   // Start scallop
      [0.8  <1, 0>]   //   flat on top
      [0.9  <0,-3>]   //     finish here.
      [0.9  <0, 0>]   // Flat remaining through 1.0
    }

  object{ My_Object
    pigment { White }
    normal {
      wood
      slope_map { Fancy_Wave }
    }
  }


7.6.2.2          Normal Maps

Most of the time you will apply single normal pattern to an entire surface
but you may also create a pattern or blend of normals using a normal map. The
syntax for a normal map is identical to a pigment map except you specify a
normal in each map entry.

A normal map is specified by...

  normal{
    PATTERN_TYPE
    normal_map {
      [ NUM_1 NORMAL_BODY_1]
      [ NUM_2 NORMAL_BODY_2]
      [ NUM_3 NORMAL_BODY_3]
       ...
    }
    NORMAL_MODIFIERS...
  }


Where NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive. A
NORMAL_BODY is anything that would normally appear inside a normal statement
but the normal keyword and {} braces are not needed. Note that the []
brackets are part of the actual statement. They are not notational symbols
denoting optional parts. The brackets surround each entry in the map. There
may be from 2 to 256 entries in the map.

For example

  normal {
    gradient x       //this is the PATTERN_TYPE
    normal_map {
      [0.3  bumps scale 2]
      [0.3  dents]
      [0.6  dents]
      [0.9  marble turbulence 1]
    }
  }


When the gradient x function returns values from 0.0 to 0.3 then the scaled
bumps normal is used. From 0.3 to 0.6 dents are From 0.6 up to 0.9 a blend of
dents and a turbulent marble is used. From 0.9 on up only the turbulent
marble is used.

Normal maps may be nested to any level of complexity you desire. The normals
in a map may have slope maps or normal maps or any type of normal you want.

A normal map is also used with the average normal type. See "Average" for
details.

Entire normals may also be used with the block patterns such as checker,
hexagon and brick. For example...

  normal {
    checker
      normal { gradient x scale .2 }
      normal { gradient y scale .2 }
    }
  }


Note that in the case of block patterns the normal wrapping is required
around the normal information.

You may not use normal_map or individual normals with a bump_map. See section
"Texture Maps" for an alternative way to do this.

7.6.2.3          Bump Maps

When all else fails and none of the above normal pattern types meets your
needs you can use a bump map to wrap a 2-D bit-mapped bump pattern around
your 3-D objects.

Instead of placing the color of the image on the shape like an image map a
bump map perturbs the surface normal based on the color of the image at that
point. The result looks like the image has been embossed into the surface. By
default, a bump map uses the brightness of the actual color of the pixel.
Colors are converted to gray scale internally before calculating height.
Black is a low spot, white is a high spot. The image's index values may be
used instead (see section "Use_Index and Use_Color" below).

7.6.2.3.1        Specifying a Bump Map

The syntax for bump_map is...

  normal {
    bump_map {
      FILE_TYPE "filename"
      BITMAP_MODIFIERS...
    }
    NORMAL_MODIFIERS...
  }


Where FILE_TYPE is one of the following keywords gif, tga, iff, ppm, pgm, png
or sys. This is followed by the name of the file using any valid string
expression. Several optional modifiers may follow the file specification. The
modifiers are described below. Note that earlier versions of POV-Ray allowed
some modifiers before the FILE_TYPE but that syntax is being phased out in
favor of the syntax described here.

Filenames specified in the bump_map statement will be searched for in the
home (current) directory first and, if not found, will then be searched for
in directories specified by any +L switches or Library_Path options. This
would facilitate keeping all your bump maps files in a separate subdirectory,
and specifying a library path to them. Note that any operating system default
paths are not searched unless you also specify them as a Library_Path.

By default, the bump pattern is mapped onto the x-y-plane. The bumps are
projected onto the object as though there were a slide projector somewhere in
the -z-direction. The bump pattern exactly fills the square area from (x,y)
coordinates (0,0) to (1,1) regardless of the bitmap's original size in
pixels. If you would like to change this default, you may translate, rotate
or scale the normal or texture to map it onto the object's surface as
desired.

The file name is optionally followed by one or more BITMAP_MODIFIERS. The
bump_size, use_color and use_index modifiers are specific to bump maps and
are discussed in the following sections. See section "Bitmap Modifiers" for
other general bitmap modifiers.

After a bump_map statement but still inside the normal statement you may
apply any legal normal modifiers except slope_map and pattern wave forms.

7.6.2.3.2        Bump_Size

The relative bump size can be scaled using the bump_size modifier. The bump
size number can be any number other than 0 but typical values are from about
0.1 to as high as 4.0 or 5.0.

  normal {
    bump_map {
      gif "stuff.gif"
      bump_size 5.0
    }
  }


Originally bump_size could only be used inside a bump map but it can now be
used with any normal. Typically it is used to override a previously defined
size. For example:

  normal {
    My_Normal   //this is a previously defined normal identifier
    bump_size 2.0
  }


7.6.2.3.3        Use_Index and Use_Color

Usually the bump map converts the color of the pixel in the map to a gray
scale intensity value in the range 0.0 to 1.0 and calculates the bumps based
on that value. If you specify use_index, the bump map uses the color's
palette number to compute as the height of the bump at that point. So, color
number 0 would be low and color number 255 would be high (if the image has
256 palette entries). The actual color of the pixels doesn't matter when
using the index. This option is only available on palette based formats. The
use_color keyword may be specified to explicitly note that the color methods
should be used instead. The alternate spelling use_colour is also valid.
These modifiers may only be used inside the bump_map statement.

7.6.3            Finish

The finish properties of a surface can greatly affect its appearance. How
does light reflect? What happens when light passes through? What kind of
highlights are visible. To answer these questions you need a finish
statement.

The finish statement is the part of a texture which defines the various
finish properties to be applied to an object. Like the pigment or normal
statement you can omit the surrounding texture block to save typing. Do not
forget however that there is a texture implied. For example...

  this...                            can be shortened to this...

  object {                           object {
    My_Object                          My_Object
    texture {                          pigment {color Purple}
      pigment {color Purple}           finish {phong 0.3}
      finish {phong 0.3}             }
    }
  }


The most complete form for defining a finish is as follows:

  finish {
    FINISH_IDENTIFIER
    [ ambient COLOR ]
    [ diffuse FLOAT ]
    [ brilliance FLOAT ]
    [ phong FLOAT ]
    [ phong_size FLOAT ]
    [ specular FLOAT ]
    [ roughness FLOAT ]
    [ metallic [ FLOAT ] ]
    [ reflection COLOR ]
    [ refraction FLOAT ]
    [ ior FLOAT ]
    [ caustics FLOAT ]
    [ fade_distance FLOAT ]
    [ fade_power FLOAT ]
    [ irid { thickness FLOAT turbulence VECTOR } ]
    [ crand FLOAT ]
  }


The FINISH_IDENTIFIER is optional but should proceed all other items. Any
items after the FINISH_IDENTIFIER modify or override settings given in the
IDENTIFIER. If no identifier is specified then the items modify the finish
values in the current default texture. Note that transformations are not
allowed inside a finish because finish items cover the entire surface
uniformly.

7.6.3.1          Ambient

The light you see in dark shadowed areas comes from diffuse reflection off of
other objects. This light cannot be directly modeled using ray-tracing.
However we can use a trick called ambient lighting to simulate the light
inside a shadowed area.

Ambient light is light that is scattered everywhere in the room. It bounces
all over the place and manages to light objects up a bit even where no light
is directly shining. Computing real ambient light would take far too much
time, so we simulate ambient light by adding a small amount of white light to
each texture whether or not a light is actually shining on that texture.

This means that the portions of a shape that are completely in shadow will
still have a little bit of their surface color. It's almost as if the texture
glows, though the ambient light in a texture only affects the shape it is
used on.

Usually a single float value is specified even though the syntax calls for a
color. For example a float value of 0.3 gets promoted to the full color
vector <0.3,0.3,0.3,0.3,0.3> which is acceptable because only the red, green
and blue parts are used.

The default value is very little ambient light (0.1). The value can range
from 0.0 to 1.0. Ambient light affects both shadowed and non-shadowed areas
so if you turn up the ambient value you may want to turn down the diffuse
value.

Note that this method doesn't account for the color of surrounding objects.
If you walk into a room that has red walls, floor and ceiling then your white
clothing will look pink from the reflected light. POV-Ray's ambient shortcut
doesn't account for this. There is also no way to model specular reflected
indirect illumination such as the flashlight shining in a mirror.

You may color the ambient light using one of two methods. You may specify a
color rather than a float after the ambient keyword in each finish statement.
For example

   finish { ambient rgb <0.3,0.1,0.1> } //a pink ambient


You may also specify the overall ambient light source used when calculating
the ambient lighting of an object using the global ambient_light setting. The
formula is given by

   AMBIENT = FINISH_AMBIENT * GLOBAL_AMBIENT_LIGHT_SOURCE


7.6.3.2          Diffuse Reflection Items

When light reflects off of a surface the laws of physics say that it should
leave the surface at the exact same angle it came in. This is similar to the
way a billiard ball bounces off a bumper of a pool table. This perfect
reflection is called specular reflection. However only very smooth polished
surfaces reflect light in this way. Most of the time, light reflects and is
scattered in all directions by the roughness of the surface. This scattering
is called diffuse reflection because the light diffuses or spreads in a
variety of directions. It accounts for the majority of the reflected light we
see.

POV-Ray and most other ray-tracers can only simulate directly one of these
three types of illumination. That is the light which comes directly from
actual light sources. Light coming from other objects such as mirrors via
specular reflection (shine a flashlight onto a mirror for example). And last
not least light coming from other objects via diffuse reflections (look at
some dark area under a desk or in a corner: even though a lamp may not
directly illuminate that spot you can still see a little bit because light
comes from diffuse reflection off of nearby objects).

7.6.3.2.1        Diffuse

The keyword diffuse is used in a finish statement to control how much of the
light coming directly from any light sources is reflected via diffuse
reflection. For example

  finish {diffuse 0.7}


means that 70% of the light seen comes from direct illumination from light
sources. The default value is diffuse 0.6.

7.6.3.2.2        Brilliance

The amount of direct light that diffuses from an object depends upon the
angle at which it hits the surface. When light hits at a shallow angle it
illuminates less. When it is directly above a surface it illuminates more.
The brilliance keyword can be used in a finish statement to vary the way
light falls off depending upon the angle of incidence. This controls the
tightness of the basic diffuse illumination on objects and slightly adjusts
the appearance of surface shininess. Objects may appear more metallic by
increasing their brilliance. The default value is 1.0. Higher values from to
about 10.0 cause the light to fall off less at medium to low angles. There
are no limits to the brilliance value. Experiment to see what works best for
a particular situation. This is best used in concert with highlighting.

7.6.3.2.3        Crand Graininess

Very rough surfaces, such as concrete or sand, exhibit a dark graininess in
their apparent color. This is caused by the shadows of the pits or holes in
the surface. The crand keyword can be added to cause a minor random darkening
in the diffuse reflection of direct illumination. Typical values range from
crand 0.01 to crand 0.5 or higher. The default value is 0. For example:

  finish { crand 0.05 }


The grain or noise introduced by this feature is applied on a pixel-by-pixel
basis. This means that it will look the same on far away objects as on close
objects. The effect also looks different depending upon the resolution you
are using for the rendering. For these reasons it is not a very accurate way
to model the rough surface effect but some objects still look better with a
little crand thrown in.

Note that this should not be used when rendering animations. This is the one
of a few truly random features in POV-Ray and will produce an annoying
flicker of flying pixels on any textures animated with a crand value.

7.6.3.3          Highlights

Highlights are the bright spots that appear when a light source reflects off
of a smooth object. They are a blend of specular reflection and diffuse
reflection. They are specular-like because they depend upon viewing angle and
illumination angle. However they are diffuse-like because some scattering
occurs. In order to exactly model a highlight you would have to calculate
specular reflection off of thousands of microscopic bumps called micro
facets. The more that micro facets are facing the viewer the shinier the
object appears and the tighter the highlights become. POV-Ray uses two
different models to simulate highlights without calculating micro facets.
They are the specular and Phong models.

Note that specular and Phong highlights are not mutually exclusive. It is
possible to specify both and they will both take effect. Normally, however,
you will only specify one or the other.

7.6.3.3.1        Phong Highlights

The phong keyword controls the amount of Phong highlighting on the object. It
causes bright shiny spots on the object that are the color of the light
source being reflected.

The Phong method measures the average of the facets facing in the mirror
direction from the light sources to the viewer.

Phong's value is typically from 0.0 to 1.0, where 1.0 causes complete
saturation to the light source's color at the brightest area (center) of the
highlight. The default phong 0.0 gives no highlight.

The size of the highlight spot is defined by the phong_size value. The larger
the phong size the tighter, or smaller, the highlight and the shinier the
appearance. The smaller the phong size the looser, or larger, the highlight
and the less glossy the appearance.

Typical values range from 1.0 (very dull) to 250 (highly polished) though any
values may be used. Default phong size is 40 (plastic) if phong_size is not
specified. For example:

  finish { phong 0.9 phong_size 60 }


7.6.3.3.2        Specular Highlight

A specular highlight is very similar to Phong highlighting but it uses
slightly different model. The specular model more closely resembles real
specular reflection and provides a more credible spreading of the highlights
occurring near the object horizons.

The specular value is typically from 0.0 to 1.0, where 1.0 causes complete
saturation to the light source's color at the brightest area (center) of the
highlight. The default specular 0.0 gives no highlight.

The size of the spot is defined by the value given for roughness. Typical
values range from 1.0 (very rough - large highlight) to 0.0005 (very smooth -
small highlight). The default value, if roughness is not specified, is 0.05
(plastic).

It is possible to specify wrong values for roughness that will generate an
error when you try to render the file. Don't use 0 and if you get errors
check to see if you are using a very, very small roughness value that may be
causing the error. For example:

  finish {specular 0.9  roughness 0.02}


7.6.3.3.3        Metallic Highlight Modifier

The keyword metallic may be used with Phong or specular highlights. This
keyword indicates that the color of the highlights will be calculated by an
empirical function that models the reflectivity of metallic surfaces.

White light reflected specularly from a metallic surface takes the color of
the surface, except then the incidence angle approaches 90 degrees, where it
becomes white again.

The metallic keyword may be follow by a numeric value to specify the
influence the above effect has (the default value is one). For example:

  finish {
    phong 0.9
    phong_size 60
    metallic
  }


7.6.3.4          Specular Reflection

When light does not diffuse and it does reflect at the same angle as it hits
an object, it is called specular reflection. Such mirror-like reflection is
controlled by the reflection keyword in a finish statement. For example:

  finish { reflection 1.0 ambient 0 diffuse 0 }


This gives the object a mirrored finish. It will reflect all other elements
in the scene. Usually a single float value is specified after the keyword
even though the syntax calls for a color. For example a float value of 0.3
gets promoted to the full color vector < 0.3,0.3,0.3,0.3,0.3> which is
acceptable because only the red, green and blue parts are used.

The value can range from 0.0 to 1.0. By default there is no reflection.

Adding reflection to a texture makes it take longer to render because an
additional ray must be traced. The reflected light may be tinted by
specifying a color rather than a float. For example

   finish { reflection rgb <1,0,0> }


gives a real red mirror that only reflects red light.

Note that although such reflection is called specular it is not controlled by
the specular keyword. That keyword controls a specular highlight.

7.6.3.5          Refraction

When light passes through a surface either into or out of a dense medium the
path of the ray of light is bent. Such bending is called refraction. Normally
transparent or semi-transparent surfaces in POV-Ray do not refract light.
Adding refraction 1.0 to the finish statement turns on refraction.

Note that it is recommended that you only use refraction 0 or refraction 1
(or even better refraction off and refraction on). Values in between will
darken the refracted light in ways that do not correspond to any physical
property. Many POV-Ray scenes were created with intermediate refraction
values before this bug was discovered so the feature has been maintained. A
more appropriate way to reduce the brightness of refracted light is to change
the filter or transmit value in the colors specified in the pigment
statement. Note also that refraction does not cause the object to be
transparent. Transparency only occurs if there is a non-zero filter or
transmit value in the color.

The amount of bending or refracting of light depends upon the density of the
material. Air, water, crystal and diamonds all have different densities and
thus refract differently. The index of  refraction or ior value is used by
scientists to describe the relative density of substances. The ior keyword is
used in POV-Ray to specify the value. For example:

  texture {
    pigment { White filter 0.9 }
    finish {
      refraction 1
      ior 1.5
    }
  }


The default ior value of 1.0 will give no refraction. The index of refraction
for air is 1.0, water is 1.33, glass is 1.5 and diamond is 2.4. The file
consts.inc pre-defines several useful values for ior.

Note that if a texture has a filter component and no value for refraction and
ior are supplied the renderer will simply transmit the ray through the
surface with no bending. In layered textures, the refraction and ior keywords
must be in the last texture, otherwise they will not take effect.

7.6.3.5.1        Light Attenuation

Light attenuation is used to model the decrease in light intensity as the
light travels through a translucent object. Its syntax is:

  finish {
    fade_distance FADE_DISTANCE
    fade_power FADE_POWER
  }


The fade_distance keyword determines the distance the light has to travel to
reach half intensity while the fade_power keyword describes how fast the
light will fall off. For realistic effects a fade power of 1 to 2 should be
used.

The attenuation is calculated by a formula similar to that used for light
source attenuation.

                                 1
  attenuation = --------------------------------------
                 1 + (d / FADE_DISTANCE) ^ FADE_POWER


7.6.3.5.2        Faked Caustics

Caustics are light effects that occur if light is reflected or refrected by
specular reflective or refractive surfaces. Imagine a glass of water standing
on a table. If sunlight falls onto the glass you will see spots of light on
the table. Some of the spots are caused by light being reflected by the glass
while some of them are caused by light being refratced by the water in the
glass.

Since it is a very difficult and time-consuming process to actually calculate
those effects (though it is not impossible) POV-Ray uses a quite simple
method to simulate caustics caused by refraction. This caustic effect is
limited to areas that are shaded by the translucent object. You'll get no
caustic effects from reflective surfaces nor in parts that are not shaded by
the object.

The syntax is:

  finish {
    caustics POWER
  }


7.6.3.6          Iridescence

Iridescence, or Newton's thin film interference, simulates the effect of
light on surfaces with a microscopic transparent film overlay. The effect is
like an oil slick on a puddle of water or the rainbow hues of a soap bubble
(see also "Irid_Wavelength").

The syntax is:

  finish {
    irid {
      AMOUNT
      thickness FLOAT
      turbulence VECTOR
    }
  }


This finish modifies the surface color as a function of the angle between the
light source and the surface. Since the effect works in conjunction with the
position and angle of the light sources to the surface it does not behave in
the same ways as a procedural pigment pattern.

The AMOUNT parameter is the contribution of the iridescence effect to the
overall surface color. As a rule of thumb keep to around 0.25 (25%
contribution) or less, but experiment. If the surface is coming out too
white, try lowering the diffuse and possibly the ambient values of the
surface.

The thickness keyword represents the film's thickness. This is an awkward
parameter to set, since the thickness value has no relationship to the
object's scale. Changing it affects the scale or busy-ness of the effect. A
very thin film will have a high frequency of color changes while a thick film
will have large areas of color.

The thickness of the film can be varied with the turbulence keyword. You can
only specify the amount of turbulence with iridescence. The octaves, lambda,
and omega values are internally set and are not adjustable by the user at
this time.

In addition, perturbing the object's surface normal through the use of bump
patterns will affect iridescence.

For the curious, thin film interference occurs because, when the ray hits the
surface of the film, part of the light is reflected from that surface, while
a portion is transmitted into the film. This subsurface ray travels through
the film and eventually reflects off the opaque substrate. The light emerges
from the film slightly out of phase with the ray that was reflected from the
surface.

This phase shift creates interference, which varies with the wavelength of
the component colors, resulting in some wavelengths being reinforced, while
others are cancelled out. When these components are recombined, the result is
iridescence.

The concept used for this feature came from the book Fundamentals  of
Three-Dimensional Computer Graphics by Alan Watt (Addison-Wesley).

7.6.4            Halo

Important notice: The halo feature in POV-Ray 3.0 are somewhat experimental.
There is a high probability that the design and implementation of these
features will be changed in future versions. We cannot guarantee that scenes
using these features in 3.0 will render identically in future releases or
that full backwards compatibility of language syntax can be maintained.

A halo is used to simulate some of the atmospheric effects that occur when
small particles interact with light or radiate on their own. Those effects
include clouds, fogs, fire, etc.

Halos are attached to an object, the so called container object, which they
completely fill. If the object is partially or completely translucent and the
object is specified to be hollow (see section "Hollow" for more details) the
halo will be visible. Thus the halo effects are limited to the space that the
object covers. This should always be kept in mind.

What the halo actually will look like depends on a lot of parameters. First
of all you have to specify which kind of effect you want to simulate. After
this you need to define the distribution of the particles. This is basically
done in two steps: a mapping function is selected and a density function is
chosen. The first function maps world coordinates onto a one-dimensional
interval while the later describes how this linear interval is mapped onto
the final density values.

The properties of the particles, such as their color and their translucency,
are given by a color map. The density values calculated by the mapping
processes are used to determine the appropriate color using this color map.

A ray marching process is used to volume sample the halo and to accumulate
the intensities and opacity of each interval.

The following sections will describe all of the halo parameters in more
detail. The complete halo syntax is given by:

  halo {
    attenuating | emitting | glowing | dust
    [ constant | linear | cubic | poly ]
    [ planar_mapping | spherical_mapping |
      cylindrical_mapping | box_mapping ]
    [ dust_type DUST_TYPE ]
    [ eccentricity ECCENTRICITY ]
    [ max_value MAX_VALUE ]
    [ exponent EXPONENT ]
    [ samples SAMPLES ]
    [ aa_level AA_LEVEL ]
    [ aa_threshold AA_THRESHOLD ]
    [ jitter JITTER ]
    [ turbulence <TURBULENCE> ]
    [ octaves OCTAVES ]
    [ omega OMEGA ]
    [ lambda LAMBDA ]
    [ colour_map COLOUR_MAP ]
    [ frequency FREQUENCY ]
    [ phase PHASE ]
    [ scale <VECTOR> ]
    [ rotate <VECTOR> ]
    [ translate <VECTOR> ]
  }


7.6.4.1          Halo Mapping

As described above the actual particle distribution and halo appearance is
influenced by a lot of parameters. The steps that are performed during the
halo calculation will be explained below. It will also be noted where the
different halo keywords will have an effect on the calculations.

  1.Depending on the current sampling position along the ray, point P
    (coordinates x, y, z) inside the halo container object is calculated. The
    actual location is influenced by the jitter keyword, the number of
  2.Point P is transformed into point Q using the (current) halo'sd).
    transformation. Here all local halo transformations come into play, i.e.
  3.Turbulence is added to point Q. The amount of turbulence is given by the
    urbulence keyword. The turbulence calculation is influenced by the
  4.Radius r is calculated depending on the specified density mapping
    (planar_mapping, spherical_mapping, cylindrical_mapping, box_mapping).
  5.The density d is calculated from the radius r using the specified density
    function (constant, linear, cubic, poly) and the maximum value given by
  6.The density d is first multiplied by the frequency value, added to the
    phase value and clipped to the range from 0 to 1 before it is used to get
    the color from the color_map . If an attenuating halo is used the color
    will be determined by the total density along the ray and not by the sum
    of the colors for each sample.


All steps are repeated for each sample point along the ray that is inside the
halo container object. Steps 2 through 6 are repeated for all halos attached
to the halo container object.

It should be noted that in order to get a finite particle distribution, i. e.
a particle distribution that vanishes outside a finite area, a finite density
mapping and a finite density function has to be used.

A finite density mapping gives the constant value one for all points outside
a finite area. The box and spherical mappings are the only finite mapping
types.

A finite density function vanishes for all parameter values above one (there
are no negative parameter values). The only infinite density function is the
constant function.

Finite particle distributions are especially useful because they can always
be transformed to stay inside the halo container object. If particles leave
the container object they become invisible and the surface of the container
will be visible due to the density discontinuity at the surface.

7.6.4.2          Multiple Halos

It is possible to put more than one halo inside a container object. This is
simply done by putting more than one halo statement inside the container
object statement like:

  sphere { 0, 1
    pigment { Clear }
    halo { here comes halo nr. 1 }
    halo { here comes halo nr. 2 }
    halo { here comes halo nr. 3 }
    ...
  }


The effects of the different halos are added. This is in fact similar to the
CSG union operation.

You should note that currently multiple attenuating halos will use the color
map of the last halo only. It is not possible to use different color maps for
multiple attenuating halos.

7.6.4.3          Halo Type

The type of the halo is defined by one of the following mutually exclusive
keywords (if more than one is specified the last will be used). The default
is attenuating.

  halo {
    attenuating | emitting | glowing | dust
  }


The halo type determines how the light will interact with the particles
inside the container object. There are two basic categories of light
interaction: self-illuminated and illuminated. The first type includes the
attenuating, emitting and glowing effects while the dust effect is of the
second type.


7.6.4.3.1        Attenuating

The attenuating halo that only absorbs light passing through it is rendered
by accumulating the particle density along a ray. The total halo color is
determined from the total, accumulated density and the specified color map
(see section "Halo Color Map" for details about the color map). The
background light, i. e. the light passing through the halo, is attenuated by
the total density and added to the total halo color to get the final color of
the halo.

This model is suited to render particle distributions with a high albedo
because the final color does not depend on the transparency of single volume
elements but only on the total transparency along the ray. The albedo of a
particle is given by the amount of light scattered by this particle in all
directions in relation to the amount of incoming light. If the particle
doesn't absorb any light the albedo is one.

Clouds and steams are two of the effects that can be rendered quite realistic
by adding enough turbulence.

7.6.4.3.2        Dust

The dust halo consists of particles that do not emit any light. They only
reflect and absorb incoming light. Its syntax is:

  halo {
    dust
    [ dust_type DUST_TYPE ]
    [ eccentricity ECCENTRICITY ]
  }


As the ray marches through the dust all light coming from any light sources
is accumulated and scattered according to the dust type and the current dust
density. Since this light accumulation includes a test for occlusion, other
objects may cast shadows into the dust.

The same scattering types that are used with the atmosphere in section
"Atmosphere" can be used with the dust (the default type is isotropic
scattering). They are:

  #declare ISOTROPIC_SCATTERING         = 1
  #declare MIE_HAZY_SCATTERING          = 2
  #declare MIE_MURKY_SCATTERING         = 3
  #declare RAYLEIGH_SCATTERING          = 4
  #declare HENYEY_GREENSTEIN_SCATTERING = 5


The Henyey-Greenstein function needs the additional parameter eccentricity
that is described in the section about atmosphere. This keyword only applies
to dust type 5, the Henyey-Greenstein scattering.

7.6.4.3.3        Emitting

Emitting halos only emit light. Every particle is a small light source that
emits some light. This light is not attenuated by the other particles because
they are assumed to be very small.

As the ray travels through the density field of an emitting halo the color of
the particles in each volume element and their differential transparency is
determined from the color map. These intensities are accumulated to get the
total color of the density field. This total intensity is added to the light
passing through the halo. The background light is attenuated by the total
density of the halo.

Since the emitted light is not attenuated it can be used to model effects
like fire, explosions, light beams, etc. By choosing a well suited color map
those effects can be rendered with a high degree of realism.

Fire is best modeled using planar mapping. Spherical mapping and high
turbulence values can be used to create explosions (it's best to use a
periodic color map and frequencies larger than one).

Emitting halos do not cast any light on other objects like light sources do,
even though they are made up of small, light-emitting particles. In order to
make them actually emit light hundreds or thousands of small light sources
would have to be used. This would slow down tracing by a degree that would
make it useless.

7.6.4.3.4        Glowing

The glowing halo is similar to the emitting halo. The difference is that the
light emitted by the particles is attenuated by the other particles. This can
be seen as a combination of the attenuating and the emitting model.

7.6.4.4          Density Mapping

The density mapping is used to map points in space onto a linear,
one-dimensional interval between 0.0 and 1.0, thus describing the appearance
of the three-dimensional particle distribution. The different mapping types
are specified by:

  halo {
    planar_mapping | spherical_mapping |
    cylindrical_mapping | box_mapping
  }


The default mapping type is planar mapping.

Since the mapping takes place in relation to the origin of the world
coordinate system the following rule must always be kept in mind: Halo
container objects ought to be unit sized objects centered at the origin. They
can be transformed later to suit the individuals needs.

The different mapping types are explained in more detail in the following
sections.

7.6.4.4.1        Box Mapping

The box mapping can be used to create a box-shaped particle distribution. The
mapping is calculated by getting the maximum of the absolute values of each
coordinate as given by the formula:

  r(x, y, z) = max(abs(x), abs(y), abs(z))


7.6.4.4.2        Cylindrical Mapping

The distance r(x,y,z) from the y-axis given by

  r(x, y, z) = sqrt(x*x + z*z)


is used to get the interval values. Values larger than one are clipped to
one.

7.6.4.4.3        Planar Mapping

The distance r(x,y,z) from the x-z-plane given by

  r(x, y, z) = abs(y)


is used to get the interval values. Values larger than one are clipped to
one.

7.6.4.4.4        Spherical Mapping

The distance r(x,y,z) from the origin given by

  r(x, y, z) = sqrt(x*x + y*y + z*z)


is used to get the interval values. Values larger than one are clipped to
one.

7.6.4.5          Density Function

The density function determines how the actual density values are calculated
from the linear, one-dimensional interval that resulted from the density
mapping.

The density function is specified by the following keywords:

  halo {
    [ constant | linear | cubic | poly ]
    [ max_value MAX_VALUE ]
    [ exponent EXPONENT ]
  }


The exponent keyword is only used together with the poly density function.

The individual functions f(r) are described in the following sections. They
all map the value r(x,y,z) calculated by the density mapping onto a suitable
density range between 0 and MAX_VALUE (specified with the keyword max_value).

7.6.4.5.1        Constant

The constant function gives the constant value MAX_VALUE regardless of the
interval value and the type of density mapping. It is calculated by the
trivial formula   f(r) = MAX_VALUE.


The constant density function.

The constant density function can be used to create a constant particle
distribution that is only constrained by the container object.

7.6.4.5.2        Linear

A linear falloff from MAX_VALUE at r=0 to zero at r=1 is created with the
linear density function. It is given by:

  f(r) = MAX_VALUE * (1 - r)


7.6.4.5.3        Cubic

The cubic function gives a smooth blend between the maximum value MAX_VALUE
at r=0 and 0 at r=1. It is given by:

  f(r) = MAX_VALUE * (2 * r  - 3) * r * r + 1


The cubic density function.


7.6.4.5.4        Poly

A polynomial function can be used to get a large variety of density
functions. All have the maximum value MAX_VALUE at r=0 and the minimum value
0 at r=1. It is given by:

  f(r) = MAX_VALUE * (1 - r) ^ EXPONENT


The polynomial density function for different exponent values.

The exponent is given by the exponent keyword. In case of EXPONENT=0 you'll
get a linear falloff.

7.6.4.6          Halo Color Map

The density f(r), which ranges from 0 to MAX_VALUE, is mapped onto the color
map to get the color and differential translucency for each volume element as
the ray marches through the density field (the final color of attenuating
halos is calculated from the total density; see section "Halo Mapping" and
section "Attenuating"). The differential translucency determines for each
value of f(r) how much the total opacity has to be increased (or decreased).

The color map is specified by:

  halo {
    [ colour_map COLOUR_MAP ]
  }


The differential translucency is stored in the transmittance channel of the
map's color entries. A simple example is given by

  colour_map {
    [0 rgbt<1, 1, 1, 1>]
    [1 rgbt<1, 1, 1, 0>]
  }


In this example areas with a low density (small f(r)) will be translucent
(large differential translucency of 1=100%) and areas with a high density
(large f(r)) will be opaque (small differential translucency of 0=0%). You
should note that negative transmittance values can be used to create very
dense fields.

In the case of the dust halo the filter channels of the colors in the color
map are used to specify the amount of light that will be filtered by the
corresponding color map entry. For all other halo types the filter value is
ignored.


7.6.4.7          Halo Sampling

The halo effects are calculated by marching through the density field along a
ray. At discrete steps samples are taken from the density field and evaluated
according to the color map and all other parameters. The effects of all
volume elements are accumulated to get the total effect.

The following parameters are used to tune the sampling process:

  halo {
    [ samples SAMPLES ]
    [ aa_level AA_LEVEL ]
    [ aa_threshold AA_THRESHOLD ]
    [ jitter JITTER ]
  }


7.6.4.7.1        Number of Samples

The number of samples that are taken along the ray inside the halo container
object is specified by the samples keyword. The greater the number of samples
the more denser the density field is sampled and the more accurate but slower
the result will be.

The default number of samples is 10. This is sufficient for simple density
fields that don't use turbulence.

High turbulence values and dust halos normally need a large number of samples
to avoid aliasing artifacts.

7.6.4.7.2        Super-Sampling

The sampling is prone to alias (like the atmosphere sampling in section
"Atmosphere"). One way to reduce possible aliasing artifacts is to use
super-sampling. If two neighboring samples differ too much an additional
sampling is taken in-between. This process recurses until the values of the
samples are close too each other or the maximum recursion level given by
aa_level is reached. The threshold to kick super-sampling in is given by
aa_threshold.

By default super-sampling is not used. The default values for aa_threshold
and aa_level are 0.3 and 3 respectively.

7.6.4.7.3        Jitter

Jitter can be used to introduce some noise to the sampling locations. This
may help to reduce aliasing artifacts at the cost of an increased noise level
in the image. Since the human visual system is much more forgiving to noise
than it is to regular patterns this is not much of a problem.

By default jittering is not used. The values should be smaller than 1.0.


7.6.4.8          Halo Modifiers

This section covers all general halo modifiers. They are:

  halo {
    [ turbulence <TURBULENCE> ]
    [ octaves OCTAVES ]
    [ omega OMEGA ]
    [ lambda LAMBDA ]
    [ frequency FREQUENCY ]
    [ phase PHASE ]
    [ scale <VECTOR> ]
    [ rotate <VECTOR> ]
    [ translate <VECTOR> ]
  }


7.6.4.8.1        Frequency Modifier

The frequency parameter adjusts the number of times the density interval is
mapped onto itself, i. e. the range from 0.0 to 1.0, before it is mapped onto
the color map. The formula doing this is:

  f_new(r) = (f(r) * FREQUENCY + PHASE) modulo 1.0


7.6.4.8.2        Phase Modifier

The phase parameter determines the offset at which the mapping of the density
field onto itself starts. See the formula in the previous section for how the
pahse is used.


7.6.4.8.3        Transformation Modifiers

Halos can be transformed using the rotate, scale and translate keywords. You
have to be careful that you don't move the density field out of the container
object though.

7.6.5            Special Textures

Special textures are complex textures made up of multiple textures. The
component textures may be plain textures or may be made up of special
textures. A plain texture has just one pigment, normal and finish statement
(and maby some halo statements). Even a pigment with a pigment map is still
one pigment and thus considered a plain texture as are normals with normal
map statements.

Special textures use either a texture_map keyword to specify a blend or
pattern of textures or they use a bitmap similar to an image map called a
material map (specified with the material_map keyword).

There are restrictions on using special textures. A special texture may not
be used as a default texture (see section "Default Directive"). A special
texture cannot be used as a layer in a layered texture however you may use
layered textures as any of the textures contained within a special texture.

7.6.5.1          Texture Maps

In addition to specifying blended color with a color map or a pigment map you
may create a blend of textures using texture_map. The syntax for a texture
map is identical to the pigment map except you specify a texture in each map
entry.

A texture map is specified by...

  texture{
    PATTERN_TYPE
    texture_map {
      [ NUM_1 TEXTURE_BODY_1]
      [ NUM_2 TEXTURE_BODY_2]
      [ NUM_3 TEXTURE_BODY_3]
       ...
    }
    TEXTURE_MODIFIERS...
  }


Where NUM_1, NUM_2, ... are float values between 0.0 and 1.0 inclusive. A
TEXTURE_BODY is anything that would normally appear inside a texture
statement but the texture keyword and {} braces are not needed. Note that the
[] brackets are part of the actual statement. They are not notational symbols
denoting optional parts. The brackets surround each entry in the map. There
may be from 2 to 256 entries in the map.

For example:

  texture {
    gradient x       //this is the PATTERN_TYPE
    texture_map {
      [0.3  pigment{Red} finish{phong 1}]
      [0.3  T_Wood11]    //this is a texture identifier
      [0.6  T_Wood11]
      [0.9  pigment{DMFWood4} finish{Shiny}]
    }
  }


When the gradient x function returns values from 0.0 to 0.3 the red
highlighted texture is used. From 0.3 to 0.6 the texture identifier T_Wood11
is used. From 0.6 up to 0.9 a blend of T_Wood11 and a shiny DMFWood4 is used.
From 0.9 on up only the shiny wood is used.

Texture maps may be nested to any level of complexity you desire. The
textures in a map may have color maps or texture maps or any type of texture
you want.

The blended area of a texture map works by fully calculating both
contributing textures in their entirety and then linearly interpolating the
apparent colors. This means that reflection, refraction and lighting
calculations are done twice for every point. This is in contrast to using a
pigment map and a normal map in a plain texture, where the pigment is
computed, then the normal, then reflection, refraction and lighting are
calculated once for that point.

Entire textures may also be used with the block patterns such as checker,
hexagon and brick. For example...

  texture {
    checker
      texture { T_Wood12 scale .8 }
      texture {
        pigment { White_Marble }
        finish { Shiny }
        scale .5
      }
    }
  }


Note that in the case of block patterns the texture wrapping is required
around the texture information. Also note that this syntax prohibits the use
of a layered texture however you can work around this by declaring a texture
identifier for the layered texture and referencing the identifier.

A texture map is also used with the average pattern type. See "Average" for
details.

7.6.5.2          Tiles

Earlier versions of POV-Ray had a special texture called tiles texture that
created a checkered pattern of textures. Although it is still supported for
backwards computability you should use a checker block texture pattern
described in section "Texture Maps" rather than tiles textures.

7.6.5.3          Material Maps

The material map special texture extends the concept of image maps to apply
to entire textures rather than solid colors. A material map allows you to
wrap a 2-D bit-mapped texture pattern around your 3-D objects.

Instead of placing a solid color of the image on the shape like an image map,
an entire texture is specified based on the index or color of the image at
that point. You must specify a list of textures to be used like a texture
palette rather than the usual color palette.

When used with mapped file types such as GIF, and some PNG and TGA images,
the index of the pixel is used as an index into the list of textures you
supply. For unmapped file types such as some PNG and TGA images the 8 bit
value of the red component in the range 0-255 is used as an index.

If the index of a pixel is greater than the number of textures in your list
then the index is taken modulo N where N is the length of your list of
textures.

7.6.5.3.1        Specifying a Material Map

The syntax of a material map is...

  texture {
    material_map {
      FILE_TYPE "filename"
      BITMAP_MODIFIERS...
      texture {...} // First used for index 0
      texture {...} // Second texture used for index 1
      texture {...} // Third texture used for index 2
      texture {...} // Fourth texture used for index 3
                    // and so on for however many used.
    }
    TRANSFORMATION...
  }


Where FILE_TYPE is one of the following keywords gif, tga, iff, ppm, pgm, png
or sys. This is followed by the name of the file using any valid string
expression. Several optional modifiers may follow the file specification. The
modifiers are described below. Note that earlier versions of POV-Ray allowed
some modifiers before the FILE_TYPE but that syntax is being phased out in
favor of the syntax described here.

Filenames specified in the material_map statements will be searched for in
the home (current) directory first and, if not found, will then be searched
for in directories specified by any +L switches or Library_Path options. This
would facilitate keeping all your material map files in a separate
subdirectory and specifying a library path to them. Note that any operating
system default paths are not searched unless you also specify them as a
Library_Path.

By default, the material is mapped onto the x-y-plane. The material is
projected onto the object as though there were a slide projector somewhere in
the -z-direction. The material exactly fills the square area from (x,y)
coordinates (0,0) to (1,1) regardless of the bitmap's original size in
pixels. If you would like to change this default you may translate, rotate or
scale the texture to map it onto the object's surface as desired.

The file name is optionally followed by one or more BITMAP_MODIFIERS. See
section "Bitmap Modifiers" for other details.

After a material_map statement but still inside the texture statement you may
apply any legal texture modifiers. Note that no other pigment, normal, finish
or halo statements may be added to the texture outside the material map. The
following is illegal:

  texture {
    material_map {
      gif "matmap.gif"
      texture {T1}
      texture {T2}
      texture {T3}
    }
    finish {phong 1.0}
  }


The finish must be individually added to each texture.

Note that earlier versions of POV-Ray allowed such specifications but they
were ignored. The above restrictions on syntax were necessary for various bug
fixes. This means some POV-Ray 1.0 scenes using material maps many need minor
modifications that cannot be done automatically with the version
compatibility mode.

If particular index values are not used in an image then it may be necessary
to supply dummy textures. It may be necessary to use a paint program or other
utility to examine the map file's palette to determine how to arrange the
texture list.

The textures within a material map texture may be layered but material map
textures do not work as part of a layered texture. To use a layered texture
inside a material map you must declare it as a texture identifier and invoke
it in the texture list.

7.6.6            Layered Textures

It is possible to create a variety of special effects using layered textures.
A layered texture consists of several textures that are partially transparent
and are laid one on top of the other to create a more complex texture. The
different texture layers show through the transparent portions to create the
appearance of one texture that is a combination of several textures.

You create layered textures by listing two or more textures one right after
the other. The last texture listed will be the top layer, the first one
listed will be the bottom layer. All textures in a layered texture other than
the bottom layer should have some transparency. For example:

  object {
    My_Object
    texture {T1}  // the bottom layer
    texture {T2}  // a semi-transparent layer
    texture {T3}  // the top semi-transparent layer
  }


In this example T2 shows only where T3 is transparent and T1 shows only where
T2 and T3 are transparent.

The color of underlying layers is filtered by upper layers but the results do
not look exactly like a series of transparent surfaces. If you had a stack of
surfaces with the textures applied to each, the light would be filtered
twice: once on the way in as the lower layers are illuminated by filtered
light and once on the way out. Layered textures do not filter the
illumination on the way in. Other parts of the lighting calculations work
differently as well. The results look great and allow for fantastic looking
textures but they are simply different from multiple surfaces. See stones.inc
in the standard include files directory for some magnificent layered
textures.

Note layered textures must use the texture wrapped around any pigment, normal
or finish statements. Do not use multiple pigment, normal or finish
statements without putting them inside the texture statement.

Layered textures may be declared. For example

  #declare Layered_Examp =
    texture {T1}
    texture {T2}
    texture {T3}


may be invoked as follows:

  object {
    My_Object
    texture {
      Layer_Examp
      // Any pigment, normal or finish here
      // modifies the bottom layer only.
    }
  }


If you wish to use a layered texture in a block pattern, such as checker,
hexagon, or brick, or in a material map, you must declare it first and then
reference it inside a single texture statement. A special texture cannot be
used as a layer in a layered texture however you may use layered textures as
any of the textures contained within a special texture.

7.6.7            Patterns

POV-Ray uses a method called three-dimensional solid texturing to define the
color, bumpiness and other properties of a surface. You specify the way that
the texture varies over a surface by specifying a pattern. Patterns are used
in pigments, normals and texture maps.

All patterns in POV-Ray are three dimensional. For every point in space, each
pattern has a unique value. Patterns do not wrap around a surface like
putting wallpaper on an object. The patterns exist in 3d and the objects are
carved from them like carving an object from a solid block of wood or stone.

Consider a block of wood. It contains light and dark bands that are
concentric cylinders being the growth rings of the wood. On the end of the
block you see these concentric circles. Along its length you see lines that
are the veins. However the pattern exists throughout the entire block. If you
cut or carve the wood it reveals the pattern inside. Similarly an onion
consists of concentric spheres that are visible only when you slice it.
Marble stone consists of wavy layers of colored sediments that harden into
rock.

These solid patterns can be simulated using mathematical functions. Other
random patterns such as granite or bumps and dents can be generated using a
random number system and a noise function.

In each case, the x, y, z coordinate of a point on a surface is used to
compute some mathematical function that returns a float value. When used with
color maps or pigment maps, that value looks up the color of the pigment to
be used. In normal statements the pattern function result modifies or
perturbs the surface normal vector to give a bumpy appearance. Used with a
texture map, the function result determines which combinations of entire
textures to be used.

The following sections describe each pattern. See the sections "Pigment" and
"Normal" for more details on how to use patterns.

7.6.7.1          Agate

The agate pattern is a banded pattern similar to marble but it uses a
specialized built-in turbulence function that is different from the
traditional turbulence. The traditional turbulence can be used as well but it
is generally not necessary because agate is already very turbulent. You may
control the amount of the built-in turbulence by adding the agate_turb
keyword followed by a float value. For example:   pigment {
    agate
    agate_turb 0.5
    color_map {
      ...
    }
  }


The agate pattern uses the ramp_wave wave type by default but may use any
wave type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.2          Average

Technically average is not a pattern type but it is listed here because the
syntax is similar to other patterns. Typically a pattern type specifies how
colors or normals are chosen from a pigment map or normal map, however
average tells POV-Ray to average together all of the patterns you specify.
Average was originally designed to be used in a normal statement with a
normal map as a method of specifying more than one normal pattern on the same
surface. However average may be used in a pigment statement with a pigment
map or in a texture statement with a texture map to average colors too.

When used with pigments, the syntax is:

  pigment {
    average
    pigment_map
    {
      [WEIGHT_1 PIGMENT_BODY_1]
      [WEIGHT_2 PIGMENT_BODY_2]
      ...
      [WEIGHT_n PIGMENT_BODY_n]
    }
    PIGMENT_MODIFIER
  }


Similarly you may use a texture map in a texture statement. All textures are
fully computed. The resulting colors are then weighted and averaged.

When used with a normal map in a normal statement, multiple copies of the
original surface normal are created and are perturbed by each pattern. The
perturbed normals are then weighted, added and normalized.

See the sections "Pigment Maps", "Normal Maps" and "Texture Maps" for more
information.

7.6.7.3          Bozo

The bozo pattern is a very smooth, random noise function that is
traditionally used with some turbulence to create clouds. The spotted pattern
is identical to bozo but in early versions of POV-Ray spotted did not allow
turbulence to be added. Turbulence can now be added to any pattern so these
are redundant but both are retained for backwards compatibility. The bumps
pattern is also identical to bozo when used anywhere except in a normal
statement. When used as a normal, bumps uses a slightly different method to
perturb the normal with a similar noise function.

The bozo noise function has the following properties:

  1.It's defined over 3D space i.e., it takes x, y, and z and returns the
  2.If two points are far apart, the noise values at those points are
  3.If two points are close together, the noise values at those points are
    close to each other.


You can visualize this as having a large room and a thermometer that ranges
from 0.0 to 1.0. Each point in the room has a temperature. Points that are
far apart have relatively random temperatures. Points that are close together
have close temperatures. The temperature changes smoothly but randomly as we
move through the room.

Now let's place an object into this room along with an artist. The artist
measures the temperature at each point on the object and paints that point a
different color depending on the temperature. What do we get? A POV-Ray bozo
texture!

The bozo pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.4          Brick

The brick pattern generates a pattern of bricks. The bricks are offset by
half a brick length on every other row in the x- and z-directions. A layer of
mortar surrounds each brick. The syntax is given by

  pigment {
    brick COLOR_1, COLOR_2
    brick_size VECTOR
    mortar FLOAT
  }


where COLOR_1 is the color of the mortar and COLOR_2 is the color of the
brick itself. If no colors are specified a default deep red and dark gray are
used. The default size of the brick and mortar together is <8, 3, 4.5> units.
The default thickness of the mortar is 0.5 units. These values may be changed
using the optional brick_size and mortar pattern modifiers. You may also use
pigment statements in place of the colors. For example:

  pigment {
    brick pigment{Jade}, pigment{Black_Marble}
  }


When used with normals, the syntax is   normal {
    brick BUMP_FLOAT
  }


Where BUMP_FLOAT is an optional bump size float value. You may also use full
normal statements. For example:

  normal {
    brick normal{bumps 0.2}, normal{granite 0.3}
  }


When used with textures, the syntax is

  texture {
    brick texture{T_Gold_1A}, texture{Stone12}
  }


This is a block pattern which cannot use wave types, color map, or slope map
modifiers.

7.6.7.5          Bumps

The bumps pattern was originally designed only to be used as a normal
pattern. It uses a very smooth, random noise function that creates the look
of rolling hills when scaled large or a bumpy orange peal when scaled small.
Usually the bumps are about 1 unit apart.

When used as a normal, bumps uses a specialized normal perturbation function.
This means that the bumps pattern cannot be used with normal map, slope map
or wave type modifiers in a normal statement.

When used as a pigment pattern or texture pattern, the bumps pattern is
identical to bozo or spotted and is similar to normal bumps but is not
identical as are most normals when compared to pigments. When used as pigment
or texture statements the bumps pattern uses the ramp_wave wave type by
default but may use any wave type. The pattern may be used with color_map,
pigment_map, and texture_map.

7.6.7.6          Checker

The checker pattern produces a checkered pattern consisting of alternating
squares of COLOR_1 and COLOR_2. If no colors are specified then default blue
and green colors are used.

  pigment { checker COLOR_1, COLOR_2 }


The checker pattern is actually a series of cubes that are one unit in size.
Imagine a bunch of 1 inch cubes made from two different colors of modeling
clay. Now imagine arranging the cubes in an alternating check pattern and
stacking them in layer after layer so that the colors still alternate in
every direction. Eventually you would have a larger cube. The pattern of
checks on each side is what the POV-Ray checker pattern produces when applied
to a box object. Finally imagine cutting away at the cube until it is carved
into a smooth sphere or any other shape. This is what the checker pattern
would look like on an object of any kind.

You may also use pigment statements in place of the colors. For example:

  pigment { checker pigment{Jade}, pigment{Black_Marble} }


When used with normals, the syntax is

  normal { checker BUMP_FLOAT }


Where BUMP_FLOAT is an optional bump size float value. You may also use full
normal statements. For example:

  normal {
    checker normal{gradient x scale .2},
            normal{gradient y scale .2}
  }


When used with textures, the syntax is...

  texture { checker texture{T_Wood_3A},texture{Stone12} }


This use of checker as a texture pattern replaces the special tiles texture
in previous versions of POV-Ray. You may still use tiles but it may be phased
out in future versions so checker textures are best.

This is a block pattern which cannot use wave types, color map, or slope map
modifiers.

7.6.7.7          Crackle

The crackle pattern is a set of random tiled polygons. With a large scale and
no turbulence it makes a pretty good stone wall or floor. With a small scale
and no turbulence it makes a pretty good crackle ceramic glaze. Using high
turbulence it makes a good marble that avoids the problem of apparent
parallel layers in traditional marble.

Mathematically, the set crackle(p)=0 is a 3D Voronoi diagram of a field of
semi random points and crackle(p) < 0 is the distance from the set along the
shortest path (a Voronoi diagram is the locus of points equidistant from
their two nearest neighbors from a set of disjoint points, like the membranes
in suds are to the centers of the bubbles).

The crackle pattern uses the ramp_wave wave type by default but may use any
wave type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.8          Dents

The dents pattern was originally designed only to be used as a normal
pattern. It is especially interesting when used with metallic textures. It
gives impressions into the metal surface that look like dents have been
beaten into the surface with a hammer. Usually the dents are about 1 unit
apart.

When used as a normal pattern, dents uses a specialized normal perturbation
function. This means that the dents pattern cannot be used with normal map,
slope map or wave type modifiers in a normal statement.

When used as a pigment pattern or texture pattern, the dents pattern is
similar to normal dents but is not identical as are most normals when
compared to pigments. When used in pigment or texture statements the dents
pattern uses the ramp_wave wave type by default but may use any wave type.
The pattern may be used with color_map, pigment_map and texture_map.

7.6.7.9          Gradient

One of the simplest patterns is the gradient pattern. It is specified as

  pigment {gradient VECTOR}


where VECTOR is a vector pointing in the direction that the colors blend. For
example    pigment { gradient x } // bands of color vary as you move
                          // along the "x" direction.


produces a series of smooth bands of color that look like layers of colors
next to each other. Points at x=0 are the first color in the color map. As
the x location increases it smoothly turns to the last color at x=1. Then it
starts over with the first again and gradually turns into the last color at
x=2. The pattern reverses for negative values of x. Using gradient y or
gradient z makes the colors blend along the y- or z-axis. Any vector may be
used but x, y and z are most common.

As a normal pattern, gradient generates a saw-tooth or ramped wave
appearance. The syntax is

   normal { gradient VECTOR, BUMP_FLOAT}


where the VECTOR giving the orientation is a required parameter but the
BUMP_FLOAT bump size which follows is optional.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.10         Granite

This pattern uses a simple 1/f fractal noise function to give a good granite
pattern. This pattern is used with creative color maps in stones.inc to
create some gorgeous layered stone textures.

As a normal pattern it creates an extremely bumpy surface that looks like a
gravel driveway or rough stone.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.11         Hexagon

The hexagon pattern is a block pattern that generates a repeating pattern of
hexagons in the x-y-plane. In this instance imagine tall rods that are
hexagonal in shape and are parallel to the y-axis and grouped in bundles like
shown in the example image. Three separate colors should be specified as
follows:

  pigment { hexagon COLOR_1, COLOR_2, COLOR_3 }


     _____
    /     \
   /   C2  _____
  |       /     \
  | _____/   C3  \
  | /            /|
   /   C1  _____/ |
  |       /|    | |
  | _____/ |    | |
  | |     | |    | |
  | |     | |    | |
  | |     | |    | |
  | |     | |    | |
  | |     | |    |
  | |     | |    |
    |     |
    |     |
The hexagon pattern.

The three colors will repeat the hexagonal pattern with hexagon COLOR_1
centered at the origin, COLOR_2 in the +z-direction and COLOR_3 to either
side. Each side of the hexagon is one unit long. The hexagonal rods of color
extend infinitely in the +y- and -y-directions. If no colors are specified
then default blue, green and red colors are used.

You may also use pigment statements in place of the colors. For example:

  pigment {
    hexagon pigment { Jade },
            pigment { White_Marble },
            pigment { Black_Marble }
  }


When used with normals, the syntax is

  normal { hexagon BUMP_FLOAT }


Where BUMP_FLOAT is an optional bump size float value. You may also use full
normal statements. For example:

  normal {
    hexagon
      normal { gradient x scale .2 },
      normal { gradient y scale .2 },
      normal { bumps scale .2 }
  }


When used with textures, the syntax is...

  texture {
    hexagon
      texture { T_Gold_3A },
      texture { T_Wood_3A },
      texture { Stone12 }
  }


This is a block pattern which cannot use wave types, color map, or slope map
modifiers.

7.6.7.12         Leopard

Leopard creates regular geometric pattern of circular spots.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.13         Mandel

The mandel pattern computes the standard Mandelbrot fractal pattern and
projects it onto the x-y-plane. It uses the x and y coordinates to compute
the Mandelbrot set. The pattern is specified with the keyword mandel followed
by an integer number. This number is the maximum number of iterations to be
used to compute the set. Typical values range from 10 up to 256 but any
positive integer may be used. For example:

  pigment {
    mandel 25
    color_map {
      [0.0  color Cyan]
      [0.3  color Yellow]
      [0.6  color Magenta]
      [1.0  color Cyan]
    }
    scale .5
  }


The value passed to the color map is computed by the formula:

  value = number_of_iterations / max_iterations


When used as a normal pattern, the syntax is...

  normal {
    mandel ITER, BUMP_AMOUNT
  }


where the required integer ITER value is optionally followed by a float bump
size.

The pattern extends infinitely in the z-direction similar to a planar image
map. The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.14         Marble

The marble pattern is very similar to the gradient x pattern. The gradient
pattern uses a default ramp_wave wave type which means it uses colors from
the color map from 0.0 up to 1.0 at location x=1 but then jumps back to the
first color for x > 1 and repeats the pattern again and again. However the
marble pattern uses the triangle_wave wave type in which it uses the color
map from 0 to 1 but then it reverses the map and blends from 1 back to zero.
For example:

  pigment {
    gradient x
    color_map {
      [0.0  color Yellow]
      [1.0  color Cyan]
    }
  }


This blends from yellow to cyan and then it abruptly changes back to yellow
and repeats. However replacing gradient x with marble smoothly blends from
yellow to cyan as the x coordinate goes from 0.0 to 0.5 and then smoothly
blends back from cyan to yellow by x=1.0.

Earlier versions of POV-Ray did not allow you to change wave types. Now that
wave types can be changed for most any pattern, the distinction between
marble and gradient x is only a matter of default wave types.

When used with turbulence and an appropriate color map, this pattern looks
like veins of color of real marble, jade or other types of stone. By default,
marble has no turbulence.

The pattern may be used with color_map, pigment_map, normal_map, slope_map
and texture_map.

7.6.7.15         Onion

Onion is a pattern of concentric spheres like the layers of an onion. Each
layer is one unit thick.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.16         Quilted

The quilted pattern was originally designed only to be used as a normal
pattern. The quilted pattern is so named because it can create a pattern
somewhat like a quilt or a tiled surface. The squares are actually 3-D cubes
that are 1 unit in size.

When used as a normal pattern it uses a specialized normal perturbation
function. This means that the quilted pattern cannot be used with normal map,
slope map or wave type modifiers in a normal statement.

When used as a pigment pattern or texture pattern, the quilted pattern is
similar to normal quilted but is not identical as are most normals when
compared to pigments. When used in pigment or texture statements the quilted
pattern uses the ramp_wave wave type by default but may use any wave type.
The pattern may be used with color_map, pigment_map and texture_map.

The two parameters control0 and control1 are used to adjust the curvature of
the seam or gouge area between the quilts. The syntax is:

  normal {
    quilted AMOUNT
    control0 C0
    control1 C1
  }


The values should generally be kept to around the 0.0 to 1.0 range. The
default value is 1.0 if none is specified. Think of this gouge between the
tiles in cross-section as a sloped line.

Quilted pattern with c0=0 and different values for c1.

Quilted pattern with c0=0.33 and different values for c1.

Quilted pattern with c0=0.67 and different values for c1.

Quilted pattern with c0=1 and different values for c1.

This straight slope can be made to curve by adjusting the two control values.
The control values adjust the slope at the top and bottom of the curve. A
control values of 0 at both ends will give a linear slope, as shown above,
yielding a hard edge. A control value of 1 at both ends will give an "s"
shaped curve, resulting in a softer, more rounded edge.

7.6.7.17         Radial

The radial pattern is a radial blend that wraps around the +y-axis. The color
for value 0.0 starts at the +x-direction and wraps the color map around from
east to west with 0.25 in the -z-direction, 0.5 in -x, 0.75 at +z and back to
1.0 at +x. Typically the pattern is used with a frequency modifier to create
multiple bands that radiate from the y-axis.

The pattern uses the ramp_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.18         Ripples

The ripples pattern was originally designed only to be used as a normal
pattern. It makes the surface look like ripples of water. The ripples radiate
from 10 random locations inside the unit cube area <0,0,0> to <1,1,1>. Scale
the pattern to make the centers closer or farther apart.

Usually the ripples from any given center are about 1 unit apart. The
frequency keyword changes the spacing between ripples. The phase keyword can
be used to move the ripples outwards for realistic animation.

The number of ripple centers can be changed with the global parameter
global_settings { number_of_waves FLOAT } somewhere in the scene. This
affects the entire scene. You cannot change the number of wave centers on
individual patterns. See section "Number_Of_Waves" for details.

When used as a normal pattern, ripples uses a specialized normal perturbation
function. This means that the ripples pattern cannot be used with normal map,
slope map or wave type modifiers in a normal statement.

When used in pigment or texture statements the ripples pattern uses the
ramp_wave wave type by default but may use any wave type. The pattern may be
used with color_map, pigment_map and texture_map.

7.6.7.19         Spiral1

The spiral1 pattern creates a spiral that winds around the y-axis similar to
a screw. Its syntax is:

  pigment {
    spiral1 NUMBER_OF_ARMS
  }


The NUMBER_OF_ARMS value determines how may arms are winding around the
y-axis.

The pattern uses the triangle_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.20         Spiral2

The spiral2 pattern is a modification of the spiral1 pattern with an
extraordinary look.

The pattern uses the triangle_wave wave type by default but may use any wave
type. The pattern may be used with color_map, pigment_map, normal_map,
slope_map and texture_map.

7.6.7.21         Spotted

The spotted pattern is identical to the bozo pattern. Early versions of
POV-Ray did not allow turbulence to be used with spotted. Now that any
pattern can use turbulence there is no difference between bozo and spotted.
See section "Bozo" for details.

7.6.7.22         Waves

The waves pattern was originally designed only to be used as a normal
pattern. The waves pattern looks similar to the ripples pattern except the
features are rounder and broader. The effect is to make waves that look more
like deep ocean waves. The waves radiate from ten random locations inside the
unit cube area <0,0,0> to <1,1,1>. Scale the pattern to make the centers
closer or farther apart.

Usually the waves from any given center are about 1 unit apart. The frequency
keyword changes the spacing between waves. The phase keyword can be used to
move the waves outwards for realistic animation.

The number of ripple centers can be changed with the global parameter
global_settings { number_of_waves FLOAT } somewhere in the scene. This
affects the entire scene. You cannot change the number of wave centers on
individual patterns. See section "Number_Of_Waves" for details.

When used as a normal pattern, waves uses a specialized normal perturbation
function. This means that the waves pattern cannot be used with normal map,
slope map or wave type modifiers in a normal statement.

When used in pigment or texture statements the waves pattern uses the
ramp_wave wave type by default but may use any wave type. The pattern may be
used with color_map, pigment_map and texture_map.

7.6.7.23         Wood

The wood pattern consists of concentric cylinders centered on the z-axis.
When appropriately colored, the bands look like the growth rings and veins in
real wood. Small amounts of turbulence should be added to make it look more
realistic. By default, wood has no turbulence.

Unlike most patterns, the wood pattern uses the triangle_wave wave type by
default. This means that like marble, wood uses color map values 0.0 to 1.0
then repeats the colors in reverse order from 1.0 to 0.0. However you may use
any wave type. The pattern may be used with color_map, pigment_map,
normal_map, slope_map and texture_map.

7.6.7.24         Wrinkles

The wrinkles pattern was originally designed only to be used as a normal
pattern. It uses a 1/f noise pattern similar to granite but the features in
wrinkles are sharper. The pattern can be used to simulate wrinkled cellophane
or foil. It also makes an excellent stucco texture.

When used as a normal pattern it uses a specialized normal perturbation
function. This means that the wrinkles pattern cannot be used with normal
map, slope map or wave type modifiers in a normal statement.

When used as a pigment pattern or texture pattern, the wrinkles pattern is
similar to normal wrinkles but is not identical as are most normals when
compared to pigments. When used in pigment or texture statements the wrinkles
pattern uses the ramp_wave wave type by default but may use any wave type.
The pattern may be used with color_map, pigment_map and texture_map.

7.6.8            Pattern Modifiers

Pattern modifiers are statements or parameters which modify how a pattern is
evaluated or tells what to do with the pattern. The modifiers color_map and
pigment_map apply only to pigments. See section "Pigment". The modifiers
bump_size, slope_map and normal_map apply only to normals. See section
"Normal". The texture_map modifier can only be used with textures. See
section "Texture Maps".

The pattern modifiers in the following section can be used with pigment,
normal or texture patterns.

7.6.8.1          Transforming Patterns

The most common pattern modifiers are the transformation modifiers translate,
rotate, scale and matrix. For details on these commands see section
"Transformations".

These modifiers may be placed inside pigment, normal and texture statements
to change the position, size and orientation of the patterns.

In general the order of transformations relative to other pattern modifiers
such as turbulence, color_map and other maps is not important. For example
scaling before or after turbulence makes no difference. The turbulence is
done first, then the scaling regardless of which is specified first. However
the order in which transformations are performed relative to warp statements
is important. See "Warps" for details.

7.6.8.2          Frequency and Phase

The frequency and phase modifiers act as a type of scale and translate
modifiers for color_map, pigment_map, normal_map, slope_map and texture_map.
This discussion uses a color map as an example but the same principles apply
to pigment maps, normal maps, slope maps and texture maps.

The frequency keyword adjusts the number of times that a color map repeats
over one cycle of a pattern. For example gradient covers color map values 0
to 1 over the range from x=0 to x=1. By adding frequency 2.0 the color map
repeats twice over that same range. The same effect can be achieved using
scale 0.5*x so the frequency keyword isn't that useful for patterns like
gradient.

However the radial pattern wraps the color map around the +y-axis once. If
you wanted two copies of the map (or 3 or 10 or 100) you'd have to build a
bigger map. Adding frequency 2.0 causes the color map to be used twice per
revolution. Try this:

  pigment {
    radial
    color_map{[0.5 color Red][0.5 color White]}
    frequency 6
  }


The result is six sets of red and white radial stripes evenly spaced around
the object.

The float after frequency can be any value. Values greater than 1.0 causes
more than one copy of the map to be used. Values from 0.0 to 1.0 cause a
fraction of the map to be used. Negative values reverses the map.

The phase value causes the map entries to be shifted so that the map starts
and ends at a different place. In the example above if you render successive
frames at phase 0 then phase 0.1, phase 0.2 etc you could create an animation
that rotates the stripes. The same effect can be easily achieved by rotating
the radial pigment using rotate  y*Angle but there are other uses where phase
can be handy.

Sometimes you create a great looking gradient or wood color map but you want
the grain slightly adjusted in or out. You could re-order the color map
entries but that's a pain. A phase adjustment will shift everything but keep
the same scale. Try animating a mandel pigment for a color palette rotation
effect.

Frequency and phase have no effect on block patterns checker, brick and
hexagon nor do they effect image maps, bump maps or material maps. They also
have no effect in normal statements when used with bumps, dents, quilted or
wrinkles because these normal patterns cannot use normal_map or slope_map.

They can be used with normal patterns ripples and waves even though these two
patterns cannot use normal_map or slope_map either. When used with ripples or
waves, frequency adjusts the space between features and phase can be adjusted
from 0.0 to 1.0 to cause the ripple or waves to move relative to their center
for animating the features.

These values work by applying the following formula

  NEW_VALUE = fmod ( OLD_VALUE * FREQUENCY + PHASE, 1.0 ).


7.6.8.3          Waveform

Most patterns that take color_map, pigment_map, slope_map, normal_map or
texture_map use the entries in the map in order from 0.0 to 1.0. The wood and
marble patterns use the map from 0.0 to 1.0 and then reverses it and runs it
from 1.0 to 0.0. The difference can easily be seen when these patterns are
used as normal patterns with no maps.

Patterns such as gradient or onion generate a grove or slot that looks like a
ramp that drops off sharply. This is called a ramp_wave wave type. However
wood and marble slope upwards to a peak, then slope down again in a
triangle_wave. In previous versions of POV-Ray there was no way to change the
wave types. You could simulate a triangle wave on a ramp wave pattern by
duplicating the map entries in reverse, however there was no way to use a
ramp wave on wood or marble.

Now any pattern that takes a map can have the default wave type overridden.
For example:

  pigment { wood color_map { MyMap } ramp_wave }


Also available are sine_wave and scallop_wave types. These types are of most
use in normal patterns as a type of built-in slope map. The sine_wave takes
the zig-zag of a ramp wave and turns it into a gentle rolling wave with
smooth transitions. The scallop_wave uses the absolute value of the sine wave
which looks like corduroy when scaled small or like a stack of cylinders when
scaled larger.

Although any of these wave types can be used for pigments, normals or
textures, the sine_wave and scallop_wave types are not as noticeable on
pigments or textures as they are for normals.

Wave types have no effect on block patterns checker, brick and hexagon nor do
they effect image maps, bump maps or material maps. They also have no effect
in normal statements when used with bumps, dents, quilted or wrinkles because
these normal patterns cannot use normal_map or slope_map.

7.6.8.4          Turbulence

The keyword turbulence followed by a float or vector may be used to stir up
any pigment, normal, texture, irid or halo. A number of optional parameters
may be used with turbulence to control how it is computed. For example:

  pigment  {
    wood color_map { MyMap }
    turbulence TURB_VECTOR
    octaves FLOAT
    omega FLOAT
    lambda FLOAT
  }


Typical turbulence values range from the default 0.0, which is no turbulence,
to 1.0 or more, which is very turbulent. If a vector is specified different
amounts of turbulence are applied in the x-, y- and z-direction. For example

  turbulence <1.0, 0.6, 0.1>


has much turbulence in the x-direction, a moderate amount in the y-direction
and a small amount in the z-direction.

Turbulence uses a random noise function called DNoise. This is similar to the
noise used in the bozo pattern except that instead of giving a single value
it gives a direction. You can think of it as the direction that the wind is
blowing at that spot. Points close together generate almost the same value
but points far apart are randomly different.

In general the order of turbulence parameters relative to other pattern
modifiers such as transformations, color maps and other maps is not
important. For example scaling before or after turbulence makes no
difference. The turbulence is done first, then the scaling regardless of
which is specified first. See section "Warps" for a way to work around this
behavior.

Turbulence uses DNoise to push a point around in several steps called
octaves. We locate the point we want to evaluate, then push it around a bit
using turbulence to get to a different point then look up the color or
pattern of the new point.

It says in effect Don't give me the color at this spot... take a  few random
steps in different directions and give me that color. Each step is typically
half as long as the one before. For example:

  P ------------------------->
           First Move        /
                            /
                           /
                          /Second
                         /  Move
                        /
                 ______/
                 \
                  \
                   Q - Final point.
Turbulence random walk.

The magnitude of these steps is controlled by the turbulence value. There are
three additional parameters which control how turbulence is computed. They
are octaves, lambda and omega. Each is optional. Each is followed by a single
float value. Each has no effect when there is no turbulence.

7.6.8.5          Octaves

The octaves value controls the number of steps of turbulence that are
computed. Legal values range from 1 to 10. The default value of 6 is a fairly
high value; you won't see much change by setting it to a higher value because
the extra steps are too small. Float values are truncated to integer. Smaller
numbers of octaves give a gentler, wavy turbulence and computes faster.
Higher octaves create more jagged or fuzzy turbulence and takes longer to
compute.

7.6.8.6          Lambda

The lambda parameter controls how statistically different the random move of
an octave is compared to its previous octave. The default value is 2.0 which
is quite random. Values close to lambda 1.0 will straighten out the
randomness of the path in the diagram above. The zig-zag steps in the
calculation are in nearly the same direction. Higher values can look more
swirly under some circumstances.

7.6.8.7          Omega

The omega value controls how large each successive octave step is compared to
the previous value. Each successive octave of turbulence is multiplied by the
omega value. The default omega 0.5 means that each octave is 1/2 the size of
the previous one. Higher omega values mean that 2nd, 3rd, 4th and up octaves
contribute more turbulence giving a sharper, crinkly look while smaller
omegas give a fuzzy kind of turbulence that gets blurry in places.

7.6.8.8          Warps

The warp statement is a pattern modifier that is similar to turbulence.
Turbulence works by taking the pattern evaluation point and pushing it about
in a series of random steps. However warps push the point in very
well-defined, non-random, geometric ways. The warp statement also overcomes
some limitations of traditional turbulence and transformations by giving the
user more control over the order in which turbulence, transformation and warp
modifiers are applied to the pattern.

Currently there are three types of warps but the syntax was designed to allow
future expansion. The first two, the repeat warp and the black_hole warp are
new features for POV-Ray that modify the pattern in geometric ways. The other
warp provides an alternative way to specify turbulence.

The syntax for using a warp statement in a pigment is

  pigment {
    PATTERN_TYPE
    PIGMENT_MODIFIERS...
    warp { WARP_ITEMS...}
    OTHER_PIGMENT_MODIFIERS...
  }


Similarly warps may be used in normals and textures. You may have as many
separate warp statements as you like in each pattern. The placement of warp
statements relative to other modifiers such as color_map or turbulence is not
important. However placement of warp statements relative to each other and to
transformations is significant. Multiple warps and transformations are
evaluated in the order in which you specify them. For example if you
translate, then warp or warp, then translate, the results can be different.

7.6.8.8.1        Black Hole Warp

A black hole is so named because of its similarity to real black holes. Just
like the real thing, you cannot actually see a black hole. The only way to
detect its presence is by the effect it has on things that surround it.
Unlike the real thing, however, it won't swallow you up and compress your
entire body to a volume of, say, 2.0 10-10 microns in diameter if you get too
close (We're working on that part).

Take, for example, a woodgrain. Using POV-Ray's normal turbulence and other
texture modifier functions, you can get a nice, random appearance to the
grain. But in its randomness it is regular - it is regularly random! Adding a
black hole allows you to create a localised disturbance in a woodgrain in
either one or multiple locations. The black hole can have the effect of
either sucking the surrounding texture into itself (like the real thing) or
pushing it away. In the latter case, applied to a woodgrain, it would look to
the viewer as if there were a knothole in the wood. In this text we use a
woodgrain regularly as an example, because it is ideally suitable to
explaining black holes. However, black holes may in fact be used with any
texture.

The effect that the black hole has on the texture can be specified. By
default, it sucks with the strength calculated exponentially
(inverse-square). You can change this if you like.

Black holes may be used anywhere a Warp is permitted. The syntax is:

  warp
  {
    black_hole <CENTER>, RADIUS
    [falloff VALUE]
    [strength VALUE]
    [repeat <VECTOR>]
    [turbulence <VECTOR>]
    [inverse]
  }


Some examples are given by

  warp
  {
    black_hole <0, 0, 0>, 0.5
  }

  warp
  {
    black_hole <0.15, 0.125, 0>, 0.5
    falloff 7
    strength 1.0
    repeat <1.25, 1.25, 0>
    turbulence <0.25, 0.25, 0>
    inverse
  }

  warp
  {
    black_hole <0, 0, 0>, 1.0
    falloff 2
    strength 2
    inverse
  }


In order to fully understand how a black hole works, it is important to know
the theory behind it. A black hole (or any warp) works by taking a point and
perturbing it to another location. The amount of perturbation depends on the
strength of the black hole at the original point passed in to it. The amount
of perturbation directly relates to the amount of visual movement that you
can see occur in a texture. The stronger the black hole at the input
co-ordinate the more that original co-ordinate is moved to another location
(either closer to or further away from the center of the black hole.)

Movement always occurs on the vector that exists between the input point and
the center of the black hole.

Black holes are considered to be spheres. For a point to be affected by a
black hole, it must be within the sphere's volume.

Suppose you have a black hole at <1,1,1> and a point at <1,2,1>. If this
point is perturbed by a total amount of +1 units its new location is <1,3,1>,
which is on a direct line extrapolated from the vector between <1,1,1> and
<1,2,1>. In this case the point is pushed away from the black hole, which is
not normal behaviour but is good for demonstration purposes.

The internal properties of a black hole are as follows.

  Falloff          The power of two by which the effect falls off (default
  Turbulence       If set, each new repeated black hole's position isem in.
  Turbulence_VectorThe maximum <x,y,z> factor for turbulence randomness.


Each of these are discussed below.

Center: A vector defining the center of the sphere that represents the black
hole. If the black hole has Repeat set it is the offset within each block.

Radius: A number giving the length, in units, of the radius of the sphere
that represents the black hole.

If a point is not within radius units of <center> it cannot be affected by
the black hole and will not be perturbed.

Falloff: The power by which the effect of the black hole falls off. The
default is two. The force of the black hole at any given point, before
applying the Strength modifier, is as follows.

First, convert the distance from the point to the center to a proportion (0
to 1) that the point is from the edge of the black hole. A point on the
perimeter of the black hole will be 0.0; a point at the centre will be 1.0; a
point exactly halfway will be 0.5, and so forth.

Mentally you can consider this to be a closeness factor. A closeness of 1.0
is as close as you can get to the center (i. e. at the center), a closeness
of 0.0 is as far away as you can get from the center and still be inside the
black hole and a closeness of 0.5 means the point is exactly halfway between
the two.

Call this value c. Raise c to the power specified in Falloff. By default
Falloff is 2, so this is c^2 or c squared. The resulting value is the force
of the black hole at that exact location and is used, after applying the
Strength scaling factor as described below, to determine how much the point
is perturbed in space.

For example, if c is 0.5 the force is 0.5^2 or 0.25. If c is 0.25 the force
is 0.125. But if c is exactly 1.0 the force is 1.0.

Recall
that as c gets smaller the point is farther from the center of the black
hole. Using the default power of 2, you can see that as c reduces, the force
reduces exponentially in an inverse-square relationship. Put in plain
english, it means that the force is much stronger (by a power of two) towards
the center than it is at the outside.

By increasing Falloff, you can increase the magnitude of the falloff. A large
value will mean points towards the perimeter will hardly be affected at all
and points towards the center will be affected strongly.

A value of 1.0 for Falloff will mean that the effect is linear. A point that
is exactly halfway to the center of the black hole will be affected by a
force of exactly 0.5.

A value of Falloff of less than one but greater than zero means that as you
get closer to the outside, the force increases rather than decreases. This
can have some uses but there is a side effect. Recall that the effect of a
black hole ceases outside its perimeter. This means that points just within
the permiter will be affected strongly and those just outside not at all.
This would lead to a visible border, shaped as a sphere.

A value for Falloff of 0 would mean that the force would be 1.0 for all
points within the black hole, since any number larger 0 raised to the power
of 0 is 1.0.

The magnitude of the movement of the point is determined basically by the
value of force after scaling. We'll consider scaling later. Lets take an
example.

Suppose we have a black hole of radius 2.0 and a point that is exactly 1.0
units from the center. That means it is exactly half-way to the center and
that c would be 0.5. If we use the default falloff of 2 the force at that
point is 0.5^2 or 0.25. What this means is that we must move the point by
0.25 of its distance from the center. In this case it is 1.0 units from the
center, so we move it by 1.0*0.25 or 0.25 units. This gives a final distance
of 1.0-(1.0*0.25) or 0.75 units from the center, on a direct line in 3D space
between the original position and the center.

If the point were part of, say, a wood grain, the wood grain would appear to
bend towards the (invisible) center of the black hole. If the Inverse flag
were set, however, it would be pushed away, meaning its final position would
be 1.0+(1.0*0.25) or 1.25 units from the center.

Strength: The Strength gives you a bit more control over how much a point is
perturbed by the black hole. Basically, the force of the black hole (as
determined above) is multiplied by the value of Strength, which defaults to
1.0. If you set Strength to 0.5, for example, all points within the black
hole will be moved by only half as much as they would have been. If you set
it to 2.0 they will be moved twice as much.

There is a rider to the latter example, though - the movement is clipped to a
maximum of the original distance from the center. That is to say, a point
that is 0.75 units from the center may only be moved by a maximum of 0.75
units either towards the center or away from it, regardless of the value of
Strength. The result of this clipping is that you will have an exclusion area
near the centre of the black hole where all points whose final force value
exceeded or equaled 1.0 were moved by a fixed amount.

Inverted: If Inverted is set points are pushed away from the center instead
of being pulled in.

Repeat: Repeat allows you to simulate the effect of many black holes without
having to explicitly declare them. Repeat is a vector that tells POV-Ray to
use this black hole at multiple locations.

If you're not interested in the theory behind all this, just skip the
following text and use the values given in the summary below.

Using Repeat logically divides your scene up into cubes, the first being
located at <0,0,0> and going to < repeat>. Suppose your repeat vector was
<1,5,2>. The first cube would be from <0,0,0> to < 1,5,2>. This cube repeats,
so there would be one at < -1,-5,-2>, <1,5,2>, <2,10,4> and so forth in all
directions, ad infinitum.

When you use Repeat, the center of the black hole does not specify an
absolute location in your scene but an offset into each block. It is only
possible to use positive offsets. Negative values will produce undefined
results.

Suppose your center was <0.5,1,0.25> and the repeat vector is <2,2,2>. This
gives us a block at < 0,0,0> and <2,2,2>, etc. The centers of the black
hole's for these blocks would be <0,0,0> + < 0.5,1.0,0.25>, i. e.
<0.5,1.0,0.25>, and < 2,2,2> + <0.5,1.0,0.25>, i. e. < 2,5,3.0,2.25>.

Due to the way repeats are calculated internally, there is a restriction on
the values you specify for the repeat vector. Basically, each black hole must
be totally enclosed within each block (or cube), with no part crossing into a
neighbouring one. This means that, for each of the x, y and z dimensions, the
offset of the center may not be less than the radius, and the repeat value
for that dimension must be >=the center plus the radius since any other
values would allow the black hole to cross a boundary. Put another way, for
each of x, y and z

radius <= offset or center <= repeat - radius.


If the repeat vector in any dimension is too small to fit this criteria, it
will be increased and a warning message issued. If the center is less than
the radius it will also be moved but no message will be issued.

Note that none of the above should be read to mean that you can't overlap
black holes. You most certainly can and in fact this can produce some most
useful effects. The restriction only applies to elements of the same black
hole which is repeating. You can declare a second black hole that also
repeats and its elements can quite happily overlap the first and causing the
appropriate interactions.

It is legal for the repeat value for any dimension to be 0, meaning that
POV-Ray will not repeat the black hole in that direction.

Turbulence: Turbulence can only be used with Repeat. It allows an element of
randomness to be inserted into the way the black holes repeat, to cause a
more natural look. A good example would be an array of knotholes in wood - it
would look rather artificial if each knothole were an exact distance from the
previous.

The turbulence vector is a measurement that is added to each individual back
hole in an array, after each axis of the vector is multiplied by a different
random amount ranging from 0 to 1.

For example, suppose you have a repeating element of a black hole that is
supposed to be at <2,2,2>. You have specified a turbulence vector of <4,5,3>,
meaning you want the position to be able to vary by no more than 1.0 units in
the X direction, 3.0 units in the Y direction and 2.0 in Z. This means that
the valid ranges of the new position are as follows

X can be from 2 to 6.

Y can be from 2 to 7.
Z can be from 2 to 5.


The resulting actual position of the black hole's center for that particular
repeat element is random (but consistent, so renders will be repeatable) and
somewhere within the above co-ordinates.

There is a rider on the use of turbulence, which basically is the same as
that of the repeat vector. You can't specify a value which would cause a
black hole to potentially cross outside of its particular block.

Since POV-Ray doesn't know in advance how much a position will be changed due
to the random nature of the changes, it enforces a rule that is similar to
the one for Repeat, except it adds the maximum possible variation for each
axis to the center. For example, suppose you had a black hole with a center
of <1.0, 1.0, 1.0>, radius of 0.5 and a turbulence of <0.5, 0.25, 0> -
normally, the minimum repeat would be <1.5, 1.5, 1.5>. However, now we take
into account the turbulence, meaning the minimum repeat vector is actually
<2.0, 1.75, 1.5>.

Repeat summarized: For each of x, y and z the offset of the center must be
>=radius and the value of the repeat must be \ge center + radius +
turbulence. The exception being that repeat may be 0 for any dimension, which
means do not repeat in that direction.

7.6.8.8.2        Repeat Warp

The repeat warp causes a section of the pattern to be repeated over and over.
It takes a slice out of the pattern and makes multiple copies of it
side-by-side. The warp has many uses but was originally designed to make it
easy to model wood veneer textures. Veneer is made by taking very thin slices
from a log and placing them side-by-side on some other backing material. You
see side-by-side nearly identical ring patterns but each will be a slice
perhaps 1/32th of an inch deeper.

The syntax for a repeat warp is

  warp { repeat VECTOR  offset VECTOR  flip VECTOR }


The repeat vector specifies the direction in which the pattern repeats and
the width of the repeated area. This vector must lie entirely along an axis.
In other words, two of its three components must be 0. For example

  pigment {
    wood
    warp {repeat 2*x}
  }


which means that from x=0 to x=2 you get whatever the pattern usually is. But
from x=2 to x=4 you get the same thing exactly shifted two units over in the
x-direction. To evaluate it you simply take the x-coordinate modulo 2.
Unfortunately you get exact duplicates which isn't very realistic. The
optional offset vector tells how much to translate the pattern each time it
repeats. For example

  pigment {
    wood
    warp {repeat x*2  offset z*0.05}
  }


means that we slice the first copy from x=0 to x=2 at z=0 but at x=2 to x=4
we offset to z=0.05. In the 4 to 6 interval we slice at z=0.10. At the n-th
copy we slice at 0.05 n z. Thus each copy is slightly different. There are no
restrictions on the offset vector.

Finally the flip vector causes the pattern to be flipped or mirrored every
other copy of the pattern. The first copy of the pattern in the positive
direction from the axis is not flipped. The next farther is, the next is not,
etc. The flip vector is a three component x, y, z vector but each component
is treated as a boolean value that tells if you should or should not flip
along a given axis. For example

  pigment {
    wood
    warp {repeat 2*x  flip <1,1,0>}
  }


means that every other copy of the pattern will be mirrored about the x- and
y- axis but not the z-axis. A non-zero value means flip and zero means do not
flip about that axis. The magnitude of the values in the flip vector doesn't
matter.

7.6.8.8.3        Turbulence Warp

The POV-Ray language contains an ambiguity and limitation on the way you
specify turbulence and transformations such as translate, rotate, scale and
matrix transforms. Usually the turbulence is done first. Then all translate,
rotate, scale and matrix operations are always done after turbulence
regardless of the order in which you specify them. For example this

 pigment {
   wood
   scale .5
   turbulence .2
 }


works exactly the same as

 pigment {
   wood
   turbulence .2
   scale .5
 }


The turbulence is always first. A better example of this limitation is with
uneven turbulence and rotations.

  pigment {
    wood
    turbulence 0.5*y
    rotate z*60
  }

  // as compared to

  pigment {
   wood
   rotate z*60
   turbulence 0.5*y
  }


The results will be the same either way even though you'd think it should
look different.

We cannot change this basic behavior in POV-Ray now because lots of scenes
would potentially render differently if suddenly the order transformation vs
turbulence suddenly mattered when in the past, it didn't.

However, by specifying our turbulence inside warp statement you tell POV-Ray
that the order in which turbulence, transformations and other warps are
applied is significant. Here's an example of a turbulence warp.

  warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }


The significance is that this

 pigment {
   wood
   translate <1,2,3> rotate x*45 scale 2
   warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }
 }


produces different results than this...

 pigment {
   wood
   warp { turbulence <0,1,1> octaves 3 lambda 1.5 omega 0.3 }
   translate <1,2,3> rotate x*45 scale 2
 }


You may specify turbulence without using a warp statement. However you cannot
control the order in which they are evaluated unless you put them in a warp.

The evaluation rules are as follows:

  1)First any turbulence not inside a warp statement is applied regardless of
  2)Next each warp statement, translate, rotate, scale or matrix one-by-one,
    is applied in the order the user specifies. If you want turbulence done
    in a specific order, you simply specify it inside a warp in the proper
place.

7.6.8.9          Bitmap Modifiers

A bitmap modifier is a modifier used inside an image_map, bump_map or
material_map to specify how the 2-D bitmap is to be applied to the 3-D
surface. Several bitmap modifiers apply to specific kinds of maps and they
are covered in the appropriate sections. The bitmap modifiers discussed in
the following sections are applicable to all three types of bitmaps.

7.6.8.9.1        The once Option

Normally there are an infinite number of repeating image maps, bump maps or
material maps created over every unit square of the x-y-plane like tiles. By
adding the once keyword after a file name you can eliminate all other copies
of the map except the one at (0,0) to (1,1). In image maps, areas outside
this unit square are treated as fully transparent. In bump maps, areas
outside this unit square are left flat with no normal modification. In
material maps, areas outside this unit square are textured with the first
texture of the texture list.

For example:

  image_map {
    gif "mypic.gif"
    once
  }


7.6.8.9.2        The "map_type" Option

The default projection of the bump onto the x-y-plane is called a planar map
type. This option may be changed by adding the map_type keyword followed by a
number specifying the way to wrap the bump around the object.

A map_type 0 gives the default planar mapping already described.

A map_type 1 gives a spherical mapping. It assumes that the object is a
sphere of any size sitting at the origin. The y-axis is the north/south pole
of the spherical mapping. The top and bottom edges of the bitmap just touch
the pole regardless of any scaling. The left edge of the bitmap begins at the
positive x-axis and wraps the pattern around the sphere from west to east in
a -y-rotation. The pattern covers the sphere exactly once. The once keyword
has no meaning for this type.

With map_type 2 you get a cylindrical mapping. It assumes that a cylinder of
any diameter lies along the y-axis. The bump pattern wraps around the
cylinder just like the spherical map but remains one unit tall from y=0 to
y=1. This band of the pattern is repeated at all heights unless the once
keyword is applied.

Finally map_type 5 is a torus or donut shaped mapping. It assumes that a
torus of major radius 1 sits at the origin in the x-z-plane. The pattern is
wrapped around similar to spherical or cylindrical maps. However the top and
bottom edges of the map wrap over and under the torus where they meet each
other on the inner rim.

Types 3 and 4 are still under development.

For example:

  sphere{<0,0,0>,1
    pigment{
      image_map {
        gif "world.gif"
        map_type 1
      }
    }
  }


7.6.8.9.3        The interpolate Option

Adding the interpolate keyword can smooth the jagged look of a bitmap. When
POV-Ray asks an image map color or a bump amount for a bump map, it often
asks for a point that is not directly on top of one pixel but sort of between
several differently colored pixels. Interpolations returns an in-between
value so that the steps between the pixels in the map will look smoother.

Although interpolate is legal in material maps the color index is
interpolated before the texture is chosen. It does not interpolate the final
color as you might hope it would. In general, interpolation of material maps
serves no useful purpose but this may be fixed in future versions.

There are currently two types of interpolation:

  Bilinear            --- interpolate 2
  Normalized Distance --- interpolate 4


For example:

  image_map {
    gif "mypic.gif"
    interpolate 2
  }


Default is no interpolation. Normalized distance is the slightly faster of
the two, bilinear does a better job of picking the between color. Normally
bilinear is used.

If your map looks jaggy, try using interpolation instead of going to a higher
resolution image. The results can be very good.

7.7              Atmospheric Effects

Atmospheric effects are a loosely-knit group of features that affect the
background and/or the atmosphere enclosing the scene. POV-Ray includes the
ability to render a number of atmospheric effects, such as fog, haze, mist,
rainbows and skies.

7.7.1            Atmosphere

Important notice: The atmosphere feature in POV-Ray 3.0 are somewhat
experimental. There is a high probability that the design and implementation
of these features will be changed in future versions. We cannot guarantee
that scenes using these features in 3.0 will render identically in future
releases or that full backwards compatibility of language syntax can be
maintained.

Computer generated images normally assume a vacuum space that does not allow
the rendering of natural phenomena like smoke, light beams, etc. A very
simple approach to add fog to a scene is explained in section "Fog". This
kind of fog does not interact with any light sources though. It will not show
light beams or other effects and is therefore not very realistic.

The atmosphere effect overcomes some of the fog's limitations by calculating
the interaction between light and the particles in the atmosphere using
volume sampling. Thus shaft of light beams will become visible and objects
will cast shadows onto smoke or fog.

The syntax of the atmosphere is:

  atmosphere {
    type TYPE
    distance DISTANCE
    [ scattering SCATTERING ]
    [ eccentricity ECCENTRICITY ]
    [ samples SAMPLES ]
    [ jitter JITTER ]
    [ aa_threshold AA_THRESHOLD ]
    [ aa_level AA_LEVEL ]
    [ colour <COLOUR> ]
  }


The type keyword determines the type of scattering model to be used. There
are five different phase functions representing the different models:
isotropic, Rayleigh, Mie (haze and murky atmosphere) and Henyey-Greenstein.

Isotropic scattering is the simplest form of scattering because it is
independent of direction. The amount of light scattered by particles in the
atmosphere does not depend on the angle between the viewing direction and the
incoming light.

Rayleigh scattering models the scattering for extremely small particles such
as molecules of the air. The amount of scattered light depends on the
incident light angle. It is largest when the incident light is parallel or
anti-parallel to the viewing direction and smallest when the incident light
is perpendicular to the viewing direction. You should note that the Rayleigh
model used in POV-Ray does not take the dependency of scattering on the
wavelength into account.

The Rayleigh scattering function.

Mie scattering is used for relatively small particles such as minuscule water
droplets of fog, cloud particles, and particles responsible for the polluted
sky. In this model the scattering is extremely directional in the forward
direction i. e. the amount of scattered light is largest when the incident
light is anti-parallel to the viewing direction (the light goes directly to
the viewer). It is smallest when the incident light is parallel to the
viewing direction. The haze and murky atmosphere models differ in their
scattering characteristics. The murky model is much more directional than the
haze model.

The Mie "haze" scattering function.

The Mie "murky" scattering function.

The Henyey-Greenstein scattering is based on an analytical function and can
be used to model a large variety of different scattering types. The function
models an ellipse with a given eccentricity e. This eccentricity is specified
by the optional keyword eccentricity which is only used for scattering type
five. An eccentricity value of zero defines isotropic scattering while
positive values lead to scattering in the direction of the light and negative
values lead to scattering in the opposite direction of the light. Larger
values of e (or smaller values in the negative case) increase the directional
property of the scattering.

The Heyney-Greenstein scattering function for different eccentricity values.


The easiest way to use the different scattering types will be to declare some
constants and use those in your atmosphere definition:

  #declare ISOTROPIC_SCATTERING         = 1
  #declare MIE_HAZY_SCATTERING          = 2
  #declare MIE_MURKY_SCATTERING         = 3
  #declare RAYLEIGH_SCATTERING          = 4
  #declare HENYEY_GREENSTEIN_SCATTERING = 5


The distance keyword is used to determine the density of the particles in the
atmosphere. This density is constant for the whole atmosphere. The distance
parameter works in the same way as the fog distance.

With the scattering keyword you can change the amount of light that is
scattered by the atmosphere, thus increasing or decreasing the brightness of
the atmosphere. Smaller scattering values decrease the brightness while
larger values increase it.

The colour or color keyword can be used to create a colored atmosphere, i. e.
it can be used to get particles that filter the light passing through. The
default color is black.

The light passing through the atmosphere (either coming from light sources or
the background) is filtered by the atmosphere's color if the specified color
has a non-zero filter value. In other words, the amount by which the light is
filtered by the atmosphere's color is given by the filter value (pretty much
in the same way as it is done for the fog). Using a color of rgbf
<1,0,0,0.25> will result in a slightly reddish atmosphere because 25% of the
light passing through the atmosphere is filtered by (multiplied with) the
color of the atmosphere, i. e. rgb <1,0,0> (and that's red).

The transmittance channel of the atmosphere's color is used to specify a
minimum translucency. If a value larger than zero is used you'll always see
that amount of the background through the atmosphere, regardless of how dense
the atmosphere is. This works in the same way as it does for fogs.

Since the atmosphere is calculated by sampling along the viewing ray and
looking for contributions from light sources, it is prone to aliasing (just
like any sampling technique). There are four parameters to minimize the
artifacts that may be visible: samples, jitter, aa_level and aa_threshold.

The samples keyword determines how many samples are calculated in one
interval along the viewing ray. The length of the interval is either the
distance as given by the distance keyword or the length of the lit part of
the viewing ray, whichever is smaller. This lit part is a section of the ray
that
is most likely lit by a light source. In the case of a spotlight it is the
part of the ray that lies in the cone of light. In other cases it becomes
more difficult. The only thing you should keep in mind is that the actual
sampling interval length is variable but there will never be fewer than the
specified samples in the specified distance.

One technique to reduce the visibility of sampling artifacts is to jitter the
sample points, i. e. to add random noise to their location. This can be done
with the jitter keyword.

Another technique is super-sampling (an anti-aliasing method). This helps to
avoid missing features by adding additional samples in places were high
intensity changes occur (e. g. the edge of a shadow). The anti-aliasing is
turned on by the aa_level keyword. If this is larger than zero super-sampling
will be used. The additional samples will be recursively placed between two
samples with a high intensity change. The level to which subdivision takes
places is specified by the aa_level keyword. Level one means one subdivision
(one additional sample), level two means two subdivisions (up to three
additional samples), etc.

The threshold for the intensity change is given by the aa_threshold keyword.
If the intensity change is greater than this threshold anti-aliasing will be
used for those two samples.

With spotlights you'll be able to create the best results because their cone
of light will become visible. Pointlights can be used to create effects like
street lights in fog. Lights can be made to not interact with the atmosphere
by adding atmosphere off to the light source. They can be used to increase
the overall light level off the scene to make it look more realistic.

You should note that the atmosphere feature will not work if the camera is
inside a non-hollow object (see section "Empty and Solid Objects" for a
detailed explanation).

7.7.2            Background

A background color can be specified if desired. Any ray that doesn't hit an
object will be colored with this color. The default background is black. The
syntax for background is:

  background { colour <COLOUR> }


7.7.3            Fog

Fog is defined by the following statement:

  fog {
    fog_type FOG_TYPE
    distance DISTANCE
    colour <COLOUR>
    [ turbulence <TURBULENCE> ]
    [ turb_depth TURB_DEPTH ]
    [ omega OMEGA ]
    [ lambda LAMBDA ]
    [ octaves OCTAVES ]
    [ fog_offset FOG_OFFSET ]
    [ fog_alt FOG_ALT ]
    [ up <FOG_UP> ]
    [ TRANSFORMATION ]
  }


The optional up vector specifies a direction pointing up, generally the same
as the camera's up vector. All calculations done during the ground fog
evaluation are done relative to this up vector, i. e. the actual heights are
calculated along this vector.

The up vector can also be modified using any of the known transformations
described in "Transformations". Though it may not be a good idea to scale the
up vector - the results are hardly predictable - it is quite useful to be
able to rotate it. You should also note that translations do not affect the
up direction (and thus don't affect the fog).

Currently there are two fog types, constant fog and ground  fog. The constant
fog has a constant density everywhere while the ground fog has a constant
density for all heights below a given point on the up axis and thins out
along this axis. The height below which the fog has constant density is
specified by the fog_offset keyword. The fog_alt keyword is used to specify
the rate by which the fog fades away. At an altitude of fog_offset+fog_alt
the fog has a density of 25%. The density of the fog at a given height y is
calculated by the formula:

           /
           |                  1
           | -------------------------------------, y > fog_alt
           |  (1 + (y - fog_offset) / fog_alt) ^2
density = -|
           |
           |                  1,                   y <= fog_alt
           |
           \


The total density along a ray is calculated by integrating from the height of
the starting point to the height of the end point.

Two constants are defined for easy use of the fog types in the file
const.inc:

   // FOG TYPE CONSTANTS
   #declare Constant_Fog = 1
   #declare Ground_Fog   = 2


The color of a pixel with an intersection depth d is calculated by

  C_pixel = exp(-d/D) * C_object + (1-exp(-d/D)) * C_fog


where D is the fog distance. At depth 0 the final color is the object's
color. If the intersection depth equals the fog distance the final color
consists of 64% of the object's color and 36% of the fog's color.

The fog color that is given by the color keyword has three purposes. First it
defines the color to be used in blending the fog and the background. Second
it is used to specify a translucency threshold. By using a transmittance
larger than zero one can make sure that at least that amount of light will be
seen through the fog. With a transmittance of 0.3 you'll see at least 30% of
the background. Third it can be used to make a filtering fog. With a filter
value larger than zero the amount of background light given by the filer
value will be multiplied with the fog color. A filter value of 0.7 will lead
to a fog that filters 70% of the background light and leaves 30% unfiltered.

Fogs may be layered. That is, you can apply as many layers of fog as you
like. Generally this is most effective if each layer is a ground fog of
different color, altitude and with different turbulence values. To use
multiple layers of fogs, just add all of them to the scene.

You may optionally stir up the fog by adding turbulence. The turbulence
keyword may be followed by a float or vector to specify an amount of
turbulence to be used. The omega, lambda and octaves turbulence parameters
may also be specified. See section "Pattern Modifiers" for details on all of
these turbulence parameters.

Additionally the fog turbulence may be scaled along the direction of the
viewing ray using the turb_depth amount. Typical values are from 0.0 to 1.0
or more. The default value is 0.5 but any float value may be used.

You should note that the fog feature will not work if the camera is inside a
non-hollow object (see section "Empty and Solid Objects" for a detailed
explanation).

7.7.4            Sky Sphere

The sky sphere is used create a realistic sky background without the need of
an additional sphere to simulate the sky. Its syntax is:

  sky_sphere {
    pigment { PIGMENT1 }
    pigment { PIGMENT2 }
    pigment { PIGMENT3 }
    ...
    [ TRANSFORMATION ]
  }


The sky sphere can contain several pigment layers with the last pigment being
at the top, i. e. it is evaluated last, and the first pigment being at the
bottom, i. e. it is evaluated first. If the upper layers contain filtering
and/or transmitting components lower layers will shine through. If not lower
layers will be invisible.

The sky sphere is calculated by using the direction vector as the parameter
for evaluating the pigment patterns. This leads to results independent from
the view point which pretty good models a real sky where the distance to the
sky is much larger than the distances between visible objects.

If you want to add a nice color blend to your background you can easily do
this by using the following example.

  sky_sphere {
    pigment {
      gradient y
      color_map {
        [ 0.5  color CornflowerBlue ]
        [ 1.0  color MidnightBlue ]
      }
      scale 2
      translate -1
    }
  }


This gives a soft blend from CornflowerBlue at the horizon to MidnightBlue at
the zenith. The scale and translate operations are used to map the direction
vector values, which lie in the range from <-1, -1, -1> to <1, 1, 1>, onto
the range from <0, 0, 0> to <1, 1, 1>. Thus a repetition of the color blend
is avoided for parts of the sky below the horizon.

In order to easily animate a sky sphere you can transform it using the known
transformations described in "Transformations". Though it may not be a good
idea to translate or scale a sky sphere - the results are hardly predictable
- it is quite useful to be able to rotate it. In an animation the color
blendings of the sky can be made to follow the rising sun for example.

You should note that only one sky sphere can be used in any scene. It also
will not work as you might expect if you use camera types like the
orthographic or cylindrical camera. The orthographic camera uses parallel
rays and thus you'll only see a very small part of the sky sphere (you'll get
one color skies in most cases). Reflections in curved surface will work
though, e. g. you will clearly see the sky in a mirrored ball.

7.7.5            Rainbow

Rainbows are implemented using fog-like, circular arcs. Their syntax is:

  rainbow {
    direction <DIR>
    angle ANGLE
    width WIDTH
    distance DISTANCE
    color_map { COLOUR_MAP }
    [ jitter JITTER ]
    [ up <UP> ]
    [ arc_angle ARC_ANGLE ]
    [ falloff_angle FALLOFF_ANGLE ]
  }


The direction vector determines the direction of the (virtual) light that is
responsible for the rainbow. Ideally this is an infinitely far away light
source like the sun that emits parallel light rays. The position and size of
the rainbow are specified by the angle and width keywords. To understand how
they work you should first know how the rainbow is calculated.

For each ray the angle between the rainbow's direction vector and the ray's
direction vector is calculated. If this angle lies in the interval from
ANGLE-WIDTH/2 to ANGLE+WIDTH/2 the rainbow is hit by the ray. The color is
then determined by using the angle as an index into the rainbow's colormap.
After the color has been determined it will be mixed with the background
color in the same way like it is done for fogs.

Thus the angle and width parameters determine the angles under which the
rainbow will be seen. The optional jitter keyword can be used to add random
noise to the index. This adds some irregularity to the rainbow that makes it
look more realistic.

The distance keyword is the same like the one used with fogs. Since the
rainbow is a fog-like effect it's possible that the rainbow is noticeable on
objects. If this effect is not wanted it can be avoided by using a large
distance value. By default a sufficiently large value is used to make sure
that this effect does not occur.

The color_map keyword is used to assign a color map that will be mapped onto
the rainbow. To be able to create realistic rainbows it is important to know
that the index into the color map increases with the angle between the ray's
and rainbow's direction vector. The index is zero at the innermost ring and
one at the outermost ring. The filter and transmittance values of the colors
in the color map have the same meaning as the ones used with fogs (see
section "Fog").

The default rainbow is a 360 degree arc that looks like a circle. This is no
problem as long as you have a ground plane that hides the lower, non-visible
part of the rainbow. If this isn't the case or if you don't want the full arc
to be visible you can use the optional keywords up, arc_angle and
falloff_angle to specify a smaller arc.

The arc_angle keyword determines the size of the arc in degrees (from 0 to
360 degrees). A value smaller than 360 degrees results in an arc that
abruptly vanishes. Since this doesn't look nice you can use the falloff_angle
keyword to specify a region in which the rainbow will smoothly blend into the
background making it vanish softly. The falloff angle has to be smaller or
equal to the arc angle.

The up keyword determines were the zero angle position is. By changing this
vector you can rotate the rainbow about its direction. You should note that
the arc goes from -ARC_ANGLE/2 to +ARC_ANGLE/2. The soft regions go from
-ARC_ANGLE/2 to -FALLOFF_ANGLE/2 and from +FALLOFF_ANGLE/2 to +ARC_ANGLE/2.

The following example generates a 120 degrees rainbow arc that has a falloff
region of 30 degrees at both ends:

  rainbow {
    direction <0, 0, 1>
    angle 42.5
    width 5
    distance 1000
    jitter 0.01
    color_map { Rainbow_Color_Map }
    up <0, 1, 0>
    arc_angle 240
    falloff_angle 60
  }


It is possible to use any number of rainbows and to combine them with other
atmospheric effects.

7.8              Global Settings

The global_settings statement is a catch-all statement that gathers together
a number of global parameters. The statement may appear anywhere in a scene
as long as its not inside any other statement. You may have multiple
global_settings statements in a scene. Whatever values were specified in the
last global_settings statement override any previous settings. Regardless of
where you specify the statement, the feature applies to the entire scene.

Note that some items which were language directives in previous versions of
POV-Ray have been moved inside the global_settings statement so that it is
more obvious to the user that their effect is global. The old syntax is
permitted but generates a warning.

  global_settings {
    adc_bailout FLOAT
    ambient_light COLOR
    assumed_gamma FLOAT
    hf_gray_16 BOOLEAN
    irid_wavelength COLOR
    max_intersections INTEGER
    max_trace_level INTEGER
    number_of_waves INTEGER
    radiosity { RADIOSITY_ITEMS... }
  }


Each item is optional and may appear in and order. If an item is specified
more than once, the last setting overrides previous values. Details on each
item are given in the following sections.

7.8.1            ADC_Bailout

In scenes with many reflective and transparent surfaces, POV-Ray can get
bogged down tracing multiple reflections and refractions that contribute very
little to the color of a particular pixel. The program uses a system called
Adaptive Depth Control (ADC) to stop computing additional reflected or
refracted rays when their contribution is insignificant.

You may use the global setting adc_bailout keyword followed by float value to
specify the point at which a ray's contribution is considered insignificant.

  global_settings { adc_bailout FLOAT }


The default value is 1/255, or approximately 0.0039, since a change smaller
than that could not be visible in a 24 bit image. Generally this setting is
perfectly adequate and should be left alone. Setting adc_bailout to 0 will
disable ADC, relying completely on max_trace_level to set an upper limit on
the number of rays spawned.

See section "Max_Trace_Level" for details on how ADC and max_trace_level
interact.

7.8.2            Ambient Light

Ambient light is used to simulate the effect of inter-diffuse reflection that
is responsible for lighting areas that partially or completely lie in shadow.
POV-Ray provides an ambient light source to let you easily change the
brightness of the ambient lighting without changing every ambient value in
all finish statements. It also lets you create interesting effects by
changing the color of the ambient light source. The syntax is:

  global_settings { ambient_light COLOR }


The default is a white ambient light source set at rgb <  1,1,1>. The actual
ambient used is:    AMBIENT = FINISH_AMBIENT * GLOBAL_AMBIENT


7.8.3            Assumed_Gamma

Many people may have noticed at one time or another that some images are too
bright or dim when displayed on their system. As a rule, Macintosh users find
that images created on a PC are too bright, while PC users find that images
created on a Macintosh are too dim.

The assumed_gamma global setting works in conjunction with the Display_Gamma
INI setting (see section "Display Hardware Settings") to ensure that scene
files render the same way across the wide variety of hardware platforms that
POV-Ray is used on. The assumed gamma setting is used in a scene file by
adding

  global_settings { assumed_gamma FLOAT }


where the assumed gamma value is the correction factor to be applied before
the pixels are displayed and/or saved to disk. For scenes created in older
versions of POV-Ray, the assumed gamma value will be the same as the display
gamma value of the system the scene was created on. For PC systems, the most
common display gamma is 2.2, while for scenes created on Macintosh systems
should use a scene gamma of 1.8. Another gamma value that sometimes occurs in
scenes is 1.0.

Scenes that do not have an assumed_gamma global setting will not have any
gamma correction performed on them, for compatibility reasons. If you are
creating new scenes or rendering old scenes, it is strongly recommended that
you put in an appropriate assumed_gamma global setting. For new scenes, you
should use an assumed gamma value of 1.0 as this models how light appears in
the real world more realistically.

The following sections explain more thoroughly what gamma is and why it is
important.

7.8.3.1          Monitor Gamma

The differences in how images are displayed is a result of how a computer
actually takes an image and displays it on the monitor. In the process of
rendering an image and displaying it on the screen, several gamma values are
important, including the POV scene file or image file gamma and the monitor
gamma.

Most image files generated by POV-Ray store numbers in the range from 0 to
255 for each of the red, green and blue components of a pixel. These numbers
represent the intensity of each color component, with 0 being black and 255
being the brightest color (either 100% red, 100% green or 100% blue). When an
image is displayed, the graphics card converts each color component into a
voltage which is sent to the monitor to light up the red, green and blue
phosphors on the screen. The voltage is usually proportional to the value of
each color component.

Gamma becomes important when displaying intensities that aren't the maximum
or minimum possible values. For example, 127 should represent 50% of the
maximum intensity for pixels stored as numbers between 0 and 255. On systems
that don't do gamma correction, 127 will be converted to 50% of the maximum
voltage, but because of the way the phosphors and the electron guns in a
monitor work, this may be only 22% of the maximum color intensity on a
monitor with a gamma of 2.2. To display a pixel which is 50% of the maximum
intensity on this monitor, we would need a voltage of 73% of the maximum
voltage, which translates to storing a pixel value of 186.

The relationship between the input pixel value and the displayed intensity
can be approximated by an exponential function

  obright = ibright ^ display_gamma


where obright is the output intensity and ibright is the input pixel
intensity. Both values are in the range from 0 to 1 (0% to 100%). Most
monitors have a fixed gamma value in the range from 1.8 to 2.6. Using the
above formula with display_gamma values greater than 1 means that the output
brightness will be less than the input brightness. In order to have the
output and input brightness be equal an overall system gamma of 1 is needed.
To do this, we need to gamma correct the input brightness in the same manner
as above but with a gamma value of 1/display_gamma before it is sent to the
monitor. To correct for a display gamma of 2.2, this pre-monitor gamma
correction uses a gamma value of 1.0/2.2 or approximately 0.45.

How the pre-monitor gamma correction is done depends on what hardware and
software is being used. On Macintosh systems, the operating system has taken
it upon itself to insulate applications from the differences in display
hardware. Through a gamma control panel the user may be able to set the
actual monitor gamma and MacOS will then convert all pixel intensities so
that the monitor will appear to have the specified gamma value. On Silicon
Graphics machines, the display adapter has built-in gamma correction
calibrated to the monitor which gives the desired overall gamma (the default
is 1.7). Unfortunately, on PCs and most UNIX systems, it is up to the
application to do any gamma correction needed.

7.8.3.2          Image File Gamma

Since most PC and UNIX applications and image file formats don't understand
display gamma, they don't do anything to correct for it. As a result, users
creating images on these systems adjust the image in such a way that it has
the correct brightness when displayed. This means that the data values stored
in the files are made brighter to compensate for the darkening effect of the
monitor. In essence, the 0.45 gamma correction is built in to the image files
created and stored on these systems. When these files are displayed on a
Macintosh system, the gamma correction built in to the file, in addition to
gamma correction built into MacOS, means that the image will be too bright.
Similarly, files that look correct on Macintosh or SGI systems because of the
built-in gamma correction will be too dark when displayed on a PC.

The new PNG format files generated by POV-Ray 3.0 overcome the problem of too
much or not enough gamma correction by storing the image file gamma (which is
1.0/display_gamma) inside the PNG file when it is generated by POV-Ray. When
the PNG file is later displayed by a program that has been set up correctly,
it uses this gamma value as well as the current display gamma to correct for
the potentially different display gamma used when originally creating the
image.

Unfortunately, of all the image file formats POV-Ray supports, PNG is the
only one that has any gamma correction features and is therefore preferred
for images that will be displayed on a wide variety of platforms.

7.8.3.3          Scene File Gamma

The image file gamma problem itself is just a result of how scenes themselves
are generated in POV-Ray. When you start out with a new scene and are placing
light sources and adjusting surface textures and colors, you generally make
several attempts before the lighting is how you like it. How you choose these
settings depends upon the preview image or the image file stored to disk,
which in turn is dependent upon the overall gamma of the display hardware
being used.

This means that as the artist you are doing gamma correction in the POV-Ray
scene file for your particular hardware. This scene file will generate an
image file that is also gamma corrected for your hardware and will display
correctly on systems similar to your own. However, when this scene is
rendered on another platform, it may be too bright or too dim, regardless of
the output file format used. Rather than have you change all the scene files
to have a single fixed gamma value (heaven forbid!), POV-Ray 3.0 allows you
to specify in the scene file the display gamma of the system that the scene
was created on.

The assumed_gamma global setting, in conjunction with the Display_Gamma INI
setting lets POV-Ray know how to do gamma correction on a given scene so that
the preview and output image files will appear the correct brightness on any
system. Since the gamma correction is done internally to POV-Ray, it will
produce output image files that are the correct brightness for the current
display, regardless of what output format is used. As well, since the gamma
correction is performed in the high-precision data format that POV-Ray uses
internally, it produces better results than gamma correction done after the
file is written to disk.

Although you may not notice any difference in the output on your system with
and without an assumed_gamma setting, the assumed gamma is important if the
scene is ever rendered on another platform.

7.8.4            HF_Gray_16

The hf_gray_16 setting is useful when using POV-Ray to generate heightfields
for use in other POV-Ray scenes. The syntax is...

  global_settings { hf_gray_16 BOOLEAN }


The boolean value turns the option on or off. If the keyword is specified
without the boolean value then the option is turned on. If hf_gray_16 is not
specified in any global_settings statement in the entire scene then the
default is off.

When hf_gray_16 is on, the output file will be in the form of a heightfield,
with the height at any point being dependent on the brightness of the pixel.
The brightness of a pixel is calculated in the same way that color images are
converted to grayscale images:

  height = 0.3 * red + 0.59 * green + 0.11 * blue


Setting the hf_gray_16 option will cause the preview display, if used, to be
grayscale rather than color. This is to allow you to see how the heightfield
will look because some file formats store heightfields in a way that is
difficult to understand afterwards. See section "Height Field" for a
description of how POV-Ray heightfields are stored for each file type.

7.8.5            Irid_Wavelength

Iridescence calculations depend upon the dominant wavelengths of the primary
colors of red, green and blue light. You may adjust the values using the
global setting irid_wavelength as follows...   global_settings { irid_wavelen


The default value is rgb <0.25,0.18,0.14> and any filter or transmit values
are ignored. These values are proportional to the wavelength of light but
they represent no real world units.

In general, the default values should prove adequate but we provide this
option as a means to experiment with other values.

7.8.6            Max_Trace_Level

In scenes with many reflective and transparent surfaces POV-Ray can get
bogged down tracing multiple reflections and refractions that contribute very
little to the color of a particular pixel. The global setting max_trace_level
defines the maximum number of recursive levels that POV-Ray will trace a ray.


  global_settings { max_trace_level INTEGER }


This is used when a ray is reflected or is passing through a transparent
object and when shadow rays are cast. When a ray hits a reflective surface,
it spawns another ray to see what that point reflects. That is trace level
one. If it hits another reflective surface another ray is spawned and it goes
to trace level two. The maximum level by default is five.

One speed enhancement added to POV-Ray in version 3.0 is Adaptive  Depth
Control (ADC). Each time a new ray is spawned as a result of reflection or
refraction its contribution to the overall color of the pixel is reduced by
the amount of reflection or the filter value of the refractive surface. At
some point this contribution can be considered to be insignificant and there
is no point in tracing any more rays. Adaptive depth control is what tracks
this contribution and makes the decision of when to bail out. On scenes that
use a lot of partially reflective or refractive surfaces this can result in a
considerable reduction in the number of rays fired and makes it safer to use
much higher max_trace_level values.

This reduction in color contribution is a result of scaling by the reflection
amount and/or the filter values of each surface, so a perfect mirror or
perfectly clear surface will not be optimizable by ADC. You can see the
results of ADC by watching the Rays Saved and Highest Trace Level displays on
the statistics screen.

The point at which a ray's contribution is considered insignificant is
controlled by the adc_bailout value. The default is 1/255 or approximately
0.0039 since a change smaller than that could not be visible in a 24 bit
image. Generally this setting is perfectly adequate and should be left alone.
Setting adc_bailout to 0 will disable ADC, relying completely on
max_trace_level to set an upper limit on the number of rays spawned.

If max_trace_level is reached before a non-reflecting surface is found and if
ADC hasn't allowed an early exit from the ray tree the color is returned as
black. Raise max_trace_level if you see black areas in a reflective surface
where there should be a color.

The other symptom you could see is with transparent objects. For instance,
try making a union of concentric spheres with a clear texture on them. Make
ten of them in the union with radius's from 1 to 10 and render the scene. The
image will show the first few spheres correctly, then black. This is because
a new level is used every time you pass through a transparent surface. Raise
max_trace_level to fix this problem.

Note that raising max_trace_level will use more memory and time and it could
cause the program to crash with a stack overflow error, although ADC will
alleviate this to a large extent. Values for max_trace_level are not
restricted, so it can be set to any number as long as you have the time and
memory. However, increasing its setting does not necessarily equate to
increased image quality unless such depths are really needed by the scene.

7.8.7            Max_Intersections

POV-Ray uses a set of internal stacks to collect ray/object intersection
points. The usual maximum number of entries in these I-Stacks is 64. Complex
scenes may cause these stacks to overflow. POV-Ray doesn't stop but it may
incorrectly render your scene. When POV-Ray finishes rendering, a number of
statistics are displayed. If you see I-Stack Overflows reported in the
statistics you should increase the stack size. Add a global setting to your
scene as follows:

  global_settings { max_intersections INTEGER }


7.8.8            Number_Of_Waves

The wave and ripples pattern are generated by summing a series of waves, each
with a slightly different center and size. By default, ten waves are summed
but this amount can be globally controlled by changing the number_of_waves
setting.

  global_settings { number_of_waves INTEGER }


Changing this value affects both waves and ripples alike on all patterns in
the scene.

7.8.9            Radiosity

Important notice: The radiosity feature in POV-Ray 3.0 are somewhat
experimental. There is a high probability that the design and implementation
of these features will be changed in future versions. We cannot guarantee
that scenes using these features in 3.0 will render identically in future
releases or that full backwards compatibility of language syntax can be
maintained.

Radiosity is an extra calculation that more realistically computes the
diffuse interreflection of light. This diffuse interreflection can be seen if
you place a white chair in a room full of blue carpet, blue walls and blue
curtains. The chair will pick up a blue tint from light reflecting off of
other parts of the room. Also notice that the shadowed areas of your
surroundings are not totally dark even if no light source shines directly on
the surface. Diffuse light reflecting off of other objects fills in the
shadows. Typically ray-tracing uses a trick called ambient light to simulate
such effects but it is not very accurate.

Radiosity is more accurate than simplistic ambient light but it takes much
longer to compute. For this reason, POV-Ray does not use radiosity by
default. Radiosity is turned on using the Radiosity INI file option or the
+QR command line switch.

The following sections describes how radiosity works, how to control it with
various global settings and tips on trading quality vs. speed.

7.8.9.1          How Radiosity Works

The problem of ray-tracing is to figure out what the light level is at each
point that you can see in a scene. Traditionally, in ray tracing, this is
broken into the sum of these components:

  - Diffuse, the effect that makes the side of things facing the light
  - Specular, the effect that makes shiny things have dings or sparkles on
  - Ambient, the general all-over light level that any scene has, which keeps
    things in shadow from being pure black.


POV's radiosity system, based on a method by Greg Ward, provides a way to
replace the last term - the constant ambient light value - with a light level
which is based on what surfaces are nearby and how bright in turn they are.

The first thing you might notice about this definition is that it is
circular: the light of everything is dependent on everything else and vice
versa. This is true in real life but in the world of ray-tracing, we can make
an approximation. The approximation that is used is: the objects you are
looking at have their ambient values calculated for you by checking the other
objects nearby. When those objects are checked during this process, however,
a traditional constant ambient term is used.

How does POV-Ray calculate the ambient term for each point? By sending out
more rays, in many different directions, and averaging the results. A typical
point might use 200 or more rays to calculate its ambient light level
correctly.

Now this sounds like it would make the ray-tracer 200 times slower. This is
true, except that the software takes advantage of the fact that ambient light
levels change quite slowly (remember, shadows are calculated separately, so
sharp shadow edges are not a problem). Therefore, these extra rays are sent
out only once in a while (about 1 time in 50), then these calculated values
are saved and reused for nearby pixels in the image when possible.

This process of saving and reusing values is what causes the need for a
variety of tuning parameters, so you can get the scene to look just the way
you want.

7.8.9.2          Adjusting Radiosity

As described earlier, radiosity is turned on by using the Radiosity INI file
option or the +QR command line switch. However radiosity has many parameters
that are specified in a radiosity statement inside a global_settings
statement as follows:

   global_settings {
     radiosity {
       brightness FLOAT
       count INTEGER
       distance_maximum FLOAT
       error_bound FLOAT
       gray_threshold FLOAT
       low_error_factor FLOAT
       minimum_reuse FLOAT
       nearest_count INTEGER
       recursion_limit INTEGER
     }
   }


Each item is optional and may appear in and order. If an item is specified
more than once the last setting overrides previous values. Details on each
item is given in the following sections.

7.8.9.2.1        brightness

This is the degree to which ambient values are brightened before being
returned upwards to the rest of the system. If an object is red < 1, 0, 0>,
with an ambient value of 0.3, in normal situations a red component of 0.3
will be added in. With radiosity on, assume it was surrounded by an object of
gra color <0.6, 0.6, 0.6>. The average color returned by the gathering
process will be the same. This will be multiplied by the texture's ambient
weight value of 0.3, returning <0.18, 0.18, 0.18>. This is much darker than
the 0.3 which would be added in normally. Therefore, all returned values are
brightened by the inverse of the average of the calculated values, so the
average ambient added in does not change. Some will be higher than specified
(higher than 0.3 in this example) and some will be lower but the overall
scene brightness will be unchanged.


7.8.9.2.2        count

The number of rays that are sent out whenever a new radiosity value has to be
calculated is given by count. Values of 100 to 150 make most scenes look
good. Higher values might be needed for scenes with high contrast between
light levels or small patches of light causing the illumination. This would
be used only for a final rendering on an image because it is very compute
intensive. Since most scenes calculate the ambient value at 1% to 2% of
pixels, as a rough estimate, your rendering will take 1% to 2% of this number
times as long. If you set it to 300 your rendering might take 3 to 6 times as
long to complete (1% to 2% times 300).

When this value is too low, the light level will tend to look a little bit
blotchy, as if the surfaces you're looking at were slightly warped. If this
is not important to your scene (as in the case that you have a bump map or if
you have a strong texture) then by all means use a lower number.


7.8.9.2.3        distance_maximum

The distance_maximum is the only tuning value that depends upon the size of
the objects in the scene. This one must be set for scenes to render
properly... the rest can be ignored for a first try. It is difficult to
describe the meaning simply but it sets the distance in model units from a
sample at which the error is guaranteed to hit 100% (radiosity_error_bound
>=1): no samples are reused at a distance larger than this from their
original calculation point.

Imagine an apple at the left edge of a table. The goal is to make sure that
samples on the surface of the table at the right are not used too close to
the apple and definitely not underneath the apple. If you had enough rays
there wouldn't be a problem since one of them would be guaranteed to hit the
apple and set the reuse radius properly for you. In practice, you must limit
this.

We use this technique: find the object in your scene which might have the
following problem: a small object on a larger flatter surface that you want
good ambient light near. Now, how far from this would you have to get to be
sure that one of your rays had a good chance of hitting it? In the
apple-on-the-table example, assuming I used one POV-Ray unit as one inch, I
might use 30 inches. A theoretically sound way (when you are running lots of
rays) is the distance at which this object's top is 5 degrees above the
horizon of the sample point you are considering. This corresponds to about 11
times the height of the object. So, for a 3-inch apple, 33 inches makes some
sense. For good behavior under and around a 1/3 inch pea, use 3 inches etc.
Another VERY rough estimate is one third the distance from your eye position
to the point you are looking at. The reasoning is that you are probably no
more than 90 inches from the apple on the table, if you care about the
shading underneath it.


7.8.9.2.4        error_bound

The error_bound is one of the two main speed/quality tuning values (the other
is of course the number of rays shot). In an ideal world, this would be the
only value needed. It is intended to mean the fraction of error tolerated.
For example, if it were set to 1 the algorithm would not calculate a new
value until the error on the last one was estimated at as high as 100%.
Ignoring the error introduced by rotation for the moment, on flat surfaces
this is equal to the fraction of the reuse distance, which in turn is the
distance to the closest item hit. If you have an old sample on the floor 10
inches from a wall, an error bound of 0.5 will get you a new sample at a
distance of about 5 inches from the wall. 0.5 is a little rough and ready,
0.33 is good for final renderings. Values much lower than 0.3 take forever.


7.8.9.2.5        gray_threshold

Diffusely interreflected light is a function of the objects around the point
in question. Since this is recursively defined to millions of levels of
recursion, in any real life scene, every point is illuminated at least in
part by every other part of the scene. Since we can't afford to compute this,
we only do one bounce and the calculated ambient light is very strongly
affected by the colors of the objects near it. This is known as color bleed
and it really happens but not as much as this calculation method would have
you believe. The gray_threshold variable grays it down a little, to make your
scene more believable. A value of .6 means to calculate the ambient value as
60% of the equivalent gray value calculated, plus 40% of the actual value
calculated. At 0%, this feature does nothing. At 100%, you always get
white/gray ambient light, with no hue. Note that this does not change the
lightness/darkness, only the strength of hue/grayness (in HLS terms, it
changes H only).


7.8.9.2.6        low_error_factor

If you calculate just enough samples, but no more, you will get an image
which has slightly blotchy lighting. What you want is just a few extra
interspersed, so that the blending will be nice and smooth. The solution to
this is the mosaic preview: it goes over the image one or more times
beforehand, calculating radiosity values. To ensure that you get a few extra,
the radiosity algorithm lowers the error bound during the pre-final passes,
then sets it back just before the final pass. This tuning value sets the
amount that the error bound is dropped during the preliminary image passes.
If your low error factor is 0.8 and your error bound is set to 0.4 it will
really use an error bound of 0.32 during the first passes and 0.4 on the
final pass.


7.8.9.2.7        minimum_reuse

The minimum effective radius ratio is set by minimum_reuse. This is the
fraction of the screen width which sets the minimum radius of reuse for each
sample point (actually, it is the fraction of the distance from the eye but
the two are roughly equal). For example, if the value is 0.02 the radius of
maximum reuse for every sample is set to whatever ground distance corresponds
to 2% of the width of the screen. Imagine you sent a ray off to the horizon
and it hits the ground at a distance of 100 miles from your eyepoint. The
reuse distance for that sample will be set to 2 miles. At a resolution of
300*400 this will correspond to (very roughly) 8 pixels. The theory is that
you don't want to calculate values for every pixel into every crevice
everywhere in the scene, it will take too long. This sets a minimum bound for
the reuse. If this value is too low, (which is should be in theory) rendering
gets slow, and inside corners can get a little grainy. If it is set too high,
you don't get the natural darkening of illumination near inside edges, since
it reuses. At values higher than 2% you start getting more just plain errors,
like reusing the illumination of the open table underneath the apple.

Remember that this is a unitless ratio.


7.8.9.2.8        nearest_count

The nearest_count value is the maximum number of old ambient values blended
together to create a new interpolated value. It will always be the n
geometrically closest reusable points that get used. If you go lower than 4,
things can get pretty patchy. This can be good for debugging, though. Must be
no more than 10, since that is the size of the array allocated.


7.8.9.2.9        radiosity_quality


7.8.9.2.10       recursion_limit

This value determines how many recursion levels are used to calculate the
diffuse inter-reflection. Valid values are one and two.


7.8.9.3          Tips on Radiosity

If you want to see where your values are being calculated set radiosity_count
down to about 20, set radiosity_nearest_count to 1 and set radiosity_gray to
0. This will make everything maximally patchy, so you'll be able to see the
borders between patches. There will have been a radiosity calculation at the
center of most patches. As a bonus, this is quick to run. You can then change
the radiosity_error_bound up and down to see how it changes things. Likewise
modify radiosity_reuse_dist_min and max.

One way to get extra smooth results: crank up the sample count (we've gone as
high as 1300) and drop the low_error_factor to something small like 0.6. Bump
up the reuse_count to 7 or 8. This will get better values, and more of them,
then interpolate among more of them on the last pass. This is not for people
with a lack of patience since it is like a squared function. If your
blotchiness is only in certain corners or near certain objects try tuning the
error bound instead. Never drop it by more than a little at a time, since the
run time will get very long.

If your scene looks good but right near some objects you get spots of the
right (usually darker) color showing on a flat surface of the wrong color
(same as far away from the object), then try dropping reuse_dist_max. If that
still doesn't work well increase your ray count by 100 and drop the error
bound just a bit. If you still have problems, drop reuse_nearest_count to
about 4.

APPENDIX A       Copyright

The following sections contain the legal information and license for the
Persistence of Vision(tm) Ray-Tracer, also called POV-Ray(tm).


APPENDIX A.1     General License Agreement

THIS NOTICE MUST ACCOMPANY ALL OFFICIAL OR CUSTOM PERSISTENCE OF  VISION
FILES. IT MAY NOT BE REMOVED OR MODIFIED. THIS INFORMATION  PERTAINS TO ALL
USE OF THE PACKAGE WORLDWIDE. THIS DOCUMENT  SUPERSEDES ALL PREVIOUS GENERAL
LICENSES OR DISTRIBUTION POLICIES.  ANY INDIVIDUALS, COMPANIES OR GROUPS WHO
HAVE BEEN GRANTED SPECIAL  LICENSES MAY CONTINUE TO DISTRIBUTE VERSION 2.x
BUT MUST RE-APPLY  FOR VERSION 3.00 OR LATER.

This document pertains to the use and distribution of the Persistence of
Vision(tm) Ray-Tracer a. k. a POV-Ray(tm). It applies to all POV-Ray program
source files, executable (binary) files, scene files, documentation files,
help file, bitmaps and INI files contained in official POV-Ray Team(tm)
archives. All of these are referred to here as the software.

All of this software is Copyright 1991,1997 by the POV-Ray Team(tm). Although
it is distributed as freeware, it is NOT Public Domain.

The copyrighted package may ONLY be distributed and/or modified according to
the license granted herein. The spirit of the license is to promote POV-Ray
as a standard ray-tracer, provide the full POV-Ray package freely to as many
users as possible, prevent POV-Ray users and developers from being taken
advantage of, enhance the life quality of those who come in contact with
POV-Ray. This license was created so these goals could be realized. You are
legally bound to follow these rules, but we hope you will follow them as a
matter of ethics, rather than fear of litigation.

APPENDIX A.2     Usage Provisions

Permission is granted to the user to use the software and associated files in
this package to create and render images. The use of this software for the
purpose of creating images is completely free. The creator of a scene file
and the image created from the scene file, retains all rights to the image
and scene file they created and may use them for any purpose commercial or
noncommercial.

The user is also granted the right to use the scenes files, fonts, bitmaps,
and include files distributed in the include, texsamps and pov3demo sub-
directories in their own scenes. Such permission does not extend to files in
the povscn sub-directory. povscn files are for your enjoyment and education
but may not be the basis of any derivative works.

APPENDIX A.3     General Rules for All Distributions

The permission to distribute this package under certain very specific
conditions is granted in advance, provided that the following conditions are
met.

These archives must not be re-archived using a different method without the
explicit permission of the POV-Team. You may rename the archives only to meet
the file name conventions of your system or to avoid file name duplications
but we ask that you try to keep file names as similar to the originals as
possible (for example: povsrc.zip to povsrc30.zip)

Ready-to-run unarchived distribution on CD-ROM is also permitted if the files
are arranged in our standard directory or folder structure as though it had
been properly installed on a hard disk.

You must distribute a full package of files as described in the next section.
No portion of this package may be separated from the package and distributed
separately other than under the conditions specified in the provisions given
below.

Non-commercial distribution in which no money or compensation is charged
(such as a user copying the software for a personal friend or colleague) is
permitted with no other restrictions.

Teachers and educational institutions may also distribute the material to
students and may charge minimal copying costs if the software is to be used
in a course.

APPENDIX A.4     Definition of "Full Package"

POV-Ray is contained in two sets of archives for each hardware platform. A
full package consists of either:

1) End user executable archives containing an executable program,
documentation, and sample scenes but no source.

- or -

2) Programmer archives containing full source code but no executable.  Also
you must include an archive containing documentation, and  sample scenes. On
some platforms, the documentation and sample  scenes are archived separately
from the source. Source alone  is not sufficient. You must have docs and
scenes.

POV-Ray is officially distributed for MS-Dos; Windows 32-bit; Linux for Intel
x86 series; Apple Macintosh; Apple PowerPC; SunOS; and Amiga. Other systems
may be added in the future.

Distributors need not support all platforms but for each platform you support
you must distribute a full package. For example a Macintosh only BBS need not
distribute the Windows versions.

This software may only be bundled with other software packages according to
the conditions specified in the provisions below.

{/HEADER 1 Conditions for Shareware/Freeware Distribution Companies/}

Shareware and freeware distribution companies may distribute the software
included in software-only compilations using media such as, but not limited
to, floppy disk, CD-ROM, tape backup, optical disks, hard disks, or memory
cards. This section only applies to distributors of collected programs.
Anyone wishing to bundle the package with a shareware product must use the
commercial bundling rules. Any bundling with books, magazines or other print
media should also use the commercial rules.

You must notify us that you are distributing POV-Ray and must provide us with
information on how to contact you should any support issues arise.

No more than five dollars U.S. ($5) can be charged per disk for the copying
of this software and the media it is provided on. Space on each disk must be
used as fully as possible. You may not spread the files over more disks than
are necessary.

Distribution on high volume media such as backup tape or CD-ROM is permitted
if the total cost to the user is no more than $0.08 U.S. dollars per megabyte
of data. For example a CD-ROM with 600 meg could cost no more than $48.00.

APPENDIX A.5     Conditions for On-Line Services and BBS's Including Internet


On-line services, BBS's and internet sites may distribute the POV-Ray
software under the conditions in this section. Sites which allow users to run
POV-Ray from remote locations must use separate provisions in the section
below.

The archives must all be easily available on the service and should be
grouped together in a similar on-line area.

It is strongly requested that sites remove prior versions of POV-Ray to avoid
user confusion and simplify or minimize our support efforts.

The site may only charge standard usage rates for the downloading of this
software. A premium may not be charged for this package. I. e. CompuServe or
America On-Line may make these archives available to their users, but they
may only charge regular usage rates for the time required to download.

APPENDIX A.6     Online or Remote Execution of POV-Ray

Some internet sites have been set up so that remote users can actually run
POV-Ray software on the internet server. Other companies sell CPU time for
running POV-Ray software on workstations or high-speed computers. Such use of
POV-Ray software is permitted under the following conditions.

Fees or charges, if any, for such services must be for connect time, storage
or processor usage ONLY. No premium charges may be assessed for use of
POV-Ray beyond that charged for use of other software. Users must be clearly
notified that they are being charged for use of the computer and not for use
of POV-Ray software.

Users must be prominently informed that they are using POV-Ray software, that
such software is free, and where they can find official POV-Ray software. Any
attempt to obscure the fact that the user is running POV-Ray is expressly
prohibited.

All files normally available in a full package distribution, especially a
copy of this license and full documentation must be available for download or
readable online so that users of an online executable have access to all of
the material of a full user package.

If the POV-Ray software has been modified in any way, it must also follow the
provisions for custom versions below.

APPENDIX A.7     Conditions for Distribution of Custom Versions

The user is granted the privilege to modify and compile the source code for
their own personal use in any fashion they see fit. What you do with the
software in your own home is your business.

If the user wishes to distribute a modified version of the software,
documentation or other parts of the package (here after referred to as a
custom version) they must follow the provisions given below. This includes
any translation of the documentation into other languages or other file
formats. These license provisions have been established to promote the growth
of POV-Ray and prevent difficulties for users and developers alike. Please
follow them carefully for the benefit of all concerned when creating a custom
version.

No portion of the POV-Ray source code may be incorporated into another
program unless it is clearly a custom version of POV-Ray that includes all of
the basic functions of POV-Ray.

All executables, documentation, modified files and descriptions of the same
must clearly identify themselves as a modified and unofficial version of
POV-Ray. Any attempt to obscure the fact that the user is running POV-Ray or
to obscure that this is an unofficial version expressly prohibited.

You must provide all POV-Ray support for all users who use your custom
version. You must provide information so that user may contact you for
support for your custom version. The POV-Ray Team is not obligated to provide
you or your users any technical support.

Include contact information in the DISTRIBUTION_MESSAGE macros in the source
file optout.h and insure that the program prominently displays this
information. Display all copyright notices and credit screens for the
official version.

Custom versions may only be distributed as freeware. You must make all of
your modifications to POV-Ray freely and publicly available with full source
code to the modified portions of POV-Ray and must freely distribute full
source to any new parts of the custom version. The goal is that users must be
able to re-compile the program themselves and to be able to further improve
the program with their own modifications.

You must provide documentation for any and all modifications that you have
made to the program that you are distributing. Include clear and obvious
information on how to obtain the official POV-Ray.

The user is encouraged to send enhancements and bug fixes to the POV-Ray
Team, but the team is in no way required to utilize these enhancements or
fixes. By sending material to the team, the contributor asserts that he owns
the materials or has the right to distribute these materials. He authorizes
the team to use the materials any way they like. The contributor still
retains rights to the donated material, but by donating, grants unrestricted,
irrevocable usage and distribution rights to the POV-Ray Team. The team
doesn't have to use the material, but if we do, you do not acquire any rights
related to POV-Ray. The team will give you credit as the creator of new code
if applicable.


APPENDIX A.8     Conditions for Commercial Bundling

Vendors wishing to bundle POV-Ray with commercial software (including
shareware) or with publications must first obtain explicit permission from
the POV-Ray Team. This includes any commercial software or publications, such
as, but not limited to, magazines, cover-disk distribution, books,
newspapers, or newsletters in print or machine readable form.

The POV-Ray Team will decide if such distribution will be allowed on a
case-by-case basis and may impose certain restrictions as it sees fit. The
minimum terms are given below. Other conditions may be imposed.

  * Purchasers of your product must not be led to believe that they are
    paying for POV-Ray. Any mention of the POV-Ray bundle on the box, in
    advertising or in instruction manuals must be clearly marked with a
    disclaimer that POV-Ray is free software and can be obtained for free or
  * Include clear and obvious information on how to obtain the official
  * You must provide all POV-Ray support for all users who acquired POV-Ray
    through your product. The POV-Ray Development Team is not obligated to
  * If you modify any portion POV-Ray for use with your hardware or software,
  * Include a full user package as described above.r product.hese rules.

APPENDIX A.9     Retail Value of this Software

Although POV-Ray is, when distributed within the terms of this agreement,
free of charge, the retail value (or price) of this program is determined as
US$20.00 per copy distributed or copied. If the software is distributed or
copied without authorization you are legally liable to this debt to the
copyright holder or any other person or organization delegated by the
copyright holder for the collection of this debt, and you agree that you are
legally bound by the above and will pay this debt within 30 days of the
event.

However, none of the above paragraph constitutes permission for you to
distribute this software outside of the terms of this agreement. In
particular, the conditions and debt mentioned above (whether paid or unpaid)
do not allow you to avoid statutory damages or other legal penalties and does
not constitute any agreement that would allow you to avoid such other legal
remedies as are available to the copyright holder.

Put simply, POV-Ray is only free if you comply with our distribution
conditions; it is not free otherwise. The copyright holder of this software
chooses to give it away free under these and only these conditions.

For the purpose of copyright regulations, the retail value of this software
is US$20.00 per copy.

APPENDIX A.10    Other Provisions

The team permits and encourages the creation of programs, including
commercial packages, which import, export or translate files in the POV-Ray
Scene Description Language. There are no restrictions on use of the language
itself. We reserve the right to add or remove or change any part of the
language.

"POV-Ray", "Persistence of Vision", "POV-Ray Team" and "POV-Help" are
trademarks of the POV-Ray Team.

While we do not claim any restrictions on the letters "POV" alone, we humbly
request that you not use POV in the name of your product. Such use tends to
imply it is a product of the POV-Ray Team. Existing programs which used "POV"
prior to the publication of this document need not feel guilty for doing so
provided that you make it clear that the program is not the work of the team
nor endorsed by us.

APPENDIX A.11    Revocation of License

VIOLATION OF THIS LICENSE IS A VIOLATION OF COPYRIGHT LAWS. IT  WILL RESULT
IN REVOCATION OF ALL DISTRIBUTION PRIVILEGES AND MAY  RESULT IN CIVIL OR
CRIMINAL PENALTY.

Such violators who are prohibited from distribution will be identified in
this document.

In this regard, "PC Format", a magazine published by Future Publishing, Ltd.
in the United Kingdom, distributed incomplete versions of POV-Ray 1.0 in
violation the license which was effect at the time. They later attempted to
distribute POV-Ray 2.2 without prior permission of the POV-Ray Team in
violation the license which was in effect at the time. There is evidence that
other Future Publishing companies have also violated our terms. Therefore "PC
Format", and any other magazine, book or CD-ROM publication owned by Future
Publishing is expressly prohibited from any distribution of POV-Ray software
until further notice.

APPENDIX A.12    Disclaimer

This software is provided as is without any guarantees or warranty. Although
the authors have attempted to find and correct any bugs in the package, they
are not responsible for any damage or losses of any kind caused by the use or
misuse of the package. The authors are under no obligation to provide
service, corrections, or upgrades to this package.

APPENDIX A.13    Technical Support

We sincerely hope you have fun with our program. If you have any problems
with the program, the team would like to hear about them. Also, if you have
any comments, questions or enhancements, please contact the POV-Ray Team in
out own forum on the CompuServe Information Service, the GO POVRAY forum.
Also check us out on the internet at http://www.povray.org or ftp.povray.org.
The USENET group comp.graphics.rendering.raytracing is a great source of
information on POV-Ray and related topics.

License enquiries should be made via email and limited technical support is
available via email to:

   Chris Young
   POV-Ray Team Coordinator
   CIS: 76702,1655
   Internet 76702.1655@compuserve.com


The following postal address is only for official license business and only
if email is impossible.

We do not provide technical support via regular mail, only email. We don't
care if you don't have a modem or online access. We will not mail you disks
with updated versions. Do not send money.

   Chris Young
   3119 Cossell Drive
   Indianapolis, IN 46224 U.S.A.


The other authors' contact information may be found in section "Authors"
(see also "Postcards for POV-Ray Team Members").

APPENDIX B       Authors

Following is a list in alphabetic order of all people who have ever worked on
the POV-Ray Team or who have made a note-worthy contribution. If you want to
contact or thank the authors read the sections "Contacting the Authors" and
"Postcards for POV-Ray Team Members".

                               Claire Amundsen
                   (Tutorials for the POV-Ray User Guide)

                                 Steve Anger
                         (POV-Ray 2.0/3.0 developer)
                               CIS: 70714,3113
                         Internet: sanger@hookup.net

                                Randy Antler
                     (IBM-PC display code enhancements)

                                 John Baily
                              (RLE targa code)

                                 Eric Barish
                              (Ground fog code)

                                Dieter Bayer
                (POV-Ray 3.0 developer and docs coordinator)
                               CIS: 104707,643

                               Kendall Bennett
                           (PMODE library support)

                                Steve Bennett
                                (GIF support)

                              Jeff Bowermaster
                                 (Beta test)

                                 David Buck
                        (Original author of DKBTrace)
                           (POV-Ray 1.0 developer)

                                 Chris Cason
         (POV-Ray 2.0/3.0 developer, POV-Help, POV-Ray for Windows)
   Internet (preferred): povray@mail.oaks.com.au or Chris.Cason@povray.org
                              CIS: 104706,3166

                                Aaron Collins
                        (Co-author of DKBTrace 2.12)
                           (POV-Ray 1.0 developer)

                                Chris Dailey
                           (POV-Ray 3.0 developer)
                                    CIS:

                                Steve Demlow
                           (POV-Ray 3.0 developer)
                                    CIS:

                               Andreas Dilger
                           (POV-Ray 3.0 developer)
                     Internet: adilger@enel.ucalgary.ca
           WWW: http://www-mddsp.enel.ucalgary.ca/People/adilger/

                           Joris van Drunen Littel
                              (Mac beta tester)

                              Alexander Enzmann
                       (POV-Ray 1.0/2.0/3.0 developer)
                               CIS: 70323,2461
                         Internet: xander@mitre.com

                                 Dan Farmer
                       (POV-Ray 1.0/2.0/3.0 developer)
                               CIS: 74431,1075

                               Charles Fusner
                   (Tutorials for the POV-Ray User Guide)

                                 David Harr
                     (Mac balloon help and palette code)

                                 Jimmy Hoeks
                   (Help file for Windows user interface)

                                Terry Kanakis
                                (Camera fix)

                            Kari Juharvi Kivisalo
                              (Ground fog code)

                                 Adam Knight
                (Mac beta tester, Mac Apple Guide developer)
                                    CIS:

                              Lutz Kretzschmar
   (IBM-PC display code [SS24 truecolor], part of the anti-aliasing code)
                              CIS: 100023,2006

                              Charles Marslett
                            (IBM-PC display code)

                              Pascal Massimino
                              (Fractal objects)

                                Jim McElhiney
                           (POV-Ray 3.0 developer)
                                    CIS:

                             Robert A. Mickelsen
                             (POV-Ray 3.0 docs)
                                    CIS:

                                 Mike Miller
                      (Artist, scene files, stones.inc)
                               CIS: 70353,100

                                Douglas Muir
                         (Bump maps, height fields)

                                Joel NewKirk
                               (Amiga Version)
                              CIS: 102627,1152

                                Jim Nitchals
                         (Mac version, scene files)

                                 Paul Novak

                           (Texture contributions)

                                  Dave Park
                       (Amiga support, AGA video code)

                                 David Payne
                              (RLE targa code)

                                 Bill Pulver
                         (Time code, IBM-PC compile)

                                 Anton Raves
             (Beta tester, helping out on several Mac thingies)
                              CIS: 100022,2603

                               Dan Richardson
                                   (Docs)
                                    CIS:

                                 Tim Rowley
             (PPM and Windows-specific BMP image format support)
                       Internet: trowley@geom.umn.edu

                              Robert Schadewald
                                (Beta tester)
                                    CIS:

                                Eduard Schwan
                     (Mac version, mosaic preview, docs)
                   CIS: 104706,3276 or POVRAYMAC or ESPSW
         Internet: povraymac@compuserve.com or espsw@compuserve.com
           WWW: http://ourworld.compuserve.com/homepages/povraymac

                               Robert Skinner
                              (Noise functions)

                              Erkki Sondergaard
                                (Scene files)
                                    CIS:

                               Zsolt Szalavari
                                 (Halo code)
                       Internet: zsolt@cg.tuwien.ac.at

                                Scott Taylor
                        (Leopard and onion textures)

                               Timothy Wegner
                       (Fractal objects, PNG support)
                               CIS: 71320,675
                        Internet: twegner@phoenix.net

                                 Drew Wells
            (POV-Ray 1.0 developer, POV-Ray 1.0 team coordinator)

                                 Chris Young
      (POV-Ray 1.0/2.0/3.0 developer, POV-Ray 2.0/3.0 team coordinator)
                               CIS: 76702,1655


APPENDIX C       Contacting the Authors

The POV-Team is a collection of volunteer programmers, designers, animators
and artists meeting via electronic mail on Compuserve's POVRAY forum (GO
POVRAY).

The POV-Team's goal is to create freely distributable, high quality rendering
and animation software written in C that can be easily ported to many
different computers.

If you have any questions about POV-Ray, please contact   Chris Young
  POV-Team Coordinator
  CIS: 76702,1655
  Internet: 76702.1655@compuserve.com


We love to hear about how you're using and enjoying the program. We also will
do our best try to solve any problems you have with POV-Ray and incorporate
good suggestions into the program.

If you have a question regarding commercial use of, distribution of, or
anything particularly sticky, please contact Chris Young, the development
team coordinator. Otherwise, spread the mail around. We all love to hear from
you!

The best method of contact is e-mail through CompuServe for most of us.
America On-Line and Internet can now send mail to CompuServe, also, just use
the Internet address and the mail will be sent through to CompuServe where we
read our mail daily.

Please do not send large files to us through the e-mail without asking first.
We pay for each minute on CompuServe and large files can get expensive. Send
a query before you send the file, thanks!

APPENDIX D       Postcards for POV-Ray Team Members

If you want to personally thank some of the POV-Ray Team members you can send
them a postcard from wherever you are. To avoid invalid addresses from
floating around (in case some of us move) the addresses listed below (in
alphabetical order) are only valid until the given date.

  Dieter Bayer
  Taeublingstr. 26
  91058 Erlangen
  Germany                                    (until 31. July 1997)

  Chris Cason                                (Windows version)
  PO Box 407
  Williamstown
  Victoria 3016
  Australia                                  (until 31. December 1998)

  Joel NewKirk
  255-9 Echelon Rd
  Voorhees, NJ, USA, 08043                   (until ---)

  Eduard Schwan                              (Macintosh version)
  1112 Oceanic Drive
  Encinitas, California, USA, 92024-4007     (until 30. June 1998)


You should also be aware that we do not answer any questions asked by regular
mail or phone, we only reply to e-mails. Send any questions you have to the
e-mail address mentioned in section "Contacting the Authors".

APPENDIX E       Credits

Credits for providing contributions to the user documentation go to (in
alphabetical order):

                               Charles Fusner
                      (Blob, lathe and prism tutorial)


APPENDIX F       Tips and Hints


APPENDIX F.1     Scene Design Tips

There are a number of excellent shareware CAD style modelers available on the
DOS platform now that will create POV-Ray scene files. The online systems
mentioned elsewhere in this document are the best places to find these.

Hundreds of special-purpose utilities have been written for POV-Ray: data
conversion programs, object generators, shell-style launchers and more. It
would not be possible to list them all here, but again, the online systems
listed will carry most of them. Most, following the POV-Ray spirit, are
freeware or inexpensive shareware.

Some extremely elaborate scenes have been designed by drafting on graph
paper. Raytracer Mike Miller recommends graph paper with a grid divided in
tenths, allowing natural decimal conversions.

Start out with a boilerplate scene file, such as a copy of basicvue.pov, and
edit that. In general, place your objects near and around the origin with the
camera in the negative z-direction, looking at the origin. Naturally, you
will break from this rule many times, but when starting out, keep things
simple.

For basic, boring, but dependable lighting, place a light source at or near
the position of the camera. Objects will look flat, but at least you will see
them. From there, you can move it slowly into a better position.

APPENDIX F.2     Scene Debugging Tips

To see a quick version of your picture, render it very small. With fewer
pixels to calculate the ray-tracer can finish more quickly. -W160 -H100 is a
good size.

Use the +Q quality switch when appropriate.

If there is a particular area of your picture that you need to see in high
resolution, perhaps with anti-aliasing on (perhaps a fine-grained wood
texture), use the +SC, +EC, +SR and +ER switches to isolate a window.

If your image contains a lot of inter-reflections, set max_trace_level to a
low value such as 1 or 2. Don't forget to put it back up when you're
finished!

Turn off any unnecessary lights. Comment out extended light keywords when not
needed for debugging. Again, don't forget to put them back in before you
retire for the night with a final render running!

If you've run into an error that is eluding you by visual examination it's
time to start bracketing your file. Use the block comment characters /* ...
*/ to disable most of your scene and try to render again. If you no longer
get an error the problem naturally lies somewhere within the disabled area.
Slow and methodical testing like this will eventually get you to a point
where you will either be able to spot the bug, or go quietly insane. Maybe
both.

If you seem to have lost yourself or an object (a common experience for
beginners) there are a few tricks that can sometimes help:

  1)Move your camera way back to provide a long range view. This may not help
    with very small objects which tend to be less visible at a distance, but
  2)Try setting the ambient value to 1.0 if you suspect that the object may
    simply be hidden from the lights. This will make it self-illuminated and
  3)Replace the object with a larger, more obvious "stand-in" object like a
    large sphere or box. Be sure that all the same transformations are
    applied to this new shape so that it ends up in the same spot.

APPENDIX F.3     Animation Tips

When animating objects with solid textures, the textures must move with the
object, i. e. apply the same rotate or translate functions to the texture as
to the object itself. This is now done automatically if the transformations
are placed after the texture block like the following example

  shape { ...
    pigment { ... }
    scale < ... >
  }


will scale the shape and pigment texture by the same amount.

  shape { ...
    scale < ... >
    pigment { ... }
  }


will scale the shape but not the pigment.

Constants can be declared for most of the data types in the program including
floats and vectors. By writing these to include files you can easily separate
the parameters for an animation into a separate file.

Some examples of declared constants would be:

   #declare Y_Rotation = 5.0 * clock
   #declare ObjectRotation = <0, Y_Rotation, 0>
   #declare MySphere = sphere { <0, 0, 0>, 1.1234 }


Other examples can be found scattered throughout the sample scene files.

A tip for MS-Dos users: Get ahold of dta.exe (Dave's Targa Animator) for
creating .FLI/.FLC animations. aaplay.exe and play.exe are common viewers for
this type of file.

When moving the camera in an animation (or placing one in a still image, for
that matter) avoid placing the camera directly over the origin. This will
cause very strange errors. Instead, move off center slightly and avoid
hovering directly over the scene.

APPENDIX F.4     Texture Tips

Wood is designed like a log with growth rings aligned along the z-axis.
Generally these will look best when scaled down by about a tenth (to a
unit-sized object). Start out with rather small value for the turbulence too
(around 0.05 is good for starters).

The marble texture is designed around a pigment primitive that is much like
an x-gradient. When turbulated, the effect is different when viewed from the
side or from the end. Try rotating it by 90 degrees on the y-axis to see the
difference.

You cannot get specular highlights on a totally black object. Try using a
very dark gray, say Gray10 or Gray15 (from colors.in), instead.

APPENDIX F.5     Height Field Tips

Try using POV-Ray itself to create images for height fields:   camera { locat
  plane { z, 0
     finish { ambient 1 }    // needs no light sources
     pigment { bozo }        // or whatever.  Experiment.
  }


That's all you'll need to create a .tga file that can then be used as a
height field in another image!

APPENDIX F.6     Converting "Handedness"

If you are importing images from other systems you may find that the shapes
are backwards (left-to-right inverted) and no rotation can make them correct.


Often, all you have to do is negate the terms in the right vector of the
camera to flip the camera left-to-right (use the right-hand coordinate
system). Some programs seem to interpret the coordinate systems differently,
however, so you may need to experiment with other camera transformations if
you want the y- and z-vectors to work as POV-Ray does.

APPENDIX G       Frequently Asked Questions

This is a collection of frequently asked questions and their answers taken
directly from messages posted in the POVRAY Forum on Compuserve and the
comp.graphics.raytracing newsgroup.

This version of the FAQ is heavily biased towards the CompuServe user of the
IBM PC version of POV-Ray. Hopefully later revisions will remove some of this
bias, but at present time, that is the largest audience.

APPENDIX G.1     General Questions


APPENDIX G.2     POV-Ray Options Questions

Q: How can I set mosaic preview to go from 8*straight to final render without
going to 4*and then 2*first? A: Use the +SPn or Preview_Start_Size option to
set the starting resolution and the +EPn or Preview_End_Size option to set
the ending resolution. With +SP8 and +EP8 it will go from 8*8 down to 8*8
(just one pass) then immediately drop into the final pass at 1*1.

Q: Should the +MB switch be used in very small scenes, i. e. with a low
number of objects. A: That depends on the number of objects and their type.
Normally it doesn't hurt to always use the bounding box hierarchy (+MB0). If
you have just one or two objects it may be better to not use automatic
bounding.

Q: Does the +MB switch affect the quality of the image? A: No. It only
affects the speed of the intersection tests.

Q: How do I avoid that the options screen scrolls off when error messages are
generated? A: Use the +P switch. Everytime POV-Ray is interrupted or the
tracing finishes you can use the cursor keys to scroll-back the options text.

APPENDIX G.3     Include File Questions

Q: In the file textures.v2, the glass textures are commented out. Why? A: The
old glass textures are duplicated in glass.inc. The old texture names didn't
fit in with the new naming scheme. Glass is now T_Glass1, Glass2 is now
T_Glass2 and Glass3 is now T_Glass3. While you can easily un-comment the old
names you're strongly encouraged to use the newer naming scheme.

APPENDIX G.4     Object Questions


APPENDIX G.4.1   Height Field Questions

Q: I have a lowly 8 meg of RAM on my computer and I ran out of memory trying
to use a 1024x768 pot file and a gif of the same resolution as height fields
(two different scenes). Is it my memory thats low or is that resolution
crazy? A: Smoothed heightfields will consume a lot more memory (about three
times as much) as one that isn't smoothed. Since smoothing really isn't
neccessary at those resolutions don't smooth (if you're smoothing).

Q: I want to use the same image for an image map and a height-field (which
gives some meaningful relationship between the height and colors). Does that
only work when using a gif or bmp format? I couldn't get the pot file to map
(format not supported). A: pot files are not supported as image maps. Their
purpose to POV-Ray is as heightfields. That doesn't prevent you from making a
matching gif in fractint that uses the continuous potential coloring that you
used for the 16 bit pot file, and using that as the image map. Remember that
both image maps and height fields are initialized in a 1*1(*1) area, with the
lower-left of the image situated at the origin. The image map is initiated in
the x-y-plane while the height field is in the x-z plane. Thus you'll have to
rotate the image map by 90 degrees around the x-axis (use rotate x*90) to get
the image map to line up.

APPENDIX G.4.2   Text Questions

Q: Is there any possibility to know the size of a font-object? A: Sadly no.
We really need it but its not easy to do. Until just days before beta release
the horizontal spacing didn't even work right. Now that we've got that fixed,
perhaps we can figure a way to get the length.

APPENDIX G.5     Atmospheric Questions


APPENDIX G.5.1   Atmosphere Questions

Q: Why is the atmosphere I added not visible? A: The most common error made
when adding an atmosphere to a scene is the missing hollow keyword in all
objects the camera currently is in. If you are inside a box that is used to
model a room you'll have to add the hollow keyword to the box statement. If a
plane is used to model the ground you'll have to make it hollow (only if you
are inside the plane, but to be sure you can always do it).

If this doesn't help there may be other problems you'll have to verify. The
distance and scattering values of the atmosphere have to be larger than zero.
Light sources that shall interact with the atmosphere mustn't contain an
atmosphere off statement.

Q: Why can't I see any atmosphere through my translucent object? A: If you
have a translucent object you (almost) always have to make it hollow by
adding the hollow keyword. Whenever an intersection is found and the ray is
inside a solid object no atmospheric effects will be calculated.

If you have a partially transparent plane for example the atmosphere on the
other side of the plane will only be visible through the plane if this plane
is hollow.

Q: Why do the lit parts of the atmosphere amplify the background? A: First,
they don't.

Second, whenever parts of the background are visible through the atmosphere
and those areas of the atmosphere are lit by any light source, the scattered
light is added to the light coming from the background. This is the reason
why the background seems to be amplified by the atmosphere. Just imagine the
followoing example: you have a blue background that is attenuated be the
atmosphere in a way that the color reaching the viewer is <0,0,0.2>. Now some
light coming from a light source is attenuated and scattered by the
atmosphere and finally reaches the viewer with a color of <0.5,0.5,0.5>.
Since we already have light coming from the background, both colors are added
to give <0.5,0.5,0.7>. Thus the light gets a blue hue. As a result you think
that the background light is amplified but it isn't as the following scene
clearly shows.

#version 3.0
  camera {
    location <0, 6, -20>
    look_at <0, 6, 0>
    angle 48
  }

  atmosphere {
    type 1
    samples 10
    distance 20
    scattering 0.3
    aa_level 3
    aa_threshold 0.1
    jitter 0.2
  }

  light_source { <0, 15, 0> color rgb .7 shadowless }

  light_source {
    <-5, 15, 0> color rgb <1, 0, 0>
    spotlight
    point_at <-5, 0, 0>
    radius 10
    falloff 15
    tightness 1
    atmospheric_attenuation on
  }

  light_source {
    <0, 15, 0> color rgb <0, 1, 0>
    spotlight
    point_at <0, 0, 0>
    radius 10
    falloff 15
    tightness 1
    atmospheric_attenuation on
  }

  light_source {
    <5, 15, 0> color rgb <0, 0, 1>
    spotlight
    point_at <5, 0, 0>
    radius 10
    falloff 15
    tightness 1
    atmospheric_attenuation on
  }

  plane { z, 10
    pigment { checker color rgb<1, 0, 0> color rgb<0, 1, 0> }
    hollow
  }


The atmosphere seems to amplify what is seen in the background.

In the background you see a red/green checkered plane. The background color
visible through the atmosphere is added to the light scattered from the
spotlights. You'll notice that even though the red squares behind the red
spotlight's cone are brighter than those outside the cone the green ones are
not. For the green spotlight the situation is turned around: the green
squares seem to be amplified while the red are not. The blue spotlight
doesn't show this effect at all.

Q: The docs say the distance parameter for atmosphere works in the same way
as fog distance. Is that right? A: Yes, that's right. Try to use a fog
instead of the atmosphere. If everything looks good, i. e. you still can see
the background or whatever you want to see, use the same distance and color
for the atmosphere.

APPENDIX G.5.2   Fog Questions

Q: I'm using moray to build a scene containing a ground fog. The problem is
that the fog fades out along the y-axis. In moray the z-axis is up, so I have
a wall of fog, rather than a layer. What to do? A: There is an up keyword
that can be used to specify the up direction the ground fog is using. Adding
the line up z to your fog will help.

APPENDIX H       Suggested Reading

Beside the POV-Ray specific books mentioned in "POV-Ray Related Books and
CD-ROMs" there are several good books or periodicals that you should be able
to locate in your local computer book store or your local university library.


  "An Introduction to Ray tracing"
  Andrew S. Glassner (editor)
  ISBN 0-12-286160-4
  Academic Press
  1989

  "3D Artist" Newsletter
  "The Only Newsletter about Affordable
   PC 3D Tools and Techniques")
  Publisher: Bill Allen
  P.O. Box 4787
  Santa Fe, NM 87502-4787
  (505) 982-3532

  "Image Synthesis:  Theory and Practice"
  Nadia Magnenat-Thalman and Daniel Thalmann
  Springer-Verlag
  1987

  "The RenderMan Companion"
  Steve Upstill
  Addison Wesley
  1989

  "Graphics Gems"
  Andrew S. Glassner (editor)
  Academic Press
  1990

  "Fundamentals of Interactive Computer Graphics"
  J. D. Foley and A. Van Dam
  ISBN 0-201-14468-9
  Addison-Wesley
  1983

  "Computer Graphics:  Principles and Practice (2nd Ed.)"
  J. D. Foley, A. van Dam, J. F. Hughes
  ISBN 0-201-12110-7
  Addison-Wesley,
  1990

  "Computers, Pattern, Chaos, and Beauty"
  Clifford Pickover
  St. Martin's Press

  "SIGGRAPH Conference Proceedings"
  Association for Computing Machinery
  Special Interest Group on Computer Graphics

  "IEEE Computer Graphics and Applications"
  The Computer Society
  10662, Los Vaqueros Circle
  Los Alamitos, CA 90720

  "The CRC Handbook of Mathematical Curves and Surfaces"
  David von Seggern
  CRC Press
  1990

  "The CRC Handbook of Standard Mathematical Tables"
  CRC Press
  The Beginning of Time


APPENDIX I       Help on Help

Using the Help Reader (POVHELP.EXE)

KNOWN INCOMPATIBILITIES

See after the Quick Intro.

Quick Intro

Use the +E option to make the help reader a pop-up program. Use Space to go
to the next section. Use Ctrl-PgUp and Ctrl-PgDn to move between sections
also. Use Tab to highlight hypertext links. Use Alt-Tab to highlight code
fragments. Use Enter to jump to a highlighted hypertext link. Use +/- to jump
to relevant sections once link jumping has started. Use BACKSPACE to return
to the last place you were before a search/jump. Use 'S' to search on a
keyword. Use 'J' to toggle text justification when reading a section. Use 'P'
to paste code into your application via the keyboard buffer.

POV-Help will handle non-standard page widths provided the BIOS column count
is correctly updated by whatever program is being used to alter it from 80
columns.

If you use POV-Help as a pop-up program, it will attempt to search on the
word under your cursor when you pop it up. Note that if you exit pop-up mode
by using the hot-key (the default is ALT-ESC), POV-Help takes this to mean
that you want to return to the same place next time and will not perform a
search. A search is only performed if you exited using ESCAPE (meaning you
have finished with the current subject.)

The history stack activated by using Backspace holds 32 entries.

KNOWN INCOMPATIBILITIES

POV-Help does not work with MS-DOS's EDIT program. [In fact, EDIT.COM is
really QBASIC.EXE with a few add ons ; EDIT needs QBASIC to run.]

If it won't work with your editor, try this (assuming you have macro
facilities) -

  o bind the macro to your key-sequence of choice.rameter


Command Line (case insensitive)

  +Tsphere or "+Tsphere"go straight to the first section found with  'sphere'
  +PH[n]                send 'n' HOME keys after each CR when pasting.
  +KALT-ESC             hot key sequence. can be CTRL|ALT|CTRL-ALT+[Any
                        character]|[ESC]. e.g. +KCTRL-ALT-P, +KCTRL-1,
  +Eabc d e             run program 'abc' with parameters 'd' and 'e'. all
  text                  same as +T unless collecting +E parameters, where it
                        is a parameter


Viewer Commands

Top Menu

  Escapewnexit help viewerem


Authors, Copyright

  EscapeRightreturn to top menu


Section

  "P"TababertrlPgDnpaste highlighted code fragment via keyboard buffer.ing)


General

The help reader wraps most text. Excluded are specified portions, lists, and
a few others. Use the left and right arrow keys to scroll these if need be.

The help reader is intended to be a 'shell' around an editor program. Some
people may prefer the term 'shim'.

Using EMS for most memory requirements, it loads itself and then runs your
editor for you, providing pop-up help facilities. It will also be able to
paste code fragments into your source. If your editor was, for example, 'ME',
you would place a batch file called 'ME.BAT' in your scene development
directory. If you use 'VI', you'd create 'VI.BAT', and so on.

(YOUR-EDITOR-NAME.BAT)

desired key sequence ----
                        |
        ----------- -------------- ----------------
povhelp |+W50 +H15³ |+KCTRL-ALT-H| |+Ed:\me\me.exe| %1 %2 %3 %4 %5
        ----------- -------------- ----------------
                |                      |
size of window --                      |
                                       |
place path to your editor here ---------


For example -

povhelp +W50 +H15 +KALT-H +Ed:\me\me.exe %1 %2 %3 %4 %5


This command line will yield a version of POV-Help with a 50x15 window,
popped-up with the ALT-H key sequence, over the editor 'd:\me\me.exe'. If you
don't specify a key sequence, POV-Help defaults to using ALT-ESC.

This would load the help reader. which would then load ME.EXE, and things
would proceed as normal. When you exit your editor, the help reader
automatically unloads. You can use the ALT-ESC key sequence to pop up
POVHELP. This is the default ; there is a way to set it. Note that no other
parameters may appear after the +E parameter as they will just be passed to
the program being run.

If you use the hotkey to pop-up, POVHELP performs a simplistic search of
sections and titles based on the word under the cursor. If found, you are
taken to that. Otherwise, you are taken to the main menu, unless you
hot-keyed out.

You can hot-key out of the actual section text, by using the same hot key
that got you in. If you press escape, you are taken back up to the top menu.
But if you hotkey out, you go back to your program. Next time you press the
hot key, you will be taken back to the same place. No search is performed in
this case.

POVHELP needs EMS if it is running as a shell program.

If
you don't specify the +E parameter, POVHELP will come up as a stand-alone
program, in which case it does not use EMS.

If you highlight a section of code using Alt-Tab, and you are using POV-Help
in pop-up mode, then you may paste the code via the keyboard buffer using
'P'.

As many editors today use auto-indentation, this may cause some problems with
column alignment. For that reason, POV-Help by default inserts a HOME key
code into the keyboard buffer after each CR. Some editors require more than
one HOME key operation to get to the left column. For this reason, the number
of HOME's sent may be adjusted from 0 (none) to 9 using the +PH[n]
command-line parameter. 'n' is any value from 0 to 9 and defaults to 1.

POV-Help was written by  Christopher J. Cason.
CIS      : 100032,1644.
Internet : cjcason@yarrow.wt.uwa.edu.au.

Converters will be available which translate POV-Help databases to other
formats such as Postscript, LaTeX, RTF, Windows Help, HTML, etc.

The format of the POV-Help database is documented and freely available.

POV-Help is free. It may not be sold. See POVLEGAL.DOC for details. The
POV-Help suite of programs is copyright  (c) 1994 C.J. Cason and the
POV-Team.


