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Matt Pharr • Greg Humphreys
Physically Based Rendering
from Theory to Implementation

Table of Contents

(† indicates advanced topics)

Foreword by Pat Hanrahan
Preface

CHAPTER 01. INTRODUCTION

• Literate Programming
  
  • Indexing and Cross-Referencing
    
• Photorealistic Rendering and the Ray-Tracing Algorithm
  • Cameras
    
  • Ray-Object Intersections
    
  • Light Distribution
    
  • Visibility
    
  • Surface Scattering
    
  • Recursive Ray Tracing
    
  • Ray Propagation
    
• pbrt: System Overview
  
  • Phases of Execution
    
  • Scene Representation
    
  • Main Rendering Loop
    
  • Scene Methods
    
  • An Integrator for Whitted-Style Ray Tracing
    
• How to Proceed through This Book
  
  • The Exercises
    
• Using and Understanding the Code
  
  • Pointer or Reference?
    
  • Code Optimization
    
  • The Book Web site
    
  • Bugs
    
• Further Reading
  
• Exercise
  
  

CHAPTER 02. GEOMETRY AND TRANSFORMATIONS

• Coordinate Systems
  
  • Coordinate System Handedness
    
• Vectors
  
  • Arithmetic
    
  • Scaling
    
  • Dot and Cross Product
    
  • Normalization
    
  • Coordinate System from a Vector
    
• Points
  
• Normals
  
• Rays
  
  • Ray Differentials
    
• Three-Dimensional Bounding Boxes
  
• Transformations
  
  • Homogeneous Coordinates
    
  • Basic Operations
    
  • Translations
    
  • Scaling
    
  • x, y, and z Axis Rotations
    
  • Rotation around an Arbitrary Axis
    
  • The Look-At Transformation
    
• Applying Transformations
  
  • Points
    
  • Vectors
    
  • Normals
    
  • Rays
    
  • Bounding Boxes
    
  • Composition of Transformations
    
  • Transformations and Coordinate System Handedness
    
• Differential Geometry
  
• Further Reading
  
• Exercises
  
  

CHAPTER 03. SHAPES

• Basic Shape Interface
  
  • Bounding
    
  • Refinement
    
  • Intersection
    
  • Avoiding Incorrect Self-Intersections
    
  • Shading Geometry
    
  • Surface Area
    
  • Sidedness
    
• Spheres
  
  • Construction
    
  • Bounding
    
  • Intersection
    
  • Partial Spheres
    
  • Partial Derivatives of Normal Vectors
    
  • DifferentialGeometry Initialization
    
  • Surface Area
    
• Cylinders
  
  • Construction
    
  • Bounding
    
  • Intersection
    
  • Partial Cylinders
    
  • Surface Area
    
• Disks
  
  • Construction
    
  • Bounding
    
  • Intersection
    
  • Surface Area
    
• Other Quadrics
  
  • Cones
    
  • Paraboloids
    
  • Hyperboloids
    
• Triangles and Meshes
  
  • Triangle
    
  • Triangle Intersection
    
  • Surface Area
    
  • Shading Geometry
    
• Subdivision Surfaces †
  
  • Mesh Representation
    
  • Bounds
    
  • Subdivison
    
• Further Reading
  
• Exercises
  
  

CHAPTER 04. PRIMITIVES AND INTERSECTION ACCELERATION

• Primitive Interface and Geometric Primitives
  
  • Geometric Primitives
    
  • Object Instancing
    
• Aggregates
  
  • Ray-Box Intersections
    
• Grid Accelerator
  
  • Creation
    
  • Traversal
    
• Kd-Tree Accelerator
  
  • Tree Representation
    
  • Tree Construction
    
  • Traversal
    
• Further Reading
  
• Exercises
  
  

CHAPTER 05. COLOR AND RADIOMETRY

• Spectral Representation
  
  • Spectrum Class
    
  • XYZ Color
    
• Basic Radiometry
  
  • Basic Quantities
    
  • Incident and Exitant Radiance Functions
    
• Working with Radiometric Integrals
  
  • Integrals over Projected Solid Angle
    
  • Integrals over Spherical Coordinates
    
  • Integrals over Area
    
• Surface Reflection and the BRDF
  
• Further Reading
  
• Exercises
  
  

CHAPTER 06. CAMERA MODELS

• Camera Model
  
  • Camera Coordinate Spaces
    
• Projective Camera Models
  
  • Orthographic Camera
    
  • Perspective Camera
    
  • Depth of Field
    
• Environment Camera
  
• Further Reading
  
• Exercises
  
  

CHAPTER 07. SAMPLING AND RECONSTRUCTION

• Sampling Theory
  
  • The Frequency Domain and the Fourier Transform
    
  • Ideal Sampling and Reconstruction
    
  • Aliasing
    
  • Antialiasing Techniques
    
  • Application to Image Synthesis
    
  • Sources of Aliasing in Rendering
    
  • Understanding Pixels
    
• Image Sampling Interface
  
  • Sample Representation and Allocation
    
• Stratified Sampling
  
• Low-Discrepancy Sampling †
  
  • Definition of Discrepancy
    
  • Constructing Low-Discrepancy Sequences
    
  • (0,2)-Sequences
    
  • The Low-Discrepancy Sampler
    
• Best-Candidate Sampling Patterns †
  
  • Generating the Best-Candidate Pattern
    
  • Using the Best-Candidate Pattern
    
• Image Reconstruction
  
  • Filter Functions
    
• Further Reading
  
• Exercises
  
  

CHAPTER 08. FILM AND THE IMAGING PIPELINE

• Film Interface
  
• Image Film
  
  • Image Output
    
• Image Pipeline
  
• Perceptual Issues and Tone Mapping †
  
  • Luminance and Photometry
    
  • Bloom
    
  • Tone Mapping Interface
    
  • Maximum to White
    
  • Contrast-Based Scale Factor
    
  • Varying Adaptation Luminance
    
  • Spatially Varying Nonlinear Scale
    
• Final Imaging Pipeline Stages
  
• Further Reading
  
• Exercises
  
  

CHAPTER 09. REFLECTION MODELS

• Basic Interface
  
  • Reflectance
    
  • BRDF>BTDF Adapter
    
• Specular Reflection and Transmission
  
  • Fresnel Reflectance
    
  • Specular Reflection
    
  • Specular Transmission
    
• Lambertian Reflection
  
• Microfacet Models
  
  • Oren-Nayar Diffuse Reflection
    
  • Torrance-Sparrow Model
    
  • Blinn Microfacet Distribution
    
  • Anisotropic Microfacet Model
    
• Lafortune Model
  
• Fresnel Incidence Effects
  
• Further Reading
  
• Exercises
  
  

CHAPTER 10. MATERIALS

• BSDFs
  
  • BSDF Memory Management
    
• Material Interface and Implementations
  
  • Matte
    
  • Plastic
    
  • Additional Materials
    
• Bump Mapping
  
• Further Reading
  
• Exercises
  
  

CHAPTER 11. TEXTURE

• Sampling and Antialiasing
  
  • Finding the Texture Sampling Rate
    
  • Filtering Texture Functions
    
  • Ray Differentials for Specular Reflection and Transmission †
    
• Texture Coordinate Generation
  
  • 2D (u, v) Mapping
    
  • Spherical Mapping
    
  • Cylindrical Mapping
    
  • Planar Mapping
    
  • 3DMapping
    
• Texture Interface and Basic Textures
  
  • Constant Texture
    
  • Scale Texture
    
  • Mix Textures
    
  • Bilinear Interpolation
    
• Image Texture
  
  • Texture Caching
    
  • MIPMaps
    
  • Isotropic Triangle Filter
    
  • Elliptically Weighted Average
    
• Solid and Procedural Texturing
  
  • UV Texture
    
  • Checkerboard
    
  • Solid Checkerboard
    
• Noise
  
  • Perlin Noise
    
  • Random Polka Dots
    
  • Noise Idioms and Spectral Synthesis
    
  • Bumpy and Wrinkled Textures
    
  • Windy Waves
    
  • Marble
    
• Further Reading
  
• Exercises
  
  

CHAPTER 12. VOLUME SCATTERING †

• Volume Scattering Processes
  
  • Absorption
    
  • Emission
    
  • Out-Scattering and Extinction
    
  • In-scattering
    
• Phase Functions
  
• Volume Interface and Homogeneous Media
  
  • Homogeneous Volumes
    
• Varying-Density Volumes
  
  • 3D Grids
    
  • Exponential Density
    
• Volume Aggregates
  
• Further Reading
  
• Exercises
  
  

CHAPTER 13. LIGHT SOURCES

• Light Interface
  
  • Visibility Testing
    
• Point Lights
  
  • Spotlights
    
  • Texture Projection Lights
    
  • Goniophotometric Diagram Lights
    
• Distant Lights
  
• Area Lights
  
• Infinite Area Lights
  
• Further Reading
  
• Exercises
  
  

CHAPTER 14. MONTE CARLO INTEGRATION I: BASIC CONCEPTS

• Background and Probability Review
  
  • Continuous Random Variables
    
  • Expected Values and Variance
    
• The Monte Carlo Estimator
  
• Sampling Random Variables
  
  • The Inversion Method
    
  • Example: Power Distribution
    
  • Example: Exponential Distribution
    
  • Example: Piecewise-Constant 1D Functions
    
  • The Rejection Method
    
  • Example: Rejection Sampling a Unit Circle
    
• Transforming between Distributions
  
  • Transformation in Multiple Dimensions
    
  • Example: Polar Coordinates
    
  • Example: Spherical Coordinates
    
• 2D Sampling with Multidimensional Transformations
  
  • Example: Uniformly Sampling a Hemisphere
    
  • Example: Sampling a Unit Disk
    
  • Example: Cosine-Weighted Hemisphere Sampling
    
  • Example: Sampling a Triangle
    
• Further Reading
  
• Exercises
  
  

CHAPTER 15. MONTE CARLO INTEGRATION II: IMPROVING EFFICIENCY

• Russian Roulette and Splitting
  
  • Splitting
    
• Careful Sample Placement
  
  • Stratified Sampling
    
  • Quasi Monte Carlo
    
  • Warping Samples and Distortion
    
• Bias
  
• Importance Sampling
  
  • Multiple Importance Sampling
    
• Sampling Reflection Functions
  
  • Sampling the Blinn Microfacet Distribution
    
  • Sampling the Anisotropic Microfacet Model
    
  • Sampling FresnelBlend
    
  • Specular Reflection and Transmission
    
  • Application: Estimating Reflectance
    
  • Sampling BSDFs
    
• Sampling Light Sources
  
  • Basic Interface
    
  • Lights with Singularities
    
  • Area Lights
    
  • ShapeSet Sampling
    
  • Infinite Area Lights
    
• Volume Scattering †
  
  • Sampling Phase Functions
    
  • Computing Optical Thickness
    
• Further Reading
  
• Exercises
  
  

CHAPTER 16. LIGHT TRANSPORT I: SURFACE REFLECTION

• Direct Lighting
  
  • Estimating the Direct Lighting Integral
    
• The Light Transport Equation
  
  • Basic Derivation
    
  • Analytic Solutions to the LTE
    
  • The Surface Form of the LTE
    
  • Integral over Paths
    
  • Delta Distributions in the Integrand
    
  • Partitioning the Integrand
    
  • The Measurement Equation and Importance
    
• Path Tracing
  
  • Overview
    
  • Path Sampling
    
  • Incremental Path Construction
    
  • Implementation
    
  • Bidirectional Path Tracing †
    
• Irradiance Caching
  
• Particle Tracing and Photon Mapping
  
  • Theoretical Basis for Particle Tracing †
    
  • Photon Integrator
    
  • Building the Photon Maps
    
  • Using the Photon Map
    
  • Photon Interpolation and Density Estimation
    
• Further Reading
  
• Exercises
  
  

CHAPTER 17. LIGHT TRANSPORT II: VOLUME RENDERING †

• The Equation of Transfer
  
• Volume Integrator Interface
  
• Emission-Only Integrator
  
• Single Scattering Integrator
  
• Further Reading
  
• Exercises
  
  

CHAPTER 18. SUMMARY AND CONCLUSION

• Design Retrospective
  
  • Abstraction versus Efficiency
    
  • Design Alternatives: Triangles Only
    
  • Design Alternatives: Streaming Computation
    
• Major Projects
  
  • Parallel Rendering
    
  • Increased Scene Complexity
    
  • Subsurface Scattering
    
  • Precomputation for Interactive Rendering
    
• Conclusion
  
  

APPENDIXES

Utilities

Scene Description Interface

Input File Format

Index of Fragments

Index of Classes and their Members

Index of Identifiers

REFERENCES
INDEX
ABOUT THE CD-ROM