Cover -- Contents -- Preface -- What's New in the Third Edition -- Contents Overview -- Website and Code Listings -- Notational Conventions -- Chapter 1 The Rendering Pipeline -- 1.1 Graphics Processors -- 1.2 Vertex Transformation -- 1.3 Rasterization and Fragment Operations -- Chapter 2 Vectors -- 2.1 Vector Properties -- 2.2 The Dot Product -- 2.3 The Cross Product -- 2.4 Vector Spaces -- Chapter 2 Summary -- Exercises for Chapter 2 -- Chapter 3 Matrices -- 3.1 Matrix Properties -- 3.2 Linear Systems -- 3.3 Matrix Inverses -- 3.4 Determinants -- 3.5 Eigenvalues and Eigenvectors -- 3.6 Diagonalization -- Chapter 3 Summary -- Exercises for Chapter 3 -- Chapter 4 Transforms -- 4.1 Linear Transformations -- 4.1.1 Orthogonal Matrices -- 4.1.2 Handedness -- 4.2 Scaling Transforms -- 4.3 Rotation Transforms -- 4.3.1 Rotation About an Arbitrary Axis -- 4.4 Homogeneous Coordinates -- 4.4.1 Four-Dimensional Transforms -- 4.4.2 Points and Directions -- 4.4.3 Geometrical Interpretation of the w Coordinate -- 4.5 Transforming Normal Vectors -- 4.6 Quaternions -- 4.6.1 Quaternion Mathematics -- 4.6.2 Rotations with Quaternions -- 4.6.3 Spherical Linear Interpolation -- Chapter 4 Summary -- Exercises for Chapter 4 -- Chapter 5 Geometry for 3D Engines -- 5.1 Lines in 3D Space -- 5.1.1 Distance Between a Point and a Line -- 5.1.2 Distance Between Two Lines -- 5.2 Planes in 3D Space -- 5.2.1 Intersection of a Line and a Plane -- 5.2.2 Intersection of Three Planes -- 5.2.3 Transforming Planes -- 5.3 The View Frustum -- 5.3.1 Field of View -- 5.3.2 Frustum Planes -- 5.4 Perspective-Correct Interpolation -- 5.4.1 Depth Interpolation -- 5.4.2 Vertex Attribute Interpolation -- 5.5 Projections -- 5.5.1 Perspective Projections -- 5.5.2 Orthographic Projections -- 5.5.3 Extracting Frustum Planes -- 5.6 Reflections and Oblique Clipping -- Chapter 5 Summary.

Exercises for Chapter 5 -- Chapter 6 Ray Tracing -- 6.1 Root Finding -- 6.1.1 Quadratic Polynomials -- 6.1.2 Cubic Polynomials -- 6.1.3 Quartic Polynomials -- 6.1.4 Newton's Method -- 6.1.5 Refinement of Reciprocals and Square Roots -- 6.2 Surface Intersections -- 6.2.1 Intersection of a Ray and a Triangle -- 6.2.2 Intersection of a Ray and a Box -- 6.2.3 Intersection of a Ray and a Sphere -- 6.2.4 Intersection of a Ray and a Cylinder -- 6.2.5 Intersection of a Ray and a Torus -- 6.3 Normal Vector Calculation -- 6.4 Reflection and Refraction Vectors -- 6.4.1 Reflection Vector Calculation -- 6.4.2 Refraction Vector Calculation -- Chapter 6 Summary -- Exercises for Chapter 6 -- Chapter 7 Lighting and Shading -- 7.1 RGB Color -- 7.2 Light Sources -- 7.2.1 Ambient Light -- 7.2.2 Directional Light Sources -- 7.2.3 Point Light Sources -- 7.2.4 Spot Light Sources -- 7.3 Diffuse Reflection -- 7.4 Specular Reflection -- 7.5 Texture Mapping -- 7.5.1 Standard Texture Maps -- 7.5.2 Projective Texture Maps -- 7.5.3 Cube Texture Maps -- 7.5.4 Filtering and Mipmaps -- 7.6 Emission -- 7.7 Shading Models -- 7.7.1 Calculating Normal Vectors -- 7.7.2 Gouraud Shading -- 7.7.3 Blinn-Phong Shading -- 7.8 Bump Mapping -- 7.8.1 Bump Map Construction -- 7.8.2 Tangent Space -- 7.8.3 Calculating Tangent Vectors -- 7.8.4 Implementation -- 7.9 A Physical Reflection Model -- 7.9.1 Bidirectional Reflectance Distribution Functions -- 7.9.2 Cook-Torrance Illumination -- 7.9.3 The Fresnel Factor -- 7.9.4 The Microfacet Distribution Function -- 7.9.5 The Geometrical Attenuation Factor -- 7.9.6 Implementation -- Chapter 7 Summary -- Exercises for Chapter 7 -- Chapter 8 Visibility Determination -- 8.1 Bounding Volume Construction -- 8.1.1 Principal Component Analysis -- 8.1.2 Bounding Box Construction -- 8.1.3 Bounding Sphere Construction -- 8.1.4 Bounding Ellipsoid Construction.

8.1.5 Bounding Cylinder Construction -- 8.2 Bounding Volume Tests -- 8.2.1 Bounding Sphere Test -- 8.2.2 Bounding Ellipsoid Test -- 8.2.3 Bounding Cylinder Test -- 8.2.4 Bounding Box Test -- 8.3 Spatial Partitioning -- 8.3.1 Octrees -- 8.3.2 Binary Space Partitioning Trees -- 8.4 Portal Systems -- 8.4.1 Portal Clipping -- 8.4.2 Reduced View Frustums -- Chapter 8 Summary -- Exercises for Chapter 8 -- Chapter 9 Polygonal Techniques -- 9.1 Depth Value Offset -- 9.1.1 Projection Matrix Modification -- 9.1.2 Offset Value Selection -- 9.1.3 Implementation -- 9.2 Decal Application -- 9.2.1 Decal Mesh Construction -- 9.2.2 Polygon Clipping -- 9.3 Billboarding -- 9.3.1 Unconstrained Quads -- 9.3.2 Constrained Quads -- 9.3.3 Polyboards -- 9.4 Polygon Reduction -- 9.5 T-Junction Elimination -- 9.6 Triangulation -- Chapter 9 Summary -- Exercises for Chapter 9 -- Chapter 10 Shadows -- 10.1 Shadow Casting Set -- 10.2 Shadow Mapping -- 10.2.1 Rendering the Shadow Map -- 10.2.2 Rendering the Main Scene -- 10.2.3 Self-Shadowing -- 10.3 Stencil Shadows -- 10.3.1 Algorithm Overview -- 10.3.2 Infinite View Frustums -- 10.3.3 Silhouette Determination -- 10.3.4 Shadow Volume Construction -- 10.3.5 Determining Cap Necessity -- 10.3.6 Rendering Shadow Volumes -- 10.3.7 Scissor Optimization -- Chapter 10 Summary -- Exercises for Chapter 10 -- Chapter 11 Curves and Surfaces -- 11.1 Cubic Curves -- 11.2 Hermite Curves -- 11.3 Bézier Curves -- 11.3.1 Cubic Bézier Curves -- 11.3.2 Bézier Curve Truncation -- 11.3.3 The de Casteljau Algorithm -- 11.4 Catmull-Rom Splines -- 11.5 Cubic Splines -- 11.6 B-Splines -- 11.6.1 Uniform B-Splines -- 11.6.2 B-Spline Globalization -- 11.6.3 Nonuniform B-Splines -- 11.6.4 NURBS -- 11.7 Bicubic Surfaces -- 11.8 Curvature and Torsion -- Chapter 11 Summary -- Exercises for Chapter 11 -- Chapter 12 Collision Detection -- 12.1 Plane Collisions.

12.1.1 Collision of a Sphere and a Plane -- 12.1.2 Collision of a Box and a Plane -- 12.1.3 Spatial Partitioning -- 12.2 General Sphere Collisions -- 12.3 Sliding -- 12.4 Collision of Two Spheres -- Chapter 12 Summary -- Exercises for Chapter 12 -- Chapter 13 Linear Physics -- 13.1 Position Functions -- 13.2 Second-Order Differential Equations -- 13.2.1 Homogeneous Equations -- 13.2.2 Nonhomogeneous Equations -- 13.2.3 Initial Conditions -- 13.3 Projectile Motion -- 13.4 Resisted Motion -- 13.5 Friction -- Chapter 13 Summary -- Exercises for Chapter 13 -- Chapter 14 Rotational Physics -- 14.1 Rotating Environments -- 14.1.1 Angular Velocity -- 14.1.2 The Centrifugal Force -- 14.1.3 The Coriolis Force -- 14.2 Rigid Body Motion -- 14.2.1 Center of Mass -- 14.2.2 Angular Momentum and Torque -- 14.2.3 The Inertia Tensor -- 14.2.4 Principal Axes of Inertia -- 14.2.5 Transforming the Inertia Tensor -- 14.3 Oscillatory Motion -- 14.3.1 Spring Motion -- 14.3.2 Pendulum Motion -- Chapter 14 Summary -- Exercises for Chapter 14 -- Chapter 15 Fluid and Cloth Simulation -- 15.1 Fluid Simulation -- 15.1.1 The Wave Equation -- 15.1.2 Approximating Derivatives -- 15.1.3 Evaluating Surface Displacement -- 15.1.4 Implementation -- 15.2 Cloth Simulation -- 15.2.1 The Spring System -- 15.2.2 External Forces -- 15.2.3 Implementation -- Chapter 15 Summary -- Exercises for Chapter 15 -- Chapter 16 Numerical Methods -- 16.1 Trigonometric Functions -- 16.2 Linear Systems -- 16.2.1 Triangular Systems -- 16.2.2 Gaussian Elimination -- 16.2.3 LU Decomposition -- 16.2.4 Error Reduction -- 16.2.5 Tridiagonal Systems -- 16.3 Eigenvalues and Eigenvectors -- 16.4 Ordinary Differential Equations -- 16.4.1 Euler's Method -- 16.4.2 Taylor Series Method -- 16.4.3 Runge-Kutta Method -- 16.4.4 Higher-Order Differential Equations -- Chapter 16 Summary -- Exercises for Chapter 16.

Appendix A: Complex Numbers -- A.1 Definition -- A.2 Addition and Multiplication -- A.3 Conjugates and Inverses -- A.4 The Euler Formula -- Appendix B: Trigonometry Reference -- B.1 Function Definitions -- B.2 Symmetry and Phase Shifts -- B.3 Pythagorean Identities -- B.4 Exponential Identities -- B.5 Inverse Functions -- B.6 Laws of Sines and Cosines -- Appendix C: Coordinate Systems -- C.1 Cartesian Coordinates -- C.2 Cylindrical Coordinates -- C.3 Spherical Coordinates -- C.4 Generalized Coordinates -- Appendix D: Taylor Series -- D.1 Derivation -- D.2 Power Series -- D.3 The Euler Formula -- Appendix E: Answers to Exercises -- Chapter 2 -- Chapter 3 -- Chapter 4 -- Chapter 5 -- Chapter 6 -- Chapter 7 -- Chapter 8 -- Chapter 9 -- Chapter 10 -- Chapter 11 -- Chapter 12 -- Chapter 13 -- Chapter 14 -- Chapter 15 -- Chapter 16 -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.