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Mathematics for 3D Game Programming and Computer Graphics, Second Edition
Eric Lengyel, 2004.
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Chapter 0: The Rendering Pipeline
Graphics Processors
Vertex Transformation
Rasterization and Fragment Operations
Chapter 1: Vectors
Vector Properties
Dot Products
Cross Products
Vector Spaces
Chapter 2: Matrices
Matrix Properties
Linear Systems
Matrix Inverses
Determinants
Eigenvalues and Eigenvectors
Diagonalization
Chapter 3: Transforms
Linear Transformations
Scaling Transforms
Rotation Transforms
Homogeneous Coordinates
Transforming Normal Vectors
Quaternions
Chapter 4: 3D Engine Geometry
Lines in 3D Space
Planes in 3D Space
The View Frustum
Perspective-Correct Interpolation
Projections
Chapter 5: Ray Tracing
Root Finding
Surface Intersections
Normal Vector Calculation
Reflection and Refraction Vectors
Chapter 6: Illumination
RGB Color
Light Sources
Diffuse Lighting
Texture Mapping
Specular Lighting
Emission
Shading
Bump Mapping
A Physical Reflection Model
Chapter 7: Visibility Determination
Bounding Volume Construction
Bounding Volume Tests
Spatial Partitioning
Portal Systems
Chapter 8: Collision Detection
Plane Collisions
General Sphere Collisions
Sliding
Collision of Two Spheres
Chapter 9: Polygonal Techniques
Depth Value Offset
Decal Application
Billboarding
Polygon Reduction
T-Junction Elimination
Triangulation
Chapter 10: Shadows
Algorithm Overview
Infinite View Frustums
Silhouette Determination
Shadow Volume Construction
Determining Cap Necessity
Rendering Shadow Volumes
Scissor Optimization
Chapter 11: Linear Physics
Position Functions
Second-Order Differential Equations
Projectile Motion
Resisted Motion
Friction
Chapter 12: Rotational Physics
Rotating Environments
Rigid Body Motion
Oscillatory Motion
Chapter 13: Fluid Simulation
The Wave Equation
Approximating Derivatives
Evaluating Surface Displacement
Implementation
Chapter 14: Numerical Methods
Linear Systems
Eigenvalues and Eigenvectors
Ordinary Differential Equations
Chapter 15: Curves and Surfaces
Cubic Curves
Hermite Curves
B�zier Curves
Catmull-Rom Splines
Cubic Splines
B-Splines
Bicubic Surfaces
Curvature and Torsion
Appendix A: Complex Numbers
Definition
Addition and Multiplication
Conjugates and Inverses
The Euler Formula
Appendix B: Trigonometry Reference
Function Definitions
Symmetry and Phase Shifts
Pythagorean Identities
Exponential Identities
Inverse Functions
Laws of Sines and Cosines
Appendix C: Coordinate Systems
Cartesian Coordinates
Cylindrical Coordinates
Spherical Coordinates
Generalized Coordinates
Appendix D: Taylor Series
Derivation
Power Series
The Euler Formula
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