Mathematics for 3D Game Programming and Computer Graphics

Lengyel, Eric
Eric Lengyel is a veteran of the computer games industry with over 16 years of experience writing game engines. He has a PhD in Computer Science from the University of California at Davis and an MS in Mathematics from Virginia Tech. Eric is the founder of Terathon Software, where he currently leads ongoing development of the C4 Engine.

Sooner or later, all game programmers run into coding issues that require an understanding of mathematics or physics concepts such as collision detection, 3D vectors, transformations, game theory, or basic calculus. Unfortunately, most programmers frequently have a limited understanding of these essential mathematics and physics concepts. MATHEMATICS AND PHYSICS FOR PROGRAMMERS, THIRD EDITION provides a simple but thorough grounding in the mathematics and physics topics that programmers require to write algorithms and programs using a non-language-specific approach. Applications and examples from game programming are included throughout, and exercises follow each chapter for additional practice. The book's companion website provides sample code illustrating the mathematical and physics topics discussed in the book.

This updated third edition addresses the mathematical skills that a programmer needs to develop a 3D game engine and computer graphics for professional-level games. MATHEMATICS FOR 3D GAME PROGRAMMING & COMPUTER GRAPHICS, THIRD EDITION is suitable for advanced programmers who are experienced with C++, DirectX, or OpenGL. The book begins at a fairly basic level, covering areas such as vector geometry and linear algebra, and then progresses to more advanced topics in 3D game programming such as illumination and visibility determination. It discusses the math first; then it presents how to translate the math into programs. By providing the math behind the effect, screenshots of the results, and samples of code that translate the math so that the effect is achieved, readers get the full story rather than only a mathematical explanation or a set of code samples that are not clearly drawn from mathematical expressions. With this revised edition, almost every chapter will provide a programming example taken directly from a real-world game programming context, and based on programs that have been written and used in game engine development.

Preface.1. The Rendering Pipeline.
2. Vectors.
3. Matrices.
4. Transforms.
5. 3D Engine Geometry.
6. Ray Tracing.
7. Illumination.
8. Visibility Determination.
9. Collision Detection.
10. Polygonal Techniques.
11. Shadows.
12. Linear Physics.
13. Rotational Physics.
14. Fluid Simulation.
15. Numerical Methods.
16. Curves and Surfaces.
Appendix A: Complex Numbers.
Appendix B: Trigonometry Reference.
Appendix C: Coordinate Systems.
Appendix D: Taylor Series.
Appendix E: Answers to Exercises.