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Mathematics for Game Developers is just that?a math book designed specifically for the game developer, not the mathematician. As a game developer, you know that math is a fundamental part of your programming arsenal. In order to program a game that goes beyond the basics, you must first master concepts such as matrices and vectors. In this book, you will find some unique solutions for dealing with real problems you?ll face when programming many types of 3D games. Not only will you learn how to solve these problems, you?ll also learn why the solution works, enabling you to apply that solution to other problems. You?ll also learn how to leverage software to help solve algebraic equations. Through numerous examples, this book clarifies how mathematical ideas fit together and how they apply to game programming.

Features

- The author introduces the major branches of mathematics that are essential for game development, and demonstrates the applications of these concepts to game programming.
- Teaches readers how to think and solve problems, thereby allowing readers to independently solve their own specific problems as they develop their own games.
- Acts as a resource for programmers needing to know how to apply mathematical concepts to game development.

Table of Contents

1. Equation Manipulation and Representation
2. The Baby Steps: Introduction to Vectors
3. M&M: Meet the Matrices, Not the Candies
4. Basic Geometric Elements
5. Screwing Things Up with 2D/3D Transformations
6. Moving to Hyperspace Vectors: Quaternions
7. Accelerated Vector Calculus for the Uninitiated
8. Gravitating Around Basic Physics
9. Springing Over to Advanced Physics
10. And Then It Hits You: You Need Collision Detection and Picking
11. Educated Guessing with Statistics and Probability
12. Closing the Gap for Numerical Approximation
13. Exploring Curvy Bodies
14. Spawning Trouble with a Graphics-Generation Engine
15. The World of the Invisible - Visibility Determination
16. Cleaning Your Room - Spatial Partitioning
17. Filling Up the Gaps with Rendering Techniques
18. Building a Light Show by Lighting the Room
19. The Quick Mind: Computational Optimizations
20. Vector/Matrix Operations Using Vectorial CPU Commands
21. Kicking the Turtle by Approximating Common and Slow Functions

Appendices

A: Notation and Conventions
B: Trigonometry
C: Integral and Derivative Table
D: Solutions to the Examples
E: References and What’s on the CD

Author Bio

Christopher Tremblay lives in the California Bay Area where he works for Motorola building a 3D graphics engine for cell phones to empower the next-generation games. He holds a degree in Software Engineering from the University of Ottawa, Canada, and is currently a semester away from a mathematics degree. His work in the games industry includes game AI, core-networking, software rendering algorithms, 3D geometry algorithms, and optimization. Although most of his work is PC-based, a fare amount of it was done on embedded devices ranging from bottom-line TI-calculators Z80 and 68K Palm processors up to speedy PocketPC strong-arm processors with games such as LemmingZ.