Essential Mathematics for Games and Interactive Applications: A Programmer’s Guide

“Even though I’ve worked with these systems for years, I found new ways of looking at several topics that make them easier to remember and use. For someone new to 3D programming, it is extremely useful-it gives them a solid background in pretty much every area they need to understand.” -Peter Lipson, Toys for Bob, Inc.

Based on the authors’ popular tutorials at the Game Developers Conference, Essential Mathematics for Games and Interactive Applications presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix manipulation and expands on this foundation to cover such topics as texture filtering, interpolation, animation, and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout.

• Covers concepts in sufficient detail for a programmer to understand the foundations of 3D without feeling overwhelmed by proofs and theory
• Companion CD-ROM with code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction
• Provides guidance for students trying to understand how games are actually developed, including optimization techniques

Table of Contents

Part I Core Mathematics
Chapter 1 Vectors and Points
Chapter 2 Linear Transformations and Matrices
Chapter 3 Affine Transformations
Chapter 4 Real-World Computer Number Representation

Part II RENDERING
Chapter 5 Viewing and Projection
Chapter 6 Geometry, Shading, and Texturing
Chapter 7 Lighting
Chapter 8 Rasterization

Part III Animation
Chapter 9 Curves
Chapter 10 Orientation Representation

Part IV Simulation
Chapter 11 Intersection Testing
Chapter 12 Rigid Body Dynamics

Appendix A Trigonometry Review
Appendix B Calculus Review