Illustrating all the mathematical techniques that software engineers, graphics programmers and game programmers should need to develop a professional-quality 3D engine, this text has been updated to cover advancements in 3D graphics technology up to the end of 2003. In addition to providing all new information on illumination, collision detection, polygonal techniques and more, there are four chapters new to this edition which cover the rendering pipeline, shadows, numerical methods and curves and surfaces. Each chapter includes summaries and exercise sets for additional practice, or for use as a textbook. The book assumes a working knowledge of calculus, trigonometry and how to use 3D graphics libraries.

Table of Contents

Chapter 0 The Rendering Pipeline Chapter 1 Vectors Chapter 2 Matrices Chapter 3 Transforms Chapter 4 3D Engine Geometry Chapter 5 Ray Tracing Chapter 6 Illumination Chapter 7 Visibility Determination Chapter 8 Collision Detection Chapter 9 Polygonal Techniques Chapter 10 Shadows Chapter 11 Linear Physics Chapter 12 Rotational Physics Chapter 13 Fluid Simulation Chapter 14 Numerical Methods Chapter 15 Curves and Surfaces Appendix A Complex Numbers Appendix B Trigonometry Reference Appendix C Coordinate Systems Appendix D Taylor Series Appendix E Answers to Exercises