Front Cover; Dedication; Contents; Acknowledgments; Introduction; 1. Cartesian Coordinate Systems; 2. Vectors; 3. Multiple Coordinate Spaces; 4. Introduction to Matrices; 5. Matrices and Linear Transformations; 6. More on Matrices; 7. Polar Coordinate Systems; 8. Rotation in Three Dimensions; 9. Geometric Primitives; 10. Mathematical Topics from 3D Graphics; 11. Mechanics 1: Linear Kinematics and Calculus; 12. Mechanics 2: Linear and Rotational Dynamics; 13. Curves in 3D; 14. Afterword; A. Geometric Tests; B. Answers to the Exercises; Bibliography; This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for game designers, including the fundamentals of coordinate spaces, vectors, and matrices. It also covers orientation in three dimensions, calculus and dynamics, graphics, and parametric curves.