Contents -- Acknowledgments -- Introduction -- Part I: General Techniques -- 1 Numbers -- Overview -- Writing Numbers -- How Computers Represent Numbers -- Exercises -- Summary -- You Should Now Know -- 2 Arithmetic -- Overview -- Fractions and Remainders -- Proportions, Ratios, and Percentages -- Exponentials -- Logarithms -- Exercises -- Summary -- You Should Now Know -- 3 Algebra -- Overview -- Basic Algebra -- Working with Equations -- Functions and Graphs -- Exercises -- Summary -- You Should Now Know -- 4 Trigonometry and Pythagoras -- Overview -- Angles -- Triangles -- Calculations with Triangles -- Rotations and Reflections -- Exercises -- Summary -- You Should Now Know -- 5 Vectors -- Overview -- Getting from Here to There -- Vector Motion -- Vector Calculations -- Matrices -- Exercises -- Summary -- You Should Now Know -- 6 Calculus -- Overview -- Differentiation and Integration -- Differential Equations -- Approximation Methods -- Exercises -- Summary -- You Should Now Know -- Part II: Ballistics and Collisions -- 7 Acceleration, Mass, and Energy -- Overview -- Ballistics -- Mass and Momentum -- Energy -- Exercises -- Summary -- You Should Now Know -- 8 Detecting Collisions Between Simple Shapes -- Overview -- Ground Rules -- When Circles Collide -- When Squares Collide -- When Ovals Collide -- When Things Collide -- Exercises -- Summary -- You Should Now Know -- 9 Resolving Collisions -- Overview -- Resolving a Single Collision -- Multiple Collisions -- Exercises -- Summary -- You Should Now Know -- 10 Detecting Collisions Between Complex Shapes -- Overview -- The Problems of a Complex Shape -- Some Reasonable Problems -- Built-In Solutions -- Exercises -- Summary -- You Should Now Know -- 11 A Simple Pool Game -- Overview -- The Rules of Engagement -- Taking a Shot -- Exercises -- Summary -- You Should Now Know.

Part III: More Complex Motion -- 12 Force and Newton's Laws -- Overview -- Force -- Gravity -- Rockets and Satellites -- Exercises -- Summary -- You Should Now Know -- 13 Angular Motion -- Overview -- The Physics of a Lever -- Spin -- Spinning Collisions -- Exercises -- Summary -- You Should Now Know -- 14 Friction -- Overview -- How Friction Works -- Friction and Angular Motion -- Exercises -- Summary -- You Should Now Know -- 15 Strings, Pulleys, and Conveyor Belts -- Overview -- Pulling Things Around -- Continuous Momentum -- Exercises -- Summary -- You Should Now Know -- 16 Oscillations -- Overview -- Springs -- Simple Harmonic Motion -- Damped Harmonic Motion -- Phenomena -- Calculating Spring Motion -- Waves -- Exercises -- Summary -- You Should Now Know -- Part IV: 3D Mathematics -- 17 3D Geometry -- Overview -- 3D Vectors -- Rendering -- Casting a Ray -- Exercises -- Summary -- You Should Now Know -- 18 Transforms -- Overview -- Describing Locations in Space -- Applying Transforms -- Exercises -- Summary -- You Should Now Know -- 19 Collision Detection in Three Dimensions -- Overview -- When Worlds Collide -- When Footballs Collide -- When Boxes Collide -- When Cans Collide -- When Stuff Collides -- Resolving Collisions in Three Dimensions -- Exercises -- Summary -- You Should Now Know -- 20 Lighting and Textures -- Overview -- Light -- Materials -- Shading -- Exercises -- Summary -- You Should Now Know -- 21 Modeling Techniques -- Overview -- Mathematical 3D Modeling -- Animated Surfaces -- Bones Animation -- Exercises -- Summary -- You Should Now Know -- Part V: Game Algorithms -- 22 Speeding Things Up -- Overview -- Cheap and Expensive -- Pseudo-Physics -- Culling -- Exercises -- Summary -- You Should Now Know -- 23 Tile-Based Games -- Overview -- Generating a Game from Bits -- Advanced Tiling -- Exercises -- Summary -- You Should Now Know.

24 Mazes -- Overview -- Classifying Mazes -- Creating Mazes -- Navigating Within Mazes -- Exercises -- Summary -- You Should Now Know -- 25 Game Theory and AI -- Overview -- Introduction to Game Theory -- Tactical AI -- Top-Down AI -- Bottom-Up AI -- Exercises -- Summary -- You Should Now Know -- 26 Search Techniques -- Overview -- Problem-Solving -- Case Study -- Genetic Algorithms -- Exercises -- Summary -- You Should Now Know -- Appendix A: Glossary of Mathematical Terms -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z -- Appendix B: Language References and Pseudocode -- Appendix C: About the CD-ROM -- Appendix D: Further Reading and Resources -- Appendix E: Answers to Exercises -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z.