What is included with this book?
Acknowledgments | p. xxv |
Introduction | p. xxvii |
General Techniques | p. 1 |
Numbers | p. 3 |
Overview | p. 3 |
Writing Numbers | p. 4 |
How Computers Represent Numbers | p. 8 |
Exercises | p. 16 |
Summary | p. 17 |
You Should Now Know | p. 17 |
Arithmetic | p. 19 |
Overview | p. 19 |
Fractions and Remainders | p. 20 |
Proportions, Ratios, and Percentages | p. 29 |
Exponentials | p. 36 |
Logarithms | p. 39 |
Exercises | p. 43 |
Summary | p. 44 |
You Should Now Know | p. 44 |
Algebra | p. 45 |
Overview | p. 45 |
Basic Algebra | p. 46 |
Working with Equations | p. 50 |
Functions and Graphs | p. 65 |
Exercises | p. 74 |
Summary | p. 74 |
You Should Now Know | p. 75 |
Trigonometry and Pythagoras | p. 77 |
Overview | p. 77 |
Angles | p. 78 |
Triangles | p. 82 |
Calculations with Triangles | p. 90 |
Rotations and Reflections | p. 94 |
Exercises | p. 101 |
Summary | p. 101 |
You Should Now Know | p. 101 |
Vectors | p. 103 |
Overview | p. 103 |
Getting from Here to There | p. 104 |
Vector Motion | p. 110 |
Vector Calculations | p. 117 |
Matrices | p. 125 |
Exercises | p. 131 |
Summary | p. 131 |
You Should Now Know | p. 132 |
Calculus | p. 133 |
Overview | p. 133 |
Differentiation and Integration | p. 134 |
Differential Equations | p. 144 |
Approximation Methods | p. 146 |
Exercises | p. 152 |
Summary | p. 152 |
You Should Now Know | p. 152 |
Ballistics and Collisions | p. 153 |
Acceleration, Mass, and Energy | p. 155 |
Overview | p. 155 |
Ballistics | p. 156 |
Mass and Momentum | p. 162 |
Energy | p. 163 |
Exercises | p. 167 |
Summary | p. 168 |
You Should Now Know | p. 169 |
Detecting Collisions Between Simple Shapes | p. 171 |
Overview | p. 171 |
Ground Rules | p. 172 |
When Circles Collide | p. 173 |
When Squares Collide | p. 182 |
When Ovals Collide | p. 190 |
When Things Collide | p. 195 |
Exercises | p. 196 |
Summary | p. 197 |
You Should Now Know | p. 197 |
Resolving Collisions | p. 199 |
Overview | p. 199 |
Resolving a Single Collision | p. 200 |
Multiple Collisions | p. 207 |
Exercises | p. 211 |
Summary | p. 212 |
You Should Now Know | p. 212 |
Detecting Collisions Between Complex Shapes | p. 213 |
Overview | p. 213 |
The Problems of a Complex Shape | p. 214 |
Some Reasonable Problems | p. 225 |
Built-In Solutions | p. 237 |
Exercises | p. 238 |
Summary | p. 239 |
You Should Now Know | p. 239 |
A Simple Pool Game | p. 241 |
Overview | p. 241 |
The Rules of Engagement | p. 242 |
Taking a Shot | p. 248 |
Exercises | p. 256 |
Summary | p. 256 |
You Should Now Know | p. 256 |
More Complex Motion | p. 257 |
Force and Newton's Laws | p. 259 |
Overview | p. 259 |
Force | p. 260 |
Gravity | p. 263 |
Rockets and Satellites | p. 267 |
Exercises | p. 269 |
Summary | p. 269 |
You Should Now Know | p. 269 |
Angular Motion | p. 271 |
Overview | p. 271 |
The Physics of a Lever | p. 272 |
Spin | p. 277 |
Spinning Collisions | p. 279 |
Exercises | p. 294 |
Summary | p. 295 |
You Should Now Know | p. 295 |
Friction | p. 297 |
Overview | p. 297 |
How Friction Works | p. 298 |
Friction and Angular Motion | p. 302 |
Exercises | p. 306 |
Summary | p. 306 |
You Should Now Know | p. 307 |
Strings, Pulleys, and Conveyor Belts | p. 309 |
Overview | p. 309 |
Pulling Things Around | p. 310 |
Continuous Momentum | p. 315 |
Exercises | p. 317 |
Summary | p. 318 |
You Should Now Know | p. 318 |
Oscillations | p. 319 |
Overview | p. 319 |
Springs | p. 320 |
Simple Harmonic Motion | p. 322 |
Damped Harmonic Motion | p. 326 |
Phenomena | p. 331 |
Calculating Spring Motion | p. 332 |
Waves | p. 337 |
Exercises | p. 344 |
Summary | p. 344 |
You Should Now Know | p. 345 |
3D Mathematics | p. 347 |
3D Geometry | p. 349 |
Overview | p. 349 |
3D Vectors | p. 350 |
Rendering | p. 357 |
Casting a Ray | p. 363 |
Exercises | p. 367 |
Summary | p. 367 |
You Should Now Know | p. 368 |
Transforms | p. 369 |
Overview | p. 369 |
Describing Locations in Space | p. 370 |
Applying Transforms | p. 375 |
Exercises | p. 382 |
Summary | p. 382 |
You Should Now Know | p. 383 |
Collision Detection in Three Dimensions | p. 385 |
Overview | p. 385 |
When Worlds Collide | p. 386 |
When Footballs Collide | p. 388 |
When Boxes Collide | p. 391 |
When Cans Collide | p. 395 |
When Stuff Collides | p. 400 |
Resolving Collisions in Three Dimensions | p. 401 |
Exercises | p. 401 |
Summary | p. 401 |
You Should Now Know | p. 402 |
Lighting and Textures | p. 403 |
Overview | p. 403 |
Light | p. 403 |
Materials | p. 407 |
Shading | p. 419 |
Exercises | p. 421 |
Summary | p. 421 |
You Should Now Know | p. 422 |
Modeling Techniques | p. 423 |
Overview | p. 423 |
Mathematical 3D Modeling | p. 424 |
Animated Surfaces | p. 432 |
Bones Animation | p. 435 |
Exercises | p. 441 |
Summary | p. 441 |
You Should Now Know | p. 442 |
Game Algorithms | p. 443 |
Speeding Things Up | p. 445 |
Overview | p. 445 |
Cheap and Expensive | p. 446 |
Pseudo-Physics | p. 452 |
Culling | p. 454 |
Exercises | p. 461 |
Summary | p. 461 |
You Should Now Know | p. 462 |
Tile-Based Games | p. 463 |
Overview | p. 463 |
Generating a Game from Bits | p. 464 |
Advanced Tiling | p. 470 |
Exercises | p. 475 |
Summary | p. 475 |
You Should Now Know | p. 476 |
Mazes | p. 477 |
Overview | p. 477 |
Classifying Mazes | p. 478 |
Creating Mazes | p. 483 |
Navigating Within Mazes | p. 492 |
Exercises | p. 501 |
Summary | p. 501 |
You Should Now Know | p. 502 |
Game Theory and AI | p. 503 |
Overview | p. 503 |
Introduction to Game Theory | p. 504 |
Tactical AI | p. 515 |
Top-Down AI | p. 518 |
Bottom-Up AI | p. 522 |
Exercises | p. 528 |
Summary | p. 528 |
You Should Now Know | p. 528 |
Search Techniques | p. 529 |
Overview | p. 529 |
Problem-Solving | p. 530 |
Case Study | p. 534 |
Genetic Algorithms | p. 538 |
Exercises | p. 545 |
Summary | p. 545 |
You Should Now Know | p. 546 |
Glossary of Mathematical Terms | p. 547 |
Language References and Pseudocode | p. 567 |
About the CD-ROM | p. 575 |
Further Reading and Resources | p. 581 |
Answers to Exercises | p. 585 |
Index | p. 593 |
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