Mathematics & Physics for Programmers

by Kodicek, Danny

• ISBN13: 9781584503309
• ISBN10: 1584503300
• Edition: 1st
• Format: Paperback
• Copyright: 2005-01-02
• Publisher: Charles River Media

Summary

Many programmers frequently have limited backgrounds in the mathematics and physics needed for game development or other complex applications. Sooner or later, all programmers run into coding issues that will require an understanding of mathematics or physics concepts like collision detection, 3D vectors, transformations, game theory, or basic calculus. This book provides a simple but thorough grounding in the mathematics and physics topics that programmers need to write these algorithms and programs, using a non-language-specific approach. Applications and examples from game programming are included throughout, and exercise sets follow each chapter for additional practice of the techniques. The CD-ROM provides simulations of the mathematical and physical principles discussed in the book along with the source code.

Author Biography

Danny Kodicek is a graduate of Cambridge University, now working as a freelance programmer and multimedia developer specializing in Web sites and games

Table of Contents

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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