9781584503309

Mathematics & Physics for Programmers

by
  • ISBN13:

    9781584503309

  • ISBN10:

    1584503300

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2005-01-02
  • Publisher: Charles River Media
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Supplemental Materials

What is included with this book?

  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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

Acknowledgmentsp. xxv
Introductionp. xxvii
General Techniquesp. 1
Numbersp. 3
Overviewp. 3
Writing Numbersp. 4
How Computers Represent Numbersp. 8
Exercisesp. 16
Summaryp. 17
You Should Now Knowp. 17
Arithmeticp. 19
Overviewp. 19
Fractions and Remaindersp. 20
Proportions, Ratios, and Percentagesp. 29
Exponentialsp. 36
Logarithmsp. 39
Exercisesp. 43
Summaryp. 44
You Should Now Knowp. 44
Algebrap. 45
Overviewp. 45
Basic Algebrap. 46
Working with Equationsp. 50
Functions and Graphsp. 65
Exercisesp. 74
Summaryp. 74
You Should Now Knowp. 75
Trigonometry and Pythagorasp. 77
Overviewp. 77
Anglesp. 78
Trianglesp. 82
Calculations with Trianglesp. 90
Rotations and Reflectionsp. 94
Exercisesp. 101
Summaryp. 101
You Should Now Knowp. 101
Vectorsp. 103
Overviewp. 103
Getting from Here to Therep. 104
Vector Motionp. 110
Vector Calculationsp. 117
Matricesp. 125
Exercisesp. 131
Summaryp. 131
You Should Now Knowp. 132
Calculusp. 133
Overviewp. 133
Differentiation and Integrationp. 134
Differential Equationsp. 144
Approximation Methodsp. 146
Exercisesp. 152
Summaryp. 152
You Should Now Knowp. 152
Ballistics and Collisionsp. 153
Acceleration, Mass, and Energyp. 155
Overviewp. 155
Ballisticsp. 156
Mass and Momentump. 162
Energyp. 163
Exercisesp. 167
Summaryp. 168
You Should Now Knowp. 169
Detecting Collisions Between Simple Shapesp. 171
Overviewp. 171
Ground Rulesp. 172
When Circles Collidep. 173
When Squares Collidep. 182
When Ovals Collidep. 190
When Things Collidep. 195
Exercisesp. 196
Summaryp. 197
You Should Now Knowp. 197
Resolving Collisionsp. 199
Overviewp. 199
Resolving a Single Collisionp. 200
Multiple Collisionsp. 207
Exercisesp. 211
Summaryp. 212
You Should Now Knowp. 212
Detecting Collisions Between Complex Shapesp. 213
Overviewp. 213
The Problems of a Complex Shapep. 214
Some Reasonable Problemsp. 225
Built-In Solutionsp. 237
Exercisesp. 238
Summaryp. 239
You Should Now Knowp. 239
A Simple Pool Gamep. 241
Overviewp. 241
The Rules of Engagementp. 242
Taking a Shotp. 248
Exercisesp. 256
Summaryp. 256
You Should Now Knowp. 256
More Complex Motionp. 257
Force and Newton's Lawsp. 259
Overviewp. 259
Forcep. 260
Gravityp. 263
Rockets and Satellitesp. 267
Exercisesp. 269
Summaryp. 269
You Should Now Knowp. 269
Angular Motionp. 271
Overviewp. 271
The Physics of a Leverp. 272
Spinp. 277
Spinning Collisionsp. 279
Exercisesp. 294
Summaryp. 295
You Should Now Knowp. 295
Frictionp. 297
Overviewp. 297
How Friction Worksp. 298
Friction and Angular Motionp. 302
Exercisesp. 306
Summaryp. 306
You Should Now Knowp. 307
Strings, Pulleys, and Conveyor Beltsp. 309
Overviewp. 309
Pulling Things Aroundp. 310
Continuous Momentump. 315
Exercisesp. 317
Summaryp. 318
You Should Now Knowp. 318
Oscillationsp. 319
Overviewp. 319
Springsp. 320
Simple Harmonic Motionp. 322
Damped Harmonic Motionp. 326
Phenomenap. 331
Calculating Spring Motionp. 332
Wavesp. 337
Exercisesp. 344
Summaryp. 344
You Should Now Knowp. 345
3D Mathematicsp. 347
3D Geometryp. 349
Overviewp. 349
3D Vectorsp. 350
Renderingp. 357
Casting a Rayp. 363
Exercisesp. 367
Summaryp. 367
You Should Now Knowp. 368
Transformsp. 369
Overviewp. 369
Describing Locations in Spacep. 370
Applying Transformsp. 375
Exercisesp. 382
Summaryp. 382
You Should Now Knowp. 383
Collision Detection in Three Dimensionsp. 385
Overviewp. 385
When Worlds Collidep. 386
When Footballs Collidep. 388
When Boxes Collidep. 391
When Cans Collidep. 395
When Stuff Collidesp. 400
Resolving Collisions in Three Dimensionsp. 401
Exercisesp. 401
Summaryp. 401
You Should Now Knowp. 402
Lighting and Texturesp. 403
Overviewp. 403
Lightp. 403
Materialsp. 407
Shadingp. 419
Exercisesp. 421
Summaryp. 421
You Should Now Knowp. 422
Modeling Techniquesp. 423
Overviewp. 423
Mathematical 3D Modelingp. 424
Animated Surfacesp. 432
Bones Animationp. 435
Exercisesp. 441
Summaryp. 441
You Should Now Knowp. 442
Game Algorithmsp. 443
Speeding Things Upp. 445
Overviewp. 445
Cheap and Expensivep. 446
Pseudo-Physicsp. 452
Cullingp. 454
Exercisesp. 461
Summaryp. 461
You Should Now Knowp. 462
Tile-Based Gamesp. 463
Overviewp. 463
Generating a Game from Bitsp. 464
Advanced Tilingp. 470
Exercisesp. 475
Summaryp. 475
You Should Now Knowp. 476
Mazesp. 477
Overviewp. 477
Classifying Mazesp. 478
Creating Mazesp. 483
Navigating Within Mazesp. 492
Exercisesp. 501
Summaryp. 501
You Should Now Knowp. 502
Game Theory and AIp. 503
Overviewp. 503
Introduction to Game Theoryp. 504
Tactical AIp. 515
Top-Down AIp. 518
Bottom-Up AIp. 522
Exercisesp. 528
Summaryp. 528
You Should Now Knowp. 528
Search Techniquesp. 529
Overviewp. 529
Problem-Solvingp. 530
Case Studyp. 534
Genetic Algorithmsp. 538
Exercisesp. 545
Summaryp. 545
You Should Now Knowp. 546
Glossary of Mathematical Termsp. 547
Language References and Pseudocodep. 567
About the CD-ROMp. 575
Further Reading and Resourcesp. 581
Answers to Exercisesp. 585
Indexp. 593
Table of Contents provided by Ingram. All Rights Reserved.

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