Mathematics and Physics for Programmers

The casual game market continues to expand, and with the use of Flash growing and the increased popularity of the iPhone and other mobile gaming devices, developers have an exciting new route to market. But many of these budding game programmers find that they're missing the core math and physics skills they need to develop even simple games. (Second Edition) teaches beginning game programmers they skills they need to develop causal games. Beginning with the basic aspects of mathematics and physics that are relevant to games, and moving on to more complex topics, the book combines theory and practice and the reader develops a number of games throughout the course of the book. With the concepts and techniques presented in the book, readers should be able to program a number of standard casual game types, including Mario-style platformers, driving simulations, puzzle games, and a simple first-person shooter. They will also gain a basic understanding of 2D and 3D geometry. Provides coverage of all the latest casual gaming technology, including mobile devices such as the iPhone. Written for beginning game programmers who need to learn the basic mathematics and physics skills necessary to develop casual games. The book covers both theory and practice through hands-on application of new skills learned. All examples and techniques are non-platform specific. An accompanying CD-ROM includes all the source code needed to create the games in the book. Cover Table of Contents Part I: Essential Topics in Mathematics Chapter 1 Numbers Overview Numbers as Written How Computers Represent Numbers Exercises Summary You Should Now Know Chapter 2 Arithmetic Overview Fractions Proportions, Ratios, and Percentages Exponentials Logarithms Exercises Summary You Should Now Know Chapter 3 Algebra Overview Basic Algebra Working with Equations Factoring and Solving Quadratic Equations Functions and Graphs Exercises Summary You Should Now Know Chapter 4 Geometry and Trigonometry Overview Angles Triangles Calculations with Triangles Rotations and Reflections Exercises Summary You Should Now Know Chapter 5 Vectors Overview Getting from Here to There Vector Motion Vector Calculations Matrices Exercises Summary You Should Now Know Chapter 6 Calculus Overview Differentiation and Integration Differential Equations Approximation Methods Exercises Summary You Should Now Know Part II: Essential Topics in Physics Chapter 7 Acceleration, Mass, and Energy Overview Ballistics Mass and Momentum Energy Exercises Summary You Should Now Know Chapter 8 Detecting Collisions Between Simple Shapes Overview Ground Rules When Circles Collide When Squares Collide When Ellipses Collide When Things Collide Exercises Summary You Should Now Know Chapter 9 Collision Resolution Overview Resolving a Single Collision Multiple Collisions Exercises Summary You Should Now Know Chapter 10 Detecting Collisions Between Complex Shapes Overview Problems with Complex Shapes Some Reasonable Problems Built-In Solutions Exercises Summary You Should Now Know Chapter 11 A Simple Pool Game Overview Primary Elements of a Simulation Taking a Shot Exercises Summary You Should Now Know Part III: Complex Motion Chapter 12 Force and Newton’s Laws Overview Force Gravity Rockets and Satellites Exercise Summary You Should Now Know Chapter 13 Angular Motion Overview The Physics of a Lever Spin Spinning Collisions Spin Applied to the Pool Game Exercises Summary You Should Now Know Chapter 14 Friction Overview How Friction Works Friction and Angular Motion Exercise Summary You Should Now Know Chapter 15 Strings, Pulleys, and Conveyor Belts Overview Pulling Things Around Continuous Momentum Exercise Summary You Should Now Know Chapter 16 Oscillations Overview Springs Simple Harmonic Motion Damped Harmonic Motion Complications of Springs Calculating Spring Motion Waves Exercise Summary You Should Now Know Part IV: 3-D Mathematics Chapter 17 3-D Geometry Overview 3-D Vectors Rendering Casting a Ray Exercise Summary You Should Now Know Chapter 18 Transforms Overview Describing Locations in Space Applying Transforms Exercise Summary You Should Now Know Chapter 19 3-D Collision Detection Overview Colliding Worlds Colliding Footballs Colliding Boxes Colliding Cans Varieties of Collisions Resolving Collisions in Three Dimensions Exercise Summary You Should Now Know Chapter 20 Lighting and Textures Overview Light Materials Shading Exercises Summary You Should Now Know Chapter 21 Modeling Techniques Overview Mathematical 3-D Modeling Animated Surfaces Bone Animations Exercises Summary You Should Now Know Part V: Game Algorithms Chapter 22 Speeding Things Up Overview Cheap and Expensive Calculations Pseudo-Physics Culling Exercises Summary You Should Now Know Chapter 23 Tile-Based Games Overview Generating a Game from Bits Advanced Tiling Exercises Summary You Should Now Know Chapter 24 Mazes Overview Classifying Mazes Creating Mazes Navigating Within Mazes Exercises Summary You Should Now Know Chapter 25 Game Theory and Artificial Intelligence Overview Introduction to Game Theory Tactical AI Top-Down AI Bottom-Up AI Exercises Summary You Should Now Know Chapter 26 Search Techniques Overview Problem Solving Case Study Genetic Algorithms Exercises Summary You Should Now Know Appendix A: Glossary of Mathematical Terms Appendix B: Code References Appendix C: The Greek Alphabet Appendix D: Learning 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 Z The casual game market continues to expand, and with the use of Flash growing and the increased popularity of the iPhone and other mobile gaming devices, developers have an exciting new route to market. But many of these budding game programmers find that they're missing the core math and physics skills they need to develop even simple games. MATHEMATICS AND PHYSICS FOR PROGRAMMERS, SECOND EDITION teaches beginning game programmers they skills they need to develop causal games. Beginning with the basic aspects of mathematics and physics that are relevant to games, and moving on to more complex topics, the book combines theory and practice and the reader develops a number of games throughout the course of the book. With the concepts and techniques presented in the book, readers should be able to program a number of standard casual game types, including Mario-style platformers, driving simulations, puzzle games, and a simple first-person shooter. They will also gain a basic understanding of 2D and 3D geometry. The casual game market continues to expand, and with the use of Flash growing and the increased popularity of the iPhone and other mobile gaming devices, developers have an exciting new route to market. But many of these budding game programmers find that they're missing the core math and physics skills they need to develop even simple games. "Mathematics & Physics For Programmers, Second Edition" teaches beginning game programming students the skills they need to develop causal games. Beginning with the basic aspects of mathematics and physics that are relevant to games, and moving on to more complex topics, the book combines theory and practice and the student develops a number of games throughout the course of the book