Physics for Game Programmers
Copyright © 2005 by Grant Palmer
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Contents at a Glance
About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
About the Technical Reviewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii
CHAPTER 1 Adding Realism to Your Games . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
CHAPTER 2 Some Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
CHAPTER 3 Basic Newtonian Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
CHAPTER 4 Basic Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
CHAPTER 5 Projectiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
CHAPTER 6 Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
CHAPTER 7 Sports Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
CHAPTER 8 Cars and Motorcycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
CHAPTER 9 Boats and Things That Float . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
CHAPTER 10 Airplanes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
CHAPTER 11 Rockets and Missiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
CHAPTER 12 The Physics of Solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
CHAPTER 13 Explosions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
CHAPTER 14 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
CHAPTER 15 Probabilistic and Monte Carlo Simulations . . . . . . . . . . . . . . . . . . . 403
■INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
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Contents
About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
About the Technical Reviewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii
■CHAPTER 1 Adding Realism to Your Games . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Physics Will Keep Your Games from Looking Fake . . . . . . . . . . . . . . . . . . . 1
Adding Physics-Based Realism Is Easier Than You Might Think . . . . . . . . 2
Adding Physics Won’t Affect Game Performance . . . . . . . . . . . . . . . . . . . . 3
Knowing Some Physics Will Make You a Better Game Programmer . . . . 4
Let’s Add Some Realism to Your Games . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
■CHAPTER 2 Some Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Systems of Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Summation Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Greek Letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Coordinate Systems and Frames of Reference . . . . . . . . . . . . . . . . . . . . . . 9
Scalars and Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Computing the Magnitude of a Vector . . . . . . . . . . . . . . . . . . . . . . . . 11
The Unit Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Vector Cross Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Matrix Multiplication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Rotation Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Contents
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