Game Physics Engine Development: How to Build a Robust Commercial-Grade Physics Engine for your Game (Second Edition)

553 Pages·2010·6.3 MB·English

by  Ian Millington

GAME PHYSICS
ENGINE
DEVELOPMENT
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GAME PHYSICS
ENGINE
DEVELOPMENT
H B R
OW TO UILD A OBUST
C -G P E
OMMERCIAL RADE HYSICS NGINE
G
FOR YOUR AME
Second Edition
IANMILLINGTON
AMSTERDAM•BOSTON•HEIDELBERG•LONDON
NEWYORK•OXFORD•PARIS•SANDIEGO
SANFRANCISCO•SINGAPORE•SYDNEY•TOKYO
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LibraryofCongressCataloging-in-PublicationData
Millington,Ian.
Gamephysicsenginedevelopment:howtobuildarobustcommercial-gradephysicsengineforyour
game/IanMillington.–2nded.
p.cm.
Includesindex.
ISBN978-0-12-381976-5(pbk.:alk.paper)
1.Computergames–Programming.2.Physics–Dataprocessing.I.Title.
QA76.76.C672M552010
794.8(cid:2)1526–dc22
2010014533
BritishLibraryCataloguing-in-PublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:978-0-12-381976-5
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Contents
List of Figures
xix
Preface to the Second Edition
xxiii
Preface to the First Edition
xxv
Acknowledgments
xxvii
About the Author
xxix
Chapter
1
Introduction
1
What Is Game Physics?
1.1 2
What Is a Physics Engine?
1.2 2
1.2.1 AdvantagesofaPhysicsEngine 3

1.2.2 WeaknessesofaPhysicsEngine 4
Approaches to Physics Engines
1.3 5
1.3.1 TypesofObjects 5
1.3.2 ContactResolution 6
1.3.3 ImpulsesandForces 6
1.3.4 WhatWe’reBuilding 7
The Mathematics of Physics Engines
1.4 8
1.4.1 TheMathYouNeedtoKnow 8
1.4.2 TheMathWe’llReview 9
1.4.3 TheMathI’llIntroduce 10
The Source Code in the Book
1.5 10
How the Book Is Structured
1.6 11
1.6.1 ExercisesandProjects 12
vii
viii
Contents
PART I Particle Physics 15
Chapter
2
The Mathematics of Particles
17
Vectors
2.1 17
2.1.1 TheHandednessofSpace 21
2.1.2 VectorsandDirections 23
2.1.3 ScalarandVectorMultiplication 25
2.1.4 VectorAdditionandSubtraction 27
2.1.5 MultiplyingVectors 29
2.1.6 TheComponentProduct 30
2.1.7 TheScalarProduct 31
2.1.8 TheVectorProduct 33
2.1.9 TheOrthonormalBasis 37
Calculus
2.2 38
2.2.1 DifferentialCalculus 38
2.2.2 IntegralCalculus 43
Summary
2.3 44
Exercises
2.4 45
Chapter
3
The Laws of Motion
47
The Particle
3.1 48
The First Two Laws
3.2 49
3.2.1 TheForceEqu ations 50
3.2.2 AddingMasstoParticles 51
3.2.3 MomentumandVelocity 52
3.2.4 TheForceofGravity 53
The Integrator
3.3 55
3.3.1 TheUpdateEquations 55
3.3.2 TheCompleteIntegrator 57
Summary
3.4 58
Exercises
3.5 59
Chapter
4
The Particle Physics Engine
61
Ballistics
4.1 61
4.1.1 SettingProjectileProperties 62
4.1.2 Implementation 63
ix
Contents
Fireworks
4.2 66
4.2.1 TheFireworksData 66
4.2.2 FireworkRules 67
4.2.3 TheImplementation 69
Summary
4.3 73
Projects
4.4 73
PART II Mass Aggregate Physics 75
Chapter
5
Adding General Forces
77
D’Alembert’s Principle
5.1 77
Force Generators
5.2 80
5.2.1 InterfacesandPolymorphism 81
5.2.2 Implementation 81
5.2.3 AGravityForceGenerator 84
5.2.4 ADragForceGenerator 85
Built-In Gravity and Damping
5.3 87
Summary
5.4 87
Exercises
5.5 88
Chapter
6
Springs and Spring-Like Things
89
Hook’s Law
6.1 89
Spring-Like Force Generators
6.2 92
6.2.1 ABasicSpringForceGenerator 92
6.2.2 AnAnchoredSpringGenerator 94
6.2.3 AnElasticBungeeGenerator 96
6.2.4 ABuoyancyForceGenerator 98
Stiff Springs
6.3 101
6.3.1 TheStiffSpringsProblem 102
6.3.2 FakingStiffSprings 104
Summary
6.4 110
Exercises
6.5 110