Simulating physics helps cutting-edge games distinguish themselves by making virtual objects behave as we expect them to in the real world. Physics engines are the software programs that run these simulations. Building an engine is difficult, however. There are a large number of new developers (and hobbyists) coming into this market who need help through this complex process. Current introductory books are inadequate; they don't bring enough real-world programming experience to the task. There is a need for an introductory book on game physics with solid coding guidance but which limits the math content. Ian Millington brings his extensive professional programming experience to this problem. He has developed games since 1987, has studied AI and mathematics at the PhD level, and founded Mindlathe Ltd., a company that designed and built commercial physics engines. Physics Engine Development carefully describes each step in the creation of a robust, usable physics engine. It introduces the mathematical concepts in a clear and simple manner, keeping to high school level topics and building a physics code library as it goes. Each new concept is explained in diagrams and code to make sure that even the most novice of game programmers understands. The companion CD-ROM includes the source code for a complete physics engine of commercial quality. This book will serve as a introduction to more mathematically advanced books on game physics, such as Dave Eberly's Game Physics.

Table of Contents:
Preface About the Author About the CD-ROM 1 Introduction 1.1 What is Game Physics 1.2 What is a Physics Engine 1.2.1 Advantages of a Physics Engine 1.2.2 Weaknessess of a Physics Engine 1.3 Approaches to Physics Engines 1.3.1 Types of Object 1.3.2 Contact Resolution 1.3.3 Impulses and Forces 1.3.4 What We're Building 1.4 The Mathematics of Physics Engines 1.4.1 The Math You Need to Know 1.4.2 The Math We'll Review 1.4.3 The Mathematics We'll Introduce 1.5 The Source Code in the Book 1.6 How the Book is Structured I Particle Physics 2 The Mathematics of Particles 2.1 Vectors 2.1.1 The Handedness of Space 2.1.2 Vectors and Directions 2.1.3 Scalar and Vector Multiplication 2.1.4 Vector Addition and Subtraction 2.1.5 Multiplying Vectors 2.1.6 The Component Product 2.1.7 The Scalar Product 2.1.8 The Vector Product 2.1.9 The Orthonormal Basis 2.2 Calculus 2.2.1 Differential Calculus 2.2.2 Integral Calculus 3 The Laws of Motion 3.1 A Particle 3.2 The First Two Laws 3.2.1 The Force Equations 3.2.2 Adding Mass to Particles 3.2.3 Momentum and Velocity 3.2.4 The Force of Gravity 3.3 The Integrator 3.3.1 The Update Equations 3.3.2 The Complete Integrator 4 The Particle Physics Engine 4.1 Ballistics 4.1.1 Setting Projectile Properties 4.1.2 Implementation 4.2 Fireworks 4.2.1 The Firework Data 4.2.2 Firework Rules 4.2.3 The Implementation II Mass Aggregate Physics 5 Adding General Forces 5.1 D'Alembert's Principle 5.2 Force Generators 5.2.1 Interfaces and Polymorphism 5.2.2 Implementation 5.2.3 A Gravity Force Generator 5.2.4 A Drag Force Generator 5.3 Built-In Gravity and Damping 6 Springs and Spring-like Things 6.1 Hook's Law 6.2 Spring-Like Force Generators 6.2.1 A Basic Spring Generator 6.2.2 An Anchored Spring Generator 6.2.3 An Elastic Bungee Generator 6.2.4 A Buoyancy Force Generator 6.3 Stiff Springs 6.3.1 The Problem of Stiff Springs 6.3.2 Faking Stiff Springs 7 Hard Constraints 7.1 Simple Collision Resolution 7.1.1 The Closing Velocity 7.1.2 The Coefficient of Restitution 7.1.3 The Collision Direction and the Contact Normal 7.1.4 Impulses 7.2 Collision Processing 7.2.1 Collision Detection 7.2.2 Resolving Interpenetration 7.2.3 Resting Contacts 7.3 The Contact Resolver Algorithm 7.3.1 Resolution Order 7.3.2 Time-Division Engines 7.4 Collision-Like Things 7.4.1 Cables 7.4.2 Rods 8 The Mass Aggregate Physics Engine 8.1 Overview of the Engine 8.2 Using the Physics Engine 8.2.1 Rope Bridges and Cables 8.2.2 Friction III Rigid Body Physics 9 The Mathematics of Rotations 9.1 Rotating Objects in 2D 9.1.1 The Mathematics of Angles 9.1.2 Angular Speed 9.1.3 The Origin and the Centre of Mass 9.2 Orientation in 3D 9.2.1 Euler Angles 9.2.2 Axis-Angle 9.2.3 Rotation Matrices 9.2.4 Quaternions 9.3 Angular Velocity and Acceleration 9.3.1 Velocity of a Point 9.3.2 Angular Acceleration 9.4 Implementing the Mathematics 9.4.1 The Matrix Classes 9.4.2 Matrix Multiplication 9.4.3 Matrix Inverse and Transpose 9.4.4 Converting a Quaternion to a Matrix 9.4.5 Transforming Vectors 9.4.6 Changing the Basis of a Matrix 9.4.7 The Quaternion Class 9.4.8 Normalising Quaternions 9.4.9 Combining Quaternions 9.4.10 Rotating 9.4.11 Updating by The Angular Velocity 10 Laws of Motion for Rigid Bodies 10.1 The Rigid Body 10.2 Newton 2 for Rotation 10.2.1 Torque 10.2.2 The Moment of Inertia 10.2.3 Inertia Tensor in World-Coordinates 10.3 D'Alembert for Rotation 10.3.1 Force Generators 10.4 The Rigid Body Integration 11 The Rigid Body Physics Engine 11.1 Overview of the Engine 11.2 Using the Physics Engine 11.2.1 A Flight Simulator 11.2.2 A Sailing Simulator IV Collision Detection 12 Collision Detection 12.1 Collision Detection Pipeline 12.2 Coarse Collision Detection 12.3 Bounding Volumes 12.3.1 Hierarchies 12.3.2 Building the Hierarchy 12.3.3 Sub-object Hierarchies 12.4 Spatial Data Structures 12.4.1 Binary Space Partitioning (BSP) 12.4.2 Oct-Trees and Quad-Trees 12.4.3 Grids 12.4.4 Multi-Resolution Maps 12.5 Summary 13 Generating Contacts 13.1 Collision Geometry 13.1.1 Primitive Assemblies 13.1.2 Generating Collision Geometry 13.2 Contact Generation 13.2.1 Contact Data 13.2.2 Point-Face Contacts 13.2.3 Edge-Edge Contacts 13.2.4 Edge-Face Contacts 13.2.5 Face-Face Contacts 13.2.6 Early Outs 13.3 Primitive Collision Algorithms 13.3.1 Colliding two Spheres 13.3.2 Colliding a Sphere and a Plane 13.3.3 Colliding a Box and a Plane 13.3.4 Colliding a Sphere and a Box 13.3.5 Colliding two Boxes V Contact Physics 14 Collision Resolution 14.1 Impulses and Implusive Torques 14.1.1 Impulsive Torque 14.1.2 Rotating Collisions 14.1.3 Handling Rotating Collisions 14.2 Collision Impluses 14.2.1 Change to Contact-coordinates 14.2.2 Velocity change by Impulse 14.2.3 Impulse change by Velocity 14.2.4 Calculating the Desired Velocity Change 14.2.5 Calculating the Impulse 14.2.6 Applying the Impulse 14.3 Resolving Interpenetration 14.3.1 Choosing a Resolution Method 14.3.2 Implementing Non-linear Projection 14.3.3 Avoiding Over-Rotation 14.4 The Collision Resolution Process 14.4.1 The Collision Resolution Pipeline 14.4.2 Preparing Contact Data 14.4.3 Resolving Penetration 14.4.4 Resolving Velocity 14.4.5 Alternative Update Algorithms 14.4.6 Summary 15 Resting Contacts and Friction 15.1 Resting Forces 15.1.1 Force Calculations 15.2 Micro-Collisions 15.2.1 Removing Accelerated Velocity 15.2.2 Lowering the Restitution 15.2.3 The New Velocity Calculation 15.3 Types of Friction 15.3.1 Static and Dynamic Friction 15.3.2 Isotropic and Anisotropic Friction 15.4 Implementing Friction 15.4.1 Friction as Impulses 15.4.2 Modifying the Velocity Resolution Algorithm 15.4.3 Putting it All Together 15.5 Friction and Sequential Contact Resolution 16 Stability and Optimization 16.1 Stability 16.1.1 Quaternion Drift 16.1.2 Interpenetration on Slopes 16.1.3 Integration Stability 16.1.4 The Benefit of Pessimistic Collision Detection 16.1.5 Changing Mathematical Accuracy 16.2 Optimizations 16.2.1 Sleep 16.2.2 Margins of Error for Penetration and Velocity 16.2.3 Contact Grouping 16.2.4 Code Optimisations 16.2.5 Optimisation Summary 17 Putting It All Together 17.1 Overview of the Engine 17.2 Using the Physics Engine 17.2.1 Ragdolls 17.2.2 Fracture Physics 17.2.3 Explosive Physics 17.3 Limitations of the Engine 17.3.1 Stacks 17.3.2 Reaction Force Friction 17.3.3 Joint Assemblies 17.3.4 Stiff Springs VI Horizons 18 Other Types of Physics 18.1 Simultaneous Contact Resolution 18.1.1 The Jacobian 18.1.2 The Linear Complimentary Problem 18.2 Reduced Coordinate Approaches 18.3 Where to Look for More Information Index