Game Physics

1st Edition

Authors: David Eberly
Print ISBN: 9781558607408
Imprint: Morgan Kaufmann
Published Date: 8th December 2003
Page Count: 816


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Several years in development, Game Physics is an introduction to the ideas and techniques necessary to create physically realistic 3D graphic environments. As a companion volume to Dave Eberly's industry standard 3D Game Engine Design, Game Physics shares a similar practical approach and format. Dave includes simulations to introduce the key problems involved, and then gradually uncovers the mathematical and physical concepts necessary to solve them. He then describes all of the algorithmic foundations, and uses code examples and working source code to show how they are implemented, culminating in a large collection of physical simulations. This book tackles the complex, challenging issues that other books avoid, including rigid body dynamics, impulse methods, resting contact, linear complementarity problems, deformable bodies, mass-spring systems, friction, numerical solution of differential equations, numerical stability and its relationship to physical stability, and Verlet integration methods. Dave even describes when real physics isn't necessary—and hacked physics will do. The extensive companion CD-ROM is by itself a major contribution to creating physically realistic behavior in a virtual 3D environment. This book will be the key reference in this field for years to come.

Table of Contents

Trademarks Figures Tables Preface About the CD-ROM

1 Introduction 1.1 A Brief History of the World 1.2 A Summary of the Topics 1.3 Examples and Exercises

2 Basic Concepts from Physics 2.1 Rigid Body Classification 2.2 Rigid Body Kinematics 2.2.1 Single Particle 2.2.2 Particle Systems and Continuous Materials 2.3 Newton's Laws 2.4 Forces 2.4.1 Gravitational Forces 2.4.2 Spring Forces 2.4.3 Friction and Other Dissipative Forces 2.4.4 Torque 2.4.5 Equilibrium 2.5 Momenta 2.5.1 Linear Momentum 2.5.2 Angular Momentum 2.5.3 Center of Mass 2.5.4 Moments and Products of Inertia 2.5.5 Mass and Inertia Tensor of a Solid Polyhedron 2.6 Energy 2.6.1 Work and Kinetic Energy 2.6.2 Conservative Forces and Potential Energy

3 Rigid Body Motion 3.1 Newtonian Dynamics 3.2 Lagrangian Dynamics 3.2.1 Equations of Motion for a Particle 3.2.2 Time-Varying Frames or Constraints 3.2.3 Interpretation of the Equations of Motion 3.2.4 Equations of Motion for a System of Particles 3.2.5 Equations of Motion for a Continuum of Mass 3.2.6 Examples with Conservative Forces 3.2.7 Examples with Dissipative Forces 3.3 Euler's Equations of Motion

4 Deformable Bodies 4.1 Elasticity, Stress, and Strain 4.2 Mas


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Morgan Kaufmann
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About the Author

David Eberly

Dave Eberly is the president of Geometric Tools, Inc. (, a company that specializes in software development for computer graphics, image analysis, and numerical methods. Previously, he was the director of engineering at Numerical Design Ltd. (NDL), the company responsible for the real-time 3D game engine, NetImmerse. He also worked for NDL on Gamebryo, which was the next-generation engine after NetImmerse. His background includes a BA degree in mathematics from Bloomsburg University, MS and PhD degrees in mathematics from the University of Colorado at Boulder, and MS and PhD degrees in computer science from the University of North Carolina at ChapelHill. He is the author of 3D Game Engine Design, 2nd Edition (2006), 3D Game Engine Architecture (2005), Game Physics (2004), and coauthor with Philip Schneider of Geometric Tools for Computer Graphics (2003), all published by Morgan Kaufmann. As a mathematician, Dave did research in the mathematics of combustion, signal and image processing, and length-biased distributions in statistics. He was an associate professor at the University of Texas at San Antonio with an adjunct appointment in radiology at the U.T. Health Science Center at San Antonio. In 1991, he gave up his tenured position to re-train in computer science at the University of North Carolina. After graduating in 1994, he remained for one year as a research associate professor in computer science with a joint appointment in the Department of Neurosurgery, working in medical image analysis. His next stop was the SAS Institute, working for a year on SAS/Insight, a statistical graphics package. Finally, deciding that computer graphics and geometry were his real calling, Dave went to work for NDL (which is now Emergent Game Technologies), then to Magic Software, Inc., which later became Geometric Tools, Inc. Dave’s participation in the newsgroup

Affiliations and Expertise

President of Geometric Tools, Inc (, a company that specializes in software development for computer graphics, image analysis, and numerical methods. Previously, he was the Director of Engineering at Numerical Design Ltd (NDL), the company responsible for the real-time 3D game engine, Netlmmerse. His background includes a BA in Mathematics from Bloomsburg U, MS and PhD degrees in Mathematics from the U of Colorado at Boulder, and MS and PhD degrees in computer science from the U of North Carolina at Chapel Hill.


"I keep at most a dozen reference texts within easy reach of my workstation computer. This book will replace two of them."—Ian Ashdown, President, byHeart Consultants Limited
"Implementing physical simulations for real-time games is a complex task that requires a solid understanding of a wide range of concepts from the fields of mathematics and physics. Previously, the relevant information could only be gleaned through obscure research papers. Thanks to Game Physics, all this information is now available in a single, easily accessible volume. Dave has yet again produced a must-have book for game technology programmers everywhere." —Christer Ericson, Technology Lead, Sony Computer Entertainment
"Game Physics is a comprehensive reference of physical simulation techniques relevant to games and also contains a clear presentation of the mathematical background concepts fundamental to most types of game programming. I wish I had this book years ago." —Naty Hoffman, Senior Software Engineer, Naughty Dog, Inc.
"Eppur si muove . . . and yet it moves. From Galileo to game development, this book will surely become a standard reference for modeling movement." —Ian Ashdown, President, byHeart Consultants Limited
"This is an excellent companion volume to Dave's earlier 3D Game Engine Design. It shares the approach and strengths of his previous book. He doesn't try to pare down to the minimum necessary information that would allow you to build something with no more than basic functionality. Instead, he gives you all you need to begin working on a professional-caliber system. He puts the concepts firmly in context with current, ongoing research, so you have plenty of guidance on where to go if you are inclined to add even more features on your own. This is not a cookbook—it's a concise presentation of all the basic concepts needed to understand and use physics in