Game Physics: 2nd Edition (Hardback) book cover

Game Physics

2nd Edition

By David H. Eberly

© 2010 – CRC Press

902 pages

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Hardback: 9780123749031
pub: 2010-04-05
eBook (VitalSource) : 9780080964072
pub: 2010-04-05
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About the Book

Create physically realistic 3D Graphics environments with this introduction to the ideas and techniques behind the process. Author David H. Eberly includes simulations to introduce the key problems involved and then gradually reveals the mathematical and physical concepts needed to solve them. He then describes all 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. The book tackles the complex, challenging issues that other books avoid, including Lagrangian dynamics, 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. This book even describes when real physics isn't necessary - and hacked physics will do.


"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

Table of Contents


A Brief History of the World

A Summary of the Topics

Examples and Exercises

Basic Concepts from Physics

Rigid Body Classification

Rigid Body Kinematics

Newton’s Laws




Rigid Body Motion

Newtonian Dynamics

Lagrangian Dynamics

Euler’s Equations of Motion

Deformable Bodies

Elasticity, Stress, and Strain

Mass–Spring Systems

Control Point Deformation

Free-Form Deformation

Implicit Surface Deformation

Fluids and Gases

Vector Calculus

Strain and Stress

Conservation Laws

A Simplified Model for Fluid Flow

Implementing the Simplified 2D Model

Implementing the Simplified 3D Model

Variations of the Simplified Model

Physics Engines

The Physics Tick

Collision Culling

Test-Intersection Queries

Collision Detection with Convex Polyhedra

Unconstrained Motion

Acceleration-Based Constrained Motion

Velocity-Based Constrained Motion


Linear Algebra

A Review of Number Systems

Systems of Linear Equations


Vector Spaces

Advanced Topics

Affine Algebra


Coordinate Systems



Barycentric Coordinates


Univariate Calculus

Multivariate Calculus



Rotation Matrices

The Classical Approach

A Linear Algebraic Approach

Interpolation of Quaternions

Derivatives of Time-Varying Quaternions

Differential Equations

First-Order Equations

Existence, Uniqueness, and Continuous Dependence

Second-Order Equations

General-Order Differential Equations

Systems of Linear Differential Equations

Equilibria and Stability

Ordinary Difference Equations


Linear Equations

Constant Coefficient Equations

Systems of Equations

Numerical Methods

Euler’s Method

Higher-Order Taylor Methods

Methods via an Integral Formulation

Runge–Kutta Methods

Multistep Methods

Predictor–Corrector Methods

Extrapolation Methods

Verlet Integration

Numerical Stability and Its Relationship to Physical Stability

Stiff Equations

Linear Complementarity and Mathematical Programming

Linear Programming

The Linear Complementarity Problem

Mathematical Programming


Contact Forces

About the Author

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

Subject Categories

BISAC Subject Codes/Headings:
ART / Digital
COMPUTERS / Programming / Games