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.
Introduction
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
Forces
Momenta
Energy
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
Variations
Linear Algebra
A Review of Number Systems
Systems of Linear Equations
Matrices
Vector Spaces
Advanced Topics
Affine Algebra
Introduction
Coordinate Systems
Subspaces
Transformations
Barycentric Coordinates
Calculus
Univariate Calculus
Multivariate Calculus
Applications
Quaternions
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
Definitions
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
Applications
Contact Forces
Biography
Dave Eberly is the president of Geometric Tools, Inc. (www.geometrictools.com), 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 comp.graphics.algorit
"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
