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 To order this title, and for more information, click here
By
David Eberly, Geometric Tools, Inc., Chapel Hill, North Carolina, U.S.A.
ACM
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, 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. He is the author of 3D Game Engine Design, 2e, and 3D Game Engine Architecture,
and co-author of Geometric Tools for Computer Graphics (all published by Morgan Kaufmann).
Description
Game Physics is an introduction to the ideas and techniques needed 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 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. This 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. Dave even describes when real physics isn't necessary?and hacked
physics will do.
Audience
Professionals or students working in game development, simulation, scientific visualization, or virtual worlds.
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 Mass-Spring Systems
4.2.1 One-Dimensional Array of Masses
4.2.2 Two-Dimensional Array of Masses
4.2.3
Three-Dimensional Array of Masses
4.2.4 Arbitrary Configurations
4.3 Control Point Deformation
4.3.1 B-Spline Curves
4.3.2 NURBS Curves
4.3.3 B-Spline Surfaces
4.3.4 NURBS Surfaces
4.3.5 Surfaces Built from Curves
4.4 Free-Form
Deformation
4.5 Implicit Surface Deformation
4.5.1 Level Set Extraction
4.5.2 Isocurve Extraction in 2D Images
4.5.3
Isosurface Extraction in 3D Images
5 Physics Engines
5.1 Unconstrained Motion
5.1.1 An Illustrative Implementation
5.1.2 A Practical Implementation
5.2 Constrained Motion
5.2.1 Collision Points
5.2.2 Collision Response for Colliding
Contact
5.2.3 Collision Response for Resting Contact
5.2.4 An Illustrative Implementation
5.2.5 Lagrangian Dynamics
5.3 Collision Detection with Convex Polyhedra
5.3.1 The Method of Separating Axes
5.3.2 Stationary Objects
5.3.3
Objects Moving with Constant Linear Velocity
5.3.4 Oriented Bounding Boxes
5.3.5 Boxes Moving with Constant Linear and Angular
Velocity
5.4 Collision Culling: Spatial and Temporal Coherence
5.4.1 Culling with Bounding Spheres
5.4.2 Culling with
Axis-Aligned Bounding Boxes
5.5 Variations
6 Physics and Shader Programs
6.1 Introduction
6.2 Vertex and Pixel Shaders
6.3 Deformation by Vertex Displacement
6.4 Skin-and-Bones Animation
6.5 Rippling Ocean Waves
6.6 Refraction
6.7 Fresnel
Reflectance
6.8 Iridescence
7 Linear Complementarity and Mathematical Programming
7.1 Linear Programming
7.1.1
A Two-Dimensional Example
7.1.2 Solution by Pairwise Intersections
7.1.3 Statement of the General Problem
7.1.4 The
Dual Problem
7.2 The Linear Complementarity Problem
7.2.1 The Lemke-Howson Algorithm
7.2.2 Zero Constant Terms
7.2.3
The Complementary Variable Cannot Leave the Diction
7.3 Mathematical Programming
7.3.1 Karush-Kuhn-Tucker Conditions
7.3.2
Convex Quadratic Programming
7.3.3 General Duality Theory
7.4 Applications
7.4.1 Distance Calculations
7.4.2 Contact
Forces
8 Differential Equations
8.1 First-Order Equations
8.2 Existence, Uniqueness, and Continuous Dependence
8.3
Second-Order Equations
8.4 General-Order Differential Equations
8.5 Systems of Linear Differential Equations
8.6 Equilibria
and Stability
8.6.1 Stability for Constant-Coefficient Linear Systems
8.6.2 Stability for General Autonomous Systems
9 Numerical Methods
9.1 Euler's Method
9.2 Higher-Order Taylor Methods
9.3 Methods Via an Integral Formulation
9.4
Runge-Kutta Methods
9.4.1 Second-Order Methods
9.4.2 Third-Order Methods
9.4.3 Fourth-Order Method
9.5 Multistep
Methods
9.6 Predictor-Corrector Methods
9.7 Extrapolation Methods
9.7.1 Richardson Extrapolation
9.7.2 Application
to Differential Equations
9.7.3 Polynomial Interpolation and Extrapolation
9.7.4 Rational Polynomial Interpolation and Extrapolation
9.7.5 Modified Midpoint Method
9.7.6 Bulirsch-Stoer Method
9.8 Verlet Integration
9.8.1 Forces without a Velocity
Component
9.8.2 Forces with a Velocity Component
9.8.3 Simulating Drag in the System
9.8.4 Leap Frog Method
9.8.5
Velocity Verlet Method
9.8.6 Gear's Fifth-Order Predictor-Corrector Method
9.9 Numerical Stability and its Relationship to Physical
Stability
9.9.1 Stability for Single-Step Methods
9.9.2 Stability for Multistep Methods
9.9.3 Choosing a Stable Step
Size
9.10 Stiff Equations
10 Quaternions
10.1 Rotation Matrices
10.2 The Classical Approach
10.2.1 Algebraic
Operations
10.2.2 Relationship of Quaternions to Rotations
10.3 A Linear Algebraic Approach
10.4 From Rotation Matrices to
Quaternions
Contributed by Ken Shoemake
10.4.1 2D Rotations
10.4.2 Linearity
10.4.3 3D Rotations: Geometry
10.4.4 4D Rotations
10.4.5 3D Rotations: Algebra
10.4.6 4D Matrix
10.4.7 Retrospect, Prospect
10.5 Interpolation
of Quaternions
10.5.1 Spherical Linear Interpolation
10.5.2 Spherical Quadratic Interpolation
10.6 Derivatives of Time-Varying
Quaternions
A Linear Algebra
A.1 A Review of Number Systems
A.1.1 The Integers
A.1.2 The Rational Numbers
A.1.3 The Real Numbers
A.1.4 The Complex Numbers
A.1.5 Fields
A.2 Systems of Linear Equations
A.2.1 A Closer
Look at Two Equations in Two Unknowns
A.2.2 Gaussian Elimination and Elementary Row Operations
A.2.3 Nonsquare Systems of
Equations
A.2.4 The Geometry of Linear Systems
A.2.5 Numerical Issues
A.2.6 Iterative Methods for Solving Linear Systems
A.3 Matrices
A.3.1 Some Special Matrices
A.3.2 Elementary Row Matrices
A.3.3 Inverse Matrices
A.3.4 Properties
of Inverses
A.3.5 Construction of Inverses
A.3.6 LU Decomposition
A.4 Vector Spaces
A.4.1 Definition of a Vector
Space
A.4.2 Linear Combinations, Spans, and Subspaces
A.4.3 Linear Independence and Bases
A.4.4 Inner Products, Length,
Orthogonality, and Projection
A.4.5 Dot Product, Cross Product, and Triple Products
A.4.6 Orthogonal Subspaces
A.4.7
The Fundamental Theorem of Linear Algebra
A.4.8 Projection and Least Squares
A.4.9 Linear Transformations
A.5 Advanced
Topics
A.5.1 Determinants
A.5.2 Eigenvalues and Eigenvectors
A.5.3 Eigendecomposition for Symmetric Matrices
A.5.4 S + N Decomposition
A.5.5 Applications
B Affine Algebra
B.1 Introduction
B.2 Coordinate Systems
B.3 Subspaces
B.4 Transformations
B.5 Barycentric Coordinates
B.5.1 Triangles
B.5.2 Tetrahedra
B.5.3 Simplices
B.5.4
Length, Area, Volume, and Hypervolume
C Calculus
C.1 Univariate Calculus
C.1.1 Limits
C.1.2 Limits of a Sequence
C.1.3 Continuity
C.1.4 Differentiation
C.1.5 L'Hôpital's Rule
C.1.6 Integration
C.2 Multivariate Calculus
C.2.1 Limits and Continuity
C.2.2 Differentiation
C.2.3 Integration
C.3 Applications
C.3.1 Optimization
C.3.2 Constrained Optimization
C.3.3 Derivative Approximations by Finite Differences
D Ordinary Difference Equations
D.1 Definitions
D.2 Linear Equations
D.2.1 First-Order Linear Equations
D.2.2 Second-Order Linear Equations
D.3
Constant Coefficient Equations
D.4 Systems of Equations
Bibliography
Index
Bibliographic & ordering Information
Hardbound, 816 pages, publication date: DEC-2003
ISBN-13: 978-1-55860-740-8
ISBN-10: 1-55860-740-4
Imprint: MORGAN KAUFFMAN
Price: Order form
GBP 48.99
USD 88.95
EUR 72.95
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Last update: 29 Aug 2008
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