Game Physics (Hardcover)
David H. Eberly
- 出版商: Morgan Kaufmann
- 出版日期: 2003-12-22
- 定價: $1,980
- 售價: 5.0 折 $990
- 語言: 英文
- 頁數: 816
- 裝訂: Hardcover
- ISBN: 1558607404
- ISBN-13: 9781558607408
-
相關分類:
物理學 Physics
-
其他版本:
Game Physics, 2/e (Hardcover)
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商品描述
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.
Features
Content
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 Relationship of Quaternions to Rotations
10.3 A
Linear Algebraic Approach.
10.4 From Rotation Matrices to
Quaternions
10.4.1 Introduction
10.4.2 2D Rotations.
10.4.3 Linearity.
10.4.4 3D Rotations: Geometry
10.4.5 4D Rotations.
10.4.6 3D
Rotations: Algebra.
10.4.7 4D Matrix
10.4.8 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