Game Physics

Game Physics

by David H. Eberly
     
 

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

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Overview

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.

Product Details

ISBN-13:
9781558607408
Publisher:
Taylor & Francis
Publication date:
12/08/2003
Series:
The Morgan Kaufmann Series in Interactive 3D Technology
Edition description:
BK&CD-ROM
Pages:
816
Product dimensions:
7.14(w) x 9.56(h) x 1.24(d)

Table of Contents

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

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