Game Physics

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.

IntroductionA Brief History of the WorldA Summary of the TopicsExamples and ExercisesBasic Concepts from PhysicsRigid Body ClassificationRigid Body KinematicsNewton’s LawsForcesMomentaEnergyRigid Body MotionNewtonian DynamicsLagrangian DynamicsEuler’s Equations of MotionDeformable BodiesElasticity, Stress, and StrainMass–Spring SystemsControl Point DeformationFree-Form DeformationImplicit Surface DeformationFluids and GasesVector CalculusStrain and StressConservation LawsA Simplified Model for Fluid FlowImplementing the Simplified 2D ModelImplementing the Simplified 3D ModelVariations of the Simplified ModelPhysics EnginesThe Physics TickCollision CullingTest-Intersection QueriesCollision Detection with Convex PolyhedraUnconstrained MotionAcceleration-Based Constrained MotionVelocity-Based Constrained MotionVariationsLinear AlgebraA Review of Number SystemsSystems of Linear EquationsMatricesVector SpacesAdvanced TopicsAffine AlgebraIntroductionCoordinate SystemsSubspacesTransformationsBarycentric CoordinatesCalculusUnivariate CalculusMultivariate CalculusApplicationsQuaternionsRotation MatricesThe Classical ApproachA Linear Algebraic ApproachInterpolation of QuaternionsDerivatives of Time-Varying QuaternionsDifferential EquationsFirst-Order EquationsExistence, Uniqueness, and Continuous DependenceSecond-Order EquationsGeneral-Order Differential EquationsSystems of Linear Differential EquationsEquilibria and StabilityOrdinary Difference EquationsDefinitionsLinear EquationsConstant Coefficient EquationsSystems of EquationsNumerical MethodsEuler’s MethodHigher-Order Taylor MethodsMethods via an Integral FormulationRunge–Kutta MethodsMultistep MethodsPredictor–Corrector MethodsExtrapolation MethodsVerlet IntegrationNumerical Stability and Its Relationship to Physical StabilityStiff EquationsLinear Complementarity and Mathematical ProgrammingLinear ProgrammingThe Linear Complementarity ProblemMathematical ProgrammingApplicationsContact Forces

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