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GAME PHYSICS 101 Mathematical Background Introduction Vectors and Points Lines and Planes Matrices and Transformations Quaternions Rigid-Body Dynamics Numerical Integration Further Reading Understanding Game Physics Artifacts Introduction Discretizalion and Linearization Time Stepping and the Well of Despair The Curse of Rotations Solver Collision Detection Joints Direct Animation Artifact Reference COLLISION DETECTION Broad Phase and Constraint Optimization for PlayStation 3 Introduction Overview of CellBE Optimization of the Broad Phase Optimization of the Constraint Solver Conclusion SAT in Narrow Phase and Contact-Manifold Generation Introduction Contact Manifold Physics Engine Pipeline SAT Basics Intuitive Gauss Map Computing Full Contact Manifolds SAT Optimizations Smooth Mesh Contacts with GJK Introduction Configuration Space Support Mappings Overview of GJK Johnson's Algorithm Continuous Collision Detection Contacts Conclusion PARTICLES Optimized SPH Introduction The SPH Equations An Algorithm for SPH Simulation The Choice of Data Structure Collapsing the SPH Algorithm Stability and Behavior Performance Conclusion Appendix: Scaling the Pressure Force Parallelizing Particle-Based Simulation on Multiple Processors Introduction Dividing Computation Data Management without Duplication Choosing an Acceleration Structure Data Transfer Using Grids Results Conclusion CONSTRAINT SOLVING Ropes as Constraints Introduction Free-Hanging Ropes Strained Ropes Quaternion-Based Constraints Introduction Notation and Definitions The Problem Constraint Definitions Matrix-Based Quaternion Algebra A New Tale on Quaternion-Based Constraints Why It Works More General Frames Limits and Drivers Examples Conclusion SOFT BODY Soft Bodies Using Finite Elements Introduction Continuum Mechanics Linear FEM Solving the Linear System Surface-Mesh Update Particle-Based Simulation Using Verlet Integration Introduction Techniques for Numerical Integration Using Relaxation to Solve Systems of Equations Rigid Bodies Articulated Bodies Miscellaneous Conclusion Keep Yer Shirt On Introduction Stable Real-Time Cloth Modeling Real Fabrics Performance Order of Cloth Update Stages Conclusion, Results, and Future SKINNING Layered Skin Simulation Introduction Layered Deformation Architecture Smooth Skinning Anatomical Collisions Relaxalion Jiggle Conclusion Dynamic Secondary Skin Deformations Introduction The Interaction Model Neighborhood Interaction Volumetric Effects Final Remarks Index A Bibliography appears at the end of each chapter.
Gino van den Bergen is an experienced 3D graphics and geometry developer working at DTECTA, which offers middleware for collision detection and custom 3D software development. He has over 15 years of experience programming 3D applications in C++ and 5 years of programming experience in the game industry. He earned a Ph.D. in computing science from Eindhoven University of Technology. Dirk Gregorius is a contractor for game studios, middleware vendors, and publishers. He has extensive experience in the computer game industry, having worked at Havok and Factor 5, where he was responsible for cloth and rigid body physics.
A fine, technical guide for any computer programmer or gamer interested in knowing more about the physics behind sports and games. -The Midwest Book Review, February 2012