Game Physics Pearls

Implementing physical simulations for real-time games is a complex task that requires a solid understanding of a wide range of concepts from the fields of mathematics, physics, and software engineering. This book is a gems-like collection of practical articles in the area of game physics. Each provides hands-on detail that can be used in practical applications. The chapters cover topics such as collision detection, particle-based simulations, constraint solving, and soft-body simulation. There is an introductory section that provides the mathematical foundations and offers some background for the problems inherent in successful physics simulation. The contributors write based on their experience in developing tools and runtime libraries either in game companies or middleware houses that produce physics software for games on PCs and consoles Content: 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.