Guide to Dynamic Simulations of Rigid Bodies and Particle Systems

This book introduces the techniques needed to produce realistic simulations and animations of particle and rigid-body systems. The text focuses on both the theoretical and practical aspects of developing and implementing physically based dynamic-simulation engines. Each chapter examines numerous algorithms, describing their design and analysis in an accessible manner, without sacrificing depth of coverage or mathematical rigor. Features: examines the problem of computing an hierarchical representation of the geometric description of each simulated object, as well as the simulated world; discusses the use of discrete and continuous collision detection to handle thin or fast-moving objects; describes the computational techniques needed for determining all impulsive and contact forces between bodies with multiple simultaneous collisions and contacts; presents techniques that can be used to dynamically simulate articulated rigid bodies; concludes each chapter with exercises.

[1]  Hans-Peter Seidel,et al.  Directed Edges - A Scalable Representation for Triangle Meshes , 1998, J. Graphics, GPU, & Game Tools.

[2]  B. Joe.  Tetrahedral mesh generation in polyhedral regions based on convex polyhedron decompositions , 1994 .

[3]  Abhinandan Jain,et al.  Spatial Operator Algebra for multibody system dynamics , 1992 .

[4]  Generating Signed Distance Fields From Triangle Meshes , 2022 .

[5]  Michael M. Stark.  Efficient Construction of Perpendicular Vectors without Branching , 2009, J. Graphics, GPU, & Game Tools.

[6]  John J. Craig Zhu,et al.  Introduction to robotics mechanics and control , 1991 .

[7]  Michael Kallay,et al.  Computing the Moment of Inertia of a Solid Defined by a Triangle Mesh , 2006, J. Graph. Tools.

[8]  Gino van den Bergen.  A Fast and Robust GJK Implementation for Collision Detection of Convex Objects , 1999, J. Graphics, GPU, & Game Tools.

[9]  James K. Hahn,et al.  Realistic animation of rigid bodies , 1988, SIGGRAPH.

[10]  J A Sethian,et al.  A fast marching level set method for monotonically advancing fronts. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[11]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[12]  Georgios Papaioannou,et al.  Intersection Test for Collision Detection in Particle Systems , 1999, J. Graphics, GPU, & Game Tools.

[13]  Hiromasa Suzuki,et al.  Simulation of rigid body motion with impulsive friction force , 1997, Proceedings of the 1997 IEEE International Symposium on Assembly and Task Planning (ISATP'97) - Towards Flexible and Agile Assembly and Manufacturing -.

[14]  Brian Mirtich,et al.  Impulse-based dynamic simulation of rigid body systems , 1996 .

[15]  S. Sathiya Keerthi,et al.  A fast procedure for computing the distance between complex objects in three-dimensional space , 1988, IEEE J. Robotics Autom..

[16]  G. Dantzig,et al.  COMPLEMENTARY PIVOT THEORY OF MATHEMATICAL PROGRAMMING , 1968 .

[17]  Grit Thürmer,et al.  Computing Vertex Normals from Polygonal Facets , 1998, J. Graphics, GPU, & Game Tools.

[18]  J. Mark Keil,et al.  Polygon Decomposition , 2000, Handbook of Computational Geometry.

[19]  Per Lötstedt.  Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics , 1984 .

[20]  David Baraff,et al.  Coping with friction for non-penetrating rigid body simulation , 1991, SIGGRAPH.

[21]  James T. Kajiya,et al.  A symbolic method for calculating the integral properties of arbitrary nonconvex polyhedra , 1984, IEEE Computer Graphics and Applications.

[22]  B. Joe.  Delaunay Triangular Meshes in Convex Polygons , 1986 .

[23]  R. B. Simpson,et al.  Triangular meshes for regions of complicated shape , 1986 .

[24]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[25]  Bernard Chazelle,et al.  Convex Partitions of Polyhedra: A Lower Bound and Worst-Case Optimal Algorithm , 1984, SIAM J. Comput..

[26]  David Baraff,et al.  Fast contact force computation for nonpenetrating rigid bodies , 1994, SIGGRAPH.

[27]  R. Brach,et al.  Mechanical Impact Dynamics: Rigid Body Collisions , 1991 .

[28]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[29]  Luiz Velho,et al.  Implicit Objects in Computer Graphics , 2002, Springer New York.

[30]  Richard W. Cottle,et al.  Linear Complementarity Problem. , 1992 .

[31]  John C. Hart,et al.  Visualizing quaternion rotation , 1994, TOGS.

[32]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[33]  P. Gill,et al.  Maintaining LU factors of a general sparse matrix , 1987 .

[34]  Philip E. Gill,et al.  Numerically stable methods for quadratic programming , 1978, Math. Program..

[35]  J. Keller.  Impact With Friction , 1986 .

[36]  David Baraff,et al.  Dynamic Simulation of Non-penetrating Rigid Bodies , 1992 .

[37]  David Baraff,et al.  Issues in computing contact forces for non-penetrating rigid bodies , 1993, Algorithmica.

[38]  Brian Mirtich.  Rigid Body Contact: Collision Detection to Force Computation , 1998 .

[39]  Brian Mirtich,et al.  V-Clip: fast and robust polyhedral collision detection , 1998, TOGS.

[40]  Steven Skiena,et al.  The Algorithm Design Manual , 2020, Texts in Computer Science.

[41]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[42]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[43]  Stephen Cameron,et al.  Enhancing GJK: computing minimum and penetration distances between convex polyhedra , 1997, Proceedings of International Conference on Robotics and Automation.

[44]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[45]  R. Featherstone.  The Calculation of Robot Dynamics Using Articulated-Body Inertias , 1983 .

[46]  John F. Hughes,et al.  Building an Orthonormal Basis from a Unit Vector , 1999, J. Graphics, GPU, & Game Tools.

[47]  Thomas Lewiner,et al.  Efficient Implementation of Marching Cubes' Cases with Topological Guarantees , 2003, J. Graphics, GPU, & Game Tools.

[48]  Andrew S. Glassner.  Useful 3D geometry , 1990 .

[49]  David Baraff,et al.  Linear-time dynamics using Lagrange multipliers , 1996, SIGGRAPH.

[50]  Ferdinand Pierre Beer,et al.  Solutions manual to accompany, Vector mechanics for engineers : dynamics , 1977 .

[51]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[52]  Erwin Coumans.  Continuous Collision Detection and Physics , 2005 .

[53]  Ronen Barzel,et al.  A modeling system based on dynamic constraints , 1988, SIGGRAPH.

[54]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[55]  A. Witkin,et al.  Partitioned Dynamics , 1997 .

[56]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[57]  Ronald Fedkiw,et al.  Nonconvex rigid bodies with stacking , 2003, ACM Trans. Graph..

[58]  Ken Shoemake,et al.  Animating rotation with quaternion curves , 1985, SIGGRAPH.

[59]  David Baraff,et al.  Analytical methods for dynamic simulation of non-penetrating rigid bodies , 1989, SIGGRAPH.

[60]  Christopher Brinks,et al.  Physically-Based Modeling , 2011 .

[61]  Brian Mirtich,et al.  Fast and Accurate Computation of Polyhedral Mass Properties , 1996, J. Graphics, GPU, & Game Tools.

[62]  Jules Bloomenthal,et al.  An Implicit Surface Polygonizer , 1994, Graphics Gems.

[63]  Barry Joe,et al.  Delaunay versus max‐min solid angle triangulations for three‐dimensional mesh generation , 1991 .

[64]  David Baraff,et al.  Curved surfaces and coherence for non-penetrating rigid body simulation , 1990, SIGGRAPH.

[65]  Chandrajit L. Bajaj,et al.  Convex Decomposition of Polyhedra and Robustness , 1992, SIAM J. Comput..

[66]  Elmer G. Gilbert,et al.  The Gilbert-Johnson-Keerthi distance algorithm: a fast version for incremental motions , 1997, Proceedings of International Conference on Robotics and Automation.

[67]  Philip W. Sharp,et al.  Completely imbedded Runge-Kutta pairs , 1994 .

[68]  Joseph O'Rourke,et al.  Computational Geometry in C. , 1995 .

[69]  M. Alonso,et al.  Fundamental University Physics , 1967 .