Efficient and accurate interference detection for polynomial deformation

We present efficient and accurate algorithms for interference detection among objects undergoing polynomial deformation. The scope of our algorithms include physically-based models undergoing dynamic simulation subject to non-penetration constraints, variational models, deformable models used in soft object animation, geometric models including polygonal meshes, parametric surfaces such as Bezier patches and B-splines, and solid models defined by such surfaces. Our algorithms use axis aligned bounding boxes and convex hulls of the objects to identify the object pairs in close vicinity. They use subdivision, convex hull properties and linear programming to perform surface intersection tests and loop intersection tests. Frame-to-frame coherence is utilized to achieve incremental computations. The resulting algorithms have been implemented and work well in practice. In particular we are able to compute all contacts accurately and at interactive speeds for flexible bodies undergoing second-order polynomial deformations.

[1]  Dinesh Manocha,et al.  A new approach for surface intersection , 1991, SMA '91.

[2]  Michael E. Hohmeyer.  A surface intersection algorithm based on loop detection , 1991, Int. J. Comput. Geom. Appl..

[3]  Demetri Terzopoulos,et al.  Modeling inelastic deformation: viscolelasticity, plasticity, fracture , 1988, SIGGRAPH.

[4]  Christoph M. Hoffmann,et al.  Geometric and Solid Modeling: An Introduction , 1989 .

[5]  Daniel Thalmann,et al.  An Adaptive Spatial Subdivision of the Object Space for Fast Collision Detection of Animated Rigid Bodies , 1995, Comput. Graph. Forum.

[6]  Ming C. Lin,et al.  A fast algorithm for incremental distance calculation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[7]  F. Frances Yao,et al.  Computational Geometry , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[8]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

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

[10]  D. Manocha,et al.  Fast Polygon Triangulation Based on Seidel's Algorithm , 1995 .

[11]  Christoph M. Hoffmann,et al.  Geometric and Solid Modeling , 1989 .

[12]  Dinesh Manocha,et al.  Incremental Algorithms for Collision Detection Between General Solid Models , 1994 .

[13]  Alex Pentland,et al.  Computational complexity versus virtual worlds , 1990, I3D '90.

[14]  David R. Forsey,et al.  Hierarchical B-spline refinement , 1988, SIGGRAPH.

[15]  Andrew P. Witkin,et al.  Fast animation and control of nonrigid structures , 1990, SIGGRAPH.

[16]  John M. Snyder,et al.  Interval methods for multi-point collisions between time-dependent curved surfaces , 1993, SIGGRAPH.

[17]  Ken-ichi Anjyo,et al.  Hair animation with collision detection , 1993 .

[18]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[19]  Dinesh Manocha,et al.  Incremental algorithms for collision detection between solid models , 1995, Symposium on Solid Modeling and Applications.

[20]  Alan H. Barr,et al.  Geometric collisions for time-dependent parametric surfaces , 1990, SIGGRAPH.

[21]  Sabine Coquillart,et al.  Extended free-form deformation: a sculpturing tool for 3D geometric modeling , 1990, SIGGRAPH.

[22]  Tom Duff,et al.  Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry , 1992, SIGGRAPH.

[23]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[24]  Nadia Magnenat-Thalmann,et al.  Versatile and efficient techniques for simulating cloth and other deformable objects , 1995, SIGGRAPH.

[25]  Daniel Thalmann,et al.  Dressing animated synthetic actors with complex deformable clothes , 1992, SIGGRAPH.

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

[27]  Andrew P. Witkin,et al.  Variational surface modeling , 1992, SIGGRAPH.

[28]  Nadia Magnenat-Thalmann,et al.  Efficient self‐collision detection on smoothly discretized surface animations using geometrical shape regularity , 1994, Comput. Graph. Forum.

[29]  Dinesh Manocha,et al.  SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS , 2002 .

[30]  Dinesh Manocha,et al.  An efficient surface intersection algorithm based on lower-dimensional formulation , 1997, TOGS.

[31]  Alan Watt,et al.  Advanced animation and rendering techniques , 1992 .

[32]  Dinesh Manocha,et al.  I-COLLIDE: an interactive and exact collision detection system for large-scale environments , 1995, I3D '95.

[33]  Raimund Seidel,et al.  Linear programming and convex hulls made easy , 1990, SCG '90.

[34]  John C. Platt,et al.  Elastically deformable models , 1987, SIGGRAPH.

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

[36]  Alex Pentland,et al.  Good vibrations: modal dynamics for graphics and animation , 1989, SIGGRAPH.

[37]  Ying Yang,et al.  An improved algorithm for collision detection in cloth animation with human body , 1993 .

[38]  Hong Qin,et al.  Dynamic NURBS with geometric constraints for interactive sculpting , 1994, TOGS.

[39]  John F. Hughes,et al.  Direct manipulation of free-form deformations , 1992, SIGGRAPH.

[40]  Dinesh Manocha,et al.  Computing selected solutions of polynomial equations , 1994, ISSAC '94.

[41]  Dinesh Manocha,et al.  Interference Detection Between Curved Objects for Computer Animation , 1993 .

[42]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[43]  Jane Wilhelms,et al.  Collision Detection and Response for Computer Animation , 1988, SIGGRAPH.

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

[45]  Andrew P. Witkin,et al.  Dynamic simulation of non-penetrating flexible bodies , 1992, SIGGRAPH.