Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition

The need to perform fast and accurate proximity queries arises frequently in physically‐based modeling, simulation, animation, real‐time interaction within a virtual environment, and game dynamics. The set of proximity queries include intersection detection, tolerance verification, exact and approximate minimum distance computation, and (disjoint) contact determination. Specialized data structures and algorithms have often been designed to perform each type of query separately. We present a unified approach to perform any of these queries seamlessly for general, rigid polyhedral objects with boundary representations which are orientable 2‐manifolds. The proposed method involves a hierarchical data structure built upon a surface decomposition of the models. Furthermore, the incremental query algorithm takes advantage of coherence between successive frames. It has been applied to complex benchmarks and compares very favorably with earlier algorithms and systems.

[1]  Nimrod Megiddo,et al.  Linear-Time Algorithms for Linear Programming in R^3 and Related Problems , 1982, FOCS.

[2]  Bernard Chazelle,et al.  Strategies for Polyhedral Surface Decomposition: an Experimental Study , 1997, Comput. Geom..

[3]  Philip M. Hubbard,et al.  Interactive collision detection , 1993, Proceedings of 1993 IEEE Research Properties in Virtual Reality Symposium.

[4]  David G. Kirkpatrick,et al.  Determining the Separation of Preprocessed Polyhedra - A Unified Approach , 1990, ICALP.

[5]  Raimund Seidel,et al.  On the difficulty of triangulating three-dimensional Nonconvex Polyhedra , 1992, Discret. Comput. Geom..

[6]  Leonidas J. Guibas,et al.  BOXTREE: A Hierarchical Representation for Surfaces in 3D , 1996, Comput. Graph. Forum.

[7]  Dinesh Manocha,et al.  Fast Proximity Queries with Swept Sphere Volumes , 1999 .

[8]  George Vanecek,et al.  Modeling contacts in a physically based simulation , 1993, Solid Modeling and Applications.

[9]  Ming C. Lin,et al.  Collision Detection between Geometric Models: A Survey , 1998 .

[10]  Leonidas J. Guibas,et al.  H-Walk: hierarchical distance computation for moving convex bodies , 1999, SCG '99.

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

[12]  John F. Canny,et al.  Impulse-based simulation of rigid bodies , 1995, I3D '95.

[13]  Joseph S. B. Mitchell,et al.  Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs , 1998, IEEE Trans. Vis. Comput. Graph..

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

[15]  Ming C. Lin,et al.  Efficient collision detection for animation and robotics , 1993 .

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

[17]  Bernard Chazelle,et al.  Triangulating a non-convex polytype , 1989, SCG '89.

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

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

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

[21]  N. Megiddo.  Linear-time algorithms for linear programming in R3 and related problems , 1982, FOCS 1982.

[22]  Dinesh Manocha,et al.  OBBTree: a hierarchical structure for rapid interference detection , 1996, SIGGRAPH.

[23]  Ming C. Lin,et al.  Accelerated proximity queries between convex polyhedra by multi-level Voronoi marching , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[24]  Ari Rappoport.  The extended convex difference tree (ECDT) representation for {$N$}-dimensional polyhedra , 1991, Int. J. Comput. Geom. Appl..

[25]  Sean Quinlan,et al.  Efficient distance computation between non-convex objects , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[26]  Nimrod Megiddo,et al.  Linear-time algorithms for linear programming in R3 and related problems , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).