Fast Proximity Queries with Swept Sphere Volumes

We present novel algorithms for fast proximity queries using swept sphere volumes. The set of proximity queries includes collision detection and both exact and approximate separation distance computation. We introduce a new family of bounding volumes that correspond to a core primitive shape grown outward by some o set. The set of core primitive shapes includes a point, line, and rectangle. This family of bounding volumes provides varying tightness of t to the underlying geometry. Furthermore, we describe e cient and accurate algorithms to perform di erent queries using these bounding volumes. We present a novel analysis of proximity queries that highlights the relationship between collision detection and distance computation. We also present traversal techniques for accelerating distance queries. These algorithms have been used to perform proximity queries for applications including virtual prototyping, dynamic simulation, and motion planning on complex models. As compared to earlier algorithms based on bounding volume hierarchies for separation distance and approximate distance computation, our algorithms Supported in part by ARO Contract DAAH04-96-1-0257, NSF Career Award CCR-9625217, NSF grants EIA-9806027 and DMI-9900157, ONR Young Investigator Award and Intel.

[1]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[2]  Peter E. Hart,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[3]  David G. Kirkpatrick,et al.  Fast Detection of Polyhedral Intersection , 1983, Theor. Comput. Sci..

[4]  James Arvo,et al.  A survey of ray tracing acceleration techniques , 1989 .

[5]  Eurographics Workshop on Animation and Simulation , 1990 .

[6]  Hans-Peter Kriegel,et al.  The R*-tree: an efficient and robust access method for points and rectangles , 1990, SIGMOD '90.

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

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

[9]  Emo Welzl,et al.  Smallest enclosing disks (balls and ellipsoids) , 1991, New Results and New Trends in Computer Science.

[10]  George Vanĕček,et al.  Collision Detection and Analysis in a Physically Based Simulation , 1991 .

[11]  Stephen Cameron,et al.  Approximation hierarchies and S-bounds , 1991, SMA '91.

[12]  Bernard Chazelle,et al.  An optimal algorithm for intersecting three-dimensional convex polyhedra , 1989, 30th Annual Symposium on Foundations of Computer Science.

[13]  Josep Tornero,et al.  Efficient distance calculation using the spherically-extended polytope (S-tope) model , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[14]  P. Gács,et al.  Algorithms , 1992 .

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

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

[17]  Jing Xiao,et al.  Towards obtaining all possible contacts-growing a polyhedron by its location uncertainty , 1994, Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'94).

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

[19]  Alejandro M. García-Alonso,et al.  Solving the collision detection problem , 1994, IEEE Computer Graphics and Applications.

[20]  Martin Held,et al.  Evaluation of Collision Detection Methods for Virtual Reality Fly-Throughs , 1995 .

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

[22]  Mark H. Overmars,et al.  Range Searching and Point Location among Fat Objects , 1996, J. Algorithms.

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

[24]  Leonidas J. Guibas,et al.  Fast collision detection among multiple moving spheres , 1997, SCG '97.

[25]  Dinesh Manocha,et al.  V-COLLIDE: accelerated collision detection for VRML , 1997, VRML '97.

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

[27]  Lydia E. Kavraki,et al.  On finding narrow passages with probabilistic roadmap planners , 1998 .

[28]  Dinesh Manocha,et al.  Spherical shell: a higher order bounding volume for fast proximity queries , 1998 .

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

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

[31]  Subhash Suri,et al.  Analysis of a bounding box heuristic for object intersection , 1999, SODA '99.

[32]  J William,et al.  IEEE Computer Graphics and Applications , 2019, Computer.