Inner sphere trees for proximity and penetration queries

We present a novel geometric data structure for approximate collision detection at haptic rates between rigid objects. Our data structure, which we call inner sphere trees, supports different kinds of queries, namely, proximity queries and a new method for interpenetration computation, the penetration volume, which is related to the water displacement of the overlapping region and, thus, corresponds to a physically motivated force. The main idea is to bound objects from the inside with a set of non-overlapping spheres. Based on such sphere packings, a “inner bounding volume hierarchy” can be constructed. In order to do so, we propose to use an AI clustering algorithm, which we extend and adapt here. The results show performance at haptic rates both for proximity and penetration volume queries for models consisting of hundreds of thousands of polygons.

[1]  Philip M. Hubbard,et al.  Collision Detection for Interactive Graphics Applications , 1995, IEEE Trans. Vis. Comput. Graph..

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

[3]  Jérémie Allard,et al.  Image-based collision detection and response between arbitrary volume objects , 2008, SCA '08.

[4]  Thomas Villmann,et al.  Magnification control for batch neural gas , 2006, ESANN.

[5]  A. Schuermann.  On packing spheres into containers (about Kepler's finite sphere packing problem) , 2005, math/0506200.

[6]  René Weller.  A Benchmarking Suite for Static Collision Detection Algorithms , 2007 .

[7]  James F. O'Brien,et al.  Graphical modeling and animation of ductile fracture , 2002, SIGGRAPH '02.

[8]  Makoto Sato,et al.  Real‐time Rigid Body Simulation for Haptic Interactions Based on Contact Volume of Polygonal Objects , 2004, Comput. Graph. Forum.

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

[10]  Jessica K. Hodgins,et al.  Graphical modeling and animation of brittle fracture , 1999, SIGGRAPH.

[11]  Blake Hannaford,et al.  Stable haptic interaction with virtual environments , 1999, IEEE Trans. Robotics Autom..

[12]  Ernesto G. Birgin,et al.  Minimizing the object dimensions in circle and sphere packing problems , 2008, Comput. Oper. Res..

[13]  Leonidas J. Guibas,et al.  Collision detection for deforming necklaces , 2002, SCG '02.

[14]  Ming C. Lin,et al.  Fast penetration depth estimation for elastic bodies using deformed distance fields , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[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]  Ming C. Lin,et al.  Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition , 2001, Comput. Graph. Forum.

[17]  Elaine Cohen,et al.  A framework for efficient minimum distance computations , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[18]  Carol O'Sullivan,et al.  Adaptive medial-axis approximation for sphere-tree construction , 2004, TOGS.

[19]  Ming C. Lin,et al.  Author manuscript, published in "Journal of graphics tools (2006)" A Fast Method for Local Penetration Depth Computation , 2009 .

[20]  Gino van den Bergen.  Proximity Queries and Penetration Depth Computation on 3D Game Objects , 2001 .

[21]  Thomas Villmann,et al.  Batch and median neural gas , 2006, Neural Networks.

[22]  Carol O'Sullivan,et al.  Interruptible collision detection for deformable objects , 2006, Comput. Graph..

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

[24]  Elmer G. Gilbert,et al.  Growth distances: new measures for object separation and penetration , 1996, IEEE Trans. Robotics Autom..

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

[26]  Jernej Barbic,et al.  Six-DoF Haptic Rendering of Contact Between Geometrically Complex Reduced Deformable Models , 2008, IEEE Transactions on Haptics.

[27]  Dan Morris.  Algorithms and Data Structures for Haptic Rendering: Curve Constraints, Distance Maps, and Data Logging , 2007 .

[28]  Bernd Gärtner,et al.  Fast and Robust Smallest Enclosing Balls , 1999, ESA.

[29]  Dinesh Manocha,et al.  Generalized penetration depth computation , 2006, SPM '06.

[30]  Thomas Martinetz,et al.  'Neural-gas' network for vector quantization and its application to time-series prediction , 1993, IEEE Trans. Neural Networks.