Inner Sphere Trees

In this chapter, we present our novel geometric data structure, the Inner Sphere Trees. It is the first data structure that is able to compute the penetration volume between a pair of colliding objects at haptic rates. This new contact information guarantees physically-plausible and continuous forces and torques for a stable collision response that is essential for stable haptic rendering. Moreover, we propose a new clustering-based algorithm for creating bounding volume hierarchies and a time-critical traversal scheme for time-budgeted collision detection scenarios.

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

[2]  Dinesh Manocha,et al.  Fast penetration depth estimation using rasterization hardware and hierarchical refinement , 2003, SCG '03.

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

[4]  Michael Ortega-Binderberger,et al.  A Six Degree-of-Freedom God-Object Method for Haptic Display of Rigid Bodies with Surface Properties , 2007, IEEE Transactions on Visualization and Computer Graphics.

[5]  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).

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

[7]  Sun-Mog Hong,et al.  A fast procedure for computing incremental growth distances , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

[8]  Gabriel Zachmann,et al.  Inner sphere trees for proximity and penetration queries , 2009, Robotics: Science and Systems.

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

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

[11]  Dinesh Manocha,et al.  Fast 3D Geometric Proximity Queries between Rigid and Deformable Models Using Graphics Hardware Acceleration , 2002 .

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

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

[14]  David H. Eberly,et al.  Geometric Tools for Computer Graphics , 2002 .

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

[16]  Gabriel Zachmann,et al.  Inner Sphere Trees and Their Application to Collision Detection , 2008, Virtual Realities.

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

[18]  Shubhabrata Sengupta,et al.  Efficient Parallel Scan Algorithms for GPUs , 2011 .

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

[21]  Fuchang Liu,et al.  Real-time collision culling of a million bodies on graphics processing units , 2010, SIGGRAPH 2010.

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

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

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

[25]  Rene Weller,et al.  A unified approach for physically-based simulations and haptic rendering , 2009, Sandbox@SIGGRAPH.

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

[28]  Michael Garland,et al.  Designing efficient sorting algorithms for manycore GPUs , 2009, 2009 IEEE International Symposium on Parallel & Distributed Processing.

[29]  Dinesh Manocha,et al.  Incremental penetration depth estimation between convex polytopes using dual-space expansion , 2004, IEEE Transactions on Visualization and Computer Graphics.

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

[31]  Dinesh Manocha,et al.  Fast penetration depth computation for physically-based animation , 2002, SCA '02.

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

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

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

[35]  Hans-Peter Kriegel,et al.  Stable Haptic Interaction with Virtual Environments Using and Adapted Voxmap-PointShell Algorithm , 2001 .

[36]  Gabriel Zachmann,et al.  Rapid collision detection by dynamically aligned DOP-trees , 1998, Proceedings. IEEE 1998 Virtual Reality Annual International Symposium (Cat. No.98CB36180).

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

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

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

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

[41]  Pierre Terdiman,et al.  Memory-optimized bounding-volume hierarchies , 2001 .

[42]  Taku Komura,et al.  Topology matching for fully automatic similarity estimation of 3D shapes , 2001, SIGGRAPH.

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

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