FoldedGI: A highly parallel algorithm for interference detection by folding a geometry image into a 1D buffer

Abstract Detecting interference between two or more 3D models plays a critical role in computer animation and virtual reality. Typical approaches are bounding volume hierarchies and spatial partitioning trees, which are mainly carried out on CPUs. The conventional approaches, due to their hierarchical structure, cannot be fully parallelized. In this paper, we propose a highly parallel method, based on geometry images, for detecting interference in real time. Our method is inspired by two important observations - one is that interference between two 3D models can be converted into finding common colors contained in the couple of resulting geometry images, and the other is that the RGB space can be mapped onto a 1D buffer. Our algorithm, called FoldedGI, is parameter free, memory efficient and outperforms the state-of-the-art in terms of speed. We demonstrate its efficacy in dynamic interference detection, penetration depth computation and boolean operations between 3D objects.

[1]  Dinesh Manocha,et al.  Collision-streams: fast GPU-based collision detection for deformable models , 2011, SI3D.

[2]  Csaba D. Tóth Binary Space Partitions: recent Developments , 2007 .

[3]  Dinesh Manocha,et al.  Fast and reliable collision culling using graphics hardware , 2006, IEEE Transactions on Visualization and Computer Graphics.

[4]  Mark de Berg,et al.  Optimal Binary Space Partitions in the Plane , 2010, COCOON.

[5]  Wenping Wang,et al.  Efficient Collision Detection Using a Dual Bounding Volume Hierarchy , 2008, GMP.

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

[7]  B. R. Schlei,et al.  A new computational framework for 2D shape-enclosing contours , 2004, Image Vis. Comput..

[8]  Pedro V. Sander,et al.  Geometry videos: a new representation for 3D animations , 2003, SCA '03.

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

[10]  Lap-Pui Chau,et al.  Spectral Geometry Image: Image Based 3D Models for Digital Broadcasting Applications , 2011, IEEE Transactions on Broadcasting.

[11]  Ricardo Quirós,et al.  Binary space partitioning trees: a multiresolution approach , 1997, Proceedings. 1997 IEEE Conference on Information Visualization (Cat. No.97TB100165).

[12]  Ronald Fedkiw,et al.  Robust treatment of collisions, contact and friction for cloth animation , 2002, SIGGRAPH Courses.

[13]  Marcus A. Magnor,et al.  The Minimal Bounding Volume Hierarchy , 2010, VMV.

[14]  Robert Bridson,et al.  Efficient geometrically exact continuous collision detection , 2012, ACM Trans. Graph..

[15]  Wolfgang Straßer,et al.  Fast and Scalable CPU/GPU Collision Detection for Rigid and Deformable Surfaces , 2010, Comput. Graph. Forum.

[16]  Jeff Erickson,et al.  Greedy optimal homotopy and homology generators , 2005, SODA '05.

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

[18]  Dinesh Manocha,et al.  GPU accelerated convex hull computation , 2012, Comput. Graph..

[19]  Geoff Leach,et al.  An adaptive octree grid for GPU-based collision detection of deformable objects , 2014, The Visual Computer.

[20]  Andrew P. Witkin,et al.  Untangling cloth , 2003, ACM Trans. Graph..

[21]  Klaus Diepold,et al.  Content Adaptive Mesh Representation of Images Using Binary Space Partitions , 2009, IEEE Transactions on Image Processing.

[22]  Kurt Mehlhorn,et al.  Boolean Operations on 3D Selective Nef Complexes: Data Structure, Algorithms, and Implementation , 2003, ESA.

[23]  Scott Schaefer,et al.  Smooth Geometry Images , 2003, Symposium on Geometry Processing.

[24]  Andrew Y. C. Nee,et al.  Interactive robot trajectory planning and simulation using Augmented Reality , 2012 .

[25]  Karthik Ramani,et al.  Deep Learning 3D Shape Surfaces Using Geometry Images , 2016, ECCV.

[26]  Michael Manzke,et al.  Hardware accelerated construction of SAH-based bounding volume hierarchies for interactive ray tracing , 2012, I3D '12.

[27]  David Bommes,et al.  Quantized global parametrization , 2015, ACM Trans. Graph..

[28]  Dinesh Manocha,et al.  Quick-CULLIDE: fast inter- and intra-object collision culling using graphics hardware , 2005, IEEE Proceedings. VR 2005. Virtual Reality, 2005..

[29]  Dinesh Manocha,et al.  Interactive collision detection between deformable models using chromatic decomposition , 2005, SIGGRAPH 2005.

[30]  George Baciu,et al.  RECODE: an image-based collision detection algorithm , 1998, Proceedings Pacific Graphics '98. Sixth Pacific Conference on Computer Graphics and Applications (Cat. No.98EX208).

[31]  Steven J. Gortler,et al.  Geometry images , 2002, SIGGRAPH.

[32]  Young J. Kim,et al.  Interactive generalized penetration depth computation for rigid and articulated models using object norm , 2014, ACM Trans. Graph..

[33]  Kamran Iqbal,et al.  Collision detection: A survey , 2007, 2007 IEEE International Conference on Systems, Man and Cybernetics.

[34]  M. Nakajima,et al.  Geometry image matching for similarity estimation of 3D shapes , 2004 .

[35]  Yu Zhang,et al.  Exploit Bounding Box Annotations for Multi-Label Object Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[36]  Markus Hadwiger,et al.  Fused Multi‐Volume DVR using Binary Space Partitioning , 2009, Comput. Graph. Forum.

[37]  Dinesh Manocha,et al.  CULLIDE: interactive collision detection between complex models in large environments using graphics hardware , 2003, HWWS '03.

[38]  Bedrich Benes,et al.  GI-COLLIDE: collision detection with geometry images , 2005, SCCG '05.

[39]  Eitan Grinspun,et al.  Mesh arrangements for solid geometry , 2016, ACM Trans. Graph..

[40]  Pedro V. Sander,et al.  Multi-Chart Geometry Images , 2003, Symposium on Geometry Processing.

[41]  Yao Wang,et al.  Collision Detection Based on Bounding Box for NC Machining Simulation , 2012 .

[42]  Bochang Moon,et al.  RACBVHs: Random-Accessible Compressed Bounding Volume Hierarchies , 2010, IEEE Trans. Vis. Comput. Graph..

[43]  M. Floater Mean value coordinates , 2003, Computer Aided Geometric Design.