A Time-Dependent Inclusion-Based Method for Continuous Collision Detection between Parametric Surfaces
Article No.: 223, Pages 1 - 11
Abstract
Continuous collision detection (CCD) between parametric surfaces is typically formulated as a five-dimensional constrained optimization problem. In the field of CAD and computer graphics, common approaches to solving this problem rely on linearization or sampling strategies. Alternatively, inclusion-based techniques detect collisions by employing 5D inclusion functions, which are typically designed to represent the swept volumes of parametric surfaces over a given time span, and narrowing down the earliest collision moment through subdivision in both spatial and temporal dimensions. However, when high detection accuracy is required, all these approaches significantly increases computational consumption due to the high-dimensional searching space. In this work, we develop a new time-dependent inclusion-based CCD framework that eliminates the need for temporal subdivision and can speedup conventional methods by a factor ranging from 36 to 138. To achieve this, we propose a novel time-dependent inclusion function that provides a continuous representation of a moving surface, along with a corresponding intersection detection algorithm that quickly identifies the time intervals when collisions are likely to occur. We validate our method across various primitive types, demonstrate its efficacy within the simulation pipeline and show that it significantly improves CCD efficiency while maintaining accuracy.
References
[1]
Robert Bridson, Ronald Fedkiw, and John Anderson. 2002. Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. Graph. 21, 3 (jul 2002), 594--603.
[2]
Tyson Brochu, Essex Edwards, and Robert Bridson. 2012. Efficient geometrically exact continuous collision detection. ACM Trans. Graph. 31, 4, Article 96 (jul 2012), 7 pages.
[3]
Christoph Buchenau and Michael Guthe. 2021. Real-Time Curvature-aware Re-Parametrization and Tessellation of Bézier Surfaces. In Vision, Modeling, and Visualization, Bjoern Andres, Marcel Campen, and Michael Sedlmair (Eds.). The Eurographics Association.
[4]
R. P. R. Cardoso and O. B. Adetoro. 2017. On contact modelling in isogeometric analysis. European Journal of Computational Mechanics 26, 5--6 (2017), 443--472.
[5]
J. Austin Cottrell, Thomas J. R. Hughes, and Yuri Bazilevs. 2009. Isogeometric Analysis: Toward Integration of CAD and FEA (1st ed.). Wiley Publishing, Hoboken, NJ, USA.
[6]
Octave Crespel, Emile Hohnadel, Thibaut Metivet, and Florence Bertails-Descoubes. 2024. Contact detection between curved fibres: high order makes a difference. ACM Trans. Graph. 43, 4, Article 132 (jul 2024), 23 pages.
[7]
Alexander Efremov, Vlastimil Havran, and Hans-Peter Seidel. 2005. Robust and numerically stable Bézier clipping method for ray tracing NURBS surfaces. In Proceedings of the 21st Spring Conference on Computer Graphics (Budmerice, Slovakia) (SCCG '05). Association for Computing Machinery, New York, NY, USA, 127--135.
[8]
Zachary Ferguson, Pranav Jain, Denis Zorin, Teseo Schneider, and Daniele Panozzo. 2023. High-Order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes. In ACM SIGGRAPH 2023 Conference Proceedings (Los Angeles, CA, USA) (SIGGRAPH '23). Association for Computing Machinery, New York, NY, USA, Article 77, 11 pages.
[9]
Zachary Ferguson, Minchen Li, Teseo Schneider, Francisca Gil-Ureta, Timothy Langlois, Chenfanfu Jiang, Denis Zorin, Danny M. Kaufman, and Daniele Panozzo. 2021. Intersection-free Rigid Body Dynamics. ACM Transactions on Graphics (SIGGRAPH) 40, 4, Article 183 (2021).
[10]
A. Galligo and J. P. Pavone. 2006. A sampling algorithm computing self-intersections of parametric surfaces. In Algebraic Geometry and Geometric Modeling, Mohamed Elkadi, Bernard Mourrain, and Ragni Piene (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 185--204.
[11]
Stefan Gottschalk. 1996. Separating axis theorem.
[12]
David Harmon, Etienne Vouga, Rasmus Tamstorf, and Eitan Grinspun. 2008. Robust treatment of simultaneous collisions. In ACM SIGGRAPH 2008 Papers (Los Angeles, California) (SIGGRAPH '08). Association for Computing Machinery, New York, NY, USA, Article 23, 4 pages.
[13]
M. Hughes, C. DiMattia, M.C. Lin, and D. Manocha. 1996. Efficient and accurate interference detection for polynomial deformation. In Proceedings Computer Animation '96. 155--166.
[14]
T.J.R. Hughes, J.A. Cottrell, and Y. Bazilevs. 2005. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering 194, 39 (2005), 4135--4195.
[15]
John Keyser, Tim Culver, Mark Foskey, Shankar Krishnan, and Dinesh Manocha. 2002. ESOLID---A System for Exact Boundary Evaluation. In Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications (Saarbrücken, Germany) (SMA '02). Association for Computing Machinery, New York, NY, USA, 23--34.
[16]
Minchen Li, Danny M. Kaufman, and Chenfanfu Jiang. 2021. Codimensional Incremental Potential Contact. ACM Trans. Graph. (SIGGRAPH) 40, 4, Article 170 (2021).
[17]
Jia Lu. 2011. Isogeometric contact analysis: Geometric basis and formulation for frictionless contact. Computer Methods in Applied Mechanics and Engineering 200, 5 (2011), 726--741.
[18]
Jia Lu and Chao Zheng. 2014. Dynamic cloth simulation by isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 268 (2014), 475--493.
[19]
Zoë Marschner, Paul Zhang, David Palmer, and Justin Solomon. 2021. Sum-of-squares geometry processing. ACM Trans. Graph. 40, 6, Article 253 (dec 2021), 13 pages.
[20]
Xingyu Ni, Xuwen Chen, Cheng yu, Bin Wang, and Baoquan Chen. 2024. Simulating Thin Shells by Bicubic Hermite Elements. Computer-Aided Design 174 (2024), 103734.
[21]
Les Piegl and Wayne Tiller. 1995. The NURBS book. Springer-Verlag, Berlin, Heidelberg.
[22]
Xavier Provot. 1997. Collision and self-collision handling in cloth model dedicated to design garments. In Computer Animation and Simulation. https://api.semanticscholar.org/CorpusID:7421415
[23]
Stéphane Redon, Abderrahmane Kheddar, and Sabine Coquillart. 2002. Fast Continuous Collision Detection between Rigid Bodies. Computer Graphics Forum 21, 3 (2002), 279--287. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/1467-8659.t01-1-00587
[24]
John M. Snyder. 1992. Interval analysis for computer graphics. In Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '92). Association for Computing Machinery, New York, NY, USA, 121--130.
[25]
John M. Snyder, Adam R. Woodbury, Kurt Fleischer, Bena Currin, and Alan H. Barr. 1993. Interval methods for multi-point collisions between time-dependent curved surfaces. In Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques (Anaheim, CA) (SIGGRAPH '93). Association for Computing Machinery, New York, NY, USA, 321--334.
[26]
Stefan Suwelack, Dimitar Lukarski, Vincent Heuveline, Rüdiger Dillmann, and Stefanie Speidel. 2013. Accurate surface embedding for higher order finite elements. In Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Anaheim, California) (SCA '13). Association for Computing Machinery, New York, NY, USA, 187--192.
[27]
Min Tang, Ruofeng Tong, Zhendong Wang, and Dinesh Manocha. 2014. Fast and exact continuous collision detection with Bernstein sign classification. ACM Trans. Graph. 33, 6, Article 186 (nov 2014), 8 pages.
[28]
M. Teschner, S. Kimmerle, B. Heidelberger, G. Zachmann, L. Raghupathi, A. Fuhrmann, M.-P. Cani, F. Faure, N. Magnenat-Thalmann, W. Strasser, and P. Volino. 2005. Collision Detection for Deformable Objects. Computer Graphics Forum 24, 1 (2005), 61--81.
[29]
Brian Von Herzen, Alan H. Barr, and Harold R. Zatz. 1990. Geometric collisions for time-dependent parametric surfaces. In Proceedings of the 17th Annual Conference on Computer Graphics and Interactive Techniques (Dallas, TX, USA) (SIGGRAPH '90). Association for Computing Machinery, New York, NY, USA, 39--48.
[30]
Bolun Wang, Zachary Ferguson, Xin Jiang, Marco Attene, Daniele Panozzo, and Teseo Schneider. 2022. Fast and Exact Root Parity for Continuous Collision Detection. Computer Graphics Forum (Proceedings of Eurographics) 41, 2 (2022), 9 pages.
[31]
Bolun Wang, Zachary Ferguson, Teseo Schneider, Xin Jiang, Marco Attene, and Daniele Panozzo. 2021. A Large-scale Benchmark and an Inclusion-based Algorithm for Continuous Collision Detection. ACM Trans. Graph. 40, 5, Article 188 (sep 2021), 16 pages.
[32]
Huamin Wang. 2014. Defending continuous collision detection against errors. ACM Trans. Graph. 33, 4, Article 122 (jul 2014), 10 pages.
[33]
Zhendong Wang, Min Tang, Ruofeng Tong, and Dinesh Manocha. 2015. TightCCD: Efficient and Robust Continuous Collision Detection using Tight Error Bounds. Computer Graphics Forum 34, 7 (2015), 289--298. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/cgf.12767
[34]
Ruicheng Xiong, Yang Lu, Cong Chen, Jiaming Zhu, Yajun Zeng, and Ligang Liu. 2023. ETER: Elastic Tessellation for Real-Time Pixel-Accurate Rendering of Large-Scale NURBS Models. ACM Trans. Graph. 42, 4, Article 133 (jul 2023), 13 pages.
[35]
Chee K. Yap. 2004. Robust geometric computation. In Handbook of Discrete and Computational Geometry, Second Edition, Jacob E. Goodman and Joseph O'Rourke (Eds.). Chapman and Hall/CRC, 927--952.
[36]
Paul Zhang, Zoë Marschner, Justin Solomon, and Rasmus Tamstorf. 2023a. Sum-of-Squares Collision Detection for Curved Shapes and Paths. In ACM SIGGRAPH 2023 Conference Proceedings (Los Angeles, CA, USA) (SIGGRAPH '23). Association for Computing Machinery, New York, NY, USA, Article 76, 11 pages.
[37]
Ran Zhang, Gang Zhao, Wei Wang, and Xiaoxiao Du. 2023b. Large deformation frictional contact formulations for isogeometric Kirchhoff-Love shell. International Journal of Mechanical Sciences 249 (2023), 108253.
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- A Time-Dependent Inclusion-Based Method for Continuous Collision Detection between Parametric Surfaces
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Published: 19 November 2024
Published in TOG Volume 43, Issue 6
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