VolCCD: Fast continuous collision culling between deforming volume meshes

Abstract

We present a novel culling algorithm to perform fast and robust continuous collision detection between deforming volume meshes. This includes a continuous separating axis test that can conservatively check whether two volume meshes overlap during a given time interval. In addition, we present efficient methods to eliminate redundant elementary tests between the features (e.g., vertices, edges, and faces) of volume elements (e.g., tetrahedra, hexahedra, triangular prisms, etc.). Our approach is applicable to various deforming meshes, including those with changing topologies, and efficiently computes the first time of contact. We are able to perform inter-object and intra-object collision queries in models represented with tens of thousands of volume elements at interactive rates on a single CPU core. Moreover, we observe more than an order of magnitude performance improvement over prior methods.

References

1. ABAQUS. 2003. ABAQUS 6.4. Analysis User's Manual. Hibbitt, Karlsson & Sorensen, Inc.
2. Allard, J., Faure, F., Courtecuisse, H., Falipou, F., Duriez, C., and Kry, P. G. 2010. Volume contact constraints at arbitrary resolution. In Proceedings of the ACM SIGGRAPH Conference. ACM, 1--10.
3. Bridson, R., Fedkiw, R., and Anderson, J. 2002. Robust treatment of collisions, contact and friction for cloth animation. ACM Trans. Graph. 21, 3, 594--603.
4. Curtis, S., Tamstorf, R., and Manocha, D. 2008. Fast collision detection for deformable models using representative-triangles. In Proceedings of the Symposium on Interactive 3D Graphics and Games. 61--69.
5. Eberly, D. H. 2000. 3D Game Engine Design: A Practical Approach to Real-Time Computer Graphics. Morgan Kaufmann.
6. Erleben, K., Dohlmann, H., and Sporring, J. 2005. The adaptive thin shell tetrahedral mesh. In J. WSCG. 17--24.
7. Faure, F., Barbier, S., Allard, J., and Falipou, F. 2008. Image-based collision detection and response between arbitrary volume objects. In Proceedings of the Symposium on Computer Animation. 155--162.
8. Fisher, S. and Lin, M. C. 2001. Deformed distance fields for simulation of non-penetrating flexible bodies. In Proceedings of the Eurographic Workshop on Computer Animation and Simulation. Springer, 99--111.
9. Fleissner, F., Eberhard, P., Bischof, C., Bcker, M., Gibbon, P., Joubert, G. R., Mohr, B., (eds, F. P., Fleissner, F., and Eberhard, P. 2007. Load balanced parallel simulation of particle-fluid dem-sph systems with moving boundaries. In Proceedings of Parallel Computing: Architectures, Algorithms and Applications Conference. 37--44.
10. Gottschalk, S., Lin, M., and Manocha, D. 1996. OBB-Tree: A hierarchical structure for rapid interference detection. In Proceedings of ACM Siggraph Conference. 171--180.
11. Govindaraju, N., Knott, D., Jain, N., Kabul, I., Tamstorf, R., Gayle, R., Lin, M., and Manocha, D. 2005. Interactive collision detection between deformable models using chromatic decomposition. ACM Trans. Graph. 24, 3, 991--999.
12. Hallquist, J. 2006. LS-DYNA Theory Manual. Livermore Software Technology Corporation.
13. Heidelberger, B., Teschner, M., and Gross, M. 2003. Real-time volumetric intersections of deforming objects. In Proceedings of Vision Modeling Visualization Conference (VMV'03). 461--468.
14. Heidelberger, B., Teschner, M., Keiser, R., Müller, M., and Gross, M. 2004. Consistent peneration depth estimation for deformable collision response. In Proceedings of Vision Modeling Visualization Conference (VMV'04). 330--346.
15. Heo, J.-P., Seong, J.-K., Kim, D., Otaduy, M. A., Hong, J.-M., Tang, M., and Yoon, S.-E. 2010. FASTCD: Fracturing-Aware stable collision detection. In Proceedings of the ACM SIGGRAPH /Eurographics Symposium on Computer Animation.
16. Hutter, M. and Fuhrmann, A. 2007. Optimized continuous collision detection for deformable triangle meshes. In Proceedings of the WSCG '07. 25--32.
17. Irving, G., Teran, J., and Fedkiw, R. 2004. Invertible finite elements for robust simulation of large deformation. In Proceedings of the Symposium on Computer Animation. 131--140.
18. Klosowski, J., Held, M., Mitchell, J., Sowizral, H., and Zikan, K. 1998. Efficient collision detection using bounding volume hierarchies of k-dops. IEEE Trans. Vis. Comput. Graph. 4, 1, 21--37.
19. Levine, R. 2000. Collisions of moving objects. http://realtime collisiondetection.net/files/levine_swept_sat.txt.
20. Lombardo, J.-C., paule Cani, M., and Neyret, F. 1999. Real-time collision detection for virtual surgery. In Proceedings of the Symposium on Computer Animation. 26--28.
21. LS-DYNA. 2001. Contact modeling in LS-DYNA. http://www.dynasupport.com/tutorial/contact-modeling-in-ls-dyna/contact-types.
22. Mathias, E. and Gu, L. 2007. Hierarchical spatial hashing for real-time collision detection. In Proceedings of the IEEE International Conference on Shape Modeling and Applications. 61--70.
23. Müller, M., McMillan, L., Dorsey, J., and Jagnow, R. 2001. Real-time simulation of deformation and fracture of stiff materials. In Proceedings of the Eurographic Workshop on Computer Animation and Simulation. 113--124.
24. National-Crash-Analysis-Center. 2010. Finite element model archive. http://www.ncac.gwu.edu/vml/models.html.
25. Nealen, A., Müller, M., Keiser, R., Boxerman, E., and Carlson, M. 2006. Physically based deformable models in computer graphics. Comput. Graph. Forum 25, 4, 809--836.
26. O'Brien, J. F. 2000. Graphical modeling and animation of brittle fracture. Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
27. O'Brien, J. F. and Hodgins, J. K. 1999. Graphical modeling and animation of brittle fracture. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques. 137--146.
28. Parker, E. G. and O'Brien, J. F. 2009. Real-Time deformation and fracture in a game environment. In Proceedings of the Symposium on Computer Animation. 165--175.
29. Plimpton, S., Attaway, S., Hendrickson, B., Swegle, J., Vaughan, C., and Gardner, D. 1998. Parallel transient dynamics simulations: Algorithms for contact detection and smoothed particle hydrodynamics. J. Parall. Distrib. Comput. 50, 1-2, 104--122.
30. Provot, X. 1997. Collision and self-collision handling in cloth model dedicated to design garment. In Proceedings of the Graph. Interface Conference. 177--189.
31. Redon, S., Kheddar, A., and Coquillart, S. 2002. Fast continuous collision detection between rigid bodies. Comput. Graph. Forum. 21, 3, 279--288.
32. Sifakis, E., Der, K. G., and Fedkiw, R. 2007. Arbitrary cutting of deformable tetrahedralized objects. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 73--80.
33. Sud, A., Govindaraju, N., Gayle, R., Kabul, I., and Manocha, D. 2006. Fast proximity computation among deformable models using discrete voronoi diagrams. In Proceedings of the ACM SIGGRAPH Conference. 1144--1153.
34. Tang, M., Curtis, S., Yoon, S.-E., and Manocha, D. 2009. ICCD: Interactive continuous collision detection between deformable models using connectivity-based culling. IEEE Trans. Vis. Comput. Graph. 15, 4, 544--557.
35. Tang, M., Kim, Y. J., and Manocha, D. 2010b. Continuous collision detection for non-rigid contact computations using local advancement. In Proceedings of International Conference on Robotics and Automation.
36. Tang, M., Manocha, D., Lin, J., and Tong, R. 2011. Collision-streams: Fast GPU-based collision detection for deformable models. In Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (I3D'11). 63--70.
37. Tang, M., Manocha, D., and Tong, R. 2010a. Fast continuous collision detection using deforming non-penetration filters. In Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games (I3D'10). ACM, New York, 7--13.
38. Teschner, M., Heidelberger, B., Müller, M., Pomeranets, D., and Gross, M. 2003. Optimized spatial hashing for collision detection of deformable objects. In Proceedings of Vision Modeling Visualization Conference (VMV'03). 47--54.
39. Teschner, M., Kimmerle, S., Heidelberger, B., Zachmann, G., Raghupathi, L., Fuhrmann, A., Cani, M.-P., Faure, F., Magnenat-Thalmann, N., Strasser, W., and Volino, P. 2005. Collision detection for deformable objects. Comput. Graph. Forum 19, 1, 61--81.
40. Volino, P. and Magnenat-Thalmann, N. 2006. Resolving surface collisions through intersection contour minimization. ACM Trans. Graph. 25, 3, 1154--1159.
41. Volino, P. and Thalmann, N. M. 1994. Efficient self-collision detection on smoothly discretized surface animations using geometrical shape regularity. Comput. Graph. Forum 13, 3, 155--166.
42. Wojtan, C., Thürey, N., Gross, M., and Turk, G. 2009. Deforming meshes that split and merge. ACM Trans. Graph. 28, 76:1--76:10.
43. Zhang, X., Redon, S., Lee, M., and Kim, Y. J. 2007. Continuous collision detection for articulated models using taylor models and temporal culling. ACM Trans. Graph. 26, 3, 15.
44. Zhu, Y., Sifakis, E., Teran, J., and Brandt, A. 2010. An efficient multigrid method for the simulation of high-resolution elastic solids. ACM Trans. Graph. 29, 2, 1--18.

Index Terms

• Computing methodologies

  • Computer graphics

    • Animation

      • Physical simulation

    • Shape modeling

• Mathematics of computing

  • Continuous mathematics

    • Topology

      • Geometric topology