Continuous penalty forces

Abstract

We present a simple algorithm to compute continuous penalty forces to determine collision response between rigid and deformable models bounded by triangle meshes. Our algorithm computes a well-behaved solution in contrast to the traditional stability and robustness problems of penalty methods, induced by force discontinuities. We trace contact features along their deforming trajectories and accumulate penalty forces along the penetration time intervals between the overlapping feature pairs. Moreover, we present a closed-form expression to compute the continuous and smooth collision response. Our method has very small additional overhead compared to previous penalty methods, and can significantly improve the stability and robustness. We highlight its benefits on several benchmarks.

References

1. Allard, J., Faure, F., Courtecuisse, H., Falipou, F., Duriez, C., and Kry, P. G. 2010. Volume contact constraints at arbitrary resolution. ACM Transactions on Graphics 29, 3.
2. Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. In Proc. of ACM SIGGRAPH, 43--54.
3. Barbič, J., and James, D. L. 2008. Six-DoF haptic rendering of contact between geometrically complex reduced deformable models. IEEE Transactions on Haptics 1, 1, 39--52.
4. Bridson, R., Fedkiw, R., and Anderson, J. 2002. Robust treament for collisions, contact and friction for cloth animation. In Proc. of ACM SIGGRAPH, 594--603.
5. Choi, K.-J., and Ko, H.-S. 2002. Stable but responsive cloth. In Proc. of ACM SIGGRAPH, 604--611.
6. Drumwright, E. 2008. A fast and stable penalty method for rigid body simulation. IEEE Transactions on Visualization and Computer Graphics 14 (January), 231--240.
7. Duriez, C., Andriot, C., and Kheddar, A. 2004. Signorini's contact model for deformable objects in haptic simulations. In Proc. of IEEE Int'l Conf. Intelligent Robots and Systems, 3232--3237.
8. Duriez, C., Dubois, F., Kheddar, A., and Andriot, C. 2006. Realistic haptic rendering of interacting deformable objects in virtual environments. IEEE Transactions on Visualization and Computer Graphics 12, 1, 36--47.
9. Ellis, R. E., Sarkar, N., and Jenkins, M. A. 1997. Numerical methods for the force reflection of contact. ASME Transactions on Dynamic Systems Measurement and Control 119, 4, 768--774.
10. Faure, F., Barbier, S., Allard, J., and Falipou, F. 2008. Image-based collision detection and response between arbitrary volumetric objects. In Proc. of ACM Siggraph/Eurographics Symp. on Computer Animation, 155--162.
11. Fisher, S., and Lin, M. C. 2001. Deformed distance fields for simulation of non-penetrating flexible bodies. In Proc. of Eurographic workshop on Computer animation & simulation, 99--111.
12. Harmon, D., Vouga, E., Smith, B., Tamstorf, R., and Grinspun, E. 2009. Asynchronous contact mechanics. In Proc. of ACM SIGGRAPH, 87:1--87:12.
13. Harmon, D., Zhou, Q., and Zorin, D. 2011. Asynchronous integration with phantom meshes. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA '11, 247--256.
14. Hasegawa, S., and Sato, M. 2004. Real-time rigid body simulation for haptic interactions based on contact volume of polygonal objects. Computer Graphics Forum 23, 3, 529--538.
15. Heidelberger, B., Teschner, M., Keiser, R., Müller, M., and Gross, M. 2004. Consistent penetration depth estimation for deformable collision response. In Proc. of Vision, Modeling, Visualization, 339--346.
16. Irving, G., Teran, J., and Fedkiw, R. 2004. Invertible finite elements for robust simulation of large deformation. In Proceedings of the 2004 ACM SIGGRAPH/Eurographics symposium on Computer animation, Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, SCA '04, 131--140.
17. Mahvash, M., and Hayward, V. 2005. High-fidelty passive force-reflecting virtual environments. IEEE Transactions on Robotics 21, 1, 38--46.
18. Mirtich, B. 1996. Impulse-based Dynamic Simulation of Rigid Body Systems. Ph. D. thesis, Dept. Elec. Engin. Comput. Sci., Univ. California, Berkeley, CA.
19. Moore, M., and Wilhelms, J. 1988. Collision detection and response for computer animation. In Proc. of ACM SIGGRAPH, 289--298.
20. Ortega, M., Redon, S., and Coquillart, S. 2007. A six degree-of-freedom god-object method for haptic display of rigid bodies with surface properties. IEEE Transactions on Visualization and Computer Graphics 13, 458--469.
21. Otaduy, M. A., Tamstorf, R., Steinemann, D., and Gross, M. 2009. Implicit contact handling for deformable objects. In Proc. of Eurographics, 559--568.
22. Pauly, M., Pai, D. K., and Guibas, L. J. 2004. Quasirigid objects in contact. In Proc. of the 2004 ACM SIGGRAPH/Eurographics Symp. Computer animation, 109--119.
23. Provot, X. 1997. Collision and self-collision handling in cloth model dedicated to design garment. Graphics Interface, 177--189.
24. Redon, S., Kim, Y. J., Lin, M. C., and Manocha, D. 2004. Fast continuous collision detection for articulated models. In Proceedings of the ninth ACM symposium on Solid modeling and applications, 145--156.
25. Rengifo, C., Aoustin, Y., Chevallereau, C., and Plestan, F. 2009. A penalty-based approach for contact forces computation in bipedal robots. In Proc. of IEEE-RAS Int'l Conf. on Humanoid Robots, 121--127.
26. Tang, M., Curtis, S., Yoon, S.-E., and Manocha, D. 2009. ICCD: Interactive continuous collision detection between deformable models using connectivity-based culling. IEEE Transactions on Visualization and Computer Graphics 15, 4, 544--557.
27. Teran, J., Sifakis, E., Irving, G., and Fedkiw, R. 2005. Robust quasistatic finite elements and flesh simulation. In Proc. of the ACM SIGGRAPH/Eurographics Symp. on Computer animation, 181--190.
28. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. In Proc. of ACM SIGGRAPH, 205--214.
29. Teschner, M., Kimmerle, S., Heidelberger, B., Zachmann, G., Raghupathi, L., Fuhrmann, A., p. Cani, M., Faure, F., Magnenat-thalmann, N., Strasser, W., and Volino, P. 2005. Collision detection for deformable objects. Computer Graphics Forum 24, 61--81.
30. Witkin, A., and Baraff, D. 1997. Physically based modeling: Principles and practice. SIGGRAPH 1997 Course.
31. Wriggers, P., Vu Van, T., and Stein, E. 1990. Finite element formulation of large deformation impact-contact problems with friction. Computers & Structures 37, 3, 319--331.
32. Wriggers, P. 2006. Computational Contact Mechanics, 2nd Edition. Springer.
33. Yamane, K., and Nakamura, Y. 2006. Stable penalty-based model of frictional contacts. In Proc. of IEEE Int'l Conf. on Robotics and Automation, 1904--1909.
34. Zhang, L., Kim, Y. J., Varadhan, G., and Manocha, D. 2007. Generalized penetration depth computation. Comput. Aided Des. 39, 625--638.

Index Terms

• Computing methodologies

  • Computer graphics

    • Animation

      • Physical simulation

    • Shape modeling

• Mathematics of computing

  • Continuous mathematics

    • Topology

      • Geometric topology