David Harmon
Breannan Smith
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We develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameter-independent guarantees: that simulations of well-posed problems (a) have no interpenetrations, (b) obey causality, momentum- and energy-conservation laws, and (c) complete in finite time. We achieve these guarantees through a novel synthesis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two- and three-dimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geometries, sharp features, and sliding during extremely tight contact.
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Auxillary Materials
- Agarwal, P., Basch, J., Guibas, L. J., Hershberger, J., and Zhang, L. 2002. Deformable free space tilings for kinetic collision detection. Intl. J. Robotics Research 21, 179--197.Google Scholar
Cross Ref
- Agarwal, P., Guibas, L., Nguyen, A., Russel, D., and Zhang, L. 2004. Collision detection for deforming necklaces. Computational Geometry: Theory and Applications 28, 137--163. Google ScholarDigital Library
- Agarwal, P. K., Har-Peled, S., and Varadarajan, K. R. 2005. Geometric approximation via coresets. In Combinatorial and Computational Geometry, J. E. Goodman, J. Pach, and E. Welzl, Eds. Cambridge University Press, New York, 1--30.Google Scholar
- Ascher, U. M., and Petzold, L. R. 1998. Computer methods for ordinary differential equations and differential-algebraic equations. Society for Industrial and Applied Mathematics, Philadelphia. Google ScholarDigital Library
- Baraff, D., Witkin, A., and Kass, M. 2003. Untangling cloth. ACM Trans. Graph. 22, 3, 862--870. Google ScholarDigital Library
- Baraff, D. 1989. Analytical methods for dynamic simulation of non-penetrating rigid bodies. In SIGGRAPH '89: Proceedings of the 16th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 223--232. Google ScholarDigital Library
- Baraff, D. 1994. Fast contact force computation for nonpenetrating rigid bodies. In SIGGRAPH '94, 23--34. Google ScholarDigital Library
- Basch, J., Guibas, L. J., and Zhang, L. 1997. Proximity problems on moving points. In Proc. 13th Annu. ACM Sympos. Comput. Geom., 344--351. Google ScholarDigital Library
- Basch, J., Guibas, L. J., and Hershberger, J. 1999. Data structures for mobile data. Journal of Algorithms 31, 1--28. Google ScholarDigital Library
- Bridson, R., Fedkiw, R., and Anderson, J. 2002. Robust treatment of collisions, contact and friction for cloth animation. In SIGGRAPH '02, 594--603. Google ScholarDigital Library
- Bridson, R., Marino, S., and Fedkiw, R. 2003. Simulation of clothing with folds and wrinkles. In SCA '03, 28--36. Google ScholarDigital Library
- Brilliantov, N. V., and Pöschel, T. 2004. Kinetic Theory of Granular Gases. Oxford University Press, USA.Google Scholar
- Celes, W. 1998. Efficient asynchronous evolution of physical simulations. In SIBGRAPI '98: Proceedings of the International Symposium on Computer Graphics, Image Processing, and Vision, IEEE Computer Society, Washington, DC, USA, 224. Google ScholarDigital Library
- Choi, K.-J., and Ko, H.-S. 2005. Stable but responsive cloth. In SIGGRAPH '05: ACM SIGGRAPH 2005 Courses, ACM, New York, NY, USA, 1. Google ScholarDigital Library
- Cirak, F., and West, M. 2005. Decomposition-based contact response (DCR) for explicit finite element dynamics. Int'l Journal for Numerical Methods in Engineering 64, 8, 1078--1110.Google ScholarCross Ref
- Debunne, G., Desbrun, M., Cani, M.-P., and Barr, A. H. 2001. Dynamic real-time deformations using space & time adaptive sampling. In SIGGRAPH '01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 31--36. Google ScholarDigital Library
- Dequidt, J., Grisoni, L., and Chaillou, C. 2004. Asynchronous interactive physical simulation. Tech. Rep. RR-5338, INRIA.Google Scholar
- Eck, C., Janušek, J., and Krbec, M. 2005. Unilateral contact problems: variational methods and existence theorems. Chapman and Hall/CRC Press, Boca Raton.Google Scholar
- English, E., and Bridson, R. 2008. Animating developable surfaces using nonconforming elements. In SIGGRAPH '08: ACM SIGGRAPH 2008 papers, ACM, New York, NY, USA, 1--5. Google ScholarDigital Library
- Erickson, J., Guibas, L. J., Stolfi, J., and Zhang, L. 1999. Separation-sensitive collision detection for convex objects. In Proc. 10th ACM-SIAM Symp. Discrete Algorithms, 102--111. Google ScholarDigital Library
- Ericson, C. 2004. Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3D Technology). Morgan Kaufmann, December. Google ScholarDigital Library
- Fong, W., Darve, E., and Lew, A. 2008. Stability of asynchronous variational integrators. J. Comput. Phys. 227, 18, 8367--8394. Google ScholarDigital Library
- Gao, J., Guibas, L., Hershberger, J., Zhang, L., and Zhu, A. 2003. Discrete mobile centers. Discrete and Computational Geometry 30, 1, 45--65.Google ScholarCross Ref
- Gao, J., Guibas, L. J., and Nguyen, A. 2005. Distributed proximity maintenance in ad hoc mobile network. In IEEE International Conference on Distributed Computing in Sensor System (DCOSS'05), 4--19. Google ScholarDigital Library
- Grinspun, E., Hirani, A., Desbrun, M., and Schröder, P. 2003. Discrete Shells. In ACM SIGGRAPH / Eurographics Symposium on Computer Animation, 62--67. Google ScholarDigital Library
- Guendelman, E., Bridson, R., and Fedkiw, R. 2003. Non-convex rigid bodies with stacking. In SIGGRAPH '03: ACM SIGGRAPH 2003 Papers, ACM, New York, NY, USA, 871--878. Google ScholarDigital Library
- Guibas, L., Xie, F., and Zhang, L. 2001. Kinetic Collision detection: Algorithms and experiments. In Proceedings of the International Conference on Robotics and Automation, 2903--2910.Google Scholar
- Guibas, L. J., Xie, F., and Zhang, L. 2001. Kinetic collision detection: Algorithms and experiments. In ICRA, 2903--2910.Google Scholar
- Guibas, L., Karaveles, M., and Russel, D. 2004. A computational framework for handling motion. In Proceedings of the Sixth Workshop on Algorithm Engineering and Experiments, 129--141.Google Scholar
- Guibas, L. J. 1998. Kinetic data structures --- a state of the art report. In Proc. 3rd Workshop on Algorithmic Foundations of Robotics (WAFR), 191--209. Google ScholarDigital Library
- Hahn, J. K. 1988. Realistic animation of rigid bodies. In SIGGRAPH '88: Proceedings of the 15th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 299--308. Google ScholarDigital Library
- Hairer, E., Lubich, C., and Wanner, G. 2002. Geometric Numerical Integration: Structure-preserving Algorithms for Ordinary Differential Equations. Springer.Google Scholar
- Harmon, D., Vouga, E., Tamstorf, R., and Grinspun, E. 2008. Robust Treatment of Simultaneous Collisions. SIGGRAPH (ACM Transactions on Graphics) 27, 3, 1--4. Google ScholarDigital Library
- Johnson, K. L. 2008. Contact mechanics. Cambridge University Press.Google Scholar
- Kaufman, D. M., Edmunds, T., and Pai, D. K. 2005. Fast frictional dynamics for rigid bodies. In SIGGRAPH '05, 946--956. Google ScholarDigital Library
- Kaufman, D. M., Sueda, S., James, D. L., and Pai, D. K. 2008. Staggered projections for frictional contact in multibody systems. In SIGGRAPH Asia '08: ACM SIGGRAPH Asia 2008 papers, ACM, New York, NY, USA, 1--11. Google ScholarDigital Library
- Kharevych, L., Yang, W., Tong, Y., Kanso, E., Marsden, J. E., Schröder, P., and Desbrun, M. 2006. Geometric, variational integrators for computer animation. In SCA '06: Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation, Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 43--51. Google ScholarDigital Library
- Klosowski, J. T., Held, M., Mitchell, J. S. B., Sowizral, H., and Zikan, K. 1998. Efficient collision detection using bounding volume hierarchies of k-dops. IEEE Transactions on Visualization and Computer Graphics 4, 1, 21--36. Google ScholarDigital Library
- Konečný, P., and Zikan, K. 1997. Lower Bound of Distance in 3D. In Proceedings of WSCG 1997, vol. 3, 640--649.Google Scholar
- Korneev, V., and Kiselev, A. 2004. Modern Microprocessors. Charles River Media. Google ScholarDigital Library
- Lew, A., Marsden, J. E., Ortiz, M., and West, M. 2003. Asynchronous variational integrators. Archive for Rational Mechanics and Analysis 167, 85--146.Google ScholarCross Ref
- Lubachevsky, B. 1991. How to simulate billiards and similar systems. Journal of Computational Physics 94, 2 (June), 255--283. Google ScholarDigital Library
- Marsden, J., Patrick, G., and Shkoller, S. 1998. Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs. Communications in Mathematical Physics 199, 2, 351--395.Google ScholarCross Ref
- Marsden, J., Pekarsky, S., Shkoller, S., and West, M. 2001. Variational methods, multisymplectic geometry and contiunuum mechanics. Journal of Geometry and Physics 38, 3--4 (June), 253--284.Google ScholarCross Ref
- Milenkovic, V. J., and Schmidl, H. 2001. Optimization-based animation. In SIGGRAPH '01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 37--46. Google ScholarDigital Library
- Mirtich, B., and Canny, J. 1995. Impulse-based dynamic simulation. In WAFR: Proceedings of the workshop on Algorithmic foundations of robotics, A. K. Peters, Ltd., Natick, MA, USA, 407--418. Google ScholarDigital Library
- Mirtich, B. 2000. Timewarp rigid body simulation. In SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 193--200. Google ScholarDigital Library
- Pfeiffer, F., and Glocker, C., Eds. 2000. Multibody Dynamics With Unilateral Contacts. Springer Wien New York, ch. 2, 69--146.Google Scholar
- Pöschel, T., and Schwager, T. 2005. Computational Granular Dynamics: Models and Algorithms. Springer.Google Scholar
- Provot, X. 1997. Collision and self-collision handling in cloth model dedicated to design garments. In Computer Animation and Simulation '97, Springer Verlag, Wien, 177--189.Google Scholar
- Schwager, T., and Pöschel, T. 2007. Coefficient of restitution and linear dashpot model revisited. Granular Matter 9, 6 (November), 465--469.Google ScholarCross Ref
- Sifakis, E., Marino, S., and Teran, J. 2008. Globally coupled collision handling using volume preserving impulses. In 2008 ACM SIGGRAPH / Eurographics Symposium on Computer Animation, 147--154. Google ScholarDigital Library
- Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. In SIGGRAPH '87: Proceedings of the 14th annual conference on Computer graphics and interactive techniques, ACM, New York, NY, USA, 205--214. Google ScholarDigital Library
- Thomaszewski, B., Pabst, S., and Strasser, W. 2008. Asynchronous cloth simulation. In Computer Graphics International.Google Scholar
- Trinkle, D. S. J. 1996. An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and coulomb friction. Intl. Journal for Numerical Methods in Engineering 39, 2673--2691.Google ScholarCross Ref
- Volino, P., and Magnenat-Thalmann, N. 2006. Resolving surface collisions through intersection contour minimization. In SIGGRAPH '06: ACM SIGGRAPH 2006 Papers, ACM, New York, NY, USA, 1154--1159. Google ScholarDigital Library
- Vouga, E., Harmon, D., Tamstorf, R., and Grinspun, E. 2009. Discrete penalty layers admit multisymplectic integration. Tech. rep., Columbia University.Google Scholar
- Weller, R., and Zachmann, G. 2006. Kinetic separation lists for continuous collision detection of deformable objects. In Third Workshop in Virtual Reality Interactions and Physical Simulation (Vriphys).Google Scholar
- Wriggers, P., and Laursen, T. A. 2007. Computational contact mechanics, vol. no. 498 of CISM courses and lectures. Springer, Wien.Google Scholar
- Wriggers, P., and Panagiotopoulos, P., Eds. 1999. New Developments in Contact Problems. Springer Wien New York, ch. 1, 1--54.Google Scholar
- Zhong, G., and Marsden, J. E. 1988. Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators. Physics Letters A 133 (Nov.), 134--139.Google ScholarCross Ref
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- Asynchronous contact mechanics
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