Abstract
We propose an approach for efficiently simulating elastic objects made of non-homogeneous, non-isotropic materials. Based on recent developments in homogenization theory, a methodology is introduced to approximate a deformable object made of arbitrary fine structures of various linear elastic materials with a dynamicallysimilar coarse model. This numerical coarsening of the material properties allows for simulation of fine, heterogeneous structures on very coarse grids while capturing the proper dynamics of the original dynamical system, thus saving orders of magnitude in computational time. Examples including inhomogeneous and/or anisotropic materials can be realistically simulated in realtime with a numerically-coarsened model made of a few mesh elements.
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Supplemental material for "Numerical Coarsening of Inhomogeneous Elastic Materials."
- An, S., Kim, T., and James, D. L. 2008. Optimizing cubature for efficient integration of subspace deformations. ACM Transactions on Graphics (SIGGRAPH Asia) 27, 4 (Dec.). Google ScholarDigital Library
- Babuška, I., and Sauter, S. A. 2008. Efficient solution of anisotropic lattice equations by the recovery method. SIAM J. Sci. Comput. 30, 5, 2386--2404. Google ScholarDigital Library
- Baraff, D., and Witkin, A. P. 1998. Large steps in cloth simulation. In ACM SIGGRAPH Proceedings, 43--54. Google ScholarDigital Library
- Barbic, J., and James, D. 2005. Real-Time Subspace Integration for St. Venant-Kirchhoff Deformable Models. ACM Trans. on Graphics 24, 3 (Aug.), 982--990. Google ScholarDigital Library
- Barr, A. H. 1989. The Einstein Summation Notation: Introduction and Extensions. ACM SIGGRAPH Course Notes #30 "Topics in Physically-based Modeling", J1--J12.Google Scholar
- Bensoussan, A., Lions, J. L., and Papanicolaou, G. 1978. Asymptotic analysis for periodic structure. North Holland, Amsterdam.Google Scholar
- Berlyand, L., and Owhadi, H. 2009. Finite dimensional approximation of solutions of divergence form systems of equations with rough and high contrast coefficients. To appear.Google Scholar
- Capell, S., Green, S., Curless, B., Duchamp, T., and Popović, Z. 2002. Interactive skeleton-driven dynamic deformations. ACM SIGGRAPH 21, 3 (July), 586--593. Google ScholarDigital Library
- Capell, S., Green, S., Curless, B., Duchamp, T., and Popović, Z. 2002. A multiresolution framework for dynamic deformations. In Symposium on Computer Animation, 41--48. Google ScholarDigital Library
- Choi, M.-G., and Ko, H.-S. 2005. Modal warping: Real-time simulation of large rotational deformation. IEEE Trans. on Visualization and Computer Graphics 11, 1, 91--101. Google ScholarDigital Library
- De Veubeke, B. F. 1976. The dynamics of flexible bodies. International Journal of Engineering Science 14, 895--913.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 ACM SIGGRAPH Proceedings, 31--36. Google ScholarDigital Library
- Farmer, C. L. 2002. Upscaling: a review. International Journal for Numerical Methods in Fluids 40, 1--2, 63--78.Google ScholarCross Ref
- Feynman, R., Leighton, R., and Sands, M. 2006. The Feynman Lectures on Physics. Addison-Wesley.Google Scholar
- Georgii, J., and Westermann, R. 2008. Corotated finite elements made fast and stable. In Proceedings of the 5th Workshop on Virtual Reality Interaction and Physical Simulation.Google Scholar
- Grinspun, E., Krysl, P., and Schröder, P. 2002. Charms: A simple framework for adaptive simulation. ACM Transactions on Graphics 21, 3 (July), 281--290. Google ScholarDigital Library
- Hauth, M., and Strasser, W. 2004. Corotational simulation of deformable solids. In Winter School on Computer Graphics, 137--144.Google Scholar
- James, D. L., and Fatahalian, K. 2003. Precomputing interactive dynamic deformable scenes. ACM Transactions on Graphics 22, 3 (July), 879--887. Google ScholarDigital Library
- James, D. L., and Pai, D. K. 1999. ArtDefo: Accurate real time deformable objects. In ACM SIGGRAPH Proceedings, 65--72. Google ScholarDigital Library
- James, D. L., and Pai, D. K. 2002. DyRT: Dynamic response textures for real time deformation simulation with graphics hardware. ACM Trans. on Graphics 21, 3 (July), 582--585. Google ScholarDigital Library
- Jikov, V. V., Kozlov, S. M., and Oleinik, O. A. 1991. Homogenization of Differential Operators and Integral Functionals. Springer-Verlag.Google Scholar
- Krysl, P., Lall, S., and Marsden, J. 2000. Dimensional Model Reduction in Non-linear Finite Element Dynamics of Solids and Structures. I.J.N.M.E. 51, 479--504.Google Scholar
- Li, R.-C., and Bai, Z. 2005. Structure preserving model reduction using a Krylov subspace projection formulation. Comm. Math. Sci. 3, 2, 179--199.Google ScholarCross Ref
- Müller, M., and Gross, M. 2004. Interactive virtual materials. In Proceedings of Graphics Interface, 239--246. Google ScholarDigital Library
- Müller, M., Dorsey, J., McMillan, L., Jagnow, R., and Cutler, B. 2002. Stable real-time deformations. In Proceedings of the Symposium on Computer Animation, 49--54. Google ScholarDigital Library
- Nesme, M., Payan, Y., and Faure, F. 2006. Animating shapes at arbitrary resolution with non-uniform stiffness. In Eurographics Workshop in Virtual Reality Interaction and Physical Simulation (VRIPHYS).Google Scholar
- Nesme, M., Kry, P. G., Jeřábková, L., and Faure, F. 2009. Preserving topology and elasticity for embedded deformable models. ACM Trans. on Graphics 28, 3 (Aug.). Google ScholarDigital Library
- Owhadi, H., and Zhang, L. 2007. Metric-based upscaling. Communications on Pure and Applied Math. 60, 675--723.Google ScholarCross Ref
- Pentland, A., and Williams, J. 1989. Good vibrations: modal dynamics for graphics and animation. In ACM SIGGRAPH Proceedings, 215--222. Google ScholarDigital Library
- Rivers, A. R., and James, D. L. 2007. Fastlsm: Fast lattice shape matching for robust real-time deformation. ACM Trans. on Graphics 26, 3 (July), 82:1--82:6. Google ScholarDigital Library
- Shu, S., Babuška, I., Xiao, Y., Xu, J., and Zikatanov, L. 2008. Multilevel preconditioning methods for discrete models of lattice block materials. SIAM Journal on Scientific Computing 31, 1, 687--707. Google ScholarDigital Library
- Treuille, A., Lewis, A., and Popović, Z. 2006. Model reduction for real-time fluids. ACM Trans. on Graphics 25, 3 (July), 826--834. Google ScholarDigital Library
- Wojtan, C., and Turk, G. 2008. Fast viscoelastic behavior with thin features. ACM Trans. on Graphics 27(3), 47 (Aug.). Google ScholarDigital Library
Index Terms
- Numerical coarsening of inhomogeneous elastic materials
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