“Sparse meshless models of complex deformable solids” by Faure, Gilles, Bousquet and Pai

  • ©François Faure, Benjamin Gilles, Michele Bousquet, and Dinesh K. Pai

Conference:


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Title:

    Sparse meshless models of complex deformable solids

Presenter(s)/Author(s):



Abstract:


    A new method to simulate deformable objects with heterogeneous material properties and complex geometries is presented. Given a volumetric map of the material properties and an arbitrary number of control nodes, a distribution of the nodes is computed automatically, as well as the associated shape functions. Reference frames attached to the nodes are used to apply skeleton subspace deformation across the volume of the objects. A continuum mechanics formulation is derived from the displacements and the material properties. We introduce novel material-aware shape functions in place of the traditional radial basis functions used in meshless frameworks. In contrast with previous approaches, these allow coarse deformation functions to efficiently resolve non-uniform stiffnesses. Complex models can thus be simulated at high frame rates using a small number of control nodes.

References:


    1. Adams, B., Ovsjanikov, M., Wand, M., Seidel, H.-P., and Guibas, L. 2008. Meshless modeling of deformable shapes and their motion. In Symposium on Computer Animation, 77–86. Google ScholarDigital Library
    2. Allard, J., Cotin, S., Faure, F., Bensoussan, P.-J., Poyer, F., Duriez, C., Delingette, H., and Grisoni, L. 2007. SOFA – an open source framework for medical simulation. In Medicine Meets Virtual Reality, MMVR 15, 2007, 1–6.Google Scholar
    3. Allard, J., Faure, F., Courtecuisse, H., Falipou, F., Duriez, C., and Kry, P. 2010. Volume contact constraints at arbitrary resolution. ACM Transactions on Graphics 29, 3. Google ScholarDigital Library
    4. An, S. S., Kim, T., and James, D. L. 2008. Optimizing cubature for efficient integration of subspace deformations. ACM Trans. Graph. 27, 5, 1–10. Google ScholarDigital Library
    5. Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. SIGGRAPH Comput. Graph. 32, 106–117. Google Scholar
    6. Barbič, J., and James, D. L. 2005. Real-time subspace integration for St. Venant-Kirchhoff deformable models. ACM Transactions on Graphics (SIGGRAPH 2005) 24, 3 (Aug.), 982–990. Google Scholar
    7. Bathe, K. 1996. Finite Element Procedures. Prentice Hall.Google Scholar
    8. Fries, T.-P., and Matthies, H. 2003. Classification and overview of meshfree methods. Tech. rep., TU Brunswick, Germany.Google Scholar
    9. Galoppo, N., Otaduy, M. A., Moss, W., Sewall, J., Curtis, S., and Lin, M. C. 2009. Controlling deformable material with dynamic morph targets. In Proc. of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. Google Scholar
    10. Gilles, B., Bousquet, G., Faure, F., and Pai, D. 2011. Frame-based elastic models. ACM Transactions on Graphics. Google Scholar
    11. Gross, M., and Pfister, H. 2007. Point-Based Graphics. Morgan Kaufmann. Google Scholar
    12. Irving, G., Teran, J., and Fedkiw, R. 2006. Tetrahedral and hexahedral invertible finite elements. Graph. Models 68, 2. Google ScholarDigital Library
    13. James, D. L., and Pai, D. K. 2003. Multiresolution green’s function methods for interactive simulation of large-scale elastostatic objects. ACM Trans. Graph. 22 (January), 47–82. Google ScholarDigital Library
    14. Kaufmann, P., Martin, S., Botsch, M., and Gross, M. 2008. Flexible simulation of deformable models using discontinuous galerkin fem. In Symposium on Computer Animation. Google ScholarDigital Library
    15. Kavan, Collins, Zara, and O’Sullivan. 2007. Skinning with dual quaternions. In Symposium on Interactive 3D graphics and games, 39–46. Google Scholar
    16. Kharevych, L., Mullen, P., Owhadi, H., and Desbrun, M. 2009. Numerical coarsening of inhomogeneous elastic materials. ACM Trans. Graph. 28 (July), 51:1–51:8. Google ScholarDigital Library
    17. Kim, T., and James, D. L. 2009. Skipping steps in deformable simulation with online model reduction. ACM Trans. Graph. 28 (December), 123:1–123:9. Google ScholarDigital Library
    18. Liu, Y., Wang, W., Lévy, B., Sun, F., Yan, D.-M., Lu, L., and Yang, C. 2009. On Centroidal Voronoi TessellationEnergy Smoothness and Fast Computation. ACM Trans. Graph. 28 (08). Google Scholar
    19. Magnenat-Thalmann, N., Laperrière, R., and Thalmann, D. 1988. Joint dependent local deformations for hand animation and object grasping. In Graphics interface, 26–33. Google Scholar
    20. Martin, S., Kaufmann, P., Botsch, M., Wicke, M., and Gross, M. 2008. Polyhedral finite elements using harmonic basis functions. Comput. Graph. Forum 27, 5. Google ScholarDigital Library
    21. Martin, S., Kaufmann, P., Botsch, M., Grinspun, E., and Gross, M. 2010. Unified simulation of elastic rods, shells, and solids. SIGGRAPH Comput. Graph. 29, 3. Google Scholar
    22. Müller, M., and Gross, M. 2004. Interactive virtual materials. In Graphics Interface.Google Scholar
    23. Müller, M., Keiser, R., Nealen, A., Pauly, M., Gross, M., and Alexa, M. 2004. Point based animation of elastic, plastic and melting objects. In Symposium on Computer Animation, 141–151. Google Scholar
    24. Müller, M., Heidelberger, B., Teschner, M., and Gross, M. 2005. Meshless deformations based on shape matching. ACM Transactions on Graphics 24, 3, 471–478. Google ScholarDigital Library
    25. Nadler, B., and Rubin, M. 2003. A new 3-d finite element for nonlinear elasticity using the theory of a cosserat point. Int. J. of Solids and Struct. 40, 4585–4614.Google ScholarCross Ref
    26. Nealen, A., Müller, M., Keiser, R., Boxerman, E., and Carlson, M. 2005. Physically based deformable models in computer graphics. In Comput. Graph. Forum, vol. 25 (4), 809–836.Google ScholarCross Ref
    27. Nesme, M., Kry, P., Jerabkova, L., and Faure, F. 2009. Preserving Topology and Elasticity for Embedded Deformable Models. SIGGRAPH Comput. Graph.. Google Scholar
    28. Powell, M. J. D. 1990. The theory of radial basis function approximation. University Numerical Analysis Report.Google Scholar
    29. Sifakis, E., Der, K. G., and Fedkiw, R. 2007. Arbitrary cutting of deformable tetrahedralized objects. In Symposium on Computer Animation. Google ScholarDigital Library
    30. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. In SIGGRAPH Comput. Graph., M. C. Stone, Ed., vol. 21, 205–214. Google ScholarDigital Library
    31. Tournois, J., Wormser, C., Alliez, P., and Desbrun, M. 2009. Interleaving delaunay refinement and optimization for practical isotropic tetrahedron mesh generation. ACM Trans. Graph. 28 (July), 75:1–75:9. Google ScholarDigital Library


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