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.
Supplemental Material
- 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
- 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
- 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
- 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
- Baraff, D., and Witkin, A. 1998. Large steps in cloth simulation. SIGGRAPH Comput. Graph. 32, 106--117. Google Scholar
- 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
- Bathe, K. 1996. Finite Element Procedures. Prentice Hall.Google Scholar
- Fries, T.-P., and Matthies, H. 2003. Classification and overview of meshfree methods. Tech. rep., TU Brunswick, Germany.Google Scholar
- 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
- Gilles, B., Bousquet, G., Faure, F., and Pai, D. 2011. Frame-based elastic models. ACM Transactions on Graphics. Google Scholar
- Gross, M., and Pfister, H. 2007. Point-Based Graphics. Morgan Kaufmann. Google Scholar
- Irving, G., Teran, J., and Fedkiw, R. 2006. Tetrahedral and hexahedral invertible finite elements. Graph. Models 68, 2. Google ScholarDigital Library
- 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
- 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
- Kavan, Collins, Zara, and O'Sullivan. 2007. Skinning with dual quaternions. In Symposium on Interactive 3D graphics and games, 39--46. Google Scholar
- 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
- 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
- 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
- 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
- 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
- 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
- Müller, M., and Gross, M. 2004. Interactive virtual materials. In Graphics Interface.Google Scholar
- 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
- 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
- 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
- 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
- Nesme, M., Kry, P., Jerabkova, L., and Faure, F. 2009. Preserving Topology and Elasticity for Embedded Deformable Models. SIGGRAPH Comput. Graph.. Google Scholar
- Powell, M. J. D. 1990. The theory of radial basis function approximation. University Numerical Analysis Report.Google Scholar
- Sifakis, E., Der, K. G., and Fedkiw, R. 2007. Arbitrary cutting of deformable tetrahedralized objects. In Symposium on Computer Animation. Google ScholarDigital Library
- 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
- 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
Index Terms
- Sparse meshless models of complex deformable solids
Recommendations
Sparse meshless models of complex deformable solids
SIGGRAPH '11: ACM SIGGRAPH 2011 papersA 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 ...
Physically based morphing of point-sampled surfaces: Animating Geometrical Models
CASA 2005This paper presents an innovative method for naturally and smoothly morphing point-sampled surfaces via dynamic meshless simulation on point-sampled surfaces. While most existing literature on shape morphing emphasizes the issue of finding a good ...
Blended Deformable Models
This paper develops a new class of parameterized models based on the linear interpolation of two parameterized shapes along their main axes, using a blending function. This blending function specifies the relative contribution of each component shape on ...
Comments