“Simulation of complex nonlinear elastic bodies using lattice deformers” – ACM SIGGRAPH HISTORY ARCHIVES

“Simulation of complex nonlinear elastic bodies using lattice deformers”

  • 2012 SA Technical Papers_Patterson_Simulation of Complex Nonlinear Elastic Bodies using Lattice Deformers

Conference:


Type(s):


Title:

    Simulation of complex nonlinear elastic bodies using lattice deformers

Session/Category Title:   Skinning


Presenter(s)/Author(s):



Abstract:


    Lattice deformers are a popular option for modeling the behavior of elastic bodies as they avoid the need for conforming mesh generation, and their regular structure offers significant opportunities for performance optimizations. Our work expands the scope of current lattice-based elastic deformers, adding support for a number of important simulation features. We accommodate complex nonlinear, optionally anisotropic materials while using an economical one-point quadrature scheme. Our formulation fully accommodates near-incompressibility by enforcing accurate nonlinear constraints, supports implicit integration for large time steps, and is not susceptible to locking or poor conditioning of the discrete equations. Additionally, we increase the accuracy of our solver by employing a novel high-order quadrature scheme on lattice cells overlapping with the model boundary, which are treated at sub-cell precision. Finally, we detail how this accurate boundary treatment can be implemented at a minimal computational premium over the cost of a voxel-accurate discretization. We demonstrate our method in the simulation of complex musculoskeletal human models.

References:


    1. Almgren, A., Bell, J., Colella, P., and Marthaler, T. 1997. A Cartesian grid projection method for the incompressible Euler equations in complex geometries. SIAM Journal on Scientific Computing 18, 5, 1289–1309.
    2. Arnold, D. N. 1990. Mixed finite element methods for elliptic problems. Computer Methods in Applied Mechanics and Engineering 82, 1–3, 281–300.
    3. Batty, C., Bertails, F., and Bridson, R. 2007. A fast variational framework for accurate solid-fluid coupling. ACM Transactions on Graphics (SIGGRAPH Proceedings) 26, 3 (July).
    4. Brezzi, F., and Fortin, M. 1991. Mixed and hybrid finite element methods. Springer-Verlag: New York.
    5. Chuang, M., Luo, L., Brown, B. J., Rusinkiewicz, S., and Kazhdan, M. 2009. Estimating the Laplace-Beltrami operator by restricting 3D functions. In Proceedings of the Symposium on Geometry Processing, 1475–1484.
    6. Daux, C., Moes, N., Dolbow, J., Sukumar, N., and Belytschko, T. 2000. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering 48, 12.
    7. English, E., and Bridson, R. 2008. Animating developable surfaces using nonconforming elements. In ACM Transactions on Graphics (SIGGRAPH Proceedings), vol. 27, 66.
    8. Fedkiw, R., Aslam, T., Merriman, B., and Osher, S. 1999. A non-oscillatory eulerian approach to interfaces in multimaterial flows (the ghost fluid method). Journal of Computational Physics 152, 2, 457–492.
    9. Freund, R., and Nachtigal, N. 1994. A new Krylov-subspace method for symmetric indefinite linear systems. In Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, IMACS: New Brunswick, NJ, 1253–1256.
    10. 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.
    11. Goldenthal, R., Harmon, D., Fattal, R., Bercovier, M., and Grinspun, E. 2007. Efficient simulation of inextensible cloth. In ACM Transactions on Graphics (TOG), vol. 26, 49.
    12. Guendelman, E., Selle, A., Losasso, F., and Fedkiw, R. 2005. Coupling water and smoke to thin deformable and rigid shells. ACM Transactions on Graphics (SIGGRAPH Proceedings) 24, 3, 973–981.
    13. Hellrung, Jr., J. L., Wang, L., Sifakis, E., and Teran, J. M. 2012. A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions. Journal of Computational Physics 231, 4, 2015–2048.
    14. Hughes, T. 1987. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice Hall.
    15. Irving, G., Schroeder, C., and Fedkiw, R. 2007. Volume conserving finite element simulations of deformable models. ACM Transactions on Graphics (SIGGRAPH Proc.) 26, 3.
    16. Kharevych, L., Mullen, P., Owhadi, H., and Desbrun, M. 2009. Numerical coarsening of inhomogeneous elastic materials. ACM Trans. on Graphics (SIGGRAPH Proc.) 28, 3, 51.
    17. Kim, J., and Pollard, N. 2011. Fast simulation of skeleton-driven deformable body characters. ACM Transactions on Graphics (TOG) 30, 5, 121.
    18. Lee, S.-H., Sifakis, E., and Terzopoulos, D. 2009. Comprehensive biomechanical modeling and simulation of the upper body. ACM Transactions on Graphics 28, 4, 1–17.
    19. Lekien, F., and Marsden, J. 2005. Tricubic interpolation in three dimensions. Journal of Numerical Methods and Engineering 63, 455–471.
    20. McAdams, A., Sifakis, E., and Teran, J. 2010. A parallel multigrid Poisson solver for fluids simulation on large grids. In Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 65–74.
    21. McAdams, A., Zhu, Y., Selle, A., Empey, M., Tamstorf, R., Teran, J., and Sifakis, E. 2011. Efficient elasticity for character skinning with contact and collisions. ACM Transactions on Graphics (SIGGRAPH Proceedings) 30, 4, 37.
    22. Müller, M., Teschner, M., and Gross, M. 2004. Physically-based simulation of objects represented by surface meshes. In Proc. Computer Graphics International, 156–165.
    23. 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).
    24. Nesme, M., Kry, P., Jeřábková, L., and Faure, F. 2009. Preserving topology and elasticity for embedded deformable models. In ACM Transactions on Graphics (SIGGRAPH Proceedings), vol. 28, 52.
    25. Quarteroni, A., and Valli, A. 1999. Domain decomposition methods for partial differential equations, vol. 10. Clarendon Press.
    26. Rivers, A., and James, D. 2007. FastLSM: fast lattice shape matching for robust real-time deformation. ACM Transactions on Graphics (SIGGRAPH Proc.) 26, 3.
    27. Sifakis, E., and Barbič, J., 2012. FEM simulation of 3D deformable solids: A practitioner’s guide to theory, discretization, and model reduction. ACM SIGGRAPH 2012 Courses. http://www.femdefo.org/.
    28. Sifakis, E., Shinar, T., Irving, G., and Fedkiw, R. 2007. Hybrid simulation of deformable solids. In Proc. of ACM SIGGRAPH/Eurographics Symp. on Comput. Anim., 81–90.
    29. Teran, J., Sifakis, E., Irving, G., and Fedkiw, R. 2005. Robust quasistatic finite elements and flesh simulation. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics symposium on Computer animation, ACM, 181–190.
    30. Terzopoulos, D., Platt, J., Barr, A., and Fleischer, K. 1987. Elastically deformable models. Computer Graphics (Proc. SIGGRAPH 87) 21, 4, 205–214.
    31. Trottenberg, U., Oosterlee, C., and Schuller, A. 2001. Multigrid. San Diego: Academic Press.
    32. Wojtan, C., and Turk, G. 2008. Fast viscoelastic behavior with thin features. In ACM Transactions on Graphics (SIGGRAPH Proc.), vol. 27, ACM, 47.
    33. Zhu, Y., Sifakis, E., Teran, J., and Brandt, A. 2010. An efficient multigrid method for the simulation of high-resolution elastic solids. ACM Transactions on Graphics (TOG) 29, 2, 16.


ACM Digital Library Publication:



Overview Page:



Submit a story:

If you would like to submit a story about this presentation, please contact us: historyarchives@siggraph.org