“Animation of Deformable Bodies with Quadratic Bézier Finite Elements” by Bargteil and Cohen

  • ©Adam Bargteil and Elaine Cohen

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    Animation of Deformable Bodies with Quadratic Bézier Finite Elements

Session/Category Title: Mesh-Based Simulation

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Abstract:


    In this article, we investigate the use of quadratic finite elements for graphical animation of deformable bodies. We consider both integrating quadratic elements with conventional linear elements to achieve a computationally efficient adaptive-degree simulation framework as well as wholly quadratic elements for the simulation of nonlinear rest shapes. In both cases, we adopt the Bézier basis functions and employ a co-rotational linear strain formulation. As with linear elements, the co-rotational formulation allows us to precompute per-element stiffness matrices, resulting in substantial computational savings. We present several examples that demonstrate the advantages of quadratic elements in general and our adaptive-degree system in particular. Furthermore, we demonstrate, for the first time in computer graphics, animations of volumetric deformable bodies with nonlinear rest shapes.

References:


    1. I. Babuška and M. Suri. 1990. The p- and h-p version of the finite element method: An overview. Comput. Methods Appl. Mech. Engin. 80, 1–3, 5–26.
    2. I. Babuška, B. A. Szabo, and I. N. Katz. 1981. The p-version of the finite element method. SIAM J. Numer. Anal. 18, 3, 515–545.
    3. D. Baraff and A. Witkin. 1998. Large steps in cloth simulation. In Proceedings of the Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques. ACM Press, New York, 43–54.
    4. J. Barbič and D. L. James. 2005. Real-time subspace integration for st. venant-kirchoff deformable models. ACM Trans. Graph. 24, 3, 982–990.
    5. B. Bickel, M. Bächer, M. A. Otaduy, W. Matusik, H. Pfister, and M. Gross. 2009. Capture and modeling of nonlinear heterogeneous soft tissue. ACM Trans. Graph. 28, 3, 89:1–89:9.
    6. J. Bonet and R. Wood. 2008. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press.
    7. M. J. Borden, M. A. Scott, J. A. Evans, and T. J. R. Hughes. 2011. Isogeometric finite element data structures based on bezier extraction of nubs. Int. J. Numer. Mech. Engin. 87, 15–47.
    8. R. Bridson, S. Marino, and R. Fedkiw. 2003. Simulation of clothing with folds and wrinkles. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 28–36.
    9. T. Brochu and R. Bridson. 2009. Robust topological operations for dynamic explicit surfaces. SIAM J. Sci. Comput. 31, 4, 2472–2493.
    10. J. Burkardt. 2007. Quadrature rules for tetrahedrons. http://people.ac.feu.edu/∼jburkardt.
    11. S. Capell, S. Green, B. Curless, T. Duchamp, and Z. Popović. 2002. Interactive skeleton-driven dynamic deformations. ACM Trans. Graph. 21, 586–593.
    12. I. Chao, U. Pinkall, P. Sanan, and P. Schröder. 2010. A simple geometric model for elastic deformations. ACM Trans. Graph. 29, 4, 38:1–38:6.
    13. G. Debunne, M. Desbrun, M.-P. Cani, and A. H. Barr. 2001. Dynamic real-time deformations using space and time adaptive sampling. In Proceedings of the Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques. ACM Press, New York, 31–36.
    14. E. Grinspun, P. Krysl, and P. Schröder. 2002. CHARMS: A simple framework for adaptive simulation. ACM Trans. Graph. 21, 3, 281–290.
    15. K. K. Hauser, C. Shen, and J. F. O’Brien. 2003. Interactive deformation using modal analysis with constraints. In Proceedings of the Graphics Interface Conference. 247–256.
    16. J. S. Hesthaven and T. Warburton. 2007. Nodal Discontinuous Galerkin Methods: Algorithms, Analysis and Applications, 1st ed. Springer.
    17. T. J. R. Hughes. 1987. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs, NJ.
    18. G. Irving, J. Teran, and R. Fedkiw. 2004. Invertible finite elements for robust simulation of large deformation. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 131–140.
    19. D. L. James and D. K. Pai. 2002. Dyrt: Dynamic response textures for real time deformation simulation with graphics hardware. ACM Trans. Graph. 21, 3, 582–585.
    20. P. Joshi, M. Meyer, T. Derose, B. Green, and T. Sanocki. 2007. Harmonic coordinates for character articulation. ACM Trans. Graph. 26, 3.
    21. T. Ju, S. Schaefer, and J. Warren. 2005. Mean value coordinates for closed triangular meshes. ACM Trans. Graph. 24, 3, 561–566.
    22. J. M. Kaldor, D. L. James, and S. Marschner. 2008. Simulating knitted cloth at the yarn level. ACM Trans. Graph. 27, 3, 65:1–65:9.
    23. P. Kaufmann, S. Martin, M. Botsch, E. Grinspun, and M. Gross. 2009a. Enrichment textures for detailed cutting of shells. ACM Trans. Graph. 28, 3, 50:1–50:10.
    24. P. Kaufmann, S. Martin, M. Botsch, and M. Gross. 2009b. Flexible simulation of deformable models using discontinuous galerkin fem. Graph. Models 71, 4, 153–167.
    25. L. Kharevych, W. Yang, Y. Tong, E. Kanso, J. E. Marsden, P. Schröder, and M. Desbrun. 2006. Geometric, variational integrators for computer animation. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 43–51.
    26. F. Labelle and J. R. Shewchuk. 2007. Isosurface stuffing: Fast tetrahedral meshes with good dihedral angles. ACM Trans. Graph. 26, 3.
    27. S. Martin, P. Kaufmann, M. Botsch, M. Wicke, and M. Gross. 2008. Polyhedral finite elements using harmonic basis functions. Comput. Graph. Forum 27, 5, 1521–1529.
    28. J. Mezger, B. Thomaszewski, S. Pabst, and W. Strasser. 2009. Interactive physically-based shape editing. Comput.-Aid. Geom. Des. 26, 6, 680–694.
    29. M. Müller, J. Dorsey, L. McMillan, R. Jagnow, and B. Cutler. 2002. Stable real-time deformations. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 49–54.
    30. M. Müller and M. Gross. 2004. Interactive virtual materials. In Proceedings of the Graphics Interface Conference. 239–246.
    31. J. F. O’Brien and J. K. Hodgins. 1999. Graphical modeling and animation of brittle fracture. In Proceedings of the Annual ACM SIGGRAPH Conference on Computer Graphics and Interactive Techniques. 137–146.
    32. S. Orszag. 1969. Numerical methods for the simulation of turbulence. Phys. Fluids Suppl. II 12, 250–257.
    33. E. G. Parker and J. F. O’Brien. 2009. Real-time deformation and fracture in a game environment. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 156–166.
    34. A. Patera. 1984. A spectral element method for fluid dynamics: Laminar flow in a chennel expansion. J. Comput. Phys. 54, 468–488.
    35. Y. Remion, J.-M. Nourrit, and D. Gillard. 1999. Dynamic animation of spline like objects. In Proceedings of the International Conference on Computer Graphics, Visualization, and Computer Vision (WSCG’99). V. Skala, Ed.
    36. S. H. M. Roth, M. H. Gross, S. Turello, and F. R. Carls. 1998. A bernstein-bzier based approach to soft tissue simulation. Comput. Graph. Forum 17, 3, 285–294.
    37. J. Schöberl. 1997. NETGEN: An advancing front 2d/3d mesh generator based on abstract rules. Comput. Vis. Sci. 1, 1, 41–52.
    38. E. Sifakis, T. Shinar, G. Irving, and R. Fedkiw. 2007. Hybrid simulation of deformable solids. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 81–90.
    39. A. Stomakhin, R. Howes, C. Schroeder, and J. M. Teran. 2012. Energetically consistent invertible elasticity. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 25–32.
    40. J. Teran, S. Blemker, V. N. T. Hing, and R. Fedkiw. 2003. Finite volume methods for the simulation of skeletal muscle. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 68–74.
    41. D. Weber, J. Bender, M. Schnoes, A. Stork, and D. Fellner. 2013. Efficient gpu data structures and methods to solve sparse linear systems in dynamics applications. Comput. Graph. Forum 32, 1, 16–26.
    42. D. Weber, T. Kalbe, A. Stork, D. Fellner, and M. Goesele. 2011. Interactive deformable models with quadratic bases in bernstein-bezier-form. Trans. Vis. Comput. 27, 473–483.
    43. M. Wicke, M. Botsch, and M. Gross. 2007. A finite element method on convex polyhedra. Comput. Graph. Forum 26, 3, 355–364.
    44. C. Wojtan and G. Turk. 2008. Fast viscoelastic behavior with thin features. ACM Trans. Graph. 27, 47:1–47:8.
    45. L. Zhang, T. Cui, and H. Liu. 2009. A set of symmetric quadrature rules on triangles and tetrahedra. J. Comput. Math. 27, 1, 89–96.

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