Advertisement

The Visual Computer

, 27:473 | Cite as

Interactive deformable models with quadratic bases in Bernstein–Bézier-form

  • Daniel Weber
  • Thomas Kalbe
  • André Stork
  • Dieter Fellner
  • Michael Goesele
Original Article

Abstract

We present a physically based interactive simulation technique for de formable objects. Our method models the geometry as well as the displacements using quadratic basis functions in Bernstein–Bézier form on a tetrahedral finite element mesh. The Bernstein–Bézier formulation yields significant advantages compared to approaches using the monomial form. The implementation is simplified, as spatial derivatives and integrals of the displacement field are obtained analytically avoiding the need for numerical evaluations of the elements’ stiffness matrices. We introduce a novel traversal accounting for adjacency in order to accelerate the reconstruction of the global matrices. We show that our proposed method can compensate the additional effort introduced by the co-rotational formulation to a large extent. We validate our approach on several models and demonstrate new levels of accuracy and performance in comparison to current state-of-the-art.

Keywords

Deformation Quadratic finite elements Interactive simulation Bernstein–Bézier form 

References

  1. 1.
    Bathe, K.-J.: Finite Element Procedures in Engineering Analysis. Prentice-Hall, New York (1982) Google Scholar
  2. 2.
    Baraff, D., Witkin, A.: Large steps in cloth simulation. Comput. Graph. 32, 43–54 (1998) Google Scholar
  3. 3.
    Bonet, J., Wood, R.D.: Nonlinear Continuum Mechanics for FEA. Cambridge University Press, New York (2008) CrossRefGoogle Scholar
  4. 4.
    Cgal, Computational Geometry Algorithms Library. http://www.cgal.org
  5. 5.
    Etzmuss, O., Keckeisen, M., Strasser, W.: A fast finite element solution for cloth modelling. In: PG (2003) Google Scholar
  6. 6.
    Farin, G.: Curves and Surfaces for CAGD: A Practical Guide. MK Publishers Inc. (2002) Google Scholar
  7. 7.
    Georgii, J., Westermann, R.: Corotated finite elements made fast and stable. In: VRIPHYS, pp. 11–19 (2008) Google Scholar
  8. 8.
    Hauth, M., Etzmuss, O., Strasser, W.: Analysis of numerical methods for the simulation of deformable models. Vis. Comput. 19(7–8), 581–600 (2003) Google Scholar
  9. 9.
    Hauth, M., Strasser, W.: Corotational simulation of deformable solids. In: WSCG, pp. 137–144 (2004) Google Scholar
  10. 10.
    Irving, G., Teran, J., Fedkiw, R.: Invertible finite elements for robust simulation of large deformation. In: SCA (2004) Google Scholar
  11. 11.
    Müller, M., Dorsey, J., McMillan, L., Jagnow, R., Cutler, B.: Stable real-time deformations. In: SCA (2002) Google Scholar
  12. 12.
    Müller, M., Gross, M.: Interactive virtual materials. In: GI, pp. 239–246 (2004) Google Scholar
  13. 13.
    Mezger, J., Strasser, W.: Interactive soft object simulation with quadratic finite elements. In: AMDO (2006) Google Scholar
  14. 14.
    Mezger, J., Thomaszewski, B., Pabst, S., Strasser, W.: Interactive physically-based shape editing. In: SPM (2008) Google Scholar
  15. 15.
    Nealen, A., Müller, M., Keiser, R., Boxerman, E., Carlson, M.: Physically based deformable models in computer graphics. Comput. Graph. Forum 25(4), 809 (2006) CrossRefGoogle Scholar
  16. 16.
    Parker, E.G., O’Brien, J.F.: Real-time deformation and fracture in a game environment. In: SCA ’09 (2009) Google Scholar
  17. 17.
    Pena Serna, S., Silva, J., Stork, A., Marcos, A.: Neighboring-based linear system for dynamic meshes. In: VRIPHYS (2009) Google Scholar
  18. 18.
    Roth, S., Gross, M., Turello, S., Carls, F.: A Bernstein-Bézier based approach to soft tissue simulation. Comput. Graph. Forum 17(3), 285–294 (1998) CrossRefGoogle Scholar
  19. 19.
    Roth, S.: Bernstein–Bézier Representations for Facial Surgery Simulation. PhD thesis, ETHZ (2002) Google Scholar
  20. 20.
    Schumaker, L.: Spline Functions on Triangulations. Cambridge University Press, Cambridge (2007) zbMATHGoogle Scholar
  21. 21.
    Terzopoulos, D., Witkin, A.: Deformable models. IEEE Comput. Graph. Appl. 8(6), 41–51 (1988) CrossRefGoogle Scholar
  22. 22.
    Zienckiewicz, O.C., Taylor, R.L.: The Finite Element Method. Butterworth/Heinemann, Soneham (2000) Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Daniel Weber
    • 1
  • Thomas Kalbe
    • 2
  • André Stork
    • 1
    • 2
  • Dieter Fellner
    • 1
    • 2
  • Michael Goesele
    • 2
  1. 1.Fraunhofer IGDDarmstadtGermany
  2. 2.GRISTU DarmstadtDarmstadtGermany

Personalised recommendations