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


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.


Deformation Quadratic finite elements Interactive simulation Bernstein–Bézier form 


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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

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