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

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.