Interactive deformable models with quadratic bases in Bernstein-Bézier form

We present a physically based interactive simulation technique for deformable objects with curved boundary surfaces. Our method models the object geometry as well as the displacements using quadratic basis functions in Bernstein-Bézier-form on a tetrahedral finite element grid. The Bernstein-Bézier formulation yields significant advantages compared to approaches with linear and quadratic bases in monomial form. Spatial derivatives and integrals of the displacement field are obtained analytically avoiding the need for numerical evaluations of the elements' stiffness matrices. We validate our approach on several different models and demonstrate state-of-the-art results in terms of accuracy and perfomance.