Physically Based Shape Matching

Abstract The shape matching method is a popular approach to simulate deformable objects in interactive applications due to its stability and simplicity. An important feature is that there is no need for a mesh since the method works on arbitrary local groups within a set of particles. A major drawback of shape matching is the fact that it is geometrically motivated and not derived from physical principles which makes calibration difficult. The fact that the method does not conserve volume can yield visual artifacts, e.g. when a tire is compressed but does not bulge. In this paper we present a new meshless simulation method that is related to shape matching but derived from continuous constitutive models. Volume conservation and stiffness can be specified with physical parameters. Further, if the elements of a tetrahedral mesh are used as groups, our method perfectly reproduces FEM based simulations.