Non-iterative computation of contact forces for deformable objects

Abstract

We present a novel approach to handle collisions of deformable objects represented by tetrahedral meshes. The scheme combines the physical correctness of constraint methods with the efficiency of penalty approaches. For a set of collided points, a collision-free state is computed that is governed by the elasticities and impulses of the collided objects. In contrast to existing constraint methods we show how to decouple the resulting system of equations in order to avoid iterative solvers. By considering the time step of the numerical integration scheme, the contact force can be analytically computed for each collided point in order to achieve the collision-free state. Since predicted information on positions, impulses, and penetration depths of the subsequent time step is considered, a collision-free state is maintained at each simulation step which is in contrast to existing penalty methods. Further, our approach does not require a user-defined stiffness constant. Our scheme can handle various underlying deformable models and numerical integration schemes. To illustrate its versatility, we have performed experiments with linear and non-linear finite element methods.