Quadratic Contact Energy Model for Multi-impact Simulation

Abstract

Simultaneous multi-impact simulation is a challenging problem that frequently arises in physically-based modeling of rigid bodies. There are several physical criteria that should be satisfied for rigid body collision handling, but existing methods generally fail to meet one or more of them. In order to capture the inner process of potential energy variation, which is the physical foundation of collisions in a multi-impact system, we present a novel quadratic contact energy model for rigid body simulation. By constructing quadratic energy functions with respect to the impulses, post-impact reactions of rigid bodies can be computed efficiently. Our model can satisfy the physical criteria and can simulate various natural phenomena including the wave effect. Also, our model can be easily combined with Linear Complementary Problem (LCP) and can provide feasible results with any restitution coefficient. In practice, our model can solve the simultaneous multi-impact problem efficiently and robustly, and we highlight its performance on different benchmarks.