Nonsmooth Newton Method for Fischer Function Reformulation of Contact Force Problems for Interactive Rigid Body Simulation

Abstract

In interactive physical simulation, contact forces are applied to prevent rigid bodies from penetrating each other. Accurate contact force determination is a computationally hard problem. Thus, in practice one trades accuracy for performance. The result is visual artifacts such as viscous or damped contact response. In this paper, we present a new approach to contact force determination. We reformulate the contact force problem as a nonlinear root search problem, using a Fischer function. We solve this problem using a generalized Newton method. Our new Fischer - Newton method shows improved qualities for specific configurations where the most widespread alternative, the Projected Gauss-Seidel method, fails. Experiments show superior convergence properties of the exact Fischer - Newton method.