Curved surfaces and coherence for non-penetrating rigid body simulation

Abstract

A formulation for the contact forces between curved surfaces in resting (non-colliding) contact is presented. In contrast to previous formulations, constraints on the allowable tangential movement between contacting surfaces are not required. Surfaces are restricted to be twice-differentiable surfaces without boundary. Only finitely many contact points between surfaces are allowed; however, the surfaces need not be convex. The formulation yields the contact forces between curved surfaces and polyhedra as well. Algorithms for performing collision detection during simulation on bodies composed of both polyhedra and strictly convex curved surfaces are also presented. The collision detection algorithms exploit the geometric coherence between successive time steps of the simulation to achieve efficient running times.