In a prior paper, we described a haptic rendering algorithm for arbitrary polygonal models using a six degree-of-freedom haptic interface. In that paper, global search for local minimum distances provided repulsive forces between models. This paper augments that system with a local tracking algorithm that quickly updates and maintains globally computed minima. The global search continuously adds and deletes local minimum distance pairs being updated by the local search. This new system supports higher haptic interaction rates on more complex scenes than the previous approach.