In this project, we have contributed a new computational algorithm for maintaining the closest points between two ore more objects modeled using tiled-together parametric surface patches. Such an algorithm is the essential core of a collision detector in any multi-body system or virtual environment simulator.

Our approach for finding and tracking the closest points between two parametric surfaces is based on the formulation of a control problem and design of a stabilizing controller. The controller simultaneously accounts for the surface shape and motion while asymptotically achieving (and maintaining) the extremal pair over the whole surface patch. This algorithm enjoys many advantages over existing published routines.

The new algorithm is especially useful when a human interacts with a model through a haptic interface. It may be used to efficiently track the maximum penetration distance and the appropriate common normal between the model and an image of the user's finger in the virtual environment. The penetration distance and normal vector may then be used to produce a reaction force through the haptic interface.