An algorithm is described for fast rendering of surfaces for haptic interaction with multiple fingers. The algorithm uses a human-defined geometrical map to quickly cache surface triangles for constant time solution of the collision detection problem. The map is a 1, 2, or 3 dimensional manifold onto which it is easy to project the haptic interaction point. Dividing it?s surface into quantized bins allows easy reference to a small set of triangles which can be checked for collision. Although the algorithm relies on some one-time manual input (i.e. defining the contact map), it represents a significant increase in speed without a substantial memory penalty.