Inner sphere trees for proximity and penetration queries

We present a novel geometric data structure for approximate collision detection at haptic rates between rigid objects. Our data structure, which we call inner sphere trees, supports different kinds of queries, namely, proximity queries and a new method for interpenetration computation, the penetration volume, which is related to the water displacement of the overlapping region and, thus, corresponds to a physically motivated force. The main idea is to bound objects from the inside with a set of non-overlapping spheres. Based on such sphere packings, a “inner bounding volume hierarchy” can be constructed. In order to do so, we propose to use an AI clustering algorithm, which we extend and adapt here. The results show performance at haptic rates both for proximity and penetration volume queries for models consisting of hundreds of thousands of polygons.