Inner Sphere Trees and Their Application to Collision Detection

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 the penetration volume, which is related to the water displacement of the overlapping region and, thus, corresponds to a physically motivated force. Moreover, we present a time-critical version of the penetration volume computation that is able to achieve very tight upper and lower bounds within a fixed budget of query time. The main idea is to bound the object from the inside with a bounding volume hierarchy, which can be constructed based on dense sphere packings. In order to build our new hierarchy, 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.

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