Spherical Shell: A Higher Order Bounding Volume for Fast Proximity Queries

Abstract

Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physically-based modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are used to test for interference or compute distance bounds between the underlying geometry. The e ciency of a hierarchy is directly proportional to the choice of a bounding volume. In this paper, we introduce spherical shells, a higher order bounding volume for fast proximity queries. Each shell corresponds to a portion of the volume between two concentric spheres. We present algorithms to compute tight tting shells and fast overlap between two shells. Moreover, we show that spherical shells provide local cubic convergence to the underlying geometry. As a result, in many cases they provide faster algorithms for interference detection and distance computation as compared to earlier methods. We also describe an implementation and compare it with other hierarchies.