Eecient Collision Detection Using Bounding Volume Hierarchies of K-dops

{ Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at real-time rates. Applications such as haptic force-feedback can require over 1000 collision queries per second. In this paper, we develop and analyze a method, based on bounding-volume hierarchies, for eecient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a \discrete orientation polytope" (\k-dop"), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small xed set of k orientations. We compare a variety of methods for constructing hierarchies (\BV-trees") of bounding k-dops. Further, we propose algorithms for maintaining an eeective BV-tree of k-dops for moving objects, as they rotate, and for performing fast collision detection using BV-trees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods. or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.