Efficient discrete-time collision detection among polyhedral objects in arbitrary motion

Abstract

This paper presents an efficient discrete-time collision detection procedure for polyhedral objects that consist of convex polygons and perform arbitrary translating and/or rotating motions in a 3-D graphical environment. The discrete-time collision detection procedure can find the exact position of a collision event for a time step, which first localized the object-to object collision events with a "space cell" method, An "azimuth-elevation map" method is then proposed to rapidly select the polygons within or across the overlap region between two possibly collided objects by presorting their vertices in the spherical coordinated system.Subsequently, a divide-and-conquer method that takes advantage of bounding box representation is devised to moderate the number of polygons needed to be checked by a polygon-to-polygon intersection test. To deal with the discrete-time collision detection, a polygon-to-polygon intersection testing method based on a hierarchical scheme is developed to diminish unnecessary computation. So far, the experimental results from our proposed methods are very encouraging