This paper presents efficient time-interrupted and time-continuous collision detection procedures for polyhedral objects which consist of convex polygons and perform arbitrary translating and/or rotating motions in a 3-D graphical environment. The time-interrupted collision detection procedure can find the exact position of a collision event in a time step while the time-continuous procedure can determine both the approximate time and position of a collision event. Each procedure first localizes the object-to-object collision events using a “space cell” method, which divides the 3-D environment into small cells in order to reduce the number of object pairs required for collision detection. An “azimuthelevation map” method is then proposed which rapidly selects the polygons within or crossing the overlap region between two possibly colliding objects by presorting their vertices in the spherical coordinates system. Subsequently, a divide-and-conquer method that takes advantage of a recursive scheme is devised to moderate the number of polygons which need to be checked by means of a polygon-to-polygon intersection test. To deal with time-interrupted and time-continuous collision detection, two respective polygon-to-polygon intersection testing methods based on a hierarchical scheme are developed to diminish the number of unnecessary computations. All the experiments were performed using computer simulation. So far, the experimental results from our proposed methods are very encouraging