A new method is suggested to compute the intersection of a set of direction cones encountered in the problem of passing a convex polyhedron through a window. The time requirement of this method is (O(nm), where n is the number of vertices of the polyhedron and m is the number of vertices of the window. Besides this time improvement, the concept of parallel congruence, which the new method is crucially based on, is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28037/1/0000476.pd