Determining the Separation of Preprocessed Polyhedra - A Unified Approach

We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries e ciently (in a number of cases, optimally). Our emphasis is i) the uniform treatment of polyhedra separation problems, ii) the use of hierarchical representations of primitive objects to provide implicit representations of composite or transformed objects, and iii) applications to natural problems in graphics and robotics. Among the speci c results is an O(log jP j log jQj) algorithm for determining the separation of polyhedra P and Q (which have been individually preprocessed in at most linear time).