Generalized Unfoldings for Shortest Paths

Abstract

We consider the problem of determining shortest paths in the presence of polyhe dral obstacles between two points in Euclidean three-space. For the special case when paths are constrained to the surfaces of three-dimensional objects, simple planar unfoldings are used to obtain the shortest path. For the general case when paths are not constrained to lie on any surface, we describe general ized unfoldings wherein the shortest path in three-space again becomes a straight line. These unfoldings of consist of multiple rotations about the edges of the polyhedral obstacles.