Computing Skeletons for Rectilinearly Convex Obstacles in the Rectilinear Plane

We introduce the concept of an obstacle skeleton , which is a set of line segments inside a polygonal obstacle ω that can be used in place of ω when performing intersection tests for obstacle-avoiding network problems in the plane. A skeleton can have significantly fewer line segments compared to the number of line segments in the boundary of the original obstacle, and therefore performing intersection tests on a skeleton (rather than the original obstacle) can significantly reduce the CPU time required by algorithms for computing solutions to obstacle-avoidance problems. A minimum skeleton is a skeleton with the smallest possible number of line segments. We provide an exact O(n^2) algorithm for computing minimum skeletons for rectilinear obstacles in the rectilinear plane that are rectilinearly convex.