Shortest paths in the plane with convex polygonal obstacles

Abstract

An algorithm is presented which computes shortest paths in the Euclidean plane that do not cross given obstacles. The set of obstacles is assumed to consist of f disjoint convex polygons with n vertices in total. After preprocessing time O(n + f 2log n), the shortest path between two arbitrary query points can be found in O(f 2 + n log n) time. The space complexity is O(n + f 2).