Time and space efficient algorithms for shortest paths between convex polygons

Abstract

Two algorithms are presented for computing shortest paths in the plane avoiding convex polygonal obstacles. For the first algorithm, the obstacles are assumed to consist of f disjoint convex polygons; for the second algorithm, the boundaries of the f polygons may intersect pairwise at most twice. For finding the shortest path between two arbitrary query points, the first algorithm takes O( fn log n) time and O( n) space, the second algorithm preprocesses the polygons in O( n log n+ f 3) time and O( n+ f 2) space. Thereafter, one query takes O( n log n+ f 2) time.