Shortest Paths for Disc Obstacles

摘要

Given a number of obstacles in a plane, the problem of computing a geodesic (or the shortest path) between two points has been studied extensively. However, the case where the obstacles are circular discs has not been explored as much as it deserves. In this paper, we present an algorithm to compute a geodesic among a set of mutually disjoint discs, where the discs can have different radii. We devise two filters, an ellipse filter and a convex hull filter, which can significantly reduce the search space. After filtering, we apply Dijkstras algorithm to the remaining discs.