Shortest Paths in the Plane with Convex Polygonal Obstacles
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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 2 log 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 ).
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