Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
On shortest paths in polyhedral spaces
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Retraction: A new approach to motion-planning
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Shortest paths in the plane with polygonal obstacles
Journal of the ACM (JACM)
Collision Detection of a Moving Polygon in the Presence of Polygonal Obstacles in the Plane
IEEE Transactions on Pattern Analysis and Machine Intelligence
Simple wriggling is hard unless you are a fat hippo
FUN'10 Proceedings of the 5th international conference on Fun with algorithms
Shortest paths with arbitrary clearance from navigation meshes
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Computing shortest paths amid pseudodisks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A near-optimal algorithm for shortest paths among curved obstacles in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
Computing shortest paths among curved obstacles in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Given a robot R, a set S of obstacles, and points p and q, the Shortest Path Problem is to find the shortest path for R to move from p to q without crashing into any of the obstacles. We show that if the problem is restricted to a disc-shaped robot in the plane with nonintersecting polygons as obstacles then the shortest path can be found in time &Ogr;(n2log n) where n is the number of edges that make up the polygonal obstacles. This matches the best time currently known for the simpler problem of finding the shortest path in the plane for a point robot.