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Computing Minimum Length Paths of a Given Homotopy Class
 Comput. Geom. Theory Appl
, 1991
"... In this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides reveal ..."
Abstract

Cited by 73 (7 self)
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In this paper, we show that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon. We optimize a given path among obstacles in the plane under the Euclidean and link metrics and under polygonal convex distance functions. Besides revealing connections between the minimum paths under these three distance functions, the framework provided by the universal cover leads to simplified lineartime algorithms for shortest path trees, for minimumlink paths in simple polygons, and for paths restricted to c given orientations. 1 Introduction If a wire, a pipe, or a robot must traverse a path among obstacles in the plane, then one might ask what is the best route to take. For the wire, perhaps the shortest distance is best; for the pipe, perhaps the fewest straightline segments. For the robot, either might be best depending on the relative costs of turning and moving. In this paper, we find shortest paths and shortest closed curve...
AN O(n log log n)TIME ALGORITHM FOR TRIANGULATING A SIMPLE POLYGON
, 1988
"... Given a simple nvertex polygon, the triangulation problem is to partition the interior of the polygon into n2 triangles by adding n3 nonintersecting diagonals. We propose an O(n log logn)time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that tria ..."
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Cited by 37 (4 self)
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Given a simple nvertex polygon, the triangulation problem is to partition the interior of the polygon into n2 triangles by adding n3 nonintersecting diagonals. We propose an O(n log logn)time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that triangulation is not as hard as sorting. Improved algorithms for several other computational geometry problems, including testing whether a polygon is simple, follow from our result.
Efficient algorithms for planning purely translational collisionfree motion in two and three dimensions
 Proc. of the IEEE Int. Conf. on Robotics and Automation, Raleigh NC
, 1987
"... In this abstract we present a collection of results representing recent progress in the design and analysis of efficient algorithms for planning purely translational collisionfree motion of rigid objects moving in ..."
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Cited by 13 (2 self)
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In this abstract we present a collection of results representing recent progress in the design and analysis of efficient algorithms for planning purely translational collisionfree motion of rigid objects moving in