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A New Approach for the Geodesic Voronoi Diagram of Points in a Simple Polygon and Other Restricted Polygonal Domains

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Abstract.

We introduce a new method for computing the geodesic Voronoi diagram of point sites in a simple polygon and other restricted polygonal domains. Our method combines a sweep of the polygonal domain with the merging step of a usual divide-and-conquer algorithm. The time complexity is O((n+k) log(n+k)) where n is the number of vertices and k is the number of points, improving upon previously known bounds. Space is O(n+k) . Other polygonal domains where our method is applicable include (among others) a polygonal domain of parallel disjoint line segments and a polygonal domain of rectangles in the L 1 metric.

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Received February 15, 1996; revised November 2, 1996.

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Papadopoulou, E., Lee, D. A New Approach for the Geodesic Voronoi Diagram of Points in a Simple Polygon and Other Restricted Polygonal Domains . Algorithmica 20, 319–352 (1998). https://doi.org/10.1007/PL00009199

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  • DOI: https://doi.org/10.1007/PL00009199

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