Voronoi Diagrams for a Moderate-Sized Point-Set in a Simple Polygon
نویسندگان
چکیده
Given a set of sites in a simple polygon, a geodesic Voronoi diagram partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple n-gon, which improve the best known ones form ≤ n/polylogn. Moreover, the algorithms for the nearest-point and farthest-point Voronoi diagrams are optimal for m ≤ n/ polylogn. This partially answers a question posed by Mitchell in the Handbook of Computational Geometry. 1998 ACM Subject Classification I.3.5 Computational Geometry and Object Modeling
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