An Efficient Implementation of Fortune’s Plane-Sweep Algorithm for Voronoi Diagrams
نویسندگان
چکیده
1 Introduction
منابع مشابه
Parallel computing 2D Voronoi diagrams using untransformed sweepcircles
Voronoi diagrams are among the most important data structures in geometric modeling. Among many efficient algorithms for computing 2D Voronoi diagrams, Fortune’s sweepline algorithm (Fortune, 1986 [5]) is popular due to its elegance and simplicity. Dehne and Klein (1987) [8] extended sweepline to sweepcircle and suggested computing a type of transformed Voronoi diagram, which is parallel in nat...
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We have extended Fortune’s sweep-line algorithm for the construction Voronoi diagrams in the plane to the surface of a sphere. Although the extension is straightforward, it requires interesting modifications. The main difference between the sweep line algorithms on plane and on the sphere is that that the beach line on the sphere is a closed curve. We have implemented this algorithm and tessell...
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The geometry of circles in the plane is inextricably tied with the group of Möbius transformations, which take circles to circles. This geometry can be seen in a more symmetric after transforming the plane to the sphere, by stereographic projection. Interpretations will be discussed for Voronoi diagrams, Delaunay triangulations,etc. from this point of view. Fortune’s algorithm for constructing ...
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The Voronoi diagram is an important data structure in computational geometry. Given n sites in the plane, the Voronoi diagram partitions the plane into n regions. The region of a site p consists of all those points that lie closer to p than to any of the other sites. For a survey on Voronoi diagrams and their applications we refer to Aurenhammer [1]. A generalization of the sweep line method of...
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