Additively Weighted Voronoi Diagram on the Oriented Projective Plane
نویسندگان
چکیده
We give a new simple on-line incremental algorithm for the additively weighted Voronoi diagram, whose primitive operations are completely based on orientation tests. It is known that the closest site diagram can be disconnected, and that the furthest site diagram can have disconnected faces. The algorithm avoids such nuisances by using the oriented projective plane as an underlying geometry. In this geometry, the closest and furthest site diagrams are antipodal. This means that they are, actually, the same diagram; which is always connected, every face is simply connected, and, as a consequence, has exactly 3n ? 6 edges and 2n ? 4 vertices, where n is the number of sites.
منابع مشابه
Additively Weighted Voronoi Diagram on the Oriented Projective Plane Additively Weighted Voronoi Diagram on the Oriented Projective Plane
We consider Voronoi diagrams deened on the oriented projective plane T 2. In this geometry, the closest and furthest site diagrams are antipodal. We give a simple on-line incremental algorithm for constructing the additively weighted diagram. This diagram, which may be disconnected in Euclidean plane, is always connected in T 2 and has exactly 3n ? 6 edges and 2n ? 4 vertices, where n is the nu...
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