Duals of Orphan-Free Anisotropic Voronoi Diagrams are Triangulations

Details Duals of Orphan-Free Anisotropic Voronoi Diagrams are Triangulations Duals of Orphan-Free Anisotropic Voronoi Diagrams are Triangulations

2011-02-17

arxiv.org/abs/1102.3673v2

Computer Science

Computational Geometry

20 pages, 8 figures

Scientific paper

We show that, under mild conditions on the underlying metric, duals of appropriately defined anisotropic Voronoi diagrams are embedded triangulations. Furthermore, they always triangulate the convex hull of the vertices, and have other properties that parallel those of ordinary Delaunay triangulations. These results apply to the duals of anisotropic Voronoi diagrams of any set of vertices, so long as the diagram is orphan-free.

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