Computing the 3D Voronoi Diagram Robustly: An Easy Explanation

Authors:
Hugo Ledoux
Affiliations:
Delft University of Technology, the Netherlands
Venue:
ISVD '07 Proceedings of the 4th International Symposium on Voronoi Diagrams in Science and Engineering
Year:
2007

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Abstract

Many algorithms exist for computing the 3D Voronoi diagram, but in most cases they assume that the input is in general position. Because of the many degeneracies that arise in 3D geometric computing, their implementation is still problematic in practice. In this paper, I describe a simple 3D Voronoi diagram (and Delaunay tetrahedralization) algorithm, and I explain, by giving as many details and insights as possible, how to ensure that it outputs a correct structure, regardless of the spatial distribution of the points in the input.