Proceedings of the twenty-sixth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
The Geometric Stability of Voronoi Diagrams with Respect to Small Changes of the Sites
Proceedings of the twenty-seventh annual symposium on Computational geometry
Mollified zone diagrams and their computation
Transactions on Computational Science XIV
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Voronoi diagrams appear in many areas in science and technology and have diverse applications. Roughly speaking, they are a certain decomposition of a given space into cells, induced by a distance function and by a tuple of subsets called the generators or the sites. Voronoi diagrams have been thesubject of extensive research during the last 35 years, and manyalgorithms for computing them have been published. However, these algorithms are for specific cases. They imposerestrictions on either the space (often $R^2$ or $R^3$), the generators (distinct points, special shapes), the distance function (Euclidean or variations thereof) and more. Moreover, their implementation is not always simple andtheirsuccess is not always guaranteed. We present an efficient and simple algorithm for computing Voronoi diagramsin general normedspaces, possibly infinite dimensional. We allow infinitely many generators of a general form. The algorithm computes each of the Voronoi cells independently of the others, and to any required precision.It can be generalized to other settings, such as manifolds, graphs and convex distance functions.