Primitives for the manipulation of general subdivisions and the computation of Voronoi
ACM Transactions on Graphics (TOG)
Two-Dimensional Voronoi Diagrams in the Lp-Metric
Journal of the ACM (JACM)
Voronoi diagrams based on convex distance functions
SCG '85 Proceedings of the first annual symposium on Computational geometry
Java applets for the dynamic visualization of Voronoi diagrams
Computer Science in Perspective
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Voronoi diagrams in the plane for strictly convex distances have been studied in [3], [5] and [7]. These distances induce the usual topology in the plane and, moreover, the Voronoi diagrams they produce enjoy many of the good properties of Euclidean Voronoi diagrams. Nevertheless, we show (Th.1) that it is not possible to transform, by means of a bijection from the plane into itself, the computation of such Voronoi diagrams to the computation of Euclidean Voronoi diagrams (except in the trivial case of the distance being affinely equivalent to the Euclidean distance). The same applies if we want to compute just the topological shape of a Voronoi diagram of at least four points (Th.2).Moreover, for any strictly convex distance not affinely equivalent to the Euclidean distance, new, non Euclidean shapes appear for Voronoi diagrams, and we show a general construction of a nine-point Voronoi diagram with non Euclidean shape (Th.3).