The predicates for the Voronoi diagram of ellipses
Proceedings of the twenty-second annual symposium on Computational geometry
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Medial axis computation for planar free-form shapes
Computer-Aided Design
Divide-and-conquer for Voronoi diagrams revisited
Proceedings of the twenty-fifth annual symposium on Computational geometry
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Divide-and-conquer for Voronoi diagrams revisited
Computational Geometry: Theory and Applications
Algorithms and theory of computation handbook
Journal of Mathematical Modelling and Algorithms
Dynamic medial axes of planar shapes
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
Transactions on Computational Science XIV
Computational and structural advantages of circular boundary representation
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Computer Aided Geometric Design
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Voronoi diagrams of curved objects can show certain phenomena that are often considered artifacts: The Voronoi diagram is not connected; there are pairs of objects whose bisector is a closed curve or even a two-dimensional object; there are Voronoi edges between different parts of the same site (so-called self-Voronoi-edges); these self-Voronoi-edges may end at seemingly arbitrary points not on a site, and, in the case of a circular site, even degenerate to a single isolated point. We give a systematic study of these phenomena, characterizing their differential-geometric and topological properties. We show how a given set of curves can be refined such that the resulting curves define a “well-behaved” Voronoi diagram. We also give a randomized incremental algorithm to compute this diagram. The expected running time of this algorithm is O(n log n).