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Abstract: For any finite point set S in E d , an oriented matroid DOM(S) can be defined in terms of how S is partitioned by Euclidean hyperspheres. This oriented matroid is related to the Delaunay triangulation of S and is realizable, because of the lifting property of Delaunay triangulations. We prove that the same construction of a Delaunay oriented matroid can be performed with respect to any smooth, strictly convex distance function in the plane E 2 (Theorem 3.5). For these distances, the... (Update)
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...to Minkowskian geometry if and only if the unit ball K is an ellipse. The construction in the proof of the following theorem is based in [9]. Asplund and Grumbaum [1] have also given a characterization of ellipses in terms of a property of triangles of the Minkowskian...
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BibTeX entry: (Update)
F. Santos, On Delaunay oriented matroids for convex distance functions, Discrete and Computational Geometry, to appear. Extended abstract in Proceedings of the 6th Canadian Conference on Computational Geometry, University of Saskatoon, August 1994. http://citeseer.nj.nec.com/santos95delaunay.html More
@article{ santos96delaunay,
author = "Santos",
title = "On Delaunay Oriented Matroids for Convex Distance Functions",
journal = "GEOMETRY: Discrete & Computational Geometry",
volume = "16",
year = "1996",
url = "citeseer.nj.nec.com/santos95delaunay.html" }
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195 Voronoi diagrams -- A survey of a Fundamental Geometric Data.. (context) - Aurenhammer - 1991
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34 Voronoi Diagrams from Convex Hulls (context) - Brown - 1979
32 Voronoi Diagrams Based on Convex Distance Functions (context) - Chew - 1985
24 Concrete and Abstract Voronoi Diagrams (context) - Klein - 1989
19 Voronoi diagrams and arrangements (context) - Edelsbruner, Seidel - 1986
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13 Axioms and Hulls (context) - Knuth - 1992
3 Convex Distance Functions in 3-space are Different - Icking, Klein et al. - 1995
2 Geometry of bisectors for strictly convex distances (context) - Corbal'an, Maz'on et al.
2 the Topological Shape of Planar Voronoi Diagrams (context) - Corbal'an, Maz'on et al. - 1993
2 Combinatorial geometry of algebraic curves and Delaunay diag.. (context) - Santos - 1995
1 On general properties of strictly convex (context) - Le - 1993
1 Homothetic Ellipsoids (context) - Goodey - 1983
1 Otdelenie Matematischeskii i Estestvennyka Nauk (context) - Delaunay, Sphere et al. - 1934
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