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Abstract: Introduction The Voronoi diagram of a set of sites partitions space into regions, one per site; the region for a site s consists of all points closer to s than to any other site. The dual of the Voronoi diagram, the Delaunay triangulation, is the unique triangulation so that the circumsphere of every triangle contains no sites in its interior. Voronoi diagrams and Delaunay triangulations have been rediscovered or applied in many areas of mathematics and the natural sciences; they are central... (Update)
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...The dimension of C is dim C = maxtor dims. The underlying space of C is [ J C = Jcc rr. Delaunay triangulation and Voronoi diagrams[23]. Let P = Pl, Pn be a set of points in 11 d. The Delaunay triangulation and Voronoi diagram can be defined as dual structures of the...
.... range queries, that is, for a set of sites in d d dimensional space (i.e. which site is nearest to a given query point [Fortune, 1992][O Rourke, 1998] An example VD is shown in Figure 5. The VD takes as input a set q of points in space called the sites, and...
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BibTeX entry: (Update)
Fortune, S., Voronoi Diagrams and Delaunay triangulations, in Computing in Euclidean Geometry, D. Z. Du, F.Hwang (eds.), World Scientific Publ., 1992, 193--223. http://citeseer.nj.nec.com/fortune95voronoi.html More
@incollection{ fortune92voronoi,
author = "Fortune",
title = "Voronoi Diagrams and Delaunay Triangulations",
booktitle = "Computing in Euclidean Geometry, Edited by Ding-Zhu Du and Frank Hwang, World Scientific, Lecture Notes Series on Computing -- Vol. 1",
year = "1992",
url = "citeseer.nj.nec.com/fortune95voronoi.html" }
Citations (may not include all citations):429 Algorithms in Combinatorial Geometry (context) - Edelsbrunner - 1987
420 Computational geometry (context) - Preparata, Shamos - 1985
272 Applications of random sampling in computational geometry - Clarkson, Shor - 1989
223 Primitives for the manipulation of general subdivisions and .. (context) - Guibas, Stolfi - 1985
203 Voronoi diagrams -- a survey of a fundamental geometric data.. (context) - Aurenhammer - 1991
157 Computational Geometry: an introduction through randomized a.. (context) - Mulmuley - 1994
69 A linear-time algorithm for computing the Voronoi diagram of.. (context) - Aggarwal, Guibas et al. - 1989
34 Higher-dimensional Voronoi diagrams in linear expected time (context) - Dwyer - 1991
32 Voronoi diagrams based on convex distance functions (context) - Chew, Drysdale - 1985
27 Output-sensitive construction of polytopes in four dimension.. (context) - Chan, Snoeyink et al. - 1995
27 An acyclicity theorem for cell complexes in d dimensions (context) - Edelsbrunner - 1990
26 Spatial Tesselations: concepts and applications of Voronoi d.. (context) - Okabe, Boots et al. - 1992
21 Optimality of the Delaunay triangulation in R d (context) - Rajan - 1994
21 Minimal roughness property of the Delaunay triangulation (context) - Rippa - 1990
19 Two-dimensional Voronoi diagrams in the L p metric (context) - Lee - 1980
18 An optimal convex hull algorithm and new results on cuttings (context) - Chazelle - 1991
17 Efficient computation of Euclidean shortest paths in the pla.. (context) - Hershberger, Suri - 1993
16 An optimal algorithm for constructing the weighted Voronoi d.. (context) - Aurenhammer, Edelsbrunner - 1984
15 Randomized incremental construction of abstract Voronoi diag.. (context) - Klein, Mehlhorn et al. - 1993
9 Progress in computational geometry (context) - Fortune - 1993
9 the geodesic Voronoi diagram of point sites in a simple poly.. (context) - Aronov - 1989
9 Power diagrams: properties (context) - Aurenhammer - 1987
4 Computing in Euclidean Geometry (context) - Fortune, diagrams et al. - 1992
4 A linear-time randomized algorithm for the bounded Voronoi d.. - Klein, Lingas - 1993
1 A simple randomized incremental algorithm for computing high.. (context) - Aurenhammer, Schwarzkopf - 1995
1 Bucketing and filtering in computational geometry (context) - Katajainen - 1987
1 Multiplicatively weighted crystal growth Voronoi diagram (context) - Schaudt, Drysdale - 1991
1 Constructing levels in arrangments and higher order Voronoi .. (context) - Agarwal, de Berg et al. - 1994
1 Natural neighbor interpolation (context) - Sibson - 1981
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