INTRODUCTION
Given a finite set S of “sites” p i located in Euclidean space ℜd, the Voronoi polyhedron V(p j) of site p j is the set of all points p ∈ ℜd which are at least as close to site p j as to any other site p i.
Such a Voronoi polyhedron (also called “ Thiessen polygon” or “ Wigner-Seitz cell”) is convex, its facets determined by perpendicular bisectors — (hyper)planes or lines of equal Euclidean distance from two distinct sites. The Voronoi polyhedra V(p i), p i ∈ S cover the space ℜd and define a polyhedral cell-complex known as a Voronoi diagram (Voronoi, 1908) or Dirichlet tesselation (Dirichlet, 1850). For a survey, consult Aurenhammer (1991); also see the texts by Okabe, Boots, and Sugihara (1992); Preparata and Shannos (1985); Edelsbrunner (1987); and Goodman and O'Rourke (1997).
The cells of the dual complex are convex and, in general, simplicial. By partitioning nonsimplicial cells of the dual complex into simplices, the Delaunay triangulation results (Figure 1). It...
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Beichl, I., Bernal, J., Witzgall, C., Sullivan, F. (2001). Voronoi constructs . In: Gass, S.I., Harris, C.M. (eds) Encyclopedia of Operations Research and Management Science. Springer, New York, NY. https://doi.org/10.1007/1-4020-0611-X_1115
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