Abstract: This chapter surveys the Voronoi diagram and related topics. The Voronoi diagram is the partition of a space according to the nearest-site rule. The concept of the Voronoi diagram is related to a wide variety of areas from the analysis of natural forms to the analysis of social and geographic systems. The chapter defines the most primitive version of the Voronoi diagram, and summarizes its basic properties together with the algorithms for constructing it. It presents various applications of the Voronoi diagram, where special emphasis is placed on offsetting and interpolations. It describes the two-dimensional Voronoi and Delaunay diagrams. Delaunay triangulation gives an optimal triangulation, in the sense that the smallest angle among all the triangles is the largest. The chapter generalizes Voronoi diagrams in various directions, and presents a framework for this generalization.
Publication Year: 2002
Publication Date: 2002-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 1
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