Voronoi Diagrams and Their Uses

Mark Burkey, Joy Bhadury () and H. A. Eiselt ()
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Joy Bhadury: University of North Carolina – Greensboro
H. A. Eiselt: University of New Brunswick

Chapter Chapter 19 in Foundations of Location Analysis, 2011, pp 445-470 from Springer

Abstract: Abstract Voronoi diagrams are a very simple geometrical construct with a large variety of applications. Simply put, the problem can be described as follows. Consider some d-dimensional space in which a number of given points (sometimes referred to as seeds, attractors, or generators) are located. To each seed we assign a set that includes all points that are closer to the seed it is assigned to than to any other seed. Such a set is called a Voronoi set. The collection of all Voronoi sets is then a Voronoi diagram. Voronoi diagrams can be constructed for a number of different metrics. Clearly, different metrics will lead to different measures of proximity that result in rather different Voronoi diagrams.

Keywords: Voronoi Diagram; Block Group; Voronoi Cell; Seed Point; Attraction Function (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/978-1-4419-7572-0_19

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