On the size distribution of Poisson Voronoi cells

Járai-Szabó Ferenc and Zoltán Néda

Physica A: Statistical Mechanics and its Applications, 2007, vol. 385, issue 2, 518-526

Abstract: Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three-dimensional (3D) spaces there is no exact result known for the size distribution of Voronoi cells. Motivated by the simple form of the distribution function in the 1D case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size-distribution function in the practically important 2D and 3D cases as well. Denoting the dimensionality of the space by d (d=1,2,3) the f(y)=Const*y(3d-1)/2exp(-(3d+1)y/2) compact form is suggested for the normalized cell-size distribution function. By using large-scale computer simulations the viability of the proposed distribution function is studied and critically discussed.

Keywords: Voronoi diagrams; Monte Carlo methods; Cell-size distribution (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:385:y:2007:i:2:p:518-526

DOI: 10.1016/j.physa.2007.07.063

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