On the size distribution of Poisson Voronoi cells |
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Authors: | Járai-Szabó Ferenc Zoltán Néda |
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Institution: | a Department of Theoretical and Computational Physics, Babe?-Bolyai University, str. Kog?lniceanu 1, RO-400084 Cluj-Napoca, Romania b Interdisciplinary Computer Simulation Group, KMEI, str. Tipografiei 12, RO-400101, Cluj-Napoca, Romania |
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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 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. |
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Keywords: | 89 75 Kd 02 50 Ng 02 10 &minus v |
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