کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
976647 | 933143 | 2007 | 9 صفحه PDF | دانلود رایگان |

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=1,2,3d=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.
Journal: Physica A: Statistical Mechanics and its Applications - Volume 385, Issue 2, 15 November 2007, Pages 518–526