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 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 one-dimensional case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size distribution function in the practically important two-and three dimensional cases as well. Denoting the dimensionality of the space by d (d = 1, 2, 3) the f (y) = Const * y (3d−1)/2 exp(−(3d + 1)y/2) compact form is suggested for the normalized cell-size distribution function. By using large-scale computer simulations the validity of the proposed distribution function is studied and critically discussed.
An analytical approximation for the Voronoi cell size has been derived in REF .
On the size-distribution of Poisson Voronoi cells
Physics Mathematics