Comparative analysis of the size distributions of linear, planar, and spatial Poisson Voronoi cells

An analysis of the different cell-size distributions obtained by computer simulations of Poisson Voronoi cell structures in 1D, 2D, and 3D space is given. The different size distributions are given on a linear as well as on a logarithmic scale and are based on approximately 0.25–1.0 × 105 cells. None of the size distributions are found to be completely lognormal. However, the size distribution of lengths, areas, and volumes in the 1D, 2D, and 3D cases, respectively, are well described by different one-parameter gamma distribution functions. These results are fully in agreement with previous findings. The size distributions of intercept lengths of 1D sections through 2D and 3D structures, and the distribution of grain section areas from 2D sections through 3D cell structures have also been analyzed. None of these distributions are found to be well fitted by gamma distribution functions. These results are in agreement with previous analytical work, but do not support previous work that has suggested these distributions should be well described by gamma distribution functions.