The geometrical properties of random 2D Voronoi tesselations for the prediction of the tempered glass fracture pattern

Abstract

ABSTRACTThis paper presents spatial statistical investigations of randomly generated 2D Voronoi tessellations of planar point distributions for the prediction of the fracture pattern of thermally tempered glasses. Statistical distributions of geometrical characteristics of two dimensional Voronoi cells for three types of point processing in the plane of homogeneous Poisson point process (HPP), Matérn Hard‐Core point process (MHCP) and Strauss point process (SP) are numerically obtained based on the computer experiments. In this paper, required parameters of the point processes are presented. Samples of Voronoi cells in two dimensional spaces are generated from the point distributions. The generated random Voronoi tessellations are examined for their uniformity in comparison to a regular honey comb with hexagonal cells. The statistical distributions of geometrical characteristics, the cell area, the cell perimeter and the number of edges per cell are presented for each of the three point processes.