Uniform random Voronoi meshes

Abstract

We generate Voronoi meshes over three dimensional domains with prescribed boundaries. Voronoi cells are clipped at one-sided domain boundaries. The seeds of Voronoi cells are generated by maximal Poisson-disk sampling. In contrast to centroidal Voronoi tessellations, our seed locations are unbiased. The exception is some bias near concave features of the boundary to ensure well-shaped cells. The method is extensible to generating Voronoi cells that agree on both sides of two-sided internal boundaries. Maximal uniform sampling leads naturally to bounds on the aspect ratio and dihedral angles of the cells. Small cell edges are removed by collapsing them; some facets become slightly non-planar. Voronoi meshes are preferred to tetrahedral or hexahedral meshes for some La-grangian fracture simulations. We may generate an ensemble of random Voronoi meshes. Point location variability models some of the material strength variability observed in physical experiments. The ensemble of simulation results defines a spectrum of possible experimental results.