A note on generating Voronoi cells with a given size distribution

TL;DR

This paper presents a straightforward method for generating random points to produce Voronoi tessellations with a specified size distribution, demonstrated in 2D with numerical verification and an implementation.

Contribution

It introduces a simple technique to generate point sets that yield Voronoi cells with a desired size distribution, including power laws.

Findings

Method effectively produces Voronoi cells with target size distributions.

Numerical verification confirms the method's accuracy in 2D.

Implementation provided for practical use.

Abstract

This note describes a simple method to draw random points such that the cells of the corresponding Voronoi tesselation (approximately) satisfy a desired size distribution, for instance, follow a power law. The method is illustrated and numerically verified in two dimensions, and we also provide a simple implementation.