On the statistics of area size in two-dimensional thick Voronoi Diagrams

TL;DR

This paper introduces the concept of thick Voronoi diagrams with non-zero edge widths and analyzes how cell area statistics change as the edge thickness varies, addressing a gap in traditional zero-width models.

Contribution

It presents a novel concept of thick Voronoi tessellations and provides an analysis of how cell area distributions are affected by edge thickness.

Findings

Cell area statistics depend on edge thickness.

Thick Voronoi diagrams differ significantly from traditional models.

The study offers insights for experimental situations with non-zero edge widths.

Abstract

Cells of Voronoi diagrams in two dimensions are usually considered as having edges of zero width. However, this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large. In this paper, the concept of a thick Voronoi tessellation, that is with edges of non-zero width, is introduced and the the statistics of cell areas, as thickness changes, are analyzed.