Set Voronoi Tessellation for Particulate Systems in Two Dimensions

TL;DR

This paper introduces Set Voronoi tessellation for analyzing the structure of non-spherical particles in two-dimensional systems, providing a computational method and open-source code applicable to various shapes like granular rods, bees, and pedestrians.

Contribution

It develops a novel Set Voronoi approach for non-point particles in 2D, with an implementation balancing accuracy and computational efficiency, and releases open-source code.

Findings

Effective structural analysis of non-spherical particles

Application to granular rods, bees, and pedestrians

Open-source Python implementation available

Abstract

Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a long history and widespread applications in diverse disciplines, from astronomy to urban planning. For particulate systems in real life, such as a pile of sand or a crowd of pedestrians, the realization of Voronoi tessellation needs to be modified to accommodate the fact that the particles cannot be simply treated as points. Here, we elucidate the use of Set Voronoi tessellation (i.e., considering for a non-spherical particle a set of points on its surface) to extract meaningful local information in a quasi-two-dimensional system of granular rods. In addition, we illustrate how it can be applied to arbitrarily shaped particles such as an assembly of honey bees or pedestrians for obtaining structural information. Details on the implementation of this algorithm with the strategy of balancing computational cost and accuracy are discussed. Furthermore, we provide our python code as open source in order to facilitate Set Voronoi calculations in two dimensions for arbitrarily shaped objects.