# Pomelo, a tool for computing Generic Set Voronoi Diagrams of Aspherical Particles of Arbitrary Shape

## TL;DR

Pomelo is a versatile software tool that efficiently computes Set Voronoi diagrams for aspherical particles, facilitating advanced analysis in granular and soft matter physics.

## Contribution

It introduces a generic, user-friendly software capable of handling arbitrary particle shapes for Set Voronoi diagram calculations, expanding analysis capabilities in complex particle systems.

## Key findings

- Enabled analysis of ellipsoidal particle packings with different friction levels
- Analyzed stable packings of tetrahedral particles
- Modeled liquid crystal systems with pear-shaped particles

## Abstract

We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to granular materials. A generalization of the conventional Voronoi diagram for points or monodisperse spheres is the Set Voronoi diagram, also known as navigational map or tessellation by zone of influence. In this construction, a Set Voronoi cell contains the volume that is closer to the surface of one particle than to the surface of any other particle. This is required for aspherical or polydisperse systems. Pomelo is designed to be easy to use and as generic as possible. It directly supports common particle shapes and offers a generic mode, which allows to deal with any type of particles that can be described mathematically. Pomelo can create output in different standard formats, which allows direct visualization and further processing. Finally, we describe three applications of the Set Voronoi code in granular and soft matter physics, namely the problem of packings of ellipsoidal particles with varying degrees of particle-particle friction, mechanical stable packings of tetrahedra and a model for liquid crystal systems of particles with shapes reminiscent of pears