Random sequential adsorption of unoriented cuboids with a square base and a comparison of cuboid-cuboid intersection tests

TL;DR

This study investigates the packing density of randomly adsorbed cuboids with square bases, finding optimal shapes for maximum packing density and comparing intersection detection methods, highlighting the efficiency of the separating axis theorem.

Contribution

The paper introduces a detailed analysis of packing densities for various cuboid shapes and compares intersection detection algorithms, identifying the most efficient method.

Findings

Maximum packing density of 0.400 for specific cuboid ratios.

Oblate and prolate cuboids achieve higher densities than cubes.

Separating axis theorem is the fastest intersection detection method.

Abstract

In the paper, packings built of identical cuboids with a square base created by random sequential adsorption are studied. The result of the study show that the packing of the highest density are obtained for oblate and prolate cuboids of the edge-edge length ratios of $0.7$ and $1.4$. For both cases, the packing fraction is $0.400 \pm 0.002$, which is approximately 8% higher than the value reported for cubes. Additionally, because the crucial part of the packing generation algorithm is the cuboid-cuboid intersection detection, several methods were tested. It appears that the fastest one is based on the separating axis theorem.