Spheroidal harmonics for generalizing the morphological decomposition of closed parametric surfaces

TL;DR

This paper introduces spheroidal harmonics as a generalization of spherical harmonics to improve morphological analysis of oblate and prolate particles, reducing distortions and oscillations in reconstruction.

Contribution

It proposes a spheroidal harmonics approach with new mapping techniques, enhancing analysis quality for non-spherical particles without heavy computational costs.

Findings

SOH reduces oscillations in particle reconstruction.

Three mapping techniques effectively handle various particle shapes.

SOH improves analysis accuracy over traditional SH methods.

Abstract

Spherical harmonics (SH) have been extensively used as a basis for analyzing the morphology of particles in granular mechanics. The use of SH is facilitated by mapping the particle coordinates onto a unit sphere, in practice often a straightforward rescaling of the radial coordinate. However, when applied to oblate- or prolate-shaped particles the SH analysis quality degenerates with significant oscillations appearing after the reconstruction. Here, we propose a spheroidal harmonics (SOH) approach for the expansion and reconstruction of prolate and oblate particles. This generalizes the SH approach by providing additional parameters that can be adjusted per particle to minimize geometric distortion, thus increasing the analysis quality. We propose three mapping techniques for handling both star-shaped and non-star-shaped particles onto spheroidal domains. The results demonstrate the ability of the SOH to overcome the shortcomings of SH without requiring computationally expensive solutions or drastic changes to existing codes and processing pipelines.