Modelling soil particles by low-resolution spherical harmonics

Abstract

The paper addresses the applicability of spherical harmonics (SH) technique to describe particles shape. It is aimed to demonstrate basic features of the low-resolution spherical harmonics limited by the expansion degree L ≤ 3 and apply them to describe specified shapes. The modelling quality was evaluated by considering selected error norms and the most important integral characteristics of a particle, the surface area and the body volume. It was shown, that the even simplest case of the suggested low-resolution harmonics technique with L = 1 shows good performance for both rounded ellipsoids as well as angular octahedrons with sharp edges. For application of SH to hexahedron shaped particles (rectangular parallelepiped) the higher L = 3 degree must be used. The low-resolution harmonics yield particle shapes with rounded angularities. Therefore, enhanced future analysis of the local surface gradients and curvatures has to be performed.