Low-resolution Spherical Harmonics Models in Application to Quasi-quadric Particle Shapes

In this paper a numerical analysis was performed developing low-resolution spherical harmonics (LRSH) models in order to describe particle shapes. The potential of LRSH, limited by the expansion degree L ≤ 3, to describe quasi-regular particle shapes was explored. The term “quasi” is used hereafter to indicate the monomeric, almost regular shaped, particle described by a single continuous function. This approach reflects the shape of a major part of soil minerals. It was shown, that even the simplest case of the suggested low-resolution harmonics technique with L = 1 showed sufficient accuracy. The main drawback of the suggested approach was that the low-resolution harmonics yield particle shapes with nearly sharp angles, there-fore, enhanced analysis of local surface curvatures becomes necessary. An application using quasi-ellipsoidal particles is enclosed.