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A three-dimensional (3D) particle surface can be mathematically represented by a spherical harmonic (SH) coefficient matrix through surface parameterisation and SH expansion. However, this matrix depends on not only the particle shape but also the size, position and orientation. This study adopts a rotation-invariant analysis to explore the relationship between SH coefficient matrices and particle shape characteristics. Particle shapes are quantified at different scales (i.e., form, roundness and compactness). These methods are applied to two groups of particles (i.e., Leighton Buzzard sand (LBS) particles and LBS fragments) with distinct shape features. By using rotation invariants, the multi-scale nature of particle shape is illustrated, and two novel shape descriptors are defined. The results in this paper serve as a starting point for the generation of particle shapes with prescribed shape features using spherical harmonic.

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