  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.
