3D generation of realistic granular samples based on random fields theory and Fourier shape descriptors

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A poly‐superellipsoid‐based approach on particle morphology for DEM modeling of granular media (2019, methodology): “It is worth noting that Equation (29) is fulfilled when Equation (28) reaches a global minimum.”
Generation of a realistic 3D sand assembly using X‐ray micro‐computed tomography and spherical harmonic‐based principal component analysis (2017, methodology): “In addition, Zhao et al. [12] noted that particle size has a significant effect on the statistical distribution of the 3D shape parameters of sand fragments during size evolution under the mechanical crushing process.”
Random generation of natural sand assembly using micro x-ray tomography and spherical harmonics (2015, methodology): “To overcome this limitation, Mollon & Zhao (2013, 2014) proposed a statistical method to generate a virtual packing of particles with realistically complex yet controllable shapes based on the theory of random fields for spherical topology combined with a Fourier shape descriptor.”
3D particle shape modelling and optimization through proper orthogonal decomposition (2017, unknown): “Sophisticated three-dimensional shape characterizations recently used include 3D extensions of Fourier descriptors [25,26], or spherical harmonics (SH) series (which appropriately generalize Fourier series in a spherical topology) [27–31].”