An in-depth comparative study of three-dimensional angularity indices of general-shape particles based on spherical harmonic reconstruction

Abstract An in-depth comparative study is conducted on four three-dimensional (3D) angularity indices, namely, the radius-based angularity index (AIr), gradient-based angularity index (AIg), deviation angle-based angularity index (AId), and Gaussian curvature-based angularity index (AIG). An innovative modification is carried out to ensure that all the indices equal zero for spheres and ellipsoids. Each AI is evaluated on particle surfaces reconstructed through spherical harmonic analyses with regular polyhedral meshes of different sizes. This comprehensive comparative study revealed that AIg and AIG better reflect the local morphological characteristics of the particles than AIr and AId. To obtain a convergent value of the overall AI of the particles, a relatively coarse mesh is sufficient for estimating AIr and AId, whereas a fine mesh is required to estimate AIG and AIg. Among the four indices, only AIG and AIg are well correlated, and their relationship can be described by a power function.