Three-Dimensional Angularity Characterization of Coarse Aggregates by the Optimal Ellipsoid Approximation Algorithm

Abstract

The three-dimensional (3D) angularity of coarse aggregates was investigated in this study by an optimal ellipsoid approximation algorithm. The minimum volume enclosing ellipsoid (MVEE) of the 3D coarse aggregate particle represented by the surface point cloud was computed by a Python program. An algorithm was proposed to compute the optimal ellipsoid that is inscribed in the aggregate particle as far as possible. In the algorithm, a fitting index was proposed and a cycle program was coded to search the optimal ellipsoid. Based on the optimal ellipsoid and the point cloud of the coarse aggregate particle, a 3D angularity index was proposed. The critical discriminant coefficient was introduced into the angularity index to filter out the tiny convex parts on the particle. Six 3D geometric models were generated and five 3D aggregate particles were randomly selected to verify the effectiveness of the angularity index. The results demonstrate that the angularity index proposed in this study can effectively distinguish the angularity of different geometric models. The effect of mesh precision on the angularity index was analyzed and the critical discriminant coefficient was studied by the parameter analysis method and Delphi expert investigation method.