Geodesy

Quantum mechanics

Root mean square

Benchmark (surveying)

Scale (ratio)

Engineering

Materials science

Surface finish

Square (algebra)

Computer science

Surface (topology)

Geology

Surface roughness

Physics

Mathematics

Geometry

Composite material

Engineering drawing

Powder Technology

Surface roughness plays an important role in macro and micro-scale granular behaviors; however, there is currently lack of a unified approach to quantify the roughness of closed outlines and surfaces, which can consider the overall morphological characteristics of particles. This paper proposes approaches that are suitable for roughness evaluation of 2D general-shape closed outlines and 3D general-shape closed surfaces. For 2D closed outlines, the roughness is evaluated by comparing the real outline with the benchmark outline reconstructed based on the Fourier analyses. For 3D closed surfaces, the roughness is calculated by comparing the real surface against the benchmark surface reconstructed by the spherical harmonic analyses. The local deviation as well as the overall roughness of 2D closed outlines, and 3D closed surfaces, can be evaluated via the approach. After analyzing the roughness of two types of particles with different morphological characteristics by the proposed approaches, it is found that the 2D arithmetic average roughness and the 2D root mean square roughness are well correlated, and so are their 3D counterparts. Nevertheless, values of the 2D and 3D indices are not well correlated for each type of particles, and the particles with different texture can be more clearly distinguished from each other based on the 3D roughness parameters than on the 2D counterparts.

Roughness analysis of general-shape particles, from 2D closed outlines to 3D closed surfaces