Describing particle shape by Fourier series

The shape of solid particles exerts a fundamental influence on the efficiency of separation processes, transport behavior, and handling properties of granular materials such as mineral ores and industrial powders. Despite its significance, quantitatively describing particle shape remains a challenging morphometric task. Fourier analysis offers a rigorous mathematical framework for representing and comparing particle contours, yet its conceptual and computational complexity often limits its adoption in engineering education. This study presents a pedagogical methodology that integrates Fourier perimetric analysis into engineering curricula, emphasizing the connection between theory and practical application. The approach is based on an interactive computational case study in which students visualize how varying the number of Fourier harmonics affects the fidelity of particle shape reconstruction. The structured learning process includes: (i) introducing perimeter parameterization, (ii) understanding the Fourier trigonometric series and its harmonic components, and (iii) exploring the impact of harmonics through an interactive visualization tool. The methodology seeks to demystify Fourier analysis, helping engineering students develop both conceptual intuition and practical skills for applying shape analysis to material characterization and classification tasks. Ultimately, this framework supports the development of data-literate engineers capable of leveraging advanced quantitative tools for sustainable process optimization.