A method that integrates elliptic Fourier and principal component analysis is a new development in the analysis of the shapes of sand grains. However, conventional elliptic Fourier and principal component analysis based on the variance-covariance matrix of the elliptic Fourier results can determine only the form of sand grains, and fails to quantify fine-scale boundary smoothness of grains. In this study, sand grains from glacial, fluvial, foreshore and aeolian environments were analysed using both elliptic Fourier and principal component analysis and an extension of elliptic Fourier and principal component analysis based on the correlation matrix to extract information on grain form (macroscopic) and grain boundary smoothness (microscopic) separately. Conventional elliptic Fourier and principal component analysis based on the variance-covariance matrix produces macroscopic particle shape descriptors, such as the elongation index and bump indices. These indices indicate that sand grains exposed to subaqueous transportation (fluvial and foreshore) have forms that are more elongated than those exposed to subaerial transportation (aeolian dunes). However, elliptic Fourier and principal component analysis based on the correlation matrix is, in addition, able to extract microscopic particle features, which can be interpreted in terms of a boundary smoothness index. The boundary smoothness index indicates that the surfaces of glacial grains are the most rugged, whereas the surfaces of aeolian grains are the smoothest. On bivariate plots of the boundary smoothness and elongation indices, samples from fluvial, foreshore, aeolian and glacial environments cluster in discrete regions. In addition, the analysis reveals that glacial grains are exposed to different morphological maturation pathways than those from fluvial, foreshore and aeolian environments.
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