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R Implementation of a Polyhedral Approximation to a 3D Set of Points Using the Alpha-Shape



Thomas V. Lafarge, Beatriz Pateiro Lopez, Antonio M. Possolo, Joy P. Dunkers


This work describes the implementation in R of the alpha-shape of a finite set of points in three-dimensional space. This geometric construct generalizes the convex hull and estimates the shape of non-convex and even non-connected sets in 3D, given random samples of points drawn from them. Besides the computation of the alpha-shape, the R package alphashape3d provides users with tools to facilitate the three-dimensional graphical visualization of the estimated set, as well as the computation of geometrical attributes that include the connected components, surface area, volume, porosity, and connectivity, among others.
Journal of Statistical Software


Shape metrology, convex hull, set estimation, polymeric scaffold.


Lafarge, T. , Pateiro, B. , Possolo, A. and Dunkers, J. (2014), R Implementation of a Polyhedral Approximation to a 3D Set of Points Using the Alpha-Shape, Journal of Statistical Software, [online], (Accessed May 20, 2024)


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Created January 1, 2014, Updated January 27, 2020