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

Thomas Lafarge, Beatriz Pateiro-López, Antonio Possolo, Joy Dunkers

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This work presents the implementation in R of the α-shape of a finite set of points in the three-dimensional space R3. This geometric structure generalizes the convex hull and allows to recover the shape of non-convex and even non-connected sets in 3D, given a random sample of points taken into it. Besides the computation of the α-shape, the R package alphashape3d provides users with tools to facilitate the three-dimensional graphical visu- alization of the estimated set as well as the computation of important characteristics such as the connected components or the volume, among others.

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