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

Abstract

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.