R implementation of a polyhedral approximation to a 3D set of points using the α-shape
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Abstract
This work presents the implementation in R of the α-shape of a nite 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 visualization 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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Lafarge, T., Pateiro-López, B., Possolo, A., Dunkers, Joy P. (2014). R implementation of a polyhedral approximation to a 3D set of points using the α-shape. "Journal of Statistical Software", 56, 4 [doi: 10.18637/jss.v056.i04]
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http://dx.doi.org/10.18637/jss.v056.i04Sponsors
This work has been partially supported by Spanish Grant MTM2008-03010 and the IAP
research network grant no. P6/03 from the Belgian government (Beatriz Pateiro-L opez), and by the Shape Metrology Innovations in Measurement Science from the National Institute of Standards and Technology (all the authors). Since the work is a work product of the National Institute of Standards and Technology, an agency of the U.S. federal government, it is not subject to copyright in the United States.
We are much indebted to Girish Kumar (currently at the Food and Drug Administration, U.S. Department of Health and Human Services, formerly in the Polymers Division, Material Measurement Laboratory, National Institute of Standards and Technology) who obtained the images of the polymeric sca old used in Section 4, and to Carl Simon and Tanya Farooque (Polymers Division, Material Measurement Laboratory, National Institute of Standards and Technology) for facilitating access to the digital data, and for suggesting substantively meaningful shape attributes to measure in polymeric sca olds. R is not a commercial product: it is a freely accessible software product. Its use here does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that it is necessarily the best available for the purpose
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Attribution 3.0 Unported (CC BY 3.0)