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Updated: May 26, 2026

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
Published on: April 26, 2016
Statistics of cross sections of Voronoi tessellations
1Dipartimento di Fisica Sperimentale and CNISM, via P. Giuria 1, I-10125 Turin, Italy. ferraro@ph.unito.it
Abstract:
In this paper, we investigate relationships between the volumes of cells of three-dimensional Voronoi tessellations and the lengths and areas of sections obtained by intersecting the tessellation with a randomly oriented plane. Here, in order to obtain analytical results, Voronoi cells are approximated to spheres. First, the probability density function for the lengths of the radii of the sections is derived and it is shown that it is related to the Meijer G function; its properties are discussed and comparisons are made with the numerical results. Next, the probability density function for the areas of cross sections is computed and compared with the results of numerical simulations.
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