…studiando 2

2 settembre, 2007

Altro passaggio che mette in relazione il diagramma di Voronoi con le bolle, nell’altro articolo consigliatomi sul forum. Si parla di una ricerca che riguarda

the modeling of the statistical properties of foams, and using the statistical properties to develop a methodology for reconstructing foams.

Il passaggio importante è questo:

We used a very simple system that is well studied to model so that we could compare our initial results with the results of others and be sure that we are on the right track. The system that we used was the two dimensional Delaunay-Voronoi Tessellation. In this system, for a given set of seed points thrown down randomly in a plane, the cells are all of the points which are closer to a particular seed point than to any other seed point in the system. The edges are the points which are equally close to two seed points and the vertices are equally close to three seed points. Despite the simplicity of the system, it actually is a good representation for a physical system. It accurately describes the structure of a two dimensional soap foam. The way such a foam is constructed is by taking two slabs of material and putting them very close together. By blowing bubbles of larger diameter than the separation of the slabs, one can generate flat bubbles in between the plates. If the density of bubbles is high, they will arrange themselves in a pattern consistent with the Voronoi tessellation. The Delaunay Triangulation is completely analogous to the Voronoi Tessellation. The Delaunay Triangulation forms lines between a seed point and each of its nearest neighbor seed points, forming triangles. Nearest neighbor seed points are completely equivalent to points which share a cell edge, hence the two tessellations are equivalent. In order to maximize data and not have issues with the edges, we used periodic boundary conditions. In order to calculate the Delaunay-Voronoi Tessellation, we used the C program QHULL, and qh-Math to port the QHULL into Mathematica.

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