Gallery: Complicated boundaries: a funnel
Update (October 2008): the software used to create the this image is now available as an open source library – see the Voro++ website.
As described in the previous image, our group makes extensive use of the Voronoi tesselation to obtain accurate measurements of the local packing fraction in a granular material, on a scale of a few particle diameters.
Several methods for computing Voronoi tesselations are available, and one is built into the popular mathematical package Matlab, which makes use of the dual Delaunay triangulation. For our purposes, we created a plane-cutting algorithm which would rapidly calculate Voronoi cells directly.
Such an algorithm lends itself well to cases where we wish to handle complicated geometries. The above image shows Voronoi cells computed for particles falling out of a conical funnel, looking up from below.
