Set Voronoi diagrams of 3D assemblies of aspherical particles - Schaller, Fabian M. and Kapfer, Sebastian C. and Evans, Myfanwy E. and Hoffmann, Matthias J. F. and Aste, Tomaso and Saadatfar, Mohammad and Mecke, Klaus and Delaney, Gary W. and Schroeder-Turk, Gerd E.
PHILOSOPHICAL MAGAZINE 93, 3993-4017 (2013)
Abstract : Several approaches to quantitative local structure characterization for
particulate assemblies, such as structural glasses or jammed packings,
use the partition of space provided by the Voronoi diagram. The
conventional construction for spherical mono-disperse particles, by
which the Voronoi cell of a particle is that of its centre point, cannot
be applied to configurations of aspherical or polydisperse particles.
Here, we discuss the construction of a Set Voronoi diagram for
configurations of aspherical particles in three-dimensional space. The
Set Voronoi cell of a given particle is composed of all points in space
that are closer to the surface (as opposed to the centre) of the given
particle than to the surface of any other; this definition reduces to
the conventional Voronoi diagram for the case of mono-disperse spheres.
An algorithm for the computation of the Set Voronoi diagram for convex
particles is described, as a special case of a Voronoi-based medial axis
algorithm, based on a triangulation of the particles' bounding surfaces.
This algorithm is further improved by a pre-processing step based on
morphological erosion, which improves the quality of the approximation
and circumvents the problems associated with small degrees of
particle-particle overlap that may be caused by experimental noise or
soft potentials. As an application, preliminary data for the volume
distribution of disordered packings of mono-disperse oblate ellipsoids,
obtained from tomographic imaging, is computed.