Set Voronoi diagrams of 3D assemblies of aspherical particles

Fabian M. Schallerab, Sebastian C. Kapferac, Myfanwy E. Evansa, Matthias J.F. Hoffmanna, Tomaso Asted, Mohammad Saadatfare, Klaus Meckea, Gary W. Delaney*, Gerd E. Schröder-Turka

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    65 Citations (Scopus)

    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 theVoronoi 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 monodisperse 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.

    Original languageEnglish
    Pages (from-to)3993-4017
    Number of pages25
    JournalPhilosophical Magazine
    Volume93
    Issue number31-33
    DOIs
    Publication statusPublished - 2013

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