Set Voronoi diagrams of 3D assemblies of aspherical particles

Schaller FM, Kapfer SC, Evans M, Hoffmann M, Aste T, Saadatfar M, Mecke K, Delaney GW, Schröder-Turk G (2013)

Publication Status: Published

Publication Type: Conference contribution

Publication year: 2013

Journal

Publisher: TAYLOR & FRANCIS LTD

Book Volume: 93

Pages Range: 3993-4017

Journal Issue: 31-33

DOI: 10.1080/14786435.2013.834389

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.

Authors with CRIS profile

Involved external institutions

Max-Planck-Institut für Dynamik und Selbstorganisation / Max Planck Institute for Dynamics and Self-Organization Germany (DE) École Normale Supérieure de Cachan France (FR) University College London (UCL) United Kingdom (GB) Australian National University (ANU) Australia (AU) Commonwealth Scientific and Industrial Research Organisation (CSIRO) Australia (AU)

How to cite

APA:

Schaller, F.M., Kapfer, S.C., Evans, M., Hoffmann, M., Aste, T., Saadatfar, M.,... Schröder-Turk, G. (2013). Set Voronoi diagrams of 3D assemblies of aspherical particles. (pp. 3993-4017). TAYLOR & FRANCIS LTD.

MLA:

Schaller, Fabian M., et al. "Set Voronoi diagrams of 3D assemblies of aspherical particles." TAYLOR & FRANCIS LTD, 2013. 3993-4017.

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