TY - JOUR
T1 - Set Voronoi diagrams of 3D assemblies of aspherical particles
AU - Schallerab, Fabian M.
AU - Kapferac, Sebastian C.
AU - Evansa, Myfanwy E.
AU - Hoffmanna, Matthias J.F.
AU - Asted, Tomaso
AU - Saadatfare, Mohammad
AU - Meckea, Klaus
AU - Delaney, Gary W.
AU - Schröder-Turka, Gerd E.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
KW - Area Voronoi diagram
KW - Aspherical particles
KW - Ellipsoid packings
KW - Medial axes and surfaces
KW - Navigation map
KW - Random close packing
KW - Set Voronoi diagram
KW - Skeleton by zone of influence
UR - http://www.scopus.com/inward/record.url?scp=84888306814&partnerID=8YFLogxK
U2 - 10.1080/14786435.2013.834389
DO - 10.1080/14786435.2013.834389
M3 - Article
SN - 1478-6435
VL - 93
SP - 3993
EP - 4017
JO - Philosophical Magazine
JF - Philosophical Magazine
IS - 31-33
ER -