Related papers: Identifying Phase Space Boundaries with Voronoi Te…
We present a method to numerically estimate the densities of a discretely sampled data based on binary space partitioning tree. We start with a root node containing all the particles and then recursively divide each node into two nodes each…
Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three dimensional…
Visual recognition of material boundaries in transparent vessels is valuable for numerous applications. Such recognition is essential for estimation of fill-level, volume and phase-boundaries as well as for tracking of such chemical…
A novel method allowing to compute density, velocity and other fields in cosmological N--body simulations with unprecedentedly high spatial resolution is described. It is based on the tessellation of the three-dimensional manifold…
The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern "random", Poisson-Voronoi tessellations (PVT), or "non-random", Non Poisson-Voronoi…
For a group of pedestrians without any spatial boundaries, the methods of density estimation is a wide area of research. Besides, there is a specific difficulty when the density along one given pedestrian trajectory is needed in order to…
We present a new particle-merging algorithm for the particle-in-cell method. Based on the concept of the Voronoi diagram, the algorithm partitions the phase space into smaller subsets, which consist of only particles that are in close…
We propose an automated method for detecting galaxy clusters in imaging surveys based on the Voronoi tessellation technique. It appears very promising, expecially for its capability of detecting clusters indipendently from their shape.…
An important open question in the modeling of biological tissues is how to identify the right scale for coarse-graining, or equivalently, the right number of degrees of freedom. For confluent biological tissues, both vertex and Voronoi…
We review the concepts of the Voronoi binning technique (Cappellari & Copin 2003), which optimally solves the problem of preserving the maximum spatial resolution of general two-dimensional data, given a constraint on the minimum…
General classical arguments on the time evolution of the phase-space density can be used to derive constraints on the mass of particle candidates for the cosmological dark matter (DM). The resulting Tremaine-Gunn limit is extremely useful…
We present a new open source code for massive parallel computation of Voronoi tessellations(VT hereafter) in large data sets. The code is focused for astrophysical purposes where VT densities and neighbors are widely used. There are several…
We describe two new -- stochastic-geometrical -- methods to obtain reliable velocity field statistics from N-body simulations and from any general density and velocity fluctuation field sampled at a discrete set of locations. These methods,…
We have recently developed a mean-field theory to estimate the packing fraction of non-spherical particles [A. Baule et al., Nature Commun. (2013)]. The central quantity in this framework is the Voronoi excluded volume, which generalizes…
The area query, to find all elements contained in a specified area from a certain set of spatial objects, is a very important spatial query widely required in various fields. A number of approaches have been proposed to implement this…
This paper introduces a new approach toward characterizing local structural features of two-dimensional particle systems. The approach can accurately identify and characterize defects in high-temperature crystals, distinguish a wide range…
The size distributions of 2D and 3D Voronoi cells and of cells of $V_p(2,3)$,--2D cut of 3D Voronoi diagram--are explored, with the single-parameter (re-scaled) gamma distribution playing a central role in the analytical fitting.…
We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random…
We prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson random sets in the plane we obtain an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. The result relies on…
Recent work on distinct multicellular organisms has revealed a hitherto unknown type of biological noise; rather than a regular arrangement, cellular neighborhood volumes, obtained by Voronoi tessellations of the cell locations, are broadly…