Related papers: Computation of Centroidal Voronoi Tessellations in…
In this paper, we construct an algorithm for determining whether a given tessellation on a sphere is a spherical Laguerre Voronoi diagram or not. For spherical Laguerre tessellations, not only the locations of the Voronoi generators, but…
We present an objective and automated procedure for detecting clusters of galaxies in imaging galaxy surveys. Our Voronoi Galaxy Cluster Finder (VGCF) uses galaxy positions and magnitudes to find clusters and determine their main features:…
Voronoi diagrams, and their more general weighted counterpart, power diagrams, are fundamental geometric constructs with wide-ranging applications. Recently, they have gained renewed attention in mesh-based neural rendering. Despite being…
A Voronoi diagram partitions the plane into convex cells, each containing the points closest to a single generator. Given such a tessellation, the inverse Voronoi problem seeks the generator set \( S \) that produced it. Our algorithm…
Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up…
We propose finite-time measures to compute the divergence, the curl and the velocity gradient tensor of the point particle velocity for two- and three-dimensional moving particle clouds. For this purpose, a tessellation of the particle…
I present a regression algorithm that provides a continuous, piecewise-smooth function approximating scattered data. It is based on composing and blending linear functions over Voronoi cells, and it scales to high dimensions. The algorithm…
Given a network, the statistical ensemble of its graph-Voronoi diagrams with randomly chosen cell centers exhibits properties convertible into information on the network's large scale structures. We define a node-pair level measure called…
We have developed a novel method of determining 2D radial density profiles for astronomical systems of discrete objects using Voronoi tessellations. This Voronoi-based method was tested against the standard annulus-based method on 5…
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small…
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.…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
A method is developed to compute the chord length distribution along a line which intersects a cellular Universe. The cellular Universe is here modeled by the Poissonian Voronoi Tessellation (PVT) and by a non-Poissonian Voronoi…
Given two sets of training samples, general method is to estimate the density function and classify the test sample according to higher values of estimated densities. Natural way to estimate the density should be histogram tending to…
We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the…
In this paper, we study a generalization of the classical Voronoi diagram, called clustering induced Voronoi diagram (CIVD). Different from the traditional model, CIVD takes as its sites the power set $U$ of an input set $P$ of objects. For…
The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in $\mathbb{R}^d$, which form a rather new, rich and flexible class of random tessellations considered in stochastic…
This note describes a simple method to draw random points such that the cells of the corresponding Voronoi tesselation (approximately) satisfy a desired size distribution, for instance, follow a power law. The method is illustrated and…
A multiresolution technique on tessellation graphs for particle dynamics is proposed. This allows to split spatial field data given on millions of discrete particle positions into scale-dependent contributions. The Delaunay tessellation is…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…