Related papers: On non-Poissonian Voronoi tessellations

We observe a realization of a stationary generalized weighted Voronoi tessellation of the d-dimensional Euclidean space within a bounded observation window. Given a geometric characteristic of the typical cell, we use the minus-sampling…

A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…

This paper deals with the typical cell in a Poisson line tessellation in the plane whose directional distribution is concentrated on three equally spread values with possibly different weights. Such a random polygon can only be a triangle,…

We study the typical cell of the Poisson-Voronoi tessellation. We show that when divided by the $d$-th root of the intensity parameter $\lambda$ of the Poisson process times the volume of the unit ball, the inradius, outradius, diameter and…

With our previous study, the Super-k algorithm, we have introduced a novel way of piecewise-linear classification. While working on the Super-k algorithm, we have found that there is a similar, and simpler way to explain for obtaining a…

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…

We use the Millennium and Millennium-II simulations to illustrate the Tessellation-Level-Tree (TLT), a hierarchical tree structure linking density peaks in a field constructed by voronoi tessellation of the particles in a cosmological…

Nowadays, big data of digital media (including images, videos and 3D graphical models) are frequently modeled as low-dimensional manifold meshes embedded in a high-dimensional feature space. In this paper, we summarized our recent work on…

Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from cells of equal…

In this paper two new classes of stationary random simplicial tessellations, the so-called $\beta$- and $\beta'$-Delaunay tessellations, are introduced. Their construction is based on a space-time paraboloid hull process and generalizes…

Consider the distances $\tilde{R}_o$ and $R_o$ from the nucleus to a uniformly random point in the 0-cell and the typical cell, respectively, of the $d$-dimensional Poisson-Voronoi (PV) tessellation. The main objective of this paper is to…

Since the seminal work by Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible, yet analytically tractable model for hierarchical spatial…

For cell-division processes in a window, Cowan introduced four selection rules and two division rules each of which stands for one cell-division model. One of these is the area-weighted in-cell model. In this model, each cell is selected…

We study the sizes of the Voronoi cells of $k$ uniformly chosen vertices in a random split tree of size $n$. We prove that, for $n$ large, the largest of these $k$ Voronoi cells contains most of the vertices, while the sizes of the…

We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained…

In various types of many-particle systems, bidispersity is frequently used to avoid spontaneous ordering in particle configuration. In this study, the relation between bidispersity and disorder degree of particle configuration is…

Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for…

Mimicking natural tessellation patterns is a fascinating multi-disciplinary problem. Geometric methods aiming at reproducing such partitions on surface meshes are commonly based on the Voronoi model and its variants, and are often faced…

Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. We compute the algebraic boundaries of these…

In coverage-oriented networks, base stations (BSs) are deployed in a way such that users at the cell boundaries achieve sufficient signal strength. The shape and size of cells vary from BS to BS, since the large-scale signal propagation…