Related papers: A dynamical system using the Voronoi tessellation
We introduce a new class of spatial-temporal point processes based on Voronoi tessellations. At each step of such a process, a point is chosen at random according to a distribution determined by the associated Voronoi cells. The point is…
Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…
Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a…
The Voronoi tessellation is a natural way of space segmentation, which has many applications in various fields of science and technology, as well as in social sciences and visual art. The varieties of the Voronoi tessellation methods are…
In this paper, we review the computational aspects of a multiscale dissipative particle dynamics model for complex fluid simulations based on the feature-rich geometry of the Voronoi tessellation. The geometrical features of the model are…
Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
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…
For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi…
Voronoi diagrams appear in many areas in science and technology and have numerous applications. They have been the subject of extensive investigation during the last decades. Roughly speaking, they are a certain decomposition of a given…
High energy experimental data can be viewed as a sampling of the relevant phase space. We point out that one can apply Voronoi tessellations in order to understand the underlying probability distributions in this phase space. Interesting…
Spatial statistical analysis of multivariate volumetric data can be challenging due to scale, complexity, and occlusion. Advances in topological segmentation, feature extraction, and statistical summarization have helped overcome the…
Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…
The purpose of this note is to clarify the effect of the finite size of spherical particles upon the characteristics of their spatial distribution through a random Poisson process (RPP). This information is of special interest when using…
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…
This article represents the computational model for spacial addresation of the sensors in the dynamically changing real-time internet of things system. The model bases on the Voronoi diagrams as a basic data structure. Problem - the correct…
The large-scale matter distribution represents a complex network of structure elements such as voids, clusters, filaments, and sheets. This network is spanned by a point distribution. The global properties of the point process can be…
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…
Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set…
We introduce a framework for the generation of grid-shell structures that is based on Voronoi diagrams and allows us to design tessellations that achieve excellent static performances. We start from an analysis of stress on the input…