相关论文: Effective transport properties of conformal Vorono…
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…
A novel algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is tested. Neighbouring tracer particles are naturally identified through…
Real complex networks are often characterized by spatial constraints such as the relative position and adjacency of nodes. The present work describes how Voronoi tessellations of the space where the network is embedded provide not only a…
In this paper, we investigate the optimization of Centroidal Voronoi Tessellations (CVT) under geometric constraints. For this purpose, we minimize a linear combination of the standard CVT energy functional with terms involving geometric…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…
We point out that interesting features in high energy physics data can be determined from properties of Voronoi tessellations of the relevant phase space. For illustration, we focus on the detection of kinematic "edges" in two dimensions,…
We present a variational framework in which Centroidal Voronoi Tessellations (CVTs) arise as local minimizers of a generalized electrostatic energy functional. By modeling interior point distributions in a convex domain as repelling charges…
We present two methods to continuously and piecewise-linearly parametrize rank-3 lattices by vectors of $\RR^{13}$, which provides an efficient way to judge if two sets of parameters provide nearly identical lattices within their margins of…
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…
We extend the Geometric Refinement Transform (GRT) by introducing centroidal Voronoi tessellations (CVTs) into the refinement process, enhancing symmetry, reconstruction accuracy, and numerical stability. By applying Lloyds algorithm at…
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…
This paper presents a range of results in partial differential equations (PDEs) in which Voronoi patterns arise. We investigate the connection between the solution to an elliptic equation and its probabilistic interpretation as a stochastic…
Dual three-dimensional networks of structural and transport elements were combined to model the effect of fracture on mass transport in quasi-brittle geomaterials. Element connectivity of the structural network, representing elasticity and…
Several systems involve spatial arrangements of elements such as molecules or cells, the characterization of which bears important implications to biological and physical investigations. Traditional approaches to quantify spatial order and…
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…
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…
High-speed stereo PIV-measurements have been performed in a turbulent boundary layer at Re$_{\theta}$ of 9800 in order to elucidate the coherent structures. Snapshot proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD)…
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…
A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in {\it ab-initio} electronic-structure calculations. We combine a weighted Voronoi tessellation with…
Given two point sets in the plane, we study the minimization of the bottleneck distance between a point set B and an equally-sized subset of a point set A under translations. We relate this problem to a Voronoi-type diagram and derive…