Related papers: Efficient Computation of Voronoi Diagrams Using Po…

VORO++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. VORO++ was released in 2009 and is based on computing the…

We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes.…

In this article, we investigate vacuum leakage detection problems in composite manufacturing. Our approach uses Voronoi diagrams, a well-known structure in discrete geometry. The Voronoi diagram of the vacuum connection positions partitions…

We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm.…

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…

Accurate cell detection and counting in the image-based ELISpot and FluoroSpot immunoassays is a challenging task. Recently proposed methodology matches human accuracy by leveraging knowledge of the underlying physical process of these…

We present an extension of Voronoi diagrams where when considering which site a client is going to use, in addition to the site distances, other site attributes are also considered (for example, prices or weights). A cell in this diagram is…

This article provides numerical evidence that under volume constraint the ball is the set which maximizes the perimeter of the least-perimeter partition into cells with prescribed areas. We introduce a numerical maximization algorithm which…

Voronoi diagrams are essential geometrical structures with numerous applications, particularly astrophysics-driven finite volume methods. While serial algorithms for constructing these entities are well-established, parallel construction…

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…

This study proposes an innovative approach to analyze spatial patterns of behavior by integrating information in weighted Voronoi diagrams. The objective of the research is to analyze the temporal distribution of an experimental subject in…

Let $G=(V,E)$ be a graph with unit-length edges and nonnegative costs assigned to its vertices. Being given a list of pairwise different vertices $S=(s_1,s_2,\ldots,s_p)$, the {\em prioritized Voronoi diagram} of $G$ with respect to $S$ is…

Voronoi tessellations are used to partition the Euclidean space into polyhedral regions, which are called Voronoi cells. Labeling the Voronoi cells with the class information, we can map any classification problem into a Voronoi…

Voronoi intensity estimators, which are non-parametric estimators for intensity functions of point processes, are both parameter-free and adaptive; the intensity estimate at a given location is given by the reciprocal size of the…

Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of…

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…

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.…

Very expensive problems are very common in practical system that one fitness evaluation costs several hours or even days. Surrogate assisted evolutionary algorithms (SAEAs) have been widely used to solve this crucial problem in the past…

We introduce the inverse Voronoi diagram problem in graphs: given a graph $G$ with positive edge-lengths and a collection $\mathbb{U}$ of subsets of vertices of $V(G)$, decide whether $\mathbb{U}$ is a Voronoi diagram in $G$ with respect to…

We study the Voronoi Diagram of Rotating Rays, a Voronoi structure where the input sites are rays and the distance function between a point and a site/ray, is the counterclockwise angular distance. This novel Voronoi diagram is motivated by…