Related papers: The Voronoi tessellation method in astronomy
Image segmentation plays a critical role in unlocking the mysteries of the universe, providing astronomers with a clearer perspective on celestial objects within complex astronomical images and data cubes. Manual segmentation, while…
In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites $P=\{p_i\}_{i=1}^m$ on the surface. We…
A review on the properties and dynamical origin and nature of the cosmic foam, the tenuous space-filling frothy network permeating the interior of the Universe. We discuss the properties of this striking and intriguing pattern, describing…
Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier…
The scatter in the apparent magnitude of type Ia supernovae induced by stochastic gravitational lensing is highly dependent on the nonlinear growth of cosmological structure. In this paper, we show that such a dependence can potentially be…
Currently, grid and glass methods are the two most popular choices to generate uniform particle distributions (i.e., pre-initial conditions) for cosmological $N$-body simulations. In this article, we introduce an alternative method called…
We dynamically simulate fractionation (partitioning of particle species) during spinodal gas-liquid separation of a size-polydisperse colloid, using polydispersity up to ~40% and a skewed parent size distribution. We introduce a novel…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
In this work, image analysis techniques used in astrophysics to detect low-contrast signals have been adapted in the processing of Computed Tomography (CT) images, combining Centroidal Voronoi Tessellation (CVT) and machine learning…
Oblique, low-velocity impacts onto extraterrestrial terrain are an inevitable occurrence during space exploration. We conduct two-dimensional discrete simulations to model such impacts into a bed of triangular grains. Finite element method…
In this work we present an alternative method to obtain a distribution of particles over an hyper surface, such that they obey a rest-mass density distribution $\rho(x^i)$. We use density profiles that can be written as…
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…
Gersho's conjecture in 3D asserts the asymptotic periodicity and structure of the optimal centroidal Voronoi tessellation. This relatively simple crystallization problem remains to date open. We prove bounds on the geometric complexity of…
The Voronoi diagrams are an important tool having theoretical and practical applications in a large number of fields. We present a new procedure, implemented as a set of CUDA kernels, which detects, in a general and efficient way,…
We review some of the scientific opportunities and technical challenges posed by the exploration of the large digital sky surveys, in the context of a Virtual Observatory (VO). The VO paradigm will profoundly change the way observational…
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…
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…
We present a novel method for particle splitting in smoothed particle hydrodynamics simulations. Our method utilizes the Voronoi diagram for a given particle set to determine the position of fine daughter particles. We perform several test…
Star clusters are often hard to find, as they may lie in a dense field of background objects or, because in the case of embedded clusters, they are surrounded by a more dispersed population of young stars. This paper discusses four…
In our recent paper [de Lacy Costello et al. 2010] we described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to…