相关论文: Calculation of the Voronoi boundary for lens-shape…

According to the von Laue condition, the volume integral of the proper pressure inside isolated particles with a fixed structure and finite mass vanishes in the Minkowski limit of general relativity. In this work, we consider a simple…

In the Hausdorff Voronoi diagram of a family of \emph{clusters of points} in the plane, the distance between a point $t$ and a cluster $P$ is measured as the maximum distance between $t$ and any point in $P$, and the diagram is defined in a…

Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…

The famous Kepler conjecture has a less spectacular, two-dimensional equivalent: The theorem of Thue states that the densest circle packing in the Euclidean plane has a hexagonal structure. A common proof uses Voronoi cells and analyzes…

In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to…

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…

This paper presents the Voronoi diagram-based evolutionary algorithm (VorEAl). VorEAl partitions input space in abnormal/normal subsets using Voronoi diagrams. Diagrams are evolved using a multi-objective bio-inspired approach in order to…

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…

In this paper, we provide an $O(n \mathrm{polylog} n)$ bound on the expected complexity of the randomly weighted Voronoi diagram of a set of $n$ sites in the plane, where the sites can be either points, interior-disjoint convex sets, or…

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…

Perturbed lattices provide simple models for studying many physical systems. In this paper we study the distribution of Voronoi chains, blocks, and clusters with prescribed combinatorial features in the perturbed square lattice,…

In this paper we study volumes of moduli spaces of hyperbolic surfaces with geodesic, cusp and cone boundary components. We compute the volumes in some new cases, in particular when there exists a large cone angle. This allows us to give…

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…

We consider the inverse problem of determining the possible presence of an inclusion in a thin plate by boundary measurements. The plate is made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. The…

We have performed direct numerical simulation of turbulent open channel flow over a smooth horizontal wall in the presence of finite-size, heavy particles. The spherical particles have a diameter of approximately 7 wall units, a density of…

It is shown that linear polarization data can be used to constrain the composition (normal or pair plasma) of pc-scale extragalactic jets. A simple criterion, based on synchrotron and Faraday depolarization properties, is established. It…

We introduce a new method for stacking voids and deriving their profile that greatly increases the potential of voids as a tool for precision cosmology. Given that voids are highly non-spherical and have most of their mass at their edge,…

In this paper, we study a partially overdetermined mixed boundary value problem in a half ball. We prove that a domain in which this partially overdetermined problem admits a solution if and only if the domain is a spherical cap…

Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up…

Shephard (Canad. J. Math. 26: 302-321, 1974) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note we prove a generalization of this theorem yielding similar formulas for their intrinsic…