منابع مشابه
Large Poisson-Voronoi Cells and Crofton Cells
It is proved that the shape of the typical cell of a stationary Poisson-Voronoi tessellation in Euclidean space, under the condition that the volume of the typical cell is large, must be close to spherical shape, with high probability. The same holds if the volume is replaced by the surface area or other suitable functionals. Similar results hold for the zero cell of a stationary and isotropic ...
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In this paper are considered one-dimensional tilings arising from some Pisot numbers encountered in quasicrystallography as the quadratic Pisot units and the cubic Pisot unit associated with 7-fold symmetry, and also the Tribonacci number. We give characterizations of the Voronoi cells of such tilings, using word combinatorics and substitutions.
متن کاملOn the measure of Voronoi cells
We study the measure of a typical cell in a Voronoi tessellation defined by n independent random points drawn from a density f in Rd. In particular, we prove that the asymptotic distribution of the measure–with respect to dμ = f(x)dx–of the cell centered at a point x ∈ Rd is independent of x and the density f . We determine all moments of the asymptotic distribution and show that the distributi...
متن کاملRefinability of splines from lattice Voronoi cells
Splines can be constructed by convolving the indicator function of the Voronoi cell of a lattice. This paper presents simple criteria that imply that only a small subset of such spline families can be refined: essentially the well-known box splines and tensor-product splines. Among the many non-refinable constructions are hex-splines and their generalization to non-Cartesian lattices. An exampl...
متن کاملDynamic Positioning Based on Voronoi Cells (DPVC)
In this paper we are proposing an approach for flexible positioning of players in Soccer Simulation in a Multi-Agent environment. We introduce Dynamic Positioning based on Voronoi Cells (DPVC) as a new method for players’ positioning which uses Voronoi Diagram for distributing agents in the field. This method also uses Attraction Vectors that indicate agents’ tendency to specific objects in the...
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ژورنال
عنوان ژورنال: Algebraic Statistics
سال: 2021
ISSN: 2693-3004,2693-2997
DOI: 10.2140/astat.2021.12.75