منابع مشابه
Symmetry-Break in Voronoi Tessellations
We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional streng...
متن کاملFrom symmetry break to Poisson point process in 2D Voronoi tessellations: the generic nature of hexagons
We bridge the properties of the regular square and honeycomb Voronoi tessellations of the plane to those of the Poisson-Voronoi case, thus analyzing in a common framework symmetry-break processes and the approach to uniformly random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions is perturbed through...
متن کاملPoisson-Voronoi Tessellations
In particular, the location of S in R d is immaterial (stationarity) and E(N(S)) = λμ =Var(N(S)) (equality of mean and variance). An alternative characterization of the Poisson process involves the limit of the uniform distribution on expanding cubes C ⊆ R . Let ν denote the volume of C. Given m independent uniformly distributed particles in C and a measurable set S ⊆ C of volume μ, the probabi...
متن کاملEdge-Weighted Centroidal Voronoi Tessellations
Most existing applications of centroidal Voronoi tessellations (CVTs) lack consideration of the length of the cluster boundaries. In this paper we propose a new model and algorithms to produce segmentations which would minimize the total energy — a sum of the classic CVT energy and the weighted length of cluster boundaries. To distinguish it with the classic CVTs, we call it an Edge-Weighted CV...
متن کاملVoronoi Tessellations for Matchbox Manifolds
Matchbox manifolds M are a special class of foliated spaces, which include as special examples the weak solenoids, suspensions of odometer and Toeplitz actions, and tiling spaces associated to aperiodic tilings with finite local complexity. They have many properties analogous to those of a compact manifold, but the additional data inherently encoded in the pseudogroup dynamics of its foliation ...
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ژورنال
عنوان ژورنال: Symmetry
سال: 2009
ISSN: 2073-8994
DOI: 10.3390/sym1010021