Anisotropic Growth of Voronoi Cells

This paper discusses a simple extension of the classical Voronoi tessellation. Instead of using the Euclidean distance to decide the domains corresponding to the cell centers, another translation-invariant distance is used. The resulting tessellation is a scaled version of the usual Voronoi tessella...

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Bibliographic Details
Published in:Advances in applied probability 1994-03, Vol.26 (1), p.43-53
Main Author: Scheike, Thomas H.
Format: Article
Language:English
Subjects:
Cell growth
Eigenvalues
Ergodic theory
Euclidean space
Geometry
Mathematical models
Mosaic
Poisson process
Probability
Statistical analysis
Stochastic Geometry and Statistical Applications
Tessellations
Vertices
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Summary:This paper discusses a simple extension of the classical Voronoi tessellation. Instead of using the Euclidean distance to decide the domains corresponding to the cell centers, another translation-invariant distance is used. The resulting tessellation is a scaled version of the usual Voronoi tessellation. Formulas for the mean characteristics (e.g. mean perimeter, surface and volume) of the cells are provided in the case of cell centers from a homogeneous Poisson process. The resulting tessellation is stationary and ergodic but not isotropic.
ISSN:0001-8678
1475-6064
DOI:10.2307/1427577