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Anisotropic Growth of Voronoi Cells

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Thomas H. Scheike
Thomas H. Scheike*
Affiliation:
University of California at Berkeley
*
* Present address: Schlegels Alle 9, 1807 Frederiksberg, Denmark.
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Abstract

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.

Keywords

MEAN CHARACTERISTICSRANDOM MOSAICSTOCHASTIC GEOMETRYVORONOI TESSELLATION

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 26 , Issue 1 , March 1994 , pp. 43 - 53
Copyright
Copyright © Applied Probability Trust 1994 

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