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Anisotropic Growth of Voronoi Cells

  • Thomas H. Scheike (a1)

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.

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* Present address: Schlegels Alle 9, 1807 Frederiksberg, Denmark.

References

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Anisotropic Growth of Voronoi Cells

  • Thomas H. Scheike (a1)

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