Acta Stereologica

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Lutz Muche

Distributional properties of the Poisson-Voronoi tessellation

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Abstract

This paper presents formulas for the Voronoi tessellation which is generated by a stationary Poisson process in Rd. Expressions are given for the chord length distribution and the edge length distribution function. Furthermore, the behaviour of the pair correlation function of the point process of vertices of the planar Voronoi tessellation for small arguments is discussed. Finally, some characteristics concerning the ”typical” edge of the spatial Voronoi tessellation are given.

Keywords : chord length, edge length, face angle, pair correlation function, Poisson-Voronoi tessellation, vertices

To cite this article

Lutz Muche, «Distributional properties of the Poisson-Voronoi tessellation», Acta Stereologica [En ligne], Volume 12 (1993), Number 2 - Proceedings of the sixth European congress for stereology - Part one - Dec. 1993, 125-130 URL : https://popups.ulg.ac.be/0351-580x/index.php?id=1469.

About: Lutz Muche

Freiberg University of Mining and Technology, Institute of Mathematics Bernhard-von-Cotta-Straβe 2, D-09596 Freiberg, Germany