An incomplete Voronoi tessellation

• Autorzy: Lutz Muche
• Języki publikacji: EN

Abstrakty

EN

This paper presents distributional properties of a random cell structure which results from a growth process. It starts at the points of a Poisson point process. The growth is spherical with identical speed for all points; it stops whenever the boundaries of different cells have contact. The whole process finally stops after time t. So the space is not completely filled with cells, and the cells have both planar and spherical boundaries. Expressions are given for contact distribution functions, the specific boundary length, the specific surface area, and the mean chord length of this cell structure in $ℝ^2$ and $ℝ^3$.

Słowa kluczowe

EN

specific surface area; contact distribution function; Boolean model; mean chord length; Poisson-Voronoi tessellation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1993-1995
• Tom: 22
• Numer: 1
• Strony: 45-53

Daty

wydano

1993

otrzymano

1992-9-2

Twórcy

autor

Lutz Muche

• Bergakademie Freiberg, Fachbereich Mathematik, D-O-9200 Freiberg, Germany

Bibliografia

• [1] L. Muche, Untersuchung von Verteilungseigenschaften des Poisson-Voronoi- Mosaiks, Technical Report, Freiberg, 1992
• [2] L. Muche and D. Stoyan, Contact and chord length distributions of the Poisson-Voronoi tessellation, J. Appl. Probab. 29 (1992), 467-471
• [3] D. Stoyan, W. S. Kendall and J. Mecke, Stochastic Geometry and Its Applications, Wiley, Chichester, 1987.