# An incomplete Voronoi tessellation

Applicationes Mathematicae (1993)

- Volume: 22, Issue: 1, page 45-53
- ISSN: 1233-7234

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topMuche, Lutz. "An incomplete Voronoi tessellation." Applicationes Mathematicae 22.1 (1993): 45-53. <http://eudml.org/doc/219082>.

@article{Muche1993,

abstract = {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 $ℝ^3$.},

author = {Muche, Lutz},

journal = {Applicationes Mathematicae},

keywords = {specific surface area; contact distribution function; Boolean model; mean chord length; Poisson-Voronoi tessellation; random cell structure; Poisson point process},

language = {eng},

number = {1},

pages = {45-53},

title = {An incomplete Voronoi tessellation},

url = {http://eudml.org/doc/219082},

volume = {22},

year = {1993},

}

TY - JOUR

AU - Muche, Lutz

TI - An incomplete Voronoi tessellation

JO - Applicationes Mathematicae

PY - 1993

VL - 22

IS - 1

SP - 45

EP - 53

AB - 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 $ℝ^3$.

LA - eng

KW - specific surface area; contact distribution function; Boolean model; mean chord length; Poisson-Voronoi tessellation; random cell structure; Poisson point process

UR - http://eudml.org/doc/219082

ER -

## References

top- [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 Zbl0753.60019
- [3] D. Stoyan, W. S. Kendall and J. Mecke, Stochastic Geometry and Its Applications, Wiley, Chichester, 1987. Zbl0622.60019

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