An incomplete Voronoi tessellation

Muche, 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 -