Geodesic
Bernoulli cluster field: Voronoi tessellations
Applications of Mathematics, Tome 47 (2002) no. 2, pp. 157-167 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A new point process is proposed which can be viewed either as a Boolean cluster model with two cluster modes or as a $p$-thinned Neyman-Scott cluster process with the retention of the original parent point. Voronoi tessellation generated by such a point process has extremely high coefficients of variation of cell volumes as well as of profile areas and lengths in the planar and line induced tessellations. An approximate numerical model of tessellation characteristics is developed for the case of small cluster size; its predictions are compared with the results of computer simulations. Tessellations of this type can be used as models of grain structures in steels.
A new point process is proposed which can be viewed either as a Boolean cluster model with two cluster modes or as a $p$-thinned Neyman-Scott cluster process with the retention of the original parent point. Voronoi tessellation generated by such a point process has extremely high coefficients of variation of cell volumes as well as of profile areas and lengths in the planar and line induced tessellations. An approximate numerical model of tessellation characteristics is developed for the case of small cluster size; its predictions are compared with the results of computer simulations. Tessellations of this type can be used as models of grain structures in steels.
DOI : 10.1023/A:1021737219136
Classification : 60D05, 60G55, 60–04
Keywords: cluster point process; Voronoi tessellation; induced tessellation; coefficients of variation of cell size characteristics 
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     title = {Bernoulli cluster field: {Voronoi} tessellations},
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     year = {2002},
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Saxl, Ivan; Ponížil, Petr. Bernoulli cluster field: Voronoi tessellations. Applications of Mathematics, Tome 47 (2002) no. 2, pp. 157-167. doi: 10.1023/A:1021737219136

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