Topological and statistical properties of a constrained Voronoi tessellation Export

@article{citeulike:4058312, abstract = {Voronoi tessellation has been used widely to approximate and model various cellular structures and stochastic patterns appearing in nature. In this work, we present an extended version of the Voronoi tessellation method that partitions the space with certain constraints commonly encountered in either experimental measurements or theoretical models, such as cell volume or size distribution. The new Voronoi method is implemented using an inverse Monte Carlo method. We calculate the topological and statistical properties of tessellated Voronoi cells in several model systems with cell volumes obeying lognormal and bimodal distributions. We also compare the results with those obtained using the conventional Poisson–Voronoi method. We observed systematic changes in the topological properties as well as deviations from some established topological relations as the parameters in the constraint were varied. The application of this constrained Voronoi method in microstructure modelling and characterization in poly- and nano-crystalline materials is briefly discussed.}, author = {Xu, T. and Li, M.}, citeulike-article-id = {4058312}, citeulike-linkout-0 = {http://dx.doi.org/10.1080/14786430802647065}, doi = {10.1080/14786430802647065}, journal = {Philosophical Magazine}, keywords = {microstructure-reconstruction}, number = {4}, pages = {349--374}, posted-at = {2009-02-16 11:11:36}, priority = {2}, publisher = {Taylor \& Francis}, title = {Topological and statistical properties of a constrained Voronoi tessellation}, url = {http://dx.doi.org/10.1080/14786430802647065}, volume = {89}, year = {2009} }

TY - JOUR ID - citeulike:4058312 L3 - citeulike-article-id:4058312 N2 - Voronoi tessellation has been used widely to approximate and model various cellular structures and stochastic patterns appearing in nature. In this work, we present an extended version of the Voronoi tessellation method that partitions the space with certain constraints commonly encountered in either experimental measurements or theoretical models, such as cell volume or size distribution. The new Voronoi method is implemented using an inverse Monte Carlo method. We calculate the topological and statistical properties of tessellated Voronoi cells in several model systems with cell volumes obeying lognormal and bimodal distributions. We also compare the results with those obtained using the conventional Poisson–Voronoi method. We observed systematic changes in the topological properties as well as deviations from some established topological relations as the parameters in the constraint were varied. The application of this constrained Voronoi method in microstructure modelling and characterization in poly- and nano-crystalline materials is briefly discussed. IS - 4 JF - Philosophical Magazine EP - 374 TI - Topological and statistical properties of a constrained Voronoi tessellation PB - Taylor & Francis VL - 89 SP - 349 KW - microstructure-reconstruction AU - Xu, T AU - Li, M PY - 2009/// UR - http://dx.doi.org/10.1080/14786430802647065 ER -