Název:
Zobecněné náhodné mozaiky, jejich vlastnosti, simulace a aplikace
Překlad názvu:
Generalized random tessellations, their properties, simulation and applications
Autoři:
Jahn, Daniel ; Beneš, Viktor (vedoucí práce) ; Rataj, Jan (oponent) Typ dokumentu: Diplomové práce
Rok:
2019
Jazyk:
eng
Abstrakt: The past few years have seen advances in modelling of polycrystalline materi- als using parametric tessellation models from stochastic geometry. A promising class of tessellations, the Gibbs-type tessellation, allows the user to specify a great variety of properties through the energy function. This text focuses solely on tetrahedrizations, a three-dimensional tessellation composed of tetrahedra. The existing results for two-dimensional Delaunay triangulations are extended to the case of three-dimensional Laguerre tetrahedrization. We provide a proof of existence, a C++ implementation of the MCMC simulation and estimation of the models parameters through maximum pseudolikelihood. 1
Klíčová slova:
algoritmus přidání a odebrání; Gibbsova zobecněná mozaika; vlastnosti stochastických modelů; Gibbs generalized tessellation; incremental-decremental algorithm; properties of stochastic models