Original title:
Voroného mozaiky
Translated title:
Voronoi tessellations
Authors:
Pohly, Jakub ; Pawlas, Zbyněk (advisor) ; Beneš, Viktor (referee) Document type: Bachelor's theses
Year:
2021
Language:
slo Abstract:
[eng][cze] In the presented work we deal with the theory of Voronoi tessellations. We deal with the properties of general Voronoi tessellations, but we focus mainly on those tessellations that are randomly generated. We study the point processes that create random Voronoi tessellations. We define the most common Poisson process. We focus on the renewal pro- cesses, specifically the ordinary renewal process, the delayed process and the equilibrium renewal process. With the help of these processes, we build a one-dimensional version of the Poisson process. We examine Voronoi tessellations primarily on a semi-straight line. Later, we generalize the obtained results for the line and the plane. In the conclusion of the work we deal with Voronoi tessellations in space. 1V predloženej práci sa zaoberáme teóriou Voroného mozaík. Zaoberáme sa vlastnos- ťami Voroného mozaík obecne, ale sústredíme sa hlavne na tie mozaiky, ktoré sú náhodne generované. Skúmame bodové procesy, ktoré náhodne Voroného mozaiky vytvárajú. De- finujeme najbežnejší Poissonov proces. Venujeme sa procesom obnovy, a to konkrétne obyčajnému procesu obnovy, modifikovanému procesu obnovy a rovnovážnemu procesu obnovy. S pomocou týchto procesov budujeme jednorozmernú verziu Poissonovho procesu. Voroného mozaiky skúmame prvotne na polpriamke. Neskôr získané výsledky zobecňu- jeme pre priamku a rovinu. V závere práce sa zaoberáme Voroného mozaikami v priestore. 1
Keywords:
tessellation|point process|Poisson process|renewal process; mozaika|bodový proces|Poissonov proces|proces obnovy
Institution: Charles University Faculties (theses)
(web)
Document availability information: Available in the Charles University Digital Repository. Original record: http://hdl.handle.net/20.500.11956/127941