Jesper Moller

Lectures on Random Voronoi Tessellations (eBook, PDF)

• Format: PDF

Produktbeschreibung

Tessellations are subdivisions of d-dimensional space into non-overlapping "cells". Voronoi tessellations are produced by first considering a set of points (known as nuclei) in d-space, and then defining cells as the set of points which are closest to each nuclei. A random Voronoi tessellation is produced by supposing that the location of each nuclei is determined by some random process. They provide models for many natural phenomena as diverse as the growth of crystals, the territories of animals, the development of regional market areas, and in subjects such as computational geometry and astrophysics. This volume provides an introduction to random Voronoi tessellations by presenting a survey of the main known results and the directions in which research is proceeding. Throughout the volume, mathematical and rigorous proofs are given making this essentially a self-contained account in which no background knowledge of the subject is assumed.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 134
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461226529
• Artikelnr.: 43986730

Inhaltsangabe

1. Introduction and background.
1.1. Definitions, assumptions, and characteristics.
1.2. History and applications.
1.3. Related tessellations.
2. Geometrical properties and other background material.
2.1. On the geometric structure of Voronoi and Delaunay tessellations.
2.2. Short diversion into integral geometry.
3. Stationary Voronoi tessellations.
3.1. Spatial point processes and stationarity.
3.2. Palm measures and intensities of cells and facets.
3.3. Mean value relations.
3.4. Flat sections.
4. Poisson
Voronoi tessellations.
4.1. The homogeneous Poisson process.
4.2. Mean value characteristics of Poisson
Voronoi facets.
4.3. On the distribution of the typical Poisson
Delaunay cell and related statistics.
4.4. On the distribution of the typical Poisson
Voronoi cell and related statistics.
4.5. Simulation procedures for Poisson
Voronoi tessellations and other related models.
References.
Subject and author index.
Notation index.