Lectures on Random Voronoi Tessellations

Jesper Moller

ISBN 10: 0387942645 / ISBN 13: 9780387942643

Editore: Springer New York, Springer New York, 1994

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9780387942643

Dati bibliografici

• Titolo: Lectures on Random Voronoi Tessellations
• Editore: Springer New York, Springer New York
• Data di pubblicazione: 1994
• Lingua: Inglese
• ISBN 10: 0387942645
• ISBN 13: 9780387942643
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 229 L x 152 A x 9 P (millimetri) 229 millimetri di larghezza per 152 millimetri di altezza per 9 millimetri di profondità
• Peso: 226 grammi

Descrizione articolo

Riassunto

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.

Contenuti

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.