Lectures on Random Voronoi Tessellations (Paperback)

Jesper Moller

ISBN 10: 0387942645 / ISBN 13: 9780387942643

Editore: Springer-Verlag New York Inc., New York, NY, 1994

Riguardo questo articolo

Paperback. 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. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9780387942643

Dati bibliografici

• Titolo: Lectures on Random Voronoi Tessellations (Paperback)
• Editore: Springer-Verlag New York Inc., New York, NY
• Data di pubblicazione: 1994
• Lingua: Inglese
• ISBN 10: 0387942645
• ISBN 13: 9780387942643
• Rilegatura: Paperback
• Condizione: new

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.