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Lectures on Random Voronoi Tessellations

  • Jesper Møller

Part of the Lecture Notes in Statistics book series (LNS, volume 87)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Jesper Møller
    Pages 1-14
  3. Jesper Møller
    Pages 43-82
  4. Jesper Møller
    Pages 83-124
  5. Back Matter
    Pages 125-137

About this book

Introduction

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.

Keywords

Division Mathematica Natural Poisson process Simula Tessellation computation computational geometry distribution geometry integral knowledge point process statistics story

Authors and affiliations

  • Jesper Møller
    • 1
  1. 1.Department of Theoretical Statistics Institute of MathematicsUniversity of AarhusAarhus CDenmark

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2652-9
  • Copyright Information Springer-Verlag New York 1994
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94264-3
  • Online ISBN 978-1-4612-2652-9
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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