Skip to main content

Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd Edition




Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd Edition

Atsuyuki Okabe, Barry Boots, Kokichi Sugihara, Sung Nok Chiu

ISBN: 978-0-471-98635-5 May 2000 696 Pages


Spatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization. With such versatility, the Voronoi diagram and its relative, the Delaunay triangulation, provide valuable tools for the analysis of spatial data. This is a rapidly growing research area and in this fully updated second edition the authors provide an up-to-date and comprehensive unification of all the previous literature on the subject of Voronoi diagrams.

* Expands on the highly acclaimed first edition
* Provides an up-to-date and comprehensive survey of the existing literature on Voronoi diagrams
* Includes a useful compendium of applications
* Contains an extensive bibliography

A wide range of applications is discussed, enabling this book to serve as an important reference volume on this topic. The text will appeal to students and researchers studying spatial data in a number of areas, in particular, applied probability, computational geometry, and Geographic Information Science (GIS). This book will appeal equally to those whose interests in Voronoi diagrams are theoretical, practical or both.
Definitions and Basic Properties of Voronoi Diagrams.

Generalizations of the Voronoi Diagram.

Algorithms for Computing Voronoi Diagrams.

Poisson Voronoi Diagrams.

Spatial Interpolation.

Models of Spatial Processes.

Point Pattern Analysis.

Locational Optimization Through Voronoi Diagrams.


"While this edition maintains the overall structure of the first, there are substantial changes in the content..." (Mathematical Reviews, Issue 2001c)

"...a must..." (Monatshefte fur Mathematik, Vol 131/2, 2000)