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.

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. References. Index.

Spatial Tessellations Concepts and Applications of Voronoi Diagrams Second Edition Atsuyuki Okabe, University of Tokyo, Japan Barry Boots, Wilfrid Laurier University, Ontario, Canada Kokichi Sugihara, University of Tokyo, Japan Sung Nok Chiu, Hong Kong Baptist University, China 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. Features: * 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 The authors guide the reader through all the necessary mathematical background, before introducing a number of generalizations of Voronoi diagrams in Chapter 3. The subsequent chapters cover algorithms, random Voronoi diagrams, spatial interpolation, multivariate data manipulation, spatial process models, point pattern analysis and locational optimization. Emphasis of a particular perspective is deliberately avoided in order to provide a comprehensive and balanced treatment of the topic. A wide range of applications are discussed, enabling this book to serve as an important reference volume on the 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.

"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)