Research Catalog

Title

Spatial tessellations : concepts and applications of Voronoi diagrams / Atsuyuki Okabe, Barry Boots, Kokichi Sugihara ; with a foreword by D.G. Kendall.

Author

Okabe, Atsuyuki, 1945-

Publication

Chichester, England ; New York : Wiley, ©1992.

Items in the Library & Off-site

Details

Additional Authors

• Boots, B. N.
• Sugihara, Kōkichi, 1948-

Description

x, 532 pages : illustrations; 24 cm

Summary

"Given a pattern of objects in continuous space, Voronoi diagrams provide a means of naturally partitioning the space into subregions. This is a rapidly expanding topic as these diagrams find application in such areas as spatial data manipulation, modelling spatial structures and spatial processes, pattern analysis and locational optimization. These areas can be found within many different scientific fields, and consequently this increases not only the use of Voronoi diagrams but also the demand for knowledge about them. This is the first book which, dealing exclusively with these diagrams, meets this demand. Material within is synthesized, unified and presented in a structured form. Emphasis of a particular perspective is deliberately avoided in order to provide a comprehensive and balanced treatment of all aspects of Voronoi diagrams. A wide range of applications drawn from over a dozen fields is discussed, enabling this book to serve as an important reference volume on this topic." "This book should appeal equally to those whose interests in Voronoi diagrams are theoretical, practical or both."--Jacket.

Series Statement

Wiley series in probability and mathematical statistics

Uniform Title

Wiley series in probability and mathematical statistics

Subject

• Voronoi polygons
• Spatial analysis (Statistics)
• Geometry > Data processing
• spatial analysis
• Programmation géométrique
• Analyse spatiale (statistique)
• Voronoi, Polygones de
• Géométrie > Informatique

Bibliography (note)

• Includes bibliographical references (p. [489]-521) and index.

Contents

• Ch. 1. Introduction -- 1.1. Outline -- 1.2. History of the concept of the Voronoi diagram -- 1.3. Mathematical preliminaries -- Ch. 2. Definitions and Basic Properties of Voronoi Diagrams -- 2.1. Definitions of the ordinary Voronoi diagram -- 2.2. Definitions of the Delaunay tessellation (triangulation) -- 2.3. Basic properties of the Voronoi diagram -- 2.4. Basic properties of the Delaunay triangulation -- 2.5. Graphs related to the Delaunay triangulation -- Ch. 3. Generalizations of the Voronoi Diagram -- 3.1. Weighted Voronoi diagrams -- 3.2. Higher-order Voronoi diagrams -- 3.3. Farthest-point Voronoi diagram and kth nearest-point Voronoi diagram -- 3.4. Voronoi diagrams with obstacles -- 3.5. Voronoi diagrams for lines -- 3.6. Voronoi diagrams for areas -- 3.7. Voronoi diagrams with V-distances -- 3.8. Network Voronoi diagrams -- 3.9. Notes on applications -- Ch. 4. Algorithms for Computing Voronoi Diagrams -- 4.1. Computational preliminaries -- 4.2. Data structure for representing a Voronoi diagram -- 4.3. Incremental method -- 4.4. Divide-and-conquer method -- 4.5. Plane sweep method -- 4.6. Practical techniques for implementing the algorithms -- 4.7. Algorithms for higher-dimensional Voronoi diagrams -- 4.8. Algorithms for generalized Voronoi diagrams -- 4.9. Approximation algorithms -- Ch. 5. Poisson Voronoi Diagrams -- 5.1. Properties of Poisson Voronoi diagrams -- 5.2. Uses of Poisson Voronoi diagrams.
• 5.3. Simulating Poisson Voronoi cells and Poisson Delaunay cells -- 5.4. Properties of Poisson Voronoi cells -- 5.5. Sectional Poisson Voronoi diagrams -- 5.6. Additively weighted Poisson Voronoi diagrams: the Johnson-Mehl model -- 5.7. Higher order Poisson Voronoi diagrams -- 5.8. Poisson Voronoi diagrams on the surface of a sphere -- 5.9. Properties of Poisson Delaunay cells -- 5.10. Other random Voronoi diagrams -- Ch. 6. Spatial Interpolation -- 6.1. Polygonal methods -- 6.2. Triangular methods -- 6.3. Modifying Delaunay triangulations -- 6.4. Approximating surfaces -- 6.5. Ordering multivariate data -- Ch. 7. Models of Spatial Processes -- 7.1. Assignment models -- 7.2. Growth models -- 7.3. Spatial-temporal processes -- 7.4. Two-species models -- 7.5. Recognizing Voronoi diagrams -- Ch. 8. Point Pattern Analysis -- 8.1. Polygon-based methods -- 8.2. Triangle-based methods -- 8.3. Nearest neighbour distance methods -- Ch. 9. Locational Optimization through Voronoi Diagrams -- 9.1. Preliminaries -- 9.2. Locational optimization of points -- 9.3. Locational optimization of lines -- 9.4. Locational optimization over time -- 9.5. Voronoi fitting and its application to locational optimization problems.

ISBN

• 0471934305
• 9780471934301

LCCN

91047687

OCLC

• ocm25205363
• 25205363
• SCSB-1968845

Owning Institutions

Princeton University Library