Spatial tessellations [[electronic resource] ] : concepts and applications of Voronoi diagrams / / Atsuyuki Okabe ... [et al.] ; with a foreword by D.G. Kendall

• Record Nr.: UNINA9910830475503321
• Autore: Okabe Atsuyuki <1945->
• Pubbl/distr/stampa: Chichester ; ; New York, : Wiley, c2000
• ISBN: 1-282-30769-X; 9786612307690; 0-470-31701-9; 0-470-31785-X
• Edizione: [2nd ed.]
• Descrizione fisica: 1 online resource (696 p.)
• Collana: Wiley series in probability and statistics
• Altri autori (Persone): OkabeAtsuyuki <1945->
• Disciplina: 519.53; 519.536
• Soggetti: Geometry - Data processing; Spatial analysis (Statistics); Voronoi polygons
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Rev. ed. of: Spatial tesselations / Atsuyuki Okabe, Barry Boots, Kokichi Sugihara.
• Nota di bibliografia: Includes bibliographical references (p. [585]-655) and index.
• Nota di contenuto: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams; Contents; Foreword to the First Edition; Preface to the Second Edition; Acknowledgements (First Edition); Acknowledgements (Second Edition); Chapter 1 Introduction; 1.1 Outline; 1.2 History of the concept of the Voronoi diagram; 1.3 Mathematical preliminaries; 1.3.1 Vector geometry; 1.3.2 Graphs; 1.3.3 Spatial stochastic point processes; 1.3.4 Efficiency of computation; Chapter 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; 2.6 Recognition of Voronoi diagrams; 2.6.1 The geometric approach; 2.6.2 The cambinatorial approach; Chapter 3 Generalizations of the Voronoi diagram; 3.1 Weighted Voronoi diagrams; 3.1.1 The multiplicatively weighted Voronoi diagram; 3.1.2 The additively weighted Voronoi ; diagram; 3.1.3 The compoundly weighted Voronoi diagram; 3.1.4 The power diagram; 3.1.5 The sectional Voronoi diagram; 3.1.6 Applications3.2 Higher-order Voronoi diagrams; 3.2.1 The order-k Voronoi diagram; 3.2.2 The ordered order-k Voronoi diagram; 3.2.3 Applications; 3.3 The Farthest-point Voronoi diagram and kth nearest-point Voronoi diagram; 3.3.1 The farthest-point Voronoi diagram; 3.3.2 The kth nearest-point Voronoi diagram; 3.3.3 Applications; 3.4 Voronoi diagrams wih obstacles; 3.4.1 The shortest-path Voronoi diagram; 3.4.2 The visibility shortest-path Voronoi diagram; 3.4.3 The constrained Delaunay triangulation; 3.4.4 SP- and VSP-Voronoi diagrams in a simple polygon; 3.4.5 Applications; 3.5 Voronoi diagrams for lines3.5.1 Voronoi diagrams for a set of points and straight line segments; 3.5.2 Voronoi diagrams for a set of points, straight line segments and circular arcs; 3.5.3 Voronoi diagrams for a set of circles; 3.5.4 Medial axis; 3.5.5 Applications; 3.6 Voronoi diagrams for areas; 3.6.1 The area Voronoi diagram; 3.6.2 Applications; 3.7 Voronoi diagrams with V-distances; 3.7.1 Voronoi diagrams with the Minkowski metric Lp; 3.7.2 Voronoi diagrams with the convex distance; 3.7.3 Voronoi diagrams with the Karlsruhe metric; 3.7.4 Voronoi diagrams with the Hausdorff distance; 3.7.5 Voronoi diagram with the boat-on-a-river distance3.7.6 Voronoi diagrams on a sphere; 3.7.7 Voronoi diagrams on a cylinder; 3.7.8 Voronoi diagrams on a cone; 3.7.9 Voronoi diagrams on a polyhedral surface; 3.7.10 Miscellany; 3.7.11. Applications; 3.8 Network Voronoi diagrams; 3.8.1 The network Voronoi node diagram; 3.8.2 The network Voronoi link diagram; 3.8.3 The network Voronoi area diagram; 3.8.4 Applications; 3.9 Voronoi diagrams for moving points; 3.9.1 Dynamic Voronoi diagrams; 3.9.2 Applications; Chapter 4 Algorithms for Computing Voronoi Diagrams; 4.1 Computational preliminaries; 4.2 Data structure for representing a Voronoi diagram
• Sommario/riassunto: 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