LEADER 05714nam 2200709Ia 450 001 9910139857603321 005 20170815110602.0 010 $a1-282-30769-X 010 $a9786612307690 010 $a0-470-31701-9 010 $a0-470-31785-X 035 $a(CKB)1000000000806858 035 $a(EBL)470072 035 $a(OCoLC)264389523 035 $a(SSID)ssj0000343129 035 $a(PQKBManifestationID)11267359 035 $a(PQKBTitleCode)TC0000343129 035 $a(PQKBWorkID)10288442 035 $a(PQKB)10180071 035 $a(MiAaPQ)EBC470072 035 $a(PPN)152555412 035 $a(EXLCZ)991000000000806858 100 $a19990222d2000 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aSpatial tessellations$b[electronic resource] $econcepts and applications of Voronoi diagrams /$fAtsuyuki Okabe ... [et al.] ; with a foreword by D.G. Kendall 205 $a2nd ed. 210 $aChichester ;$aNew York $cWiley$dc2000 215 $a1 online resource (696 p.) 225 1 $aWiley series in probability and statistics 300 $aRev. ed. of: Spatial tesselations / Atsuyuki Okabe, Barry Boots, Kokichi Sugihara. 311 $a0-471-98635-6 320 $aIncludes bibliographical references (p. [585]-655) and index. 327 $aSpatial 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 327 $a2.2 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 327 $a3.1.6 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 327 $a3.5 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 327 $a3.7.5 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 327 $a4.2 Data structure for representing a Voronoi diagram 330 $aSpatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization. With such versatility, the Voronoi diagram and its relative, the Delaunay triangulation, provide valuable tools for the analysis of spatial data. This is a rapidly growing research area and in this fully updated second edition the authors provide an up-to-date and comprehensive unification of all the previous literature on the subject of Voronoi 410 0$aWiley series in probability and statistics. 606 $aGeometry$xData processing 606 $aSpatial analysis (Statistics) 606 $aVoronoi polygons 615 0$aGeometry$xData processing. 615 0$aSpatial analysis (Statistics) 615 0$aVoronoi polygons. 676 $a519.53 676 $a519.536 700 $aOkabe$b Atsuyuki$f1945-$0871584 701 $aOkabe$b Atsuyuki$f1945-$0871584 701 $aOkabe$b Atsuyuki$f1945-$0871584 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139857603321 996 $aSpatial tessellations$92187051 997 $aUNINA