Spatial tessellations: concepts and applications of Voronoi diagrams
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2000
|
| Edition: | 2. ed. |
| Series: | Wiley series in probality and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 671 S. graph. Darst. |
| ISBN: | 0471986356 9780471986355 |
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Record in the Search Index
| _version_ | 1804127979892113408 |
|---|---|
| adam_text | Contents
Foreword to the First Edition xi
Preface to the Second Edition xiii
Acknowledgements (First Edition) xv
Acknowledgements (Second Edition) xvi
Chapter 1 Introduction 1
1.1 Outline 3
1.2 History of the concept of the Voronoi diagram 6
1.3 Mathematical preliminaries 12
1.3.1 Vector geometry 12
1.3.2 Graphs 24
1.3.3 Spatial stochastic point processes 31
1.3.4 Efficiency of computation 41
Chapter 2 Definitions and Basic Properties of Voronoi Diagrams 43
2.1 Definitions of the ordinary Voronoi diagram 43
2.2 Definitions of the Delaunay tessellation
(triangulation) 52
2.3 Basic properties of the Voronoi diagram 57
2.4 Basic properties of the Delaunay triangulation 70
2.5 Graphs related to the Delaunay triangulation 97
2.6 Recognition of Voronoi diagrams 103
2.6.1 The geometric approach 104
2.6.2 The combinatorial approach 106
Chapter 3 Generalizations of the Voronoi diagram 113
3.1 Weighted Voronoi diagrams 119
3.1.1 The multiplicatively weighted Voronoi diagram 120
3.1.2 The additively weighted Voronoi diagram 123
3.1.3 The compoundly weighted Voronoi diagram 127
3.1.4 The power diagram 128
3.1.5 The sectional Voronoi diagram 131
3.1.6 Applications 133
CONTENTS
3.2 Higher-order Voronoi diagrams 134
3.2.1 The order-it Voronoi diagram 135
3.2.2 The ordered order-/fc Voronoi diagram 144
3.2.3 Applications 150
3.3 The farthest-point Voronoi diagram and the fcth
nearest-point Voronoi diagram 151
3.3.1 The farthest-point Voronoi diagram 151
3.3.2 The fcth nearest-point Voronoi diagram 155
3.3.3 Applications 157
3.4 Voronoi diagrams with obstacles 158
3.4.1 The shortest-path Voronoi diagram 158
3.4.2 The visibility shortest-path Voronoi diagram 163
3.4.3 The constrained Delaunay triangulation 165
3.4.4 SP- and VSP-Voronoi diagrams in a simple polygon 168
3.4.5 Applications 168
3.5 Voronoi diagrams for lines 169
3.5.1 Voronoi diagrams for a set of points and straight
line segments 171
3.5.2 Voronoi diagrams for a set of points, straight line
segments and circular arcs 176
3.5.3 Voronoi diagrams for a set of circles 178
3.5.4 Medial axis 181
3.5.5 Applications 184
3.6 Voronoi diagrams for areas 186
3.6.1 The area Voronoi diagram 186
3.6.2 Applications 188
3.7 Voronoi diagrams with V-distances 189
3.7.1 Voronoi diagrams with the Minkowski metric Lp 189
3.7.2 Voronoi diagrams with the convex distance 194
3.7.3 Voronoi diagrams with the Karlsruhe metric 201
3.7.4 Voronoi diagrams with the Hausdorff distance 202
3.7.5 Voronoi diagram with the boat-on-a-river distance 204
3.7.6 Voronoi diagrams on a sphere 206
3.7.7 Voronoi diagrams on a cylinder 209
3.7.8 Voronoi diagrams on a cone 210
3.7.9 Voronoi diagrams on a polyhedral surface 211
3.7.10 Miscellany 212
3.7.11 Applications 215
3.8 Network Voronoi diagrams 218
3.8.1 The network Voronoi node diagram 219
3.8.2 The network Voronoi link diagram 220
3.8.3 The network Voronoi area diagram 221
3.8.4 Applications 224
3.9 Voronoi diagrams for moving points 224
3.9.1 Dynamic Voronoi diagrams 224
3.9.2 Applications 227
CONTENTS VÜ
Chapter 4 Algorithms for Computing Yoronoi Diagrams 229
4.1 Computational preliminaries 229
4.2 Data structure for representing a Voronoi diagram 235
4.3 The incremental method 242
4.4 The divide-and-conquer method 251
4.5 The plane sweep method 257
4.6 Practical techniques for implementing the algorithms 264
4.6.1 Inconsistency caused by numerical errors 264
4.6.2 Construction of an error-free world 265
4.6.3 Topology-oriented approach 269
4.7 Algorithms for higher-dimensional Voronoi diagrams 275
4.8 Algorithms for generalized Voronoi diagrams 280
4.9 Approximation algorithms 287
Chapter 5 Poisson Voronoi Diagrams 291
5.1 Properties of infinite Voronoi diagrams 295
5.2 Properties of Poisson Voronoi diagrams 299
5.3 Uses of Poisson Voronoi diagrams 300
5.4 Simulating Poisson Voronoi and Delaunay cells 306
5.5 Properties of Poisson Voronoi cells 311
5.5.1 Moments of the characteristics of Poisson
Voronoi cells 311
5.5.2 Conditional moments of the characteristics of
Poisson Voronoi cells 315
5.5.3 Conditional moments of the characteristics of
the neighbouring cells of a Poisson Voronoi cell 324
5.5.4 Distributional properties 331
5.6 Stochastic processes induced by Poisson Voronoi
diagrams 350
5.6.1 Point processes of centroids of faces 350
5.6.2 Voronoi growth modeis 357
5.6.3 The Stienen model 360
5.6.4 Percolation on Poisson Voronoi diagrams and
Poisson Delaunay tessellations 361
5.7 Sectional Voronoi diagrams 363
5.8 Additively weighted Poisson Voronoi diagrams:
the Johnson-Mehl model 374
5.9 Higher order Poisson Voronoi diagrams 385
5.10 Poisson Voronoi diagrams on the surface of a sphere 389
5.11 Properties of Poisson Delaunay cells 389
5.12 Other random Voronoi diagrams 404
CONTENTS
Spatial Interpolation
6.1 Polygonal methods 416
6.1.1 Nearest neighbour interpolation 417
6.1.2 Natural neighbour interpolation 418
6.2 Triangulär methods 427
6.3 Modifying Delaunay triangulations 434
6.4 Approximating surfaces 437
6.5 Delaunay meshes for finite element methods 439
6.5.1 Two-dimensional Delaunay meshes 440
6.5.2 Three-dimensional Delaunay meshes 442
6.6 Ordering multivariate data 446
Models of Spatial Processes 453
7.1 Assignment modeis 454
7.2 Growth modeis 476
7.3 Spatial-temporal processes 482
7.3.1 Spatial competition modeis: the Hotelling process 482
7.3.2 Adjustment modeis 489
7.4 Two-species modeis 491
Point Pattem Analysis 495
8.1 Polygon-based methods 498
8.1.1 Direct approach 498
8.1.2 Indirect approaches 502
8.2 Triangle-based methods 506
8.3 Nearest neighbour distance methods 512
8.3.1 Nearest neighbour distance method for
point-like objects 514
8.3.2 Nearest neighbour distance method for
line-like objects 517
8.3.3 Nearest neighbour distance method for
area-like objects 520
8.3.4 Multi nearest neighbour distance method 521
8.4 The shape of a point pattern 521
8.4.1 Internal shape 521
8.4.2 Exteraal shape 523
8.5 Spatial intensity 525
8.6 Segmenting point patterns 527
8.7 Modelling point processes 529
CONTENTS ix
Chapter 9 Locational Optimization Through Voronoi Diagrams 531
9.1 Preliminaries 532
9.1.1 The non-linear, non-convex programming problem 532
9.1.2 The descent method 534
9.1.3 The penalty function method 538
9.2 Locational optimization of points 541
9.2.1 Locational optimization of point-like facilities used
by independent users 542
9.2.2 Locational optimization of points in a three-
dimensional space 548
9.2.3 Locational optimization of point-like facilities used
by groups 549
9.2.4 Locational optimization of a hierarchical facility 551
9.2.5 Locational optimization of observation points for
estimating the total quantity of a spatial variable
continuously distributed over a plane 555
9.2.6 Locational optimization of service points of a
mobile facility 558
9.2.7 Locational optimization of terminal points through
which users go to the central point 559
9.2.8 Locational optimization of points on a continuous
network 563
9.3 Locational optimization of lines 564
9.3.1 Locational optimization of a service route 564
9.3.2 Locational optimization of a network 567
9.3.3 Euclidean Steiner minimum tree 570
9.4 Locational optimization over time 575
9.4.1 Multi-stage locational optimization 575
9.4.2 Periodic locational optimization 578
9.5 Voronoi fitting and its application to locational
optimization problems 581
9.5.1 Method of fitting a Voronoi diagram to a polygonal
tessellation 581
9.5.2 Locational optimization for minimizing restricted
areas 584
References 585
Index 657
|
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| discipline | Informatik Mathematik |
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| id | DE-604.BV013222076 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:41:57Z |
| institution | BVB |
| isbn | 0471986356 9780471986355 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009009677 |
| oclc_num | 40890923 |
| open_access_boolean | |
| owner | DE-384 DE-91G DE-BY-TUM DE-20 DE-19 DE-BY-UBM DE-29T DE-83 DE-188 DE-523 |
| owner_facet | DE-384 DE-91G DE-BY-TUM DE-20 DE-19 DE-BY-UBM DE-29T DE-83 DE-188 DE-523 |
| physical | XII, 671 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probality and statistics |
| spelling | Spatial tessellations concepts and applications of Voronoi diagrams Atsuyuki Okabe ... 2. ed. Chichester [u.a.] Wiley 2000 XII, 671 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probality and statistics Analyse spatiale (Statistique) Analyse spatiale (Statistique) ram Géométrie - Informatique Géométrie - Informatique ram Processos estocasticos larpcal Ruimtelijke analyse gtt Tessellations gtt Voronoi, Polygones de Voronoi, Polygones de ram analyse image inriac analyse spatiale inriac diagramme Voronoi inriac géométrie algorithmique inriac interpolation spatiale inriac optimisation inriac Datenverarbeitung Geometry Data processing Spatial analysis (Statistics) Voronoi polygons Voronoi-Diagramm (DE-588)4226013-9 gnd rswk-swf Räumliche Verteilung (DE-588)4121550-3 gnd rswk-swf Polygon (DE-588)4175197-8 gnd rswk-swf Überdeckung (DE-588)4186550-9 gnd rswk-swf Voronoi-Diagramm (DE-588)4226013-9 s DE-604 Räumliche Verteilung (DE-588)4121550-3 s 1\p DE-604 Überdeckung (DE-588)4186550-9 s 2\p DE-604 Polygon (DE-588)4175197-8 s 3\p DE-604 Okabe, Atsuyuki 1945- Sonstige (DE-588)135700043 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009009677&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Spatial tessellations concepts and applications of Voronoi diagrams Analyse spatiale (Statistique) Analyse spatiale (Statistique) ram Géométrie - Informatique Géométrie - Informatique ram Processos estocasticos larpcal Ruimtelijke analyse gtt Tessellations gtt Voronoi, Polygones de Voronoi, Polygones de ram analyse image inriac analyse spatiale inriac diagramme Voronoi inriac géométrie algorithmique inriac interpolation spatiale inriac optimisation inriac Datenverarbeitung Geometry Data processing Spatial analysis (Statistics) Voronoi polygons Voronoi-Diagramm (DE-588)4226013-9 gnd Räumliche Verteilung (DE-588)4121550-3 gnd Polygon (DE-588)4175197-8 gnd Überdeckung (DE-588)4186550-9 gnd |
| subject_GND | (DE-588)4226013-9 (DE-588)4121550-3 (DE-588)4175197-8 (DE-588)4186550-9 |
| title | Spatial tessellations concepts and applications of Voronoi diagrams |
| title_auth | Spatial tessellations concepts and applications of Voronoi diagrams |
| title_exact_search | Spatial tessellations concepts and applications of Voronoi diagrams |
| title_full | Spatial tessellations concepts and applications of Voronoi diagrams Atsuyuki Okabe ... |
| title_fullStr | Spatial tessellations concepts and applications of Voronoi diagrams Atsuyuki Okabe ... |
| title_full_unstemmed | Spatial tessellations concepts and applications of Voronoi diagrams Atsuyuki Okabe ... |
| title_short | Spatial tessellations |
| title_sort | spatial tessellations concepts and applications of voronoi diagrams |
| title_sub | concepts and applications of Voronoi diagrams |
| topic | Analyse spatiale (Statistique) Analyse spatiale (Statistique) ram Géométrie - Informatique Géométrie - Informatique ram Processos estocasticos larpcal Ruimtelijke analyse gtt Tessellations gtt Voronoi, Polygones de Voronoi, Polygones de ram analyse image inriac analyse spatiale inriac diagramme Voronoi inriac géométrie algorithmique inriac interpolation spatiale inriac optimisation inriac Datenverarbeitung Geometry Data processing Spatial analysis (Statistics) Voronoi polygons Voronoi-Diagramm (DE-588)4226013-9 gnd Räumliche Verteilung (DE-588)4121550-3 gnd Polygon (DE-588)4175197-8 gnd Überdeckung (DE-588)4186550-9 gnd |
| topic_facet | Analyse spatiale (Statistique) Géométrie - Informatique Processos estocasticos Ruimtelijke analyse Tessellations Voronoi, Polygones de analyse image analyse spatiale diagramme Voronoi géométrie algorithmique interpolation spatiale optimisation Datenverarbeitung Geometry Data processing Spatial analysis (Statistics) Voronoi polygons Voronoi-Diagramm Räumliche Verteilung Polygon Überdeckung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009009677&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT okabeatsuyuki spatialtessellationsconceptsandapplicationsofvoronoidiagrams |