Voronoi diagrams and Delaunay triangulations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2013
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Literaturverz. S. 275 - 327 |
| Beschreibung: | VIII, 337 S. graph. Darst. |
| ISBN: | 9789814447638 |
Internformat
MARC
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|---|---|---|---|
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| 100 | 1 | |a Aurenhammer, Franz |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Voronoi diagrams and Delaunay triangulations |c Franz Aurenhammer ; Rolf Klein ; Der-Tsai Lee |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2013 | |
| 300 | |a VIII, 337 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 275 - 327 | ||
| 650 | 4 | |a Voronoi polygons | |
| 650 | 4 | |a Spatial analysis (Statistics) | |
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| 650 | 0 | 7 | |a Triangulation |0 (DE-588)4186017-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Voronoi-Diagramm |0 (DE-588)4226013-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Voronoi-Diagramm |0 (DE-588)4226013-9 |D s |
| 689 | 0 | 1 | |a Triangulation |0 (DE-588)4186017-2 |D s |
| 689 | 0 | |5 DE-604 | |
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| 689 | 1 | 1 | |a Delaunay-Triangulierung |0 (DE-588)4628829-6 |D s |
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| 700 | 1 | |a Lee, Der-Tsai |d 1949- |e Sonstige |0 (DE-588)122392612 |4 oth | |
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| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026101005&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026101005 | ||
Datensatz im Suchindex
| _version_ | 1804150515510018048 |
|---|---|
| adam_text | CONTENTS
1.
Introduction
1
2.
Elementary Properties
7
2.1.
Voronoi diagram
.......................... 7
2.2.
Delaunay
triangulation
...................... 11
3.
Basic Algorithms
15
3.1.
A lower time bound
........................ 16
3.2.
Incremental construction
..................... 18
3.3.
Divide
&
conquer
......................... 24
3.4.
Plane sweep
............................ 28
3.5.
Lifting to 3-space
......................... 31
4.
Advanced Properties
35
4.1.
Characterization of Voronoi diagrams
.............. 35
4.2.
Delaunay optimization properties
................ 41
5.
Generalized Sites
47
5.1.
Line segment Voronoi diagram
.................. 47
5.2.
Convex polygons
.......................... 53
5.3.
Straight skeletons
......................... 54
5.4.
Constrained Delaunay and relatives
............... 62
5.5.
Voronoi diagrams for curved objects
............... 66
5.5.1.
Splitting the Voronoi edge graph
............ 67
5.5.2.
Medial axis algorithm
................... 70
6.
Higher Dimensions
75
6.1.
Voronoi and Delaunay tessellations in 3-space
......... 75
6.1.1.
Structure and size
..................... 75
r¡
Contents
6.1.2.
Insertion algorithm
.................... 77
6.1.3.
Starting tetrahedron
................... 79
6.2.
Power diagrams
.......................... 81
6.2.1.
Basic properties
...................... 81
6.2.2.
Polyhedra and convex hulls
............... 83
6.2.3.
Related diagrams
..................... 85
6.3.
Regular simplicial complexes
................... 87
6.3.1.
Characterization
...................... 88
6.3.2.
Polytope representation in weight space
......... 89
6.3.3.
Flipping and lifting cell complexes
............ 90
6.4.
Partitioning theorems
....................... 93
6.4.1.
Least-squares clustering
................. 94
6.4.2.
Two algorithms
...................... 97
6.4.3.
More applications
..................... 100
6.5.
Higher-order Voronoi diagrams
.................. 103
6.5.1.
Farthest-site diagram
................... 103
6.5.2. Hyperplane
arrangements and /c-sets
.......... 106
6.5.3.
Computing a single diagram
............... 109
6.5.4.
Cluster Voronoi diagrams
................. 112
6.6.
Medial axis in three dimensions
................. 114
6.6.1.
Approximate construction
................ 114
6.6.2.
Union of balls and weighted
α
-shapes..........
117
6.6.3.
Voronoi diagram for spheres
............... 120
7.
General Spaces
&
Distances
123
7.1.
Generalized spaces
......................... 123
7.1.1.
Voronoi diagrams on surfaces
.............. 123
7.1.2.
Specially placed sites
................... 128
7.2.
Convex distance functions
.................... 129
7.2.1.
Convex distance Voronoi diagrams
........... 130
7.2.2.
Shape Delaunay tessellations
............... 136
7.2.3.
Situation in 3-space
.................... 141
7.3.
Nice metrics
............................ 144
7.3.1.
The concept
........................ 144
7.3.2.
Very nice metrics
..................... 148
7.4.
Weighted distance functions
................... 152
7.4.1.
Additive weights
...................... 152
7.4.2.
Multiplicative weights
................... 156
7.4.3.
Modifications
....................... 160
7.4.4. Anisotropie
Voronoi diagrams
.............. 163
7.4.5.
Quadratic-form distances
................. 165
7.5.
Abstract Voronoi diagrams
.................... 167
7.5.1.
Voronoi surfaces
...................... 167
7.5.2.
Admissible bisector systems
............... 168
7.5.3.
Algorithms and extensions
................ 172
7.6.
Time distances
........................... 175
7.6.1.
Weighted region problems
................ 175
Contents
vii
7.6.2.
City Voronoi
diagram...................
176
7.6.3.
Algorithm and variants
.................. 180
8.
Applications and Relatives
183
8.1.
Distance problems
......................... 183
8.1.1.
Post office problem
.................... 183
8.1.2.
Nearest neighbors and the closest pair
......... 186
8.1.3.
Largest empty and smallest enclosing circle
...... 189
8.2.
Subgraphs of Delaunay
triangulations
.............. 194
8.2.1.
Minimum spanning trees and cycles
........... 195
8.2.2.
α
-shapes and shape recovery
............... 200
8.2.3.
/3-skeletons
and relatives
................. 202
8.2.4.
Paths and spanners
.................... 205
8.3.
Supergraphs of Delaunay
triangulations
............. 207
8.3.1.
Higher-order Delaunay graphs
.............. 207
8.3.2.
Witness Delaunay graphs
................. 210
8.4.
Geometric clustering
........................ 211
8.4.1.
Partitional clustering
................... 212
8.4.2.
Hierarchical clustering
.................. 214
8.5.
Motion planning
.......................... 216
8.5.1.
Retraction
......................... 217
8.5.2.
Translating polygonal robots
............... 219
8.5.3.
Clearance and path length
................ 220
8.5.4.
Roadmaps and corridors
................. 222
9.
Miscellanea
225
9.1.
Voronoi diagram of changing sites
................ 225
9.1.1.
Dynamization
....................... 225
9.1.2.
Kinetic Voronoi diagrams
................. 226
9.2.
Voronoi region placement
..................... 228
9.2.1.
Maximizing a region
................... 229
9.2.2.
Voronoi game
....................... 232
9.2.3.
Hotelling game
...................... 235
9.2.4.
Separating regions
..................... 236
9.3.
Zone diagrams and relatives
................... 238
9.3.1.
Zone diagram
....................... 238
9.3.2.
Territory diagram
..................... 241
9.3.3.
Root finding diagram
................... 242
9.3.4.
Centroidal Voronoi diagram
............... 244
9.4.
Proximity structures on graphs
.................. 246
9.4.1.
Voronoi diagrams on graphs
............... 246
9.4.2.
Delaunay structures for graphs
.............. 248
10.
Alternative Solutions in Kd
251
10.1.
Exponential lower size bound
................... 251
10.2.
Embedding into low-dimensional space
............. 252
10.3.
Well-separated pair decomposition
................ 254
viii Contents
10.4.
Post office revisited
........................ 258
10.4.1.
Exact solutions
...................... 258
10.4.2.
Approximate solutions
.................. 259
10.5.
Abstract simplicial complexes
.................. 261
11.
Conclusions
267
11.1.
Sparsely covered topics
...................... 267
11.2.
Implementation issues
....................... 269
11.3.
Some open questions
....................... 272
Bibliography
275
Index
329
DELAUNAY
TRIANGULATIONS
Voronoi diagrams
partition
space according to the influence certain
sites exert on their environment. Since the 17th century, such
structures play an important role in many areas like Astronomy,
Physics, Chemistry, Biology, Ecology, Economics, Mathematics
and Computer Science. They help to describe zones of political
influence, to determine the hospital nearest to an accident site,
to compute collision-free paths for mobile robots, to reconstruct
curves and surfaces from sample points, to refine triangular meshes,
and to design location strategies for competing markets.
This unique book offers a state-of-the-art view of Voronoi diagrams
and their structure, and it provides efficient algorithms towards
their computation.
Readers with an entry-level background in algorithms can
enjoy a guided tour of gently increasing difficulty through a
fascinating area. Lecturers might find this volume a welcome
source for their courses on computational geometry. Experts are
offered a broader view, including many alternative solutions,
and up-to-date references to the existing literature; they might
benefit in their own research or application development.
|
| any_adam_object | 1 |
| author | Aurenhammer, Franz |
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| author_role | aut |
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| classification_tum | MAT 525f DAT 756f MAT 052f |
| ctrlnum | (OCoLC)859372045 (DE-599)BVBBV041125066 |
| dewey-full | 516.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.22 |
| dewey-search | 516.22 |
| dewey-sort | 3516.22 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV041125066 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:40:09Z |
| institution | BVB |
| isbn | 9789814447638 |
| language | English |
| lccn | 2013018154 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026101005 |
| oclc_num | 859372045 |
| open_access_boolean | |
| owner | DE-188 DE-703 DE-20 DE-83 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-523 |
| owner_facet | DE-188 DE-703 DE-20 DE-83 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-523 |
| physical | VIII, 337 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Aurenhammer, Franz Verfasser aut Voronoi diagrams and Delaunay triangulations Franz Aurenhammer ; Rolf Klein ; Der-Tsai Lee Singapore [u.a.] World Scientific 2013 VIII, 337 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 275 - 327 Voronoi polygons Spatial analysis (Statistics) Delaunay-Triangulierung (DE-588)4628829-6 gnd rswk-swf Triangulation (DE-588)4186017-2 gnd rswk-swf Voronoi-Diagramm (DE-588)4226013-9 gnd rswk-swf Voronoi-Diagramm (DE-588)4226013-9 s Triangulation (DE-588)4186017-2 s DE-604 Delaunay-Triangulierung (DE-588)4628829-6 s Klein, Rolf 1953- Sonstige (DE-588)13607958X oth Lee, Der-Tsai 1949- Sonstige (DE-588)122392612 oth Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026101005&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026101005&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Aurenhammer, Franz Voronoi diagrams and Delaunay triangulations Voronoi polygons Spatial analysis (Statistics) Delaunay-Triangulierung (DE-588)4628829-6 gnd Triangulation (DE-588)4186017-2 gnd Voronoi-Diagramm (DE-588)4226013-9 gnd |
| subject_GND | (DE-588)4628829-6 (DE-588)4186017-2 (DE-588)4226013-9 |
| title | Voronoi diagrams and Delaunay triangulations |
| title_auth | Voronoi diagrams and Delaunay triangulations |
| title_exact_search | Voronoi diagrams and Delaunay triangulations |
| title_full | Voronoi diagrams and Delaunay triangulations Franz Aurenhammer ; Rolf Klein ; Der-Tsai Lee |
| title_fullStr | Voronoi diagrams and Delaunay triangulations Franz Aurenhammer ; Rolf Klein ; Der-Tsai Lee |
| title_full_unstemmed | Voronoi diagrams and Delaunay triangulations Franz Aurenhammer ; Rolf Klein ; Der-Tsai Lee |
| title_short | Voronoi diagrams and Delaunay triangulations |
| title_sort | voronoi diagrams and delaunay triangulations |
| topic | Voronoi polygons Spatial analysis (Statistics) Delaunay-Triangulierung (DE-588)4628829-6 gnd Triangulation (DE-588)4186017-2 gnd Voronoi-Diagramm (DE-588)4226013-9 gnd |
| topic_facet | Voronoi polygons Spatial analysis (Statistics) Delaunay-Triangulierung Triangulation Voronoi-Diagramm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026101005&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026101005&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT aurenhammerfranz voronoidiagramsanddelaunaytriangulations AT kleinrolf voronoidiagramsanddelaunaytriangulations AT leedertsai voronoidiagramsanddelaunaytriangulations |