Triangulations and applications:
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Elektronisch E-Book |
Sprache: | English |
Veröffentlicht: |
Berlin ; Heidelberg ; New York
Springer
2006
|
Schriftenreihe: | Mathematics and visualization
|
Schlagworte: | |
Online-Zugang: | BTU01 TUM01 UBA01 UBM01 UBR01 UBT01 UPA01 Volltext Inhaltsverzeichnis |
Beschreibung: | Literaturverz. S. 223 - 227 |
Beschreibung: | 1 Online-Ressource (XI, 234 S.) graph. Darst. |
ISBN: | 354033260X 9783540332602 9783540332619 |
DOI: | 10.1007/3-540-33261-8 |
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Datensatz im Suchindex
_version_ | 1804136433056743424 |
---|---|
adam_text | 0YVIN
D HJELLE
MORTEN DAEHLEN
TRIANGULATIONS
AND APPLICATIONS
WITH 126 FIGURES
J SPRINGE
R
CONTENTS
TRIANGLES AND TRIANGULATIONS
1
1.1 TRIANGLES , 1
1.2 TRIANGULATIONS 5
1.3 SOME PROPERTIES OF TRIANGULATIONS 7
1.4 A TRIANGULATION ALGORITHM 10
1.5 EDGE INSERTION 16
1.6 USING TRIANGULATIONS 18
1.7 EXERCISES 20
GRAPHS AND DAT
A STRUCTURE
S
23
2.1 GRAPH THEORETIC CONCEPTS 23
2.2 GENERALIZED MAPS (G-MAPS) 25
2.3 DATA STRUCTURES FOR TRIANGULATIONS 29
2.4 A MINIMAL TRIANGLE-BASED DATA STRUCTURE 31
2.5 TRIANGLE-BASED DATA STRUCTURE WITH NEIGHBORS 32
2.6 VERTEX-BASED DATA STRUCTURE WITH NEIGHBORS 33
2.7 HALF-EDGE DAT
A STRUCTURE 35
2.8 DART-BASED DATA STRUCTURE 37
2.9 TRIANGLES FOR VISUALIZATION 38
2.10 BINARY TRIANGULATIONS 41
2.11 EXERCISES 45
DELAUNA
Y TRIANGULATIONS AND VORONOI DIAGRAM
S
47
3.1 OPTIMAL TRIANGULATIONS 47
3.2 THE NEUTRAL CASE 50
3.3 VORONOI DIAGRAMS 51
3.4 DELAUNAY TRIANGULATION AS THE DUAL OF THE VORONOI DIAGRAM . . 54
3.5 THE CIRCLE CRITERION 57
3.6 EQUIVALENCE OF THE DELAUNAY CRITERIA
FOR STRICTLY CONVEX QUADRILATERALS 59
X CONTENTS
3.7 COMPUTING THE CIRCUMCIRCLE TEST 62
3.8 THE LOCAL OPTIMIZATION PROCEDURE (LOP) 64
3.9 GLOBAL PROPERTIES OF THE DELAUNAY TRIANGULATION 66
3.10 EXERCISES
71
4 ALGORITHM
S FOR DELAUNA
Y TRIANGULATION
73
4.1 A SIMPLE ALGORITHM BASED ON PREVIOUS RESULTS 73
4.2 RADIAL SWEEP 74
4.3 A STEP-BY-STEP APPROACH FOR MAKING DELAUNAY TRIANGLES ...
. 75
4.4 INCREMENTAL ALGORITHMS
-YY
78
4.5 INSERTING A POINT INTO A DELAUNAY TRIANGULATION 79
4.6 POINT INSERTION AND EDGE-SWAPPING 81
4.7 RUNNING TIME OF INCREMENTAL ALGORITHMS 87
4.8 DIVIDE-AND-CONQUER 89
4.9 EXERCISES 92
5 DAT
A DEPENDEN
T TRIANGULATIONS
95
5.1 MOTIVATION 95
5.2 OPTIMAL TRIANGULATIONS REVISITED 96
5.3 THE GENERAL CONCEPT 98
5.4 DAT
A DEPENDENT SWAPPING CRITERIA 101
5.5 ON IMPLEMENTATION OF THE LOP 105
5.6 MODIFIED LOCAL OPTIMIZATION PROCEDURES (MLOP) 106
5.7 SIMULATED ANNEALING 106
5.8 EXERCISES 112
6 CONSTRAINE
D DELAUNA
Y TRIANGULATION
113
6.1 DELAUNAY TRIANGULATION OF A PLANAR STRAIGHT-LINE GRAPH 113
6.2 GENERALIZATION OF DELAUNAY TRIANGULATION 115
6.3 ALGORITHMS FOR CONSTRAINED DELAUNAY TRIANGULATION 118
6.4 INSERTING AN EDGE INTO A CDT 119
6.5 EDGE INSERTION AND SWAPPING . . 123
6.6 INSERTING A POINT INTO A CDT 127
6.7 EXERCISES 129
7 DELAUNA
Y REFINEMENT MES
H GENERATIO
N
; 131
7.1 INTRODUCTION 131
7.2 GENERAL REQUIREMENTS FOR MESHES 132
7.3 NODE INSERTION 134
7.4 SPLITTING ENCROACHED SEGMENTS 139
7.5 THE DELAUNAY REFINEMENT ALGORITHM 142
7.6 MINIMUM EDGE LENGTH AND TERMINATION 145
7.7 CORNER-LOPPING FOR HANDLING SMALL INPUT ANGLES 152
7.8 SPATIAL GRADING 154
7.9 EXERCISES 154
CONTENTS XI
8 LEAST SQUARES APPROXIMATIO
N OF SCATTERE
D DAT
A
157
8.1 ANOTHER FORMULATION OF SURFACE TRIANGULATIONS 157
8.2 APPROXIMATION OVER TRIANGULATIONS OF SUBSETS OF DATA . 160
8.3 EXISTENCE AND UNIQUENESS 163
8.4 SPARSITY AND SYMMETRY 164
8.5 PENALIZED LEAST SQUARES 166
8.6 SMOOTHING TERMS FOR PENALIZED LEAST SQUARES 168
8.7 APPROXIMATION OVER GENERAL TRIANGULATIONS 175
8.8 WEIGHTED LEAST SQUARES 178
8.9 CONSTRAINED LEAST SQUARES 180
8.10 APPROXIMATION OVER BINARY TRIANGULATIONS 182
8.11 NUMERICAL EXAMPLES FOR BINARY TRIANGULATIONS 185
8.12 EXERCISES 191
9 PROGRAMMIN
G TRIANGULATIONS:
TH
E TRIANGULATION TEMPLAT
E LIBRARY (TTL
)
193
9.1 IMPLEMENTATION OF THE HALF-EDGE DATA STRUCTURE 194
9.2 THE OVERALL DESIGN AND THE ADAPTATION LAYER 197
9.3 TOPOLOGICAL QUERIES AND THE DART CLASS 199
9.4 SOME ITERATOR CLASSES 203
9.5 GEOMETRIC QUERIES AND THE TRAITS CLASS 205
9.6 GEOMETRIC AND TOPOLOGICAL MODIFIERS 211
9.7 GENERIC DELAUNAY TRIANGULATION 213
9.8 EXERCISES 221
REFERENCES
223
INDE
X
229
|
adam_txt |
0YVIN
D HJELLE
MORTEN DAEHLEN
TRIANGULATIONS
AND APPLICATIONS
WITH 126 FIGURES
J SPRINGE
R
CONTENTS
TRIANGLES AND TRIANGULATIONS
1
1.1 TRIANGLES , 1
1.2 TRIANGULATIONS 5
1.3 SOME PROPERTIES OF TRIANGULATIONS 7
1.4 A TRIANGULATION ALGORITHM 10
1.5 EDGE INSERTION 16
1.6 USING TRIANGULATIONS 18
1.7 EXERCISES 20
GRAPHS AND DAT
A STRUCTURE
S
23
2.1 GRAPH THEORETIC CONCEPTS 23
2.2 GENERALIZED MAPS (G-MAPS) 25
2.3 DATA STRUCTURES FOR TRIANGULATIONS 29
2.4 A MINIMAL TRIANGLE-BASED DATA STRUCTURE 31
2.5 TRIANGLE-BASED DATA STRUCTURE WITH NEIGHBORS 32
2.6 VERTEX-BASED DATA STRUCTURE WITH NEIGHBORS 33
2.7 HALF-EDGE DAT
A STRUCTURE 35
2.8 DART-BASED DATA STRUCTURE 37
2.9 TRIANGLES FOR VISUALIZATION 38
2.10 BINARY TRIANGULATIONS 41
2.11 EXERCISES 45
DELAUNA
Y TRIANGULATIONS AND VORONOI DIAGRAM
S
47
3.1 OPTIMAL TRIANGULATIONS 47
3.2 THE NEUTRAL CASE 50
3.3 VORONOI DIAGRAMS 51
3.4 DELAUNAY TRIANGULATION AS THE DUAL OF THE VORONOI DIAGRAM . . 54
3.5 THE CIRCLE CRITERION 57
3.6 EQUIVALENCE OF THE DELAUNAY CRITERIA
FOR STRICTLY CONVEX QUADRILATERALS 59
X CONTENTS
3.7 COMPUTING THE CIRCUMCIRCLE TEST 62
3.8 THE LOCAL OPTIMIZATION PROCEDURE (LOP) 64
3.9 GLOBAL PROPERTIES OF THE DELAUNAY TRIANGULATION 66
3.10 EXERCISES
71
4 ALGORITHM
S FOR DELAUNA
Y TRIANGULATION
73
4.1 A SIMPLE ALGORITHM BASED ON PREVIOUS RESULTS 73
4.2 RADIAL SWEEP 74
4.3 A STEP-BY-STEP APPROACH FOR MAKING DELAUNAY TRIANGLES .
. 75
4.4 INCREMENTAL ALGORITHMS
-YY
78
4.5 INSERTING A POINT INTO A DELAUNAY TRIANGULATION 79
4.6 POINT INSERTION AND EDGE-SWAPPING 81
4.7 RUNNING TIME OF INCREMENTAL ALGORITHMS 87
4.8 DIVIDE-AND-CONQUER 89
4.9 EXERCISES 92
5 DAT
A DEPENDEN
T TRIANGULATIONS
95
5.1 MOTIVATION 95
5.2 OPTIMAL TRIANGULATIONS REVISITED 96
5.3 THE GENERAL CONCEPT 98
5.4 DAT
A DEPENDENT SWAPPING CRITERIA 101
5.5 ON IMPLEMENTATION OF THE LOP 105
5.6 MODIFIED LOCAL OPTIMIZATION PROCEDURES (MLOP) 106
5.7 SIMULATED ANNEALING 106
5.8 EXERCISES 112
6 CONSTRAINE
D DELAUNA
Y TRIANGULATION
113
6.1 DELAUNAY TRIANGULATION OF A PLANAR STRAIGHT-LINE GRAPH 113
6.2 GENERALIZATION OF DELAUNAY TRIANGULATION 115
6.3 ALGORITHMS FOR CONSTRAINED DELAUNAY TRIANGULATION 118
6.4 INSERTING AN EDGE INTO A CDT 119
6.5 EDGE INSERTION AND SWAPPING . . 123
6.6 INSERTING A POINT INTO A CDT 127
6.7 EXERCISES 129
7 DELAUNA
Y REFINEMENT MES
H GENERATIO
N
; 131
7.1 INTRODUCTION 131
7.2 GENERAL REQUIREMENTS FOR MESHES 132
7.3 NODE INSERTION 134
7.4 SPLITTING ENCROACHED SEGMENTS 139
7.5 THE DELAUNAY REFINEMENT ALGORITHM 142
7.6 MINIMUM EDGE LENGTH AND TERMINATION 145
7.7 CORNER-LOPPING FOR HANDLING SMALL INPUT ANGLES 152
7.8 SPATIAL GRADING 154
7.9 EXERCISES 154
CONTENTS XI
8 LEAST SQUARES APPROXIMATIO
N OF SCATTERE
D DAT
A
157
8.1 ANOTHER FORMULATION OF SURFACE TRIANGULATIONS 157
8.2 APPROXIMATION OVER TRIANGULATIONS OF SUBSETS OF DATA . 160
8.3 EXISTENCE AND UNIQUENESS 163
8.4 SPARSITY AND SYMMETRY 164
8.5 PENALIZED LEAST SQUARES 166
8.6 SMOOTHING TERMS FOR PENALIZED LEAST SQUARES 168
8.7 APPROXIMATION OVER GENERAL TRIANGULATIONS 175
8.8 WEIGHTED LEAST SQUARES 178
8.9 CONSTRAINED LEAST SQUARES 180
8.10 APPROXIMATION OVER BINARY TRIANGULATIONS 182
8.11 NUMERICAL EXAMPLES FOR BINARY TRIANGULATIONS 185
8.12 EXERCISES 191
9 PROGRAMMIN
G TRIANGULATIONS:
TH
E TRIANGULATION TEMPLAT
E LIBRARY (TTL
)
193
9.1 IMPLEMENTATION OF THE HALF-EDGE DATA STRUCTURE 194
9.2 THE OVERALL DESIGN AND THE ADAPTATION LAYER 197
9.3 TOPOLOGICAL QUERIES AND THE DART CLASS 199
9.4 SOME ITERATOR CLASSES 203
9.5 GEOMETRIC QUERIES AND THE TRAITS CLASS 205
9.6 GEOMETRIC AND TOPOLOGICAL MODIFIERS 211
9.7 GENERIC DELAUNAY TRIANGULATION 213
9.8 EXERCISES 221
REFERENCES
223
INDE
X
229 |
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author | Hjelle, Øyvind Daehlen, Morten 1959- |
author_GND | (DE-588)132114976 (DE-588)115422390 |
author_facet | Hjelle, Øyvind Daehlen, Morten 1959- |
author_role | aut aut |
author_sort | Hjelle, Øyvind |
author_variant | ø h øh m d md |
building | Verbundindex |
bvnumber | BV022377846 |
classification_rvk | SK 380 |
classification_tum | MAT 000 |
collection | ZDB-2-SMA |
ctrlnum | (OCoLC)873408114 (DE-599)BVBBV022377846 |
discipline | Mathematik |
discipline_str_mv | Mathematik |
doi_str_mv | 10.1007/3-540-33261-8 |
format | Electronic eBook |
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index_date | 2024-07-02T17:10:01Z |
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language | English |
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oclc_num | 873408114 |
open_access_boolean | |
owner | DE-739 DE-355 DE-BY-UBR DE-634 DE-91 DE-BY-TUM DE-384 DE-703 DE-83 DE-19 DE-BY-UBM |
owner_facet | DE-739 DE-355 DE-BY-UBR DE-634 DE-91 DE-BY-TUM DE-384 DE-703 DE-83 DE-19 DE-BY-UBM |
physical | 1 Online-Ressource (XI, 234 S.) graph. Darst. |
psigel | ZDB-2-SMA |
publishDate | 2006 |
publishDateSearch | 2006 |
publishDateSort | 2006 |
publisher | Springer |
record_format | marc |
series2 | Mathematics and visualization |
spelling | Hjelle, Øyvind Verfasser (DE-588)132114976 aut Triangulations and applications Øyvind Hjelle ; Morten Daehlen Berlin ; Heidelberg ; New York Springer 2006 1 Online-Ressource (XI, 234 S.) graph. Darst. txt rdacontent c rdamedia cr rdacarrier Mathematics and visualization Literaturverz. S. 223 - 227 Triangulation (DE-588)4186017-2 gnd rswk-swf Triangulation (DE-588)4186017-2 s DE-604 Daehlen, Morten 1959- Verfasser (DE-588)115422390 aut https://doi.org/10.1007/3-540-33261-8 Verlag Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015586887&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Hjelle, Øyvind Daehlen, Morten 1959- Triangulations and applications Triangulation (DE-588)4186017-2 gnd |
subject_GND | (DE-588)4186017-2 |
title | Triangulations and applications |
title_auth | Triangulations and applications |
title_exact_search | Triangulations and applications |
title_exact_search_txtP | Triangulations and applications |
title_full | Triangulations and applications Øyvind Hjelle ; Morten Daehlen |
title_fullStr | Triangulations and applications Øyvind Hjelle ; Morten Daehlen |
title_full_unstemmed | Triangulations and applications Øyvind Hjelle ; Morten Daehlen |
title_short | Triangulations and applications |
title_sort | triangulations and applications |
topic | Triangulation (DE-588)4186017-2 gnd |
topic_facet | Triangulation |
url | https://doi.org/10.1007/3-540-33261-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015586887&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT hjelleøyvind triangulationsandapplications AT daehlenmorten triangulationsandapplications |