CGAL arrangements and their applications: a step-by-step guide
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2012
|
| Schriftenreihe: | Geometry and computing
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIX, 293 S. Ill., graph. Darst. |
| ISBN: | 9783642172823 3642172822 9783642172830 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text |
IMAGE 1
CONTENTS
PREFACE XIWHAT THIS BOOK CONTAINS XIWHAT YOU SHOULD KNOW BEFORE READING
THIS BOOK XIHOW TO OBTAIN AND INSTALL CGAL XIILICENSE XVISTYLE
CONVENTIONS XVIEXERCISES XVIICOVER XVIIERRATA XVIIACKNOWLEDGMENTS XVII 1
INTRODUCTION 1 1.1 ARRANGEMENTS 11.2 GENERIC PROGRAMMING 21.2.1 CONCEPTS
AND MODELS 21.2.2 TRAITS CLASSES 31.2.3 GENERIC AND OBJECT-ORIENTED
PROGRAMMING 51.2.4 LIBRARIES 71.3 GEOMETRIC COMPUTING 71.3.1 SEPARATION
OF TOPOLOGY AND GEOMETRY 81.3.2 EXACT GEOMETRIC COMPUTATION 81.3.3
WELL-BEHAVED CURVES 91.4 THE COMPUTATIONAL GEOMETRY ALGORITHM LIBRARY
101.4.1 CGAL CHRONICLES 101.4.2 CGAL CONTENT 101.4.3 THE ALGEBRAIC
FOUNDATIONS OF CGAL 111.4.4 THE GEOMETRY KERNEL OF CGAL 121.4.5 THE
STATE OF CGAL 141.4.6 THE NAMESPACE OF CGAL 151.5 OUTLINE OF THE BOOK
151.6 FURTHER READING 172 BASIC ARRANGEMENTS 192.1 REPRESENTATION OF
ARRANGEMENTS: THE DCEL 192.2 THE MAIN ARRANGEMENT CLASS 202.2.1
TRAVERSING THE ARRANGEMENT 222.2.2 MODIFYING THE ARRANGEMENT 262.2.3
INPUT/OUTPUT FUNCTIONS 332.3 APPLICATION: OBTAINING SILHOUETTES OF
POLYTOPES 362.4 BIBLIOGRAPHIC NOTES AND REMARKS 402.5 EXERCISES 41
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1007777524 DIGITALISIERT
DURCH
IMAGE 2
VIII CONTENTS
3 QUERIES AND FREE FUNCTIONS 43
3.1 ISSUING QUERIES ON AN ARRANGEMENT 43
3.1.1 POINT-LOCATION QUERIES 43
3.1.2 VERTICAL RAY SHOOTING 47
3.2 TWO ALGORITHMIC FRAMEWORKS: PLANE SWEEP AND ZONE CONSTRUCTION 48
3.3 BATCHED POINT-LOCATION 50
3.4 FREE INSERTION FUNCTIONS 51
3.4.1 INCREMENTAL INSERTION FUNCTIONS 52
3.4.2 AGGREGATE INSERTION FUNCTIONS 55
3.5 REMOVING VERTICES AND EDGES 57
3.6 VERTICAL DECOMPOSITION 58
3.6.1 APPLICATION: DECOMPOSING AN ARRANGEMENT OF LINE SEGMENTS 59 3.7
BIBLIOGRAPHIC NOTES AND REMARKS 63
3.8 EXERCISES 64
4 ARRANGEMENTS OF UNBOUNDED CURVES 67
4.1 REPRESENTING ARRANGEMENTS OF UNBOUNDED CURVES 67
4.1.1 BASIC MANIPULATION AND TRAVERSAL METHODS 69
4.1.2 FREE FUNCTIONS 72
4.2 POINT-LINE DUALITY 73
4.2.1 APPLICATION: MINIMUM-AREA TRIANGLE 74
4.2.2 A NOTE ON THE INPUT PRECISION 79
4.3 BIBLIOGRAPHIC NOTES AND REMARKS 81
4.4 EXERCISES 81
5 ARRANGEMENT-TRAITS CLASSES 83
5.1 THE HIERARCHY OF TRAITS-CLASS CONCEPTS 83
5.1.1 THE BASIC CONCEPT 84
5.1.2 SUPPORTING INTERSECTIONS 85
5.1.3 SUPPORTING ARBITRARY CURVES 87
5.1.4 THE LANDMARK CONCEPT 88
5.1.5 SUPPORTING UNBOUNDED CURVES 89
5.1.6 THE TRAITS ADAPTOR 91
5.2 TRAITS CLASSES FOR LINE SEGMENTS AND LINEAR OBJECTS 91
5.2.1 THE CACHING SEGMENT-TRAITS CLASS 92
5.2.2 THE NON-CACHING SEGMENT-TRAITS CLASS 92
5.2.3 THE LINEAR-TRAITS CLASS 94
5.3 THE POLYLINE-TRAITS CLASS 94
5.4 TRAITS CLASSES FOR ALGEBRAIC CURVES 97
5.4.1 A TRAITS CLASS FOR CIRCULAR ARCS AND LINE SEGMENTS 98
5.4.2 A TRAITS CLASS FOR CONIC ARCS 102
5.4.3 A TRAITS CLASS FOR ARCS OF RATIONAL FUNCTIONS 105
5.4.4 A TRAITS CLASS FOR PLANAR BEZIER CURVES 109
5.4.5 A TRAITS CLASS FOR PLANAR ALGEBRAIC CURVES OF ARBITRARY DEGREE I
LL
5.5 TRAITS-CLASS DECORATORS 117
5.6 APPLICATION: POLYGON ORIENTATION 121
5.7 BIBLIOGRAPHIC NOTES AND REMARKS 124
5.8 EXERCISES 126
6 EXTENDING THE ARRANGEMENT 129
6.1 THE NOTIFICATION MECHANISM 129
6.2 EXTENDING THE DCEL 132
6.2.1 EXTENDING THE DCEL FACES 132
6.2.2 EXTENDING ALL THE DCEL RECORDS 134
IMAGE 3
CONTENTS IX
6.2.3 INPUT/OUTPUT FOR ARRANGEMENTS WITH AUXILIARY DATA 137
6.3 OVERLAYING ARRANGEMENTS 138
6.4 STORING THE CURVE HISTORY 146
6.4.1 TRAVERSING AN ARRANGEMENT WITH HISTORY 147
6.4.2 MODIFYING AN ARRANGEMENT WITH HISTORY 148
6.4.3 INPUT/OUTPUT FOR ARRANGEMENTS WITH CURVE HISTORY 151
6.5 APPLICATION: POLYGON REPAIRING AND WINDING NUMBERS 152
6.6 BIBLIOGRAPHIC NOTES AND REMARKS 157
6.7 EXERCISES 158
7 ADAPTING TO B O O ST GRAPHS 161
7.1 THE PRIMAL ARRANGEMENT REPRESENTATION 161
7.2 THE DUAL ARRANGEMENT REPRESENTATION 164
7.3 APPLICATION: LARGEST COMMON POINT SETS UNDER E-CONGRUENCE 166
7.4 BIBLIOGRAPHIC NOTES AND REMARKS 171
7.5 EXERCISES 172
8 OPERATIONS ON (CURVED) POLYGONS 175
8.1 OPERATIONS ON LINEAR POLYGONS 177
8.1.1 POLYGONS WITH HOLES 178
8.1.2 OPERATIONS ON POLYGONS WITH HOLES 181
8.1.3 POINT CONTAINMENT AND NON-REGULARIZED OPERATIONS 183
8.1.4 CONNECTING HOLES 184
8.1.5 OPERATIONS ON POLYGON SETS 184
8.1.6 A SEQUENCE OF SET OPERATIONS 185
8.1.7 INSERTING NON-INTERSECTING POLYGONS 187
8.1.8 PERFORMING MULTIWAY OPERATIONS 189
8.2 OPERATIONS ON CURVED POLYGONS 189
8.2.1 THE TRAITS-CLASS CONCEPTS 190
8.2.2 OPERATIONS ON POLYGONS WITH CIRCULAR ARCS 192
8.2.3 GENERAL-POLYGON SET TRAITS-ADAPTOR 194
8.3 APPLICATION: MULTIWAY OPERATIONS ON GENERAL POLYGONS 198
8.4 APPLICATION: OBTAINING SILHOUETTES OF POLYHEDRA 203
8.5 BIBLIOGRAPHIC NOTES AND REMARKS 205
8.6 EXERCISES 207
9 MINKOWKSI SUMS AND OFFSET POLYGONS 209
9.1 COMPUTING THE MINKOWSKI SUM OF TWO POLYGONS 209
9.1.1 COMPUTING MINKOWSKI SUM USING CONVOLUTIONS 211
9.1.2 DECOMPOSITION STRATEGIES 213
9.2 OFFSETTING A POLYGON 214
9.2.1 APPROXIMATING THE OFFSET WITH A GUARANTEED ERROR BOUND 215
9.2.2 COMPUTING THE EXACT OFFSET 217
9.3 MOTION-PLANNING APPLICATIONS 219
9.3.1 APPLICATION: A TRANSLATING POLYGONAL ROBOT 220
9.3.2 APPLICATION: COORDINATING TWO DISC ROBOTS 227
9.4 BIBLIOGRAPHIC NOTES AND REMARKS 237
9.5 EXERCISES 239
10 ENVELOPES 241
10.1 ENVELOPES OF CURVES IN THE PLANE 241
10.1.1 REPRESENTING THE ENVELOPE 241
10.1.2 CONSTRUCTING THE ENVELOPE DIAGRAM 242
10.1.3 THE ENVELOPE-SOFTWARE COMPONENTS 243
IMAGE 4
X CONTENTS
10.1.4 USING THE TRAITS CLASSES 244
10.2 APPLICATION: NEAREST JEEP OVER TIME 248
10.3 ENVELOPES OF SURFACES IN 3-SPACE 250
10.3.1 THE ENVELOPE-TRAITS CONCEPT 252
10.3.2 USING THE ENVELOPE-TRAITS CLASSES 254
10.4 APPLICATION: LOCATING THE FARTHEST POINT 257
10.5 BIBLIOGRAPHIC NOTES AND REMARKS 259
10.6 EXERCISES 260
11 PROSPECTS 263
11.1 ARRANGEMENTS ON CURVED SURFACES 263
11.2 HIGHER-DIMENSIONAL ARRANGEMENTS 265
11.3 FIXED-PRECISION GEOMETRIC COMPUTING 267
11.4 MORE APPLICATIONS 268
11.5 EXERCISES 269
BIBLIOGRAPHY 271
INDEX 285 |
| any_adam_object | 1 |
| author | Fogel, Efi Halperin, Dan Wein, Ron |
| author_GND | (DE-588)1019257415 (DE-588)1019423536 (DE-588)101942379X |
| author_facet | Fogel, Efi Halperin, Dan Wein, Ron |
| author_role | aut aut aut |
| author_sort | Fogel, Efi |
| author_variant | e f ef d h dh r w rw |
| building | Verbundindex |
| bvnumber | BV040097218 |
| classification_rvk | ST 320 ST 601 |
| classification_tum | DAT 537f DAT 316f DAT 756f |
| ctrlnum | (OCoLC)778375692 (DE-599)DNB1007777524 |
| dewey-full | 006.66 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.66 |
| dewey-search | 006.66 |
| dewey-sort | 16.66 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV040097218 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:30:29Z |
| institution | BVB |
| isbn | 9783642172823 3642172822 9783642172830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024953870 |
| oclc_num | 778375692 |
| open_access_boolean | |
| owner | DE-703 DE-83 DE-91G DE-BY-TUM |
| owner_facet | DE-703 DE-83 DE-91G DE-BY-TUM |
| physical | XIX, 293 S. Ill., graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series | Geometry and computing |
| series2 | Geometry and computing |
| spelling | Fogel, Efi Verfasser (DE-588)1019257415 aut CGAL arrangements and their applications a step-by-step guide Efi Fogel ; Dan Halperin ; Ron Wein Berlin ; Heidelberg Springer 2012 XIX, 293 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geometry and computing 7 Programmbibliothek (DE-588)4121521-7 gnd rswk-swf Geometrische Programmierung (DE-588)4570183-0 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Generische Programmierung (DE-588)4431718-9 gnd rswk-swf C++ (DE-588)4193909-8 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 s Algorithmische Geometrie (DE-588)4130267-9 s Geometrische Programmierung (DE-588)4570183-0 s Programmbibliothek (DE-588)4121521-7 s C++ (DE-588)4193909-8 s Generische Programmierung (DE-588)4431718-9 s DE-604 Halperin, Dan Verfasser (DE-588)1019423536 aut Wein, Ron Verfasser (DE-588)101942379X aut Erscheint auch als Online-Ausgabe CGAL Arrangements and Their Applications Geometry and computing 7 (DE-604)BV022959018 7 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3552153&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024953870&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fogel, Efi Halperin, Dan Wein, Ron CGAL arrangements and their applications a step-by-step guide Geometry and computing Programmbibliothek (DE-588)4121521-7 gnd Geometrische Programmierung (DE-588)4570183-0 gnd Geometrische Modellierung (DE-588)4156717-1 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Generische Programmierung (DE-588)4431718-9 gnd C++ (DE-588)4193909-8 gnd |
| subject_GND | (DE-588)4121521-7 (DE-588)4570183-0 (DE-588)4156717-1 (DE-588)4130267-9 (DE-588)4431718-9 (DE-588)4193909-8 |
| title | CGAL arrangements and their applications a step-by-step guide |
| title_auth | CGAL arrangements and their applications a step-by-step guide |
| title_exact_search | CGAL arrangements and their applications a step-by-step guide |
| title_full | CGAL arrangements and their applications a step-by-step guide Efi Fogel ; Dan Halperin ; Ron Wein |
| title_fullStr | CGAL arrangements and their applications a step-by-step guide Efi Fogel ; Dan Halperin ; Ron Wein |
| title_full_unstemmed | CGAL arrangements and their applications a step-by-step guide Efi Fogel ; Dan Halperin ; Ron Wein |
| title_short | CGAL arrangements and their applications |
| title_sort | cgal arrangements and their applications a step by step guide |
| title_sub | a step-by-step guide |
| topic | Programmbibliothek (DE-588)4121521-7 gnd Geometrische Programmierung (DE-588)4570183-0 gnd Geometrische Modellierung (DE-588)4156717-1 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Generische Programmierung (DE-588)4431718-9 gnd C++ (DE-588)4193909-8 gnd |
| topic_facet | Programmbibliothek Geometrische Programmierung Geometrische Modellierung Algorithmische Geometrie Generische Programmierung C++ |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3552153&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024953870&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022959018 |
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