Computational geometry: an introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1988
|
| Ausgabe: | Corr. and expanded 2. print. |
| Schriftenreihe: | Texts and monographs in computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 398 S. graph. Darst. |
| ISBN: | 0387961313 3540961313 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804115728290283520 |
|---|---|
| adam_text | COMPUTATIONAL GEOMETRY AN INTRODUCTION FRANCO P. PREPARATA MICHAEL LAN
SHAMOS WITH 234 ILLUSTRATION SPRINGER CONTENTS CHAPTER1 INTRODUCTION 1
1.1 HISTORICAL PERSPECTIVE 1 1.1.1 COMPLEXITY NOTIONS IN CLASSICAL
GEOMETRY 2 1.1.2 THE THEORY OF CONVEX SETS, METRIC AND COMBINATORIAL
GEOMETRY 4 1.1.3 PRIOR RELATED WORK 5 1.1.4 TOWARD COMPUTATIONAL
GEOMETRY 6 1.2 ALGORITHMIC BACKGROUND 6 1.2.1 ALGORITHMS: THEIR
EXPRESSION AND PERFORMANCE EVALUATION 7 1.2.2 SOME CONSIDERATIONS ON
GENERAL ALGORITHMIC TECHNIQUES 10 1.2.3 DATA STRUCTURES 11 1.2.3.1 THE
SEGMENT TREE 13 1.2.3.2 THE DOUBLY-CONNECTED-EDGE-LIST (DCEL) 15 1.3
GEOMETRIE PRELIMINARIES 17 1.3.1 GENERAL DEFINITIONS AND NOTATIONS 17
1.3.2 INVARIANTS UNDER GROUPS OF LINEAR TRANSFORMATIONS S 19 1.3.3
GEOMETRY DUALITY. POLARITY 24 1.4 MODELS OF COMPUTATION 26 CHAPTER 2
GEOMETRIE SEARCHING 36 2.1 INTRODUCTION TO GEOMETRIE SEARCHING 36 2.2
POINT-LOCATION PROBLEMS 41 2.2.1 GENERAL CONSIDERATIONS. SIMPLE CASES 41
2.2.2 LOCATION OF A POINT IN A PLANAR SUBDIVISION 45 2.2.2.1 THE SLAB
METHOD 45 XII CONTENTS 2.2.2.2 THE CHAIN METHOD 48 2.2.2.3 OPTIMAL
TECHNIQUES: THE PLANAR-SEPARATOR METHOD, THE TRIANGULATION REFINEMENT
METHOD, AND THE BRIDGED CHAIN METHOD 56 2.2.2.4 THE TRAPEZOID METHOD 63
2.3 RANGE-SEARCHING PROBLEMS 70 2.3.1 GENERAL CONSIDERATIONS 70 2.3.2
THE METHOD OF THE MULTIDIMENSIONAL BINARY TREE (K-D TREE) 74 2.3.3 A
DIRECT ACCESS METHOD AND ITS VARIANTS 79 2.3.4 THE RANGE-TREE METHOD AND
ITS VARIANTS 83 2.4 ITERATED SEARCH AND FRACTIONAL CASCADING 88 2.5
NOTES AND COMMENTS 92 2.6 EXERCISES 94 CHAPTER 3 CONVEX HULLS: BASIC
ALGORITHMS 95 3.1 PRELIMINARIES 96 3.2 PROBLEM STATEMENT AND LOWER
BOUNDS 99 3.3 CONVEX HUELL ALGORITHMS IN THE PLANE 104 3.3.1 EARLY
DEVELOPMENT OF A CONVEX HUELL ALGORITHM 104 3.3.2 GRAHAM S SCAN 106 3.3.3
JARVIS S MARCH 110 3.3.4 QUICKHULL TECHNIQUES 112 3.3.5
DIVIDE-AND-CONQUER ALGORITHMS 114 3.3.6 DYNAMIC CONVEX HUELL ALGORITHMS
117 3.3.7 A GENERALIZATION: DYNAMIC CONVEX HUELL MAINTENANCE 124 3.4
CONVEX HULLS IN MORE THAN TWO DIMENSIONS 131 3.4.1 THE GIFT-WRAPPING
METHOD 131 3.4.2 THE BENEATH-BEYOND METHOD 137 3.4.3 CONVEX HULLS IN
THREE DIMENSIONS 141 3.5 NOTES AND COMMENTS 146 3.6 EXERCISES 148
CHAPTER 4 CONVEX HULLS: EXTENSIONS AND APPLICATIONS 150 150 150 154 157
166 171 171 174 176 182 183 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 4.2.1 4.2.2
4.2.3 4.3 4.4 EXTENSIONS AND VANANTS AVERAGE-CASE ANALYSIS APPROXIMATION
ALGORITHMS FOR CONVEX HUELL THE PROBLEM OF THE MAXIMA OF A POINT SET
CONVEX HUELL OF A SIMPLE POLYGON APPLICATIONS TO STATISTICS ROBUST
ESTIMATION ISOTONIC REGRESSION CLUSTERING (DIAMETER OF A POINT SET)
NOTES AND COMMENTS EXERCISES CONTENTS XL CHAPTER 5 PROXIMITY:
FUNDAMENTAL ALGORITHMS 185 5.1 A COLLECTION OF PROBLEMS 186 5.2 A
COMPUTATIONAL PROTOTYPE: ELEMENT UNIQUENESS 191 5.3 LOWERBOUNDS 192 5.4
THE CLOSEST PAIR PROBLEM: A DIVIDE-AND-CONQUER APPROACH 195 5.5 THE
LOCUS APPROACH TO PROXIMITY PROBLEMS: THE VORONOI DIAGRAM 204 5.5.1
ACATALOGOF VORONOI PROPERTIES 205 5.5.2 CONSTRUCTING THE VORONOI DIAGRAM
211 5.5.2.1 CONSTRUCTING THE DIVIDING CHAIN 216 5.6 PROXIMITY PROBLEMS
SOLVED BY THE VORONOI DIAGRAM 220 5.7 NOTES AND COMMENTS 222 5.8
EXERCISES 223 CHAPTER 6 PROXIMITY: VARIANTS AND GENERALIZATIONS 226 6.1
EUCLIDEAN MINIMUM SPANNING TREES 226 6.1.1 EUCLIDEAN TRAVELING SALESMAN
230 6.2 PLANAR TRIANGULATIONS 234 6.2.1 THE GREEDY TRIANGULATION 235
6.2.2 CONSTRAINED TRIANGULATIONS 237 6.2.2.1 TRIANGULATING A MONOTONE
POLYGON 239 6.3 GENERALIZATIONS OF THE VORONOI DIAGRAM 241 6.3.1.
HIGHER-ORDER VORONOI DIAGRAMS (IN THE PLANE) 242 6.3.1.1 ELEMENTS OF
INVERSIVE GEOMETRY 243 6.3.1.2 THE STRUCTURE OF HIGHER-ORDER VORONOI
DIAGRAMS 244 6.3.1.3 CONSTRUCTION OF THE HIGHER-ORDER VORONOI DIAGRAMS
249 6.3.2 MULTIDIMENSIONAL CLOSEST-POINT AND FARTHEST-POINT VORONOI
DIAGRAMS 253 6.4 GAPS AND COVERS 255 6.5 NOTES AND COMMENTS 262 6.6
EXERCISES 264 CHAPTER7 INTERSECTIONS * 266 7.1 A SAMPLE OF APPLICATIONS
267 7.1.1 THE HIDDEN-LINE AND HIDDEN-SURFACE PROBLEMS 267 7.1.2 PATTERN
RECOGNITION 268 7.1.3 WIRE AND COMPONENT LAYOUT 269 7.1.4 LINEAR
PROGRAMMING AND COMMON IN TERSECTION OF HALF-SPACES 270 7.2 PLANAR
APPLICATIONS 271 7.2.1 INTERSECTION OF CONVEX POLYGONS 271 7.2.2
INTERSECTION OF STAR-SHAPED POLYGONS 277 7.2.3 INTERSECTION OF LINE
SEGMENTS 278 XIV CONTENTS 7.2.3.1 APPLICATIONS 278 7.2.3.2 SEGMENT
INTERSECTION ALGORITHMS 279 7.2.4 INTERSECTION OFHALF-PLANES 287 7.2.5
TWO-VARIABLE LINEAR PROGRAMMING 290 7.2.6 KERNEL OF A PLANE POLYGON 299
7.3 THREE-DIMENSIONAL APPLICATIONS 306 7.3.1 INTERSECTION OF CONVEX
POLYHEDRA 306 7.3.2 INTERSECTION OF HALF-SPACES 315 7.4 NOTES AND
COMMENTS 320 7.5 EXERCISES 322 CHAPTER 8 THE GEOMETRY OF RECTANGLES 323
8.1 SOME APPLICATIONS OF THE GEOMETRY OF RECTANGLES 323 8.1.1 AIDS FOR
VLSI DESIGN 323 8.1.2 CONCURRENCY CONTROLS IN DATABASES 325 8.2 DOMAIN
OF VALIDITY OF THE RESULTS 328 8.3 GENERAL CONSIDERATIONS ON STATIC-MODE
ALGORITHMS 330 8.4 MEASURE AND PERIMETER OF A UNION OF RECTANGLES 332
8.5 THE CONTOUR OF A UNION OF RECTANGLES 340 8.6 THE CLOSURE OF A UNION
OF RECTANGLES 348 8.7 THE EXTERNAL CONTOUR OF A UNION OF RECTANGLES 353
8.8 INTERSECTIONS OF RECTANGLES AND RELATED PROBLEMS 359 8.8.1
INTERSECTIONS OF RECTANGLES 359 8.8.2 THE RECTANGLE INTERSECTION PROBLEM
REVISITED 363 8.8.3 ENCLOSURE OF RECTANGLES 366 8.9 NOTES AND COMMENTS
372 8.10 EXERCISES 373 REFERENCES 374 AUTHOR INDEX 385 SUBJECT INDEX 390
|
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| edition | Corr. and expanded 2. print. |
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| spelling | Preparata, Franco P. Verfasser aut Computational geometry an introduction Franco P. Preparata ; Michael Ian Shamos Corr. and expanded 2. print. New York u.a. Springer 1988 XIV, 398 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts and monographs in computer science Matematica larpcal Datenverarbeitung Geometry Data processing Geometrie (DE-588)4020236-7 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Algorithmische Geometrie (DE-588)4130267-9 s DE-604 Geometrie (DE-588)4020236-7 s 2\p DE-604 Shamos, Michael Ian Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000798249&sequence=000001&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 |
| spellingShingle | Preparata, Franco P. Shamos, Michael Ian Computational geometry an introduction Matematica larpcal Datenverarbeitung Geometry Data processing Geometrie (DE-588)4020236-7 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4130267-9 (DE-588)4113937-9 |
| title | Computational geometry an introduction |
| title_auth | Computational geometry an introduction |
| title_exact_search | Computational geometry an introduction |
| title_full | Computational geometry an introduction Franco P. Preparata ; Michael Ian Shamos |
| title_fullStr | Computational geometry an introduction Franco P. Preparata ; Michael Ian Shamos |
| title_full_unstemmed | Computational geometry an introduction Franco P. Preparata ; Michael Ian Shamos |
| title_short | Computational geometry |
| title_sort | computational geometry an introduction |
| title_sub | an introduction |
| topic | Matematica larpcal Datenverarbeitung Geometry Data processing Geometrie (DE-588)4020236-7 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd |
| topic_facet | Matematica Datenverarbeitung Geometry Data processing Geometrie Algorithmische Geometrie Hochschulschrift |
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