Curves and surfaces in geometric modeling: theory and algorithms
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Francisco, Calif.
Morgan Kaufmann
2000
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| Schriftenreihe: | The Morgan Kaufmann series in computer graphics and geometric modeling
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 491 S. graph. Darst. |
| ISBN: | 1558605991 |
Internformat
MARC
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| 100 | 1 | |a Gallier, Jean H. |d 1949- |e Verfasser |0 (DE-588)122585615 |4 aut | |
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| 264 | 1 | |a San Francisco, Calif. |b Morgan Kaufmann |c 2000 | |
| 300 | |a XV, 491 S. |b graph. Darst. | ||
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| 490 | 0 | |a The Morgan Kaufmann series in computer graphics and geometric modeling | |
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| 650 | 4 | |a Courbes algébriques - Informatique | |
| 650 | 7 | |a Curvas algébricas |2 larpcal | |
| 650 | 7 | |a Geometria computacional (modelagem) |2 larpcal | |
| 650 | 7 | |a Geometrische methoden |2 gtt | |
| 650 | 7 | |a Krommen |2 gtt | |
| 650 | 7 | |a Oppervlakte (wiskunde) |2 gtt | |
| 650 | 4 | |a Surfaces (Mathématiques) - Informatique | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Computer-aided design | |
| 650 | 4 | |a Curves, Algebraic |x Data processing | |
| 650 | 4 | |a Surfaces |x Data processing | |
| 650 | 0 | 7 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804127765558984704 |
|---|---|
| adam_text | CURVES AND SURFACES IN GEOMETRIC MODELING THEORY AND ALGORITHMS JEAN
GALLIER 3 UNIVERSITY OF PENNSYLVANIA MORGAN KAUFMANN PUBLISHERS SAN
FRANCISCO, CALIFORNIA CONTENTS PREFACE XI INTRODUCTION 1 1.1 GEOMETRIC
METHODS IN ENGINEERING 1 1.2 EXAMPLES OF PROBLEMS USING GEOMETRIC
MODELING BASICS OF AFFINE GEOMETRY 5 C;: _._ JL BASICS OF AFFINE
GEOMETRY 7 2.1 AFFINE SPACES 7 2.2 EXAMPLES OF AFFINE SPACES 15 2.3
CHASLES S IDENTITY 16 2.4 AFFINE COMBINATIONS, BARYCENTERS 17 2.5 AFFINE
SUBSPACES 20 2.6 -AFFINE INDEPENDENCE AND AFFINE FRAMES 26 2.7 AFFINE
MAPS 31 2.8 AFFINE GROUPS 38 2.9 AFFINE HYPERPLANES 40 PROBLEMS 42
POLYNOMIAL CURVES AND SPLINE CURVES 53 INTRODUCTION TO THE ALGORITHMIC
GEOMETRY OF POLYNOMIAL CURVES 55 3.1 WHY PARAMETERIZED POLYNOMIAL
CURVES? 55 3.2 POLYNOMIAL CURVES OF DEGREE 1 AND 2 66 3.3 FIRST
ENCOUNTER WITH POLAR FORMS (BLOSSOMING) 69 VU VIII CONTENTS 3.4 FIRST
ENCOUNTER WITH THE DE CASTELJAU ALGORITHM 73 3.5 POLYNOMIAL CURVES OF
DEGREE 3 78 3.6 CLASSIFICATION OF THE POLYNOMIAL CUBICS 84 3.7 SECOND
ENCOUNTER WITH POLAR FORMS (BLOSSOMING) 88 3.8 SECOND ENCOUNTER WITH THE
DE CASTELJAU ALGORITHM 91 3.9 EXAMPLES OF CUBICS DEFINED BY CONTROL
POINTS 95 PROBLEMS 103 MULTIAFFINE MAPS AND POLAR FORMS 107 4.1
MULTIAFFINE MAPS 107 4.2 AFFINE POLYNOMIALS AND POLAR FORMS 114 4.3
POLYNOMIAL CURVES AND CONTROL POINTS 119 4.4 UNIQUENESS OF THE POLAR
FORM OF AN AFFINE POLYNOMIAL MAP 122 4.5 POLARIZING POLYNOMIALS IN ONE
OR SEVERAL VARIABLES 123 PROBLEMS 128 POLYNOMIAL CURVES AS BEZIER CURVES
131 5.1 THE DE CASTELJAU ALGORITHM 131 X 5.2 SUBDIVISION ALGORITHMS FOR
POLYNOMIAL CURVES 144 5.3 THE PROGRESSIVE VERSION OF THE DE CASTELJAU
ALGORITHM (THE DE BOOR ALGORITHM) 153 5.4 DERIVATIVES OF POLYNOMIAL
CURVES 158 5.5 JOINING AFFINE POLYNOMIAL FUNCTIONS 160 PROBLEMS 166 B
-SPLINE CURVES 171 6.1 INTRODUCTION: KNOT SEQUENCES, DE BOOR CONTROL
POINTS 171 6.2 INFINITE KNOT SEQUENCES, OPEN B-SPLINE CURVES 181 6.3
FINITE KNOT SEQUENCES, FINITE B-SPLINE CURVES 192 6.4 CYCLIC KNOT
SEQUENCES, CLOSED (CYCLIC) FI-SPLINE CURVES 201 6.5 THE DE BOOR
ALGORITHM 209 6.6 THE DE BOOR ALGORITHM AND KNOT INSERTION 212 6.7 POLAR
FORMS OF FI-SPLINES 216 6.8 CUBIC SPLINE INTERPOLATION 222 PROBLEMS 230
CONTENTS IX POLYNOMIAL SURFACES AND SPLINE SURFACES 237 :.L POLYNOMIAL
SURFACES 239 7.1 POLARIZING POLYNOMIAL SURFACES 239 7.2 BIPOLYNOMIAL
SURFACES IN POLAR FORM 249 7.3 THE DE CASTELJAU ALGORITHM FOR
RECTANGULAR SURFACE PATCHES 254 7.4 TOTAL DEGREE SURFACES IN POLAR FORM
258 7.5 THE DE CASTELJAU ALGORITHM FOR TRIANGULAR SURFACE PATCHES 262
7.6 DIRECTIONAL DERIVATIVES OF POLYNOMIAL SURFACES 264 PROBLEMS 269 MSS
SUBDIVISION ALGORITHMS FOR POLYNOMIAL SURFACES 275 8.1. SUBDIVISION
ALGORITHMS FOR TRIANGULAR PATCHES 275 8.2 SUBDIVISION ALGORITHMS FOR
RECTANGULAR PATCHES 300 PROBLEMS 306 - 9 POLYNOMIAL SPLINE SURFACES AND
SUBDIVISION SURFACES 311 9.1 JOINING POLYNOMIAL SURFACES 311 9.2 SPLINE
SURFACES WITH TRIANGULAR PATCHES 316 9.3 SPLINE SURFACES WITH
RECTANGULAR PATCHES 323 9.4 SUBDIVISION SURFACES 326 [ PROBLEMS 342 10
EMBEDDING AN AFFINE SPACE IN A VECTOR SPACE 345 10.1 THE HAT
CONSTRUCTION, OR HOMOGENIZING 345 10.2 AFFINE FRAMES OF E AND BASES OF
E 353 ; 10.3 EXTENDING AFFINE MAPS TO LINEAR MAPS 356 ; 10.4 FROM
MULTIAFFINE MAPS TO MULTILINEAR MAPS 359 . 10.5 DIFFERENTIATING AFFINE
POLYNOMIAL FUNCTIONS USING THEIR HOMOGENIZED POLAR FORMS, OSCULATING
FLATS 362 : I PROBLEMS 371 11 TENSOR PRODUCTS AND SYMMETRIC TENSOR
PRODUCTS 373 11.1 TENSOR PRODUCTS 373 X CONTENTS 11.2 SYMMETRIC TENSOR
PRODUCTS 380 11.3 AFFINE SYMMETRIC TENSOR PRODUCTS 383 11.4 PROPERTIES
OF SYMMETRIC TENSOR PRODUCTS 386 11.5 POLAR FORMS REVISITED 389 PROBLEMS
396 PART IV APPENDICES 399 APP. A LINEAR ALGEBRA 401 A.I VECTOR SPACES
401 A.2 LINEAR MAPS 408 A.3 QUOTIENT SPACES 412 A.4 DIRECT SUMS 413 A.5
HYPERPLANES AND LINEAR FORMS 421 COMPLEMENTS OF AFFINE GEOMETRY 425 B.I
AFFINE AND MULTIAFFINE MAPS 425 B.2 HOMOGENIZING MULTIAFFINE MAPS 432
B.3 INTERSECTION AND DIRECT SUMS OF AFFINE SPACES 434 B.4 OSCULATING
FLATS REVISITED 438 TOPOLOGY 445 C.I METRIC SPACES AND NORMED VECTOR
SPACES 445 C.2 CONTINUOUS FUNCTIONS, LIMITS 450 C.3 NORMED AFFINE SPACES
450 DIFFERENTIAL CALCULUS 453 D.I DIRECTIONAL DERIVATIVES, TOTAL
DERIVATIVES 453 D.2 JACOBIAN MATRICES. 461 BIBLIOGRAPHY 467 INDEX 473
ABOUT THE AUTHOR 491
|
| any_adam_object | 1 |
| author | Gallier, Jean H. 1949- |
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| author_facet | Gallier, Jean H. 1949- |
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| building | Verbundindex |
| bvnumber | BV013068458 |
| callnumber-first | Q - Science |
| callnumber-label | QA567 |
| callnumber-raw | QA567 |
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| callnumber-sort | QA 3567 |
| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)247094860 (DE-599)BVBBV013068458 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:33Z |
| institution | BVB |
| isbn | 1558605991 |
| language | English |
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| physical | XV, 491 S. graph. Darst. |
| publishDate | 2000 |
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| publisher | Morgan Kaufmann |
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| spelling | Gallier, Jean H. 1949- Verfasser (DE-588)122585615 aut Curves and surfaces in geometric modeling theory and algorithms Jean Gallier San Francisco, Calif. Morgan Kaufmann 2000 XV, 491 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Morgan Kaufmann series in computer graphics and geometric modeling Algoritmen gtt Conception assistée par ordinateur Courbes algébriques - Informatique Curvas algébricas larpcal Geometria computacional (modelagem) larpcal Geometrische methoden gtt Krommen gtt Oppervlakte (wiskunde) gtt Surfaces (Mathématiques) - Informatique Datenverarbeitung Computer-aided design Curves, Algebraic Data processing Surfaces Data processing Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008903247&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gallier, Jean H. 1949- Curves and surfaces in geometric modeling theory and algorithms Algoritmen gtt Conception assistée par ordinateur Courbes algébriques - Informatique Curvas algébricas larpcal Geometria computacional (modelagem) larpcal Geometrische methoden gtt Krommen gtt Oppervlakte (wiskunde) gtt Surfaces (Mathématiques) - Informatique Datenverarbeitung Computer-aided design Curves, Algebraic Data processing Surfaces Data processing Geometrische Modellierung (DE-588)4156717-1 gnd |
| subject_GND | (DE-588)4156717-1 |
| title | Curves and surfaces in geometric modeling theory and algorithms |
| title_auth | Curves and surfaces in geometric modeling theory and algorithms |
| title_exact_search | Curves and surfaces in geometric modeling theory and algorithms |
| title_full | Curves and surfaces in geometric modeling theory and algorithms Jean Gallier |
| title_fullStr | Curves and surfaces in geometric modeling theory and algorithms Jean Gallier |
| title_full_unstemmed | Curves and surfaces in geometric modeling theory and algorithms Jean Gallier |
| title_short | Curves and surfaces in geometric modeling |
| title_sort | curves and surfaces in geometric modeling theory and algorithms |
| title_sub | theory and algorithms |
| topic | Algoritmen gtt Conception assistée par ordinateur Courbes algébriques - Informatique Curvas algébricas larpcal Geometria computacional (modelagem) larpcal Geometrische methoden gtt Krommen gtt Oppervlakte (wiskunde) gtt Surfaces (Mathématiques) - Informatique Datenverarbeitung Computer-aided design Curves, Algebraic Data processing Surfaces Data processing Geometrische Modellierung (DE-588)4156717-1 gnd |
| topic_facet | Algoritmen Conception assistée par ordinateur Courbes algébriques - Informatique Curvas algébricas Geometria computacional (modelagem) Geometrische methoden Krommen Oppervlakte (wiskunde) Surfaces (Mathématiques) - Informatique Datenverarbeitung Computer-aided design Curves, Algebraic Data processing Surfaces Data processing Geometrische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008903247&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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