Multivariate spline functions and their applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Beijing
Science Press [u.a.]
2001
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| Schriftenreihe: | Mathematics and its applications
529 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 511 S. graph. Darst. |
| ISBN: | 079236967X 7030078977 1880132753 |
Internformat
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Datensatz im Suchindex
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| adam_text | MULTIVARIATE SPLINE FUNCTIONS AND THEIR APPLICATIONS BY REN-HONG WANG
INSTITUTE OF APPLIED MATHEMATICS, DALIAN UNIVERSITY OF TECHNOLOGY,
DALIAN, P. R. CHINA. ILLL SCIENCE PRESS BEIJING/NEW YORK, KLUWER
ACADEMIC PUBLISHERS DORDRECHT/BOSTON/LONDON CONTENTS CHAPTER 1
INTRODUCTION TO MULTIVARIATE SPLINE FUNCTIONS 1 1.1 BASIC FRAME OF
MULTIVARIATE SPLINE FUNCTIONS 2 1.2 GENERALIZED TRUNCATED POWER FUNCTION
AND GENERAL REPRE- SENTATION OF MULTIVARIATE SPLINE FUNCTIONS 10 1.3
INTERPOLATION BY MULTIVARIATE SPLINE FUNCTIONS . . . . . . . . 13 1.4
WEIGHTED SPLINE AND SPLINES WITH DIFFERENT SMOOTHNESS ... 18 1.5
INTRODUCTION TO MULTIVARIATE RATIONAL SPLINES 21 1.6 ./V-DIMENSIONAL
SPLINE FUNCTIONS . . . . . . . . . . . . . . . 22 CHAPTER 2 MULTIVARIATE
SPLINE SPACES 27 2.1 MULTIVARIATE SPLINE SPACES ON CROSS-CUT PARTITIONS
27 2.2 SPLINE SPACES ON RECTANGULAR AND SIMPLE CROSS-CUT PARTITIONS 41
2.3 SPLINE SPACES ON TYPE-1 TRIANGULATIONS 45 2.4 SPLINE SPACES ON
TYPE-2 TRIANGULATIONS 57 2.5 SPLINE SPACES ON SOME NON-UNIFORM
TRIANGULATIONS 68 2.6 SPLINE SPACES WITH BOUNDARY CONDITIONS ON UNIFORM
TYPE-1 AND TYPE-2 TRIANGULATIONS 76 2.7 SPLINE SPACES WITH BOUNDARY
CONDITIONS ON NON-UNIFORM TYPE-2 TRIANGULATIONS 89 2.8 DIMENSION OF
SPLINE SPACE S (A) ON TRIANGULATIONS 92 2.9 DECOMPOSITION METHOD FOR
STUDYING MULTIVARIATE SPLINES . . ILL 2.9.1 EXAMPLES . 115 CHAPTER 3
OTHER METHODS FOR STUDYING MULTIVARIATE SPLINE FUNCTIONS 119 3.1
5-SPLINE METHOD 119 3.2 B-NET METHOD 134 3.3 THE INTEGRAL METHODS TO
CONSTRUCT BIVARIATE SPLINES 149 CHAPTER 4 HIGHER-DIMENSIONAL SPLINE
SPACES 163 4.1 INTERPOLATION-CONFORMING METHOD 164 4.2 THE DIMENSION OF
HIGHER DIMENSIONAL SPLINE SPACES 185 4.3 THE DIMENSION OF HIGHER
DIMENSIONAL SPLINE SPACES ON A STAR 198 VI CONTENTS 4.4
PARAMETER-INTRODUCING SKILL FOR COMPUTING DIMENSION OF SPLINE SPACES 212
4.5 SPLINE FUNCTIONS DEFINED ON BIVARIATE DOMAIN WITH HOLES AND ON
TRIVARIATE TYPE-2 TRIANGULATIONS 231 4.5.1 THE DIMENSION OF SPLINE
SPACES ON DOMAIN WITH HOLES 231 4.5.2 THE THREE DIMENSIONAL SPLINE
SPACES ON TYPE-2 PAR- TITIONS 239 CHAPTER 5 RATIONAL SPLINE FUNCTIONS
247 5.1 C RATIONAL FUNCTIONS OVER ARBITRARY CONVEX POLYGONS . . . . 249
5.2 C 1 RATIONAL INTERPOLATION SPLINE FUNCTIONS OVER TRIANGULATIONS254
5.3 C 2 RATIONAL INTERPOLATION SPLINE FUNCTIONS OVER TRIANGULATIONS264
5.4 C^ RATIONAL INTERPOLATION SPLINE FUNCTIONS OVER TRIANGULATIONS273
5.5 INTERPOLATION RATIONAL SPLINES OVER REGULAR QUADRILATERAL PAR-
TITIONS . . . . 282 5.5.1 C 1 GENERALIZED WEDGE FUNCTIONS OVER
QUADRILATERAL ELEMENTS 282 5.5.2 FINDING SOLUTIONS OF CONFORMING
EQUATIONS AND CON- STRUCTING C 1 GENERALIZED WEDGE FUNCTIONS . . . . . .
286 5.5.3 C 1 INTERPOLATION RATIONAL APPROXIMATION OPERATORS OVER
QUADRILATERAL ELEMENTS 293 5.5.4 THE EQUIVALENT EXPRESSION OF C 1
PIECEWISE RATIONAL FUNCTIONS 295 5.5.5 THE BLENDING TECHNIQUE FOR C 1
STRUCTURE OVER QUADRI- LATERAL ELEMENTS 298 CHAPTER 6 PIECEWISE
ALGEBRAIC CURVES AND SURFACES 301 6.1 ALGEBRAIC VARIETY .,...., 302 6.2
SMOOTHING CONNECTION CONDITIONS OF ALGEBRAIC VARIETY . . . . 309 6.3
PIECEWISE ALGEBRAIC VARIETY 318 6.4 THE APPROXIMATIONS OF ALGEBRAIC
CURVES AND SURFACES . . . . 326 6.4.1 THE PARAMETRIC APPROXIMATIONS ON
CONIES 327 6.4.2 PARAMETRIC APPROXIMATIONS ON CONIC POLYNOMIALS . . 332
6.4.3 GENERIC APPROXIMATIONS OF ALGEBRAIC CURVES AND SUR- FACES 339 6.5
ON PIECEWISE ALGEBRAIC CURVE 353 6.5.1 SOME EXAMPLES 359 6.5.2
INTERSECTION OF PIECEWISE ALGEBRAIC CURVES 360 CONTENTS VII 6.5.3 LOCAL
BRANCHES OF PIECEWISE ALGEBRAIC CURVES 364 6.6 BEZOUT NUMBER OF
PIECEWISE ALGEBRAIC CURVES 365 6.6.1 BEZOUT S NUMBER BN(1,0; 1,0) 367
6.6.2 THE BEZOUT NUMBER OF S^ (A) AND S(A) 369 CHAPTER 7 APPLICATIONS
OF MULTIVARIATE SPLINE FUNCTIONS IN FINITE ELEMENT METHOD AND CAGD 373
7.1 MULTIVARIATE INTERPOLATED SMOOTH SPLINE FUNCTIONS 375 7.1.1
ZENISEK S THEOREM ON INTERPOLATED FINITE ELEMENT . . 375 7.1.2 HCT
SCHEME AND HCT TYPE INTERPOLATIONS 381 7.1.3 POWELL-SABIN SCHEME 388
7.1.4 THE S +1 (A*) SPACE SCHEME 400 7.1.5 FRAEIJS DE VEUBECK-SANDER
SCHEME^ 151 405 7.1.6 OTHER REFINEMENT INTERPOLATION SCHEMES 407 7.2
PARAMETRIC SURFACES 414 7.2.1 THE SMOOTH PARAMETRIC SURFACE FITTING 414
7.2.2 TENSOR-PRODUCT TYPE PARAMETRIC SURFACES 422 7.2.3 SEVERAL SPECIAL
PARAMETRIC SURFACES 425 7.2.4 PARAMETRIC SURFACE FITTINGS 436 7.3
SMOOTH SURFACE FITTINGS OF SCATTERED DATA 439 7.3.1 TRIANGULATION 440
7.3.2 SOME COMMONLY USED METHODS TO EVALUATE PARTIAL DERIVATIVES AND
DIRECTIONAL DERIVATIVES 444 7.3.3 THE LEAST SQUARE APPROXIMATION 447 7.4
HIGHER DIMENSIONAL HCT AND PS FINITE ELEMENTS 451 7.5 HIERARCHICAL BASIS
IN FINITE ELEMENT METHODS 465 7.6 AUTOMATIC MESH GENERATIONS AND THEIR
APPLICATIONS 485 REFERENCES 495 INDEX 509
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:58:00Z |
| institution | BVB |
| isbn | 079236967X 7030078977 1880132753 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009674867 |
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| physical | XI, 511 S. graph. Darst. |
| publishDate | 2001 |
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| publishDateSort | 2001 |
| publisher | Science Press [u.a.] |
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| series2 | Mathematics and its applications |
| spelling | Wang, Ren-Hong Verfasser aut Multivariate spline functions and their applications Ren-Hong Wang Beijing Science Press [u.a.] 2001 XI, 511 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 529 Splines, Théorie des ram Spline theory Spline-Funktion (DE-588)4056332-7 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 s Mehrere Variable (DE-588)4277015-4 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009674867&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wang, Ren-Hong Multivariate spline functions and their applications Splines, Théorie des ram Spline theory Spline-Funktion (DE-588)4056332-7 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4056332-7 (DE-588)4277015-4 |
| title | Multivariate spline functions and their applications |
| title_auth | Multivariate spline functions and their applications |
| title_exact_search | Multivariate spline functions and their applications |
| title_full | Multivariate spline functions and their applications Ren-Hong Wang |
| title_fullStr | Multivariate spline functions and their applications Ren-Hong Wang |
| title_full_unstemmed | Multivariate spline functions and their applications Ren-Hong Wang |
| title_short | Multivariate spline functions and their applications |
| title_sort | multivariate spline functions and their applications |
| topic | Splines, Théorie des ram Spline theory Spline-Funktion (DE-588)4056332-7 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | Splines, Théorie des Spline theory Spline-Funktion Mehrere Variable |
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