Wavelet subdivision methods: GEMS for rendering curves and surfaces
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
CRC Press
2011
|
| Schriftenreihe: | A Chapman & Hall book
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020438738&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXIV, 455 S. graph. Darst. |
| ISBN: | 9781439812150 1439812152 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819329823177179136 |
|---|---|
| adam_text | Titel: Wavelet subdivision methods
Autor: Chui, Charles K
Jahr: 2011
Contents
List of Figures xi
List of Tables xv
Foreword xvii
Preface xix
Teaching and Reading Guides xxiii
1 OVERVIEW 1
LI Curve representation and drawing............... 2
1.2 Free-form parametric curves .................. 5
1.3 From subdivision to basis functions .............. 11
1.4 Wavelet subdivision and editing ................ 16
1.5 Surface subdivision ....................... 29
1.6 Exercises ............................. 32
2 BASIS FUNCTIONS FOR CURVE REPRESENTATION 37
2.1 Refinability and scaling functions ............... 39
2.2 Generation of smooth basis functions ............. 46
2.3 Cardinal IJ-splines........................ 52
2.4 Stable bases for integer-shift Spaces .............. 56
2.5 Splines and polynomial reproduction ............. 62
2.6 Exercises ............................. 67
3 CURVE SUBDIVISION SCHEMES 75
3.1 Subdivision matrices and stencils................ 76
3.2 B-spline subdivision schemes.................. 85
3.3 Closed curve rendering ..................... 95
3.4 Open curve rendering ...................... 106
3.5 Exercises ............................. 129
4 BASIS FUNCTIONS GENERATED BY SUBDIVISION
MATRICES 133
4.1 Subdivision Operators ...................... 134
4.2 The up-sampling convolution Operation ............ 138
vii
4.3 Scaling functions from subdivision matrices.......... 141
4.4 Convergence of subdivision schemes .............. 154
4.5 Uniqueness and symmetry ................... 160
4.6 Exercises ............................. 163
QUASI-INTERPOLATION 169
5.1 Sum-rule orders and discrete moments............. 170
5.2 Representation of polynomials ................. 173
5.3 Characterization of sum-rule orders .............. 178
5.4 Quasi-interpolants........................ 182
5.5 Exercises ............................. 198
CONVERGENCE AND REGULARITY ANALYSIS 205
6.1 Cascade Operators........................ 206
6.2 Sufficient conditions for convergence.............. 211
6.3 Holder regularity......................... 218
6.4 Positive refinement sequences.................. 225
6.5 Convergence and regularity governed by two-scale symbols . 233
6.6 A one-parameter family..................... 244
6.7 Stability of the one-parameter family ............. 255
6.8 Exercises ............................. 260
ALGEBRAIC POLYNOMIAL IDENTITIES 271
7.1 Fundamental existence and uniqueness theorem ....... 272
7.2 Normalized binomial symbols.................. 280
7.3 Behavior on the unit circle in the complex plane....... 288
7.4 Exercises ............................. 291
INTERPOLATORY SUBDIVISION 295
8.1 Scaling functions generated by interpolatory refinement se-
quences .............................. 296
8.2 Convergence, regularity, and symmetry ............ 302
8.3 Rendering of closed and open interpolatory curves...... 312
8.4 A one-parameter family of interpolatory subdivision Operators 322
8.5 Exercises ............................. 333
WAVELETS FOR SUBDIVISION 339
9.1 From scaling functions to synthesis wavelets ......... 340
9.2 Synthesis wavelets with prescribed vanishing moments .... 351
9.3 Robust stability of synthesis wavelets ............. 364
9.4 Spline-wavelets.......................... 370
9.5 Interpolation wavelets...................... 385
9.6 Wavelet subdivision and editing ................ 401
9.7 Exercises ............................. 406
IX
10 SURFACE SUBDIVISION 411
10.1 Control nets and net refinement ................ 413
10.2 Box splines as basis functions.................. 422
10.3 Surface subdivision masks and stencils ............ 427
10.4 Wavelet surface subdivision................... 437
10.5 Exercises ............................. 442
11 EPILOGUE 445
Supplementary Readings 449
Index 451
|
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| author | Chui, Charles K. 1940- |
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| author_facet | Chui, Charles K. 1940- |
| author_role | aut |
| author_sort | Chui, Charles K. 1940- |
| author_variant | c k c ck ckc |
| building | Verbundindex |
| bvnumber | BV036516609 |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)700639752 (DE-599)BVBBV036516609 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV036516609 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:36:08Z |
| institution | BVB |
| isbn | 9781439812150 1439812152 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020438738 |
| oclc_num | 700639752 |
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| owner_facet | DE-384 DE-19 DE-BY-UBM DE-634 DE-83 DE-188 DE-824 |
| physical | XXIV, 455 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | CRC Press |
| record_format | marc |
| series2 | A Chapman & Hall book |
| spellingShingle | Chui, Charles K. 1940- Wavelet subdivision methods GEMS for rendering curves and surfaces Wavelets (Mathematics) Subdivision surfaces (Geometry) Oberfläche (DE-588)4042907-6 gnd Wavelet-Analyse (DE-588)4760859-6 gnd Parametrisierung (DE-588)4402701-1 gnd Kurve (DE-588)4033824-1 gnd Unterteilungsalgorithmus (DE-588)4753239-7 gnd |
| subject_GND | (DE-588)4042907-6 (DE-588)4760859-6 (DE-588)4402701-1 (DE-588)4033824-1 (DE-588)4753239-7 |
| title | Wavelet subdivision methods GEMS for rendering curves and surfaces |
| title_auth | Wavelet subdivision methods GEMS for rendering curves and surfaces |
| title_exact_search | Wavelet subdivision methods GEMS for rendering curves and surfaces |
| title_full | Wavelet subdivision methods GEMS for rendering curves and surfaces Charles Chui ; Johan de Villiers |
| title_fullStr | Wavelet subdivision methods GEMS for rendering curves and surfaces Charles Chui ; Johan de Villiers |
| title_full_unstemmed | Wavelet subdivision methods GEMS for rendering curves and surfaces Charles Chui ; Johan de Villiers |
| title_short | Wavelet subdivision methods |
| title_sort | wavelet subdivision methods gems for rendering curves and surfaces |
| title_sub | GEMS for rendering curves and surfaces |
| topic | Wavelets (Mathematics) Subdivision surfaces (Geometry) Oberfläche (DE-588)4042907-6 gnd Wavelet-Analyse (DE-588)4760859-6 gnd Parametrisierung (DE-588)4402701-1 gnd Kurve (DE-588)4033824-1 gnd Unterteilungsalgorithmus (DE-588)4753239-7 gnd |
| topic_facet | Wavelets (Mathematics) Subdivision surfaces (Geometry) Oberfläche Wavelet-Analyse Parametrisierung Kurve Unterteilungsalgorithmus |
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