Bezier and B-spline techniques:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Mathematics and visualization
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XIV, 304 S. graph. Darst. |
| ISBN: | 3540437614 9783642078422 |
Internformat
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| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 DAT 756f 2001 A 27858 |
|---|---|
| DE-BY-TUM_katkey | 1397219 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040020127637 |
| _version_ | 1821939347940704257 |
| adam_text | HARTMUT PRAUTZSCH WOLFGANG BOEHM MARCO PALUSZNY BEZIER AND B-SPLINE
TECHNIQUES WITH 182 FIGURES SPRINGER CONTENTS I CURVES 1 GEOMETRIC
FUNDAMENTALS 1.1 AFFINE SPACES 3 1.2 AFFINE COMBINATIONS 4 1.3 AFFINE
MAPS 5 1.4 PARAMETRIC CURVES AND SURFACES 6 1.5 PROBLEMS 7 2 BEZIER
REPRESENTATION 2.1 BERNSTEIN POLYNOMIALS 9 2.2 BEZIER REPRESENTATION 11
2.3 THE DE CASTELJAU ALGORITHM 13 2.4 DERIVATIVES 15 2.5 SINGULAR
PARAMETRIZATION 17 2.6 A TETRAHEDRAL ALGORITHM 17 2.7 INTEGRATION 19 2.8
CONVERSION TO BEZIER REPRESENTATION 20 2.9 CONVERSION TO MONOMIAL FORM
22 2.10 PROBLEMS 22 3 BEZIER TECHNIQUES 3.1 SYMMETRIC POLYNOMIALS 25 3.2
THE MAIN THEOREM 27 3.3 SUBDIVISION 27 3.4 CONVERGENCE UNDER
SUBDIVISION 29 3.5 CURVE GENERATION BY SUBDIVISION 30 3.6 CURVE
GENERATION BY FORWARD DIFFERENCES 32 3.7 INTERSECTIONS 32 3.8 THE
VARIATION DIMINISHING PROPERTY * 34 3.9 THE SYMMETRIC POLYNOMIAL OF THE
DERIVATIVE 35 3.10 SIMPLE C R JOINTS 36 X CONTENTS 3.11 DEGREE
ELEVATION 37 3.12 CONVERGENCE UNDER DEGREE ELEVATION 39 3.13 PROBLEMS 40
4 INTERPOLATION AND APPROXIMATION 4.1 INTERPOLATION 43 4.2 LAGRANGE FORM
44 4.3 NEWTON FORM 47 4.4 HERMITE INTERPOLATION 48 4.5 PIECEWISE CUBIC
HERMITE INTERPOLATION 49 4.6 APPROXIMATION 52 4.7 LEAST SQUARES FITTING
53 4.8 IMPROVING THE PARAMETER 55 4.9 PROBLEMS 56 5 B-SPLINE
REPRESENTATION 5.1 SPLINES 59 5.2 B-SPLINES 60 5.3 A RECURSIVE
DEFINITION OF B-SPLINES 61 5.4 THE DE BOOR ALGORITHM 63 5.5 THE MAIN
THEOREM IN ITS GENERAL FORM 65 5.6 DERIVATIVES AND SMOOTHNESS 67 5.7
B-SPLINE PROPERTIES 68 5.8 CONVERSION TO B-SPLINE FORM 69 5.9 THE
COMPLETE DE BOOR ALGORITHM 70 5.10 CONVERSIONS BETWEEN BEZIER AND
B-SPLINE REPRESENTATIONS 72 5.11 B-SPLINES AS DIVIDED DIFFERENCES 73
5.12 PROBLEMS 74 6 B-SPLINE TECHNIQUES 6.1 KNOT INSERTION 77 6.2 THE
OSLO ALGORITHM 79 6.3 CONVERGENCE UNDER KNOT INSERTION 80 6.4 A DEGREE
ELEVATION ALGORITHM 81 6.5 A DEGREE ELEVATION FORMULA 82 6.6 CONVERGENCE
UNDER DEGREE ELEVATION 83 6.7 INTERPOLATION 84 6.8 CUBIC SPLINE
INTERPOLATION 86 6.9 PROBLEMS 88 CONTENTS . XI 7 SMOOTH CURVES 7.1
CONTACT OF ORDER R 91 7.2 ARC LENGTH PARAMETRIZATION 93 7.3
GAMMA-SPLINES 94 7.4 GAMMA B-SPLINES 95 7.5 NU-SPLINES 96 7.6 THE FRENET
FRAME 97 7.7 FRENET FRAME CONTINUITY 98 7.8 OSCULANTS AND SYMMETRIC
POLYNOMIALS 100 7.9 GEOMETRIC MEANING OF THE MAIN THEOREM 102 7.10
SPLINES WITH ARBITRARY CONNECTION MATRICES 103 7.11 KNOT INSERTION 105
7.12 BASIS SPLINES 105 7.13 PROBLEMS 106 8 UNIFORM SUBDIVISION 8.1
UNIFORM B-SPLINES 109 8.2 UNIFORM SUBDIVISION 110 8.3 REPEATED
SUBDIVISION 112 8.4 THE SUBDIVISION MATRIX 114 8.5 DERIVATIVES 115 8.6
STATIONARY SUBDIVISION 115 8.7 CONVERGENCE THEOREMS 116 8.8 COMPUTING
THE DIFFERENCE SCHEME 117 8.9 THE FOUR-POINT SCHEME 119 8.10 ANALYZING
THE FOUR-POINT SCHEME 120 8.11 PROBLEMS 120 II SURFACES 9 TENSOR PRODUCT
SURFACES 9.1 TENSOR PRODUCTS 125 9.2 TENSOR PRODUCT BEZIER SURFACES 127
9.3 TENSOR PRODUCT POLAR FORMS 130 9.4 CONVERSION TO AND FROM MONOMIAL
FORM 131 9.5 THE DE CASTELJAU ALGORITHM 132 9.6 DERIVATIVES . 133 9.7
SIMPLE C R JOINTS , 135 9.8 PIECEWISE BICUBIC C 1 INTERPOLATION 135 XII
CONTENTS 9.9 SURFACES OF ARBITRARY TOPOLOGY 136 9.10 SINGULAR
PARAMETRIZATION 138 9.11 BICUBIC C 1 SPLINES OF ARBITRARY TOPOLOGY 139
9.12 PROBLEMS 140 10 BEZIER REPRESENTATION OF TRIANGULAR PATCHES 10.1
BERNSTEIN POLYNOMIALS 141 10.2 BEZIER SIMPLICES 143 10.3 LINEAR
PRECISION 145 10.4 THE DE CASTELJAU ALGORITHM 146 10.5 DERIVATIVES 147
10.6 CONVEXITY 149 10.7 LIMITATIONS OF THE CONVEXITY PROPERTY 150 10.8
PROBLEMS 152 11 BEZIER TECHNIQUES FOR TRIANGULAR PATCHES 11.1 SYMMETRIC
POLYNOMIALS 155 11.2 THE MAIN THEOREM 157 11.3 * SUBDIVISION AND
REPARAMETRIZATION 158 11.4 CONVERGENCE UNDER SUBDIVISION 160 11.5
SURFACE GENERATION 160 11.6 THE SYMMETRIC POLYNOMIAL OF THE DERIVATIVE
162 11.7 SIMPLE C R JOINTS 162 11.8 DEGREE ELEVATION 164 11.9
CONVERGENCE UNDER DEGREE ELEVATION 165 11.10 CONVERSION TO TENSOR
PRODUCT BEZIER REPRESENTATION 166 11.11 CONVERSION TO TRIANGULAR BEZIER
REPRESENTATION 167 11.12 PROBLEMS 168 12 INTERPOLATION 12.1 TRIANGULAR
HERMITE INTERPOLATION 171 12.2 THE CLOUGH-TOCHER INTERPOLANT 172 12.3
THE POWELL-SABIN INTERPOLANT 173 12.4 SURFACES OF ARBITRARY TOPOLOGY 174
12.5 SINGULAR PARAMETRIZATION 175 12.6 QUINTIC C 1 SPLINES OF ARBITRARY
TOPOLOGY 176 12.7 PROBLEMS 178 13 CONSTRUCTING SMOOT H SURFACES 13.1 THE
GENERAL C 1 JOINT 179 CONTENTS XIII 13.2 JOINING TWO TRIANGULAR
CUBIC PATCHES 181 13.3 A TRIANGULAR G 1 INTERPOLANT 183 13.4 THE VERTEX
ENCLOSURE PROBLEM 184 13.5 THE PARITY PHENOMENON 185 13.6 PROBLEMS 186
14 G K -CONSTRUCTIONS 14.1 THE GENERAL C K JOINT 189 14.2 G K JOINTS BY
CROSS CURVES * 190 14.3 G K JOINTS BY THE CHAIN RULE 192 14.4 G K
SURFACES OF ARBITRARY TOPOLOGY 193 14.5 SMOOTH N-SIDED PATCHES 198 14.6
MULTI-SIDED PATCHES IN THE PLANE 201 14.7 PROBLEMS 203 15 STATIONARY
SUBDIVISION FOR REGULAR NETS 15.1 TENSOR PRODUCT SCHEMES 205 15.2
GENERAL STATIONARY SUBDIVISION AND MASKS 207 15.3 CONVERGENCE THEOREMS
209 15.4 INCREASING AVERAGES 211 15.5 COMPUTING THE DIFFERENCE SCHEMES
212 15.6 COMPUTING THE AVERAGING SCHEMES 214 15.7 SUBDIVISION FOR
TRIANGULAR NETS 215 15.8 BOX SPLINES OVER TRIANGULAR GRIDS 218 15.9
SUBDIVISION FOR HEXAGONAL NETS * 219 15.10 HALF-BOX SPLINES OVER
TRIANGULAR GRIDS 221 15.11 PROBLEMS - 222 16 STATIONARY SUBDIVISION FOR
ARBITRARY NETS 16.1 THE MIDPOINT SCHEME 225 16.2 THE LIMITING SURFACE
227 16.3 THE STANDARD PARAMETRIZATION 229 16.4 THE SUBDIVISION MATRIX
230 16.5 CONTINUITY OF SUBDIVISION SURFACES 231 16.6 THE CHARACTERISTIC
MAP 232 16.7 HIGHER ORDER SMOOTHNESS 232 16.8 TRIANGULAR AND HEXAGONAL
NETS 234 16.9 PROBLEMS . 235 17 BOX 17.1 17.2 17.3 17.4 17.5 17.6 17.7
17.8 17.9 17.10 SPLINES DEFINITION OF BOX SPLINES BOX SPLINES AS SHADOWS
PROPERTIES OF BOX SPLINES DERIVATIVES OF BOX SPLINES BOX SPLINE SURFACES
SUBDIVISION FOR BOX SPLINE SURFACES CONVERGENCE UNDER SUBDIVISION
HALF-BOX SPLINES HALF-BOX SPLINE SURFACES PROBLEMS XIV : CONTENTS III
MULTIVARIATE SPLINES 239 240 242 243 244 247 249 251 253 256 18 SIMPLEX
SPLINES 18.1 SHADOWS OF SIMPLICES 259 18.2 PROPERTIES OF SIMPLEX SPLINES
260 18.3 NORMALIZED SIMPLEX SPLINES 262 18.4 KNOT INSERTION 263 18.5 A
RECURRENCE RELATION 265 18.6 DERIVATIVES 267 18.7 PROBLEMS 268 19
MULTIVARIATE SPLINES 19.1 GENERALIZING DE CASTELJAU S ALGORITHM 271 19.2
B-POLYNOMIALS AND B-PATCHES 273 19.3 LINEAR PRECISION 274 19.4
DERIVATIVES OF A B-PATCH 275 19.5 MULTIVARIATE B-SPLINES 277 19.6
LINEAR COMBINATIONS OF B-SPLINES 279 19.7 A RECURRENCE RELATION 280 19.8
DERIVATIVES OF A SPLINE 282 19.9 THE MAIN THEOREM 283 19.10 PROBLEMS 284
REFERENCES 287 INDEX 297
|
| any_adam_object | 1 |
| author | Prautzsch, Hartmut Böhm, Wolfgang 1928-2018 Paluszny, Marco |
| author_GND | (DE-588)119040956 |
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| dewey-ones | 511 - General principles of mathematics |
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| dewey-search | 511/.42 |
| dewey-sort | 3511 242 |
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| discipline | Informatik Mathematik |
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| id | DE-604.BV014443895 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:04:20Z |
| institution | BVB |
| isbn | 3540437614 9783642078422 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009873331 |
| oclc_num | 49936094 |
| open_access_boolean | |
| owner | DE-703 DE-824 DE-91G DE-BY-TUM DE-739 DE-634 DE-11 DE-20 |
| owner_facet | DE-703 DE-824 DE-91G DE-BY-TUM DE-739 DE-634 DE-11 DE-20 |
| physical | XIV, 304 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Mathematics and visualization |
| spellingShingle | Prautzsch, Hartmut Böhm, Wolfgang 1928-2018 Paluszny, Marco Bezier and B-spline techniques Computer graphics Computer-aided design Spline theory Graphic methods B-Spline (DE-588)4384798-5 gnd Bézier-Fläche (DE-588)4293190-3 gnd Bézier-Kurve (DE-588)4308681-0 gnd |
| subject_GND | (DE-588)4384798-5 (DE-588)4293190-3 (DE-588)4308681-0 |
| title | Bezier and B-spline techniques |
| title_auth | Bezier and B-spline techniques |
| title_exact_search | Bezier and B-spline techniques |
| title_full | Bezier and B-spline techniques Hartmut Prautzsch ; Wolfgang Boehm ; Marco Paluszny |
| title_fullStr | Bezier and B-spline techniques Hartmut Prautzsch ; Wolfgang Boehm ; Marco Paluszny |
| title_full_unstemmed | Bezier and B-spline techniques Hartmut Prautzsch ; Wolfgang Boehm ; Marco Paluszny |
| title_short | Bezier and B-spline techniques |
| title_sort | bezier and b spline techniques |
| topic | Computer graphics Computer-aided design Spline theory Graphic methods B-Spline (DE-588)4384798-5 gnd Bézier-Fläche (DE-588)4293190-3 gnd Bézier-Kurve (DE-588)4308681-0 gnd |
| topic_facet | Computer graphics Computer-aided design Spline theory Graphic methods B-Spline Bézier-Fläche Bézier-Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT prautzschhartmut bezierandbsplinetechniques AT bohmwolfgang bezierandbsplinetechniques AT palusznymarco bezierandbsplinetechniques |
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Teilbibliothek Mathematik & Informatik
| Signatur: |
0102 DAT 756f 2001 A 27858 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |