Curves and surfaces for computer aided geometric design: a practical guide
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Academic Press
1990
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Computer science and scientific computing
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 413 - 433 |
| Beschreibung: | XVII, 444 S. Ill., graph. Darst. |
| ISBN: | 0122490517 |
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| 245 | 1 | 0 | |a Curves and surfaces for computer aided geometric design |b a practical guide |c Gerald Farin |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b Academic Press |c 1990 | |
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Datensatz im Suchindex
| _version_ | 1804119700262617088 |
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| adam_text | Titel: Curves and surfaces for computer aided geometric design
Autor: Farin, Gerald E
Jahr: 1990
Contents Preface xv 1 P. Bezier: How a Simple System Was Born 1 2 Introductory Material 13 2.1 Points and Vectors...................... 13 2.2 Affine Maps.......................... 17 2.3 Linear Interpolation..................... 19 2.4 Piecewise Linear Interpolation................ 22 2.5 Menelaos’ Theorem...................... 22 2.6 Function Spaces........................ 24 2.7 Problems ........................... 26 3 The de Casteljau Algorithm 27 3.1 Parabolas........................... 27 3.2 The de Casteljau Algorithm................. 29 3.3 Some Properties of Bezier Curves.............. 30 3.4 Implementation........................ 33 3.5 Problems ........................... 35 4 The Bernstein Form of a Bezier Curve 37 4.1 Bernstein Polynomials.................... 37 vii
viii Contents 4.2 Properties of Bezier Curves................. 40 4.3 The Derivative of a Bezier Curve.............. 42 4.4 Higher Order Derivatives................... 44 4.5 Derivatives and the de Casteljau Algorithm........ 45 4.6 The Matrix Form of a Bezier Curve............. 46 4.7 Implementation....................... 47 4.8 Problems ........................... 49 5 Bezier Curve Topics 51 5.1 Degree Elevation................. 51 5.2 Repeated Degree Elevation ................. 53 5.3 The Variation Diminishing Property . 54 5.4 Degree Reduction....................... 54 5.5 Nonparametric Curves.................... 56 5.6 Cross Plots....... 57 5.7 Integrals............................ 58 5.8 The Bezier Form of a Bezier Curve............. 60 5.9 The Barycentric Form of a Bezier Curve.......... 61 5.10 The Weierstrass Approximation Theorem......... 63 5.11 Formulas for Bernstein Polynomials............. 64 5.12 Implementation........................ 65 5.13 Problems .......................... • 66 6 Polynomial Interpolation 67 6.1 Aitken’s Algorithm................ 67 6.2 Lagrange Polynomials.................... 71 6.3 The Vandermonde Approach ................ 72 6.4 Limits of Lagrange Interpolation ........ 73 6.5 Cubic Hermite Interpolation............. 75 6.6 Quintic Hermite Interpolation................ 79 6.7 The Newton Form and Forward Differencing........ 80 6.8 Implementation........................ 82 6.9 Problems ........................... 83 7 Spline Curves in Bezier Form 85 7.1 Global and Local Parameters............ 85 7.2 Subdivision I...................... 87 7.3 Subdivision II......................... 89 7.4 Smoothness Conditions.................... 91 7.5 C 1 Continuity......................... 93 7.6 C 2 Continuity......................... 94 7.7 Finding a C 1 Parametrization................ 95
Contents IX 7.8 C l Quadratic B-spline Curves................ 97 7.9 C 2 Cubic B-spline Curves.................. 101 7.10 Parametrizations................ 103 7.11 Design and Inverse Design.................. 104 7.12 Implementation........................ 107 7.13 Problems ........................... 109 8 Piecewise Cubic Interpolation 111 8.1 C 1 Piecewise Cubic Hermite Interpolation ......... Ill 8.2 C 1 Piecewise Cubic Interpolation I............. 113 8.3 C 1 Piecewise Cubic Interpolation II............ 116 8.4 Point-Normal Interpolation................. 119 8.5 Problems ........................... 120 9 Cubic Spline Interpolation 121 9.1 The B-spline Form............ .......... 121 9.2 The Hermite Form.......... 125 9.3 End Conditions........................ 127 9.4 The Parametrization............. 130 9.5 The Minimum Property ................... 135 9.6 Implementation . . . ..................... 139 9.7 Problems ........................... 145 10 B-splines 147 10.1 Motivation................. 148 10.2 Knot Insertion ................. 149 10.3 The de Boor Algorithm ................... 154 10.4 Smoothness of B-spline Curves............... 158 10.5 The B-spline Basis...................... 158 10.6 Two Recursion Formulas................... 161 10.7 Repeated Knot Insertion.......... 164 10.8 Additional Material...................... 166 10.9 B-spline Basics......................... 168 10.10 Implementation........................ 170 10.11 Problems ............ 171 11 W. Boehm: Differential Geometry I 173 11.1 Parametric Curves and Arc Length ............ 173 11.2 The Frenet Frame....................... 175 11.3 Moving the Frame ...................... 176 11.4 The Osculating Circle..... 178 11.5 Nonparametric Curves.................... 181
x Contents 11.6 Composite Curves ...................... 182 12 Geometric Continuity I 185 12.1 Motivation........................... 185 12.2 A Characterization of G 2 Curves.............. 186 12.3 Nu-splines........................... 188 12.4 G 2 Piecewise Bezier Curves................. 191 12.5 Direct G 2 Cubic Splines................... 194 12.6 Implementation........................ 195 12.7 Problems ........................... 197 13 Geometric Continuity II 199 13.1 Gamma-splines............. .~r-. . ........ 199 13.2 Local Basis Functions for G 2 Splines............ 202 13.3 Beta-splines.......................... 205 13.4 Higher Order Geometric Continuity............. 207 13.5 Implementation........................ 209 13.6 Problems ........................... 211 14 Conic Sections 213 14.1 Projective Maps of the Real Line.............. 213 14.2 Conics as Rational Quadratics................ 217 14.3 A de Casteljau Algorithm................. . 222 14.4 Derivatives .......................... 223 14.5 The Implicit Form...................... 224 14.6 Two Classic Problems..................... 226 14.7 Classification......................... 227 14.8 Problems ........................... 229 15 Rational Bezier and B-spline Curves 231 15.1 Rational Bezier Curves.................... 231 15.2 The de Casteljau Algorithm................. 234 15.3 Derivatives ....... 235 15.4 Oscillatory Interpolation .................. 237 15.5 Reparametrization and Degree Elevation.......... 237 15.6 Rational Cubic B-spline Curves............... 240 15.7 Interpolation with Rational Cubics............. 242 15.8 Rational B-splines of Arbitrary Degree........... 243 15.9 Implementation........................ 244 15.10 Problems ........................... 247 16 Tensor Product Bezier Surfaces 249 16.1 Bilinear Interpolation..................... 249
Contents xi 16.2 The Direct de Casteljau Algorithm ............. 252 16.3 The Tensor Product Approach ............... 254 16.4 Properties........................... 257 16.5 Degree Elevation................ 258 16.6 Derivatives .......................... 259 16.7 Normal Vectors........................ 261 16.8 Twists............................. 263 16.9 The Matrix Form of a Bezier Patch............. 265 16.10 Nonparametric Patches.................... 266 16.11 Implementation........................ 267 16.12 Problems ........................... 269 17 Composite Surfaces and Spline Interpolation 271 17.1 Smoothness and Subdivision ................ 271 17.2 Bicubic B-spline Surfaces ........,,......... 273 17.3 Twist Estimation............. 276 17.4 Tensor Product Interpolants ................. 281 17.5 The Parametrization..................... 284 17.6 Bicubic Hermite Patches................... 286 17.7 Rational Bezier and B-spline Surfaces ........... 288 17.8 Volume Deformations . .................... 292 17.9 Trimmed Surfaces....................... 295 17.10 Implementation........................ 296 17.11 Problems ........................... 300 18 Bezier Triangles 303 18.1 Barycentric Coordinates and Linear Interpolation.....304 18.2 The de Casteljau Algorithm................. 306 18.3 Bernstein Polynomials.................... 308 18.4 Derivatives .......................... 310 18.5 Subdivision.................... 315 18.6 Differentiability........................ 317 18.7 Degree Elevation....................... 320 18.8 Nonparametric Patches .................... 322 18.9 Rational Bezier Triangles .................. 324 18.10 Quadrics.............................326 18.11 Problems ........................... 329 19 Geometric Continuity for Surfaces 331 19.1 Introduction.......................... 331 19.2 Triangle-Triangle....................... 332 19.3 Rectangle-Rectangle............... 336
Contents xii 19.4 Rectangle-Triangle ...................... 337 19.5 “Filling inâ€
|
| any_adam_object | 1 |
| author | Farin, Gerald E. 1953- |
| author_GND | (DE-588)109438760 |
| author_facet | Farin, Gerald E. 1953- |
| author_role | aut |
| author_sort | Farin, Gerald E. 1953- |
| author_variant | g e f ge gef |
| building | Verbundindex |
| bvnumber | BV005485664 |
| callnumber-first | T - Technology |
| callnumber-label | T385 |
| callnumber-raw | T385 |
| callnumber-search | T385 |
| callnumber-sort | T 3385 |
| callnumber-subject | T - General Technology |
| classification_rvk | SK 910 ST 320 |
| classification_tum | TEC 630f DAT 810f DAT 756f |
| ctrlnum | (OCoLC)22579010 (DE-599)BVBBV005485664 |
| dewey-full | 006.6 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 006 - Special computer methods |
| dewey-raw | 006.6 |
| dewey-search | 006.6 |
| dewey-sort | 16.6 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Technik Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV005485664 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:30:21Z |
| institution | BVB |
| isbn | 0122490517 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003434419 |
| oclc_num | 22579010 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-739 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-824 DE-20 DE-19 DE-BY-UBM DE-83 DE-11 |
| owner_facet | DE-91G DE-BY-TUM DE-739 DE-898 DE-BY-UBR DE-355 DE-BY-UBR DE-824 DE-20 DE-19 DE-BY-UBM DE-83 DE-11 |
| physical | XVII, 444 S. Ill., graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Academic Press |
| record_format | marc |
| series2 | Computer science and scientific computing |
| spelling | Farin, Gerald E. 1953- Verfasser (DE-588)109438760 aut Curves and surfaces for computer aided geometric design a practical guide Gerald Farin 2. ed. Boston [u.a.] Academic Press 1990 XVII, 444 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Computer science and scientific computing Literaturverz. S. 413 - 433 B-spline inriac Infographie Infographie ram algorithme Casteljau inriac courbe Bézier inriac géométrie algorithmique inriac géométrie différentielle inriac infographie inriac interpolation inriac modélisation géométrique inriac programmation graphique inriac spline inriac surface Bézier inriac Fläche (DE-588)4129864-0 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Computergrafik (DE-588)4010450-3 gnd rswk-swf CAD (DE-588)4069794-0 gnd rswk-swf Flächendarstellung (DE-588)4232296-0 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf Fläche (DE-588)4129864-0 s Computergrafik (DE-588)4010450-3 s DE-604 Kurve (DE-588)4033824-1 s Geometrische Modellierung (DE-588)4156717-1 s 1\p DE-604 Flächendarstellung (DE-588)4232296-0 s 2\p DE-604 CAD (DE-588)4069794-0 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003434419&sequence=000002&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Farin, Gerald E. 1953- Curves and surfaces for computer aided geometric design a practical guide B-spline inriac Infographie Infographie ram algorithme Casteljau inriac courbe Bézier inriac géométrie algorithmique inriac géométrie différentielle inriac infographie inriac interpolation inriac modélisation géométrique inriac programmation graphique inriac spline inriac surface Bézier inriac Fläche (DE-588)4129864-0 gnd Geometrische Modellierung (DE-588)4156717-1 gnd Computergrafik (DE-588)4010450-3 gnd CAD (DE-588)4069794-0 gnd Flächendarstellung (DE-588)4232296-0 gnd Kurve (DE-588)4033824-1 gnd |
| subject_GND | (DE-588)4129864-0 (DE-588)4156717-1 (DE-588)4010450-3 (DE-588)4069794-0 (DE-588)4232296-0 (DE-588)4033824-1 |
| title | Curves and surfaces for computer aided geometric design a practical guide |
| title_auth | Curves and surfaces for computer aided geometric design a practical guide |
| title_exact_search | Curves and surfaces for computer aided geometric design a practical guide |
| title_full | Curves and surfaces for computer aided geometric design a practical guide Gerald Farin |
| title_fullStr | Curves and surfaces for computer aided geometric design a practical guide Gerald Farin |
| title_full_unstemmed | Curves and surfaces for computer aided geometric design a practical guide Gerald Farin |
| title_short | Curves and surfaces for computer aided geometric design |
| title_sort | curves and surfaces for computer aided geometric design a practical guide |
| title_sub | a practical guide |
| topic | B-spline inriac Infographie Infographie ram algorithme Casteljau inriac courbe Bézier inriac géométrie algorithmique inriac géométrie différentielle inriac infographie inriac interpolation inriac modélisation géométrique inriac programmation graphique inriac spline inriac surface Bézier inriac Fläche (DE-588)4129864-0 gnd Geometrische Modellierung (DE-588)4156717-1 gnd Computergrafik (DE-588)4010450-3 gnd CAD (DE-588)4069794-0 gnd Flächendarstellung (DE-588)4232296-0 gnd Kurve (DE-588)4033824-1 gnd |
| topic_facet | B-spline Infographie algorithme Casteljau courbe Bézier géométrie algorithmique géométrie différentielle infographie interpolation modélisation géométrique programmation graphique spline surface Bézier Fläche Geometrische Modellierung Computergrafik CAD Flächendarstellung Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003434419&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT faringeralde curvesandsurfacesforcomputeraidedgeometricdesignapracticalguide |