Curves and surfaces for computer aided geometric design: a practical guide
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| New Title: | Curves and surfaces for computer aided geometric design |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Acad. Press
1993
|
| Edition: | 3. ed. |
| Series: | Computer science and scientific computing
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 473 S. Ill., zahlr. graph. Darst. 1 Diskette, 5,25" |
| ISBN: | 0122490525 |
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Record in the Search Index
| _version_ | 1804122675070631936 |
|---|---|
| adam_text | 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 AffineMaps 17
2.3 Linear Interpolation 20
2.4 Piecewise Linear Interpolation 23
2.5 Menelaos Theorem 24
2.6 Function Spaces 25
2.7 Problems 27
3 The de Casteljau Algorithm 29
3.1 Parabolas 29
3.2 The de Casteljau Algorithm 31
3.3 Some Properties of Bezier Curves 32
3.4 The Blossom 36
3.5 Implementation 39
3.6 Problems 40
4 The Bernstein Form of a Bezier Curve 41
4.1 Bernstein Polynomials 41
4.2 Properties of Bezier Curves 44
4.3 The Derivative of a Bezier Curve 46
4.4 Higher Order Derivatives 47
4.5 Derivatives and the de Casteljau Algorithm 50
4.6 Subdivision 51
4.7 Blossom and Polar 56
vii
viii CONTENTS
4.8 The Matrix Form of a Bezier Curve 58
4.9 Implementation 59
4.10 Problems 62
5 Bezier Curve Topics 65
5.1 Degree Elevation 65
5.2 Repeated Degree Elevation 66
5.3 The Variation Diminishing Property 67
5.4 Degree Reduction 68
5.5 Nonparametric Curves 70
5.6 Cross Plots 72
5.7 Integrals 72
5.8 The Bezier Form of a Bezier Curve 74
5.9 The Barycentric Form of a Bezier Curve 75
5.10 The Weierstrass Approximation Theorem 78
5.11 Formulas for Bernstein Polynomials 79
5.12 Implementation 80
5.13 Problems 81
6 Polynomial Interpolation 83
6.1 Aitken s Algorithm 83
6.2 Lagrange Polynomials 86
6.3 The Vandermonde Approach 88
6.4 Limits of Lagrange Interpolation 89
6.5 Cubic Hermite Interpolation 91
6.6 Quintic Hermite Interpolation 96
6.7 The Newton Form and Forward Differencing 96
6.8 Implementation 99
6.9 Problems 99
7 Spline Curves in Bezier Form 101
7.1 Global and Local Parameters 101
7.2 Smoothness Conditions 103
7.3 C1 Continuity 105
7.4 C2 Continuity 106
7.5 Finding a C1 Parametrization 107
7.6 C1 Quadratic B spline Curves 109
7.7 C2 Cubic B spline Curves 115
7.8 Parametrizations 117
CONTENTS ix
7.9 Design and Inverse Design 118
7.10 Implementation 119
7.11 Problems 120
8 Piecewise Cubic Interpolation 121
8.1 C1 Piecewise Cubic Hermite Interpolation 121
8.2 C1 Piecewise Cubic Interpolation I 123
8.3 C1 Piecewise Cubic Interpolation II 126
8.4 Point Normal Interpolation 129
8.5 Font Generation 130
8.6 Problems 130
9 Cubic Spline Interpolation 133
9.1 The B spline Form 133
9.2 The Hermite Form 137
9.3 End Conditions 139
9.4 Parametrization 144
9.5 The Minimum Property 148
9.6 Implementation 152
9.7 Problems 154
10 B splines 157
10.1 Motivation 158
10.2 Knot Insertion 159
10.3 The de Boor Algorithm 165
10.4 Smoothness of B spline Curves 168
10.5 The B spline Basis 169
10.6 Two Recursion Formulas 172
10.7 Repeated Knot Insertion 175
10.8 Additional Material 178
10.9 B spline Blossoms 181
10.10 B spline Basics 184
10.11 Implementation 185
10.12 Problems 186
11 W. Boehm: Differential Geometry I 189
11.1 Parametric Curves and Arc Length 189
11.2 The Frenet Frame 191
11.3 Moving the Frame 192
x CONTENTS
11.4 The Osculating Circle 194
11.5 Nonparametric Curves 197
11.6 Composite Curves 197
12 Geometric Continuity I 201
12.1 Motivation 201
12.2 A Characterization of G2 Curves 202
12.3 Nu splines 204
12.4 G2 Piecewise Bezier Curves 207
12.5 Direct G2 Cubic Splines 210
12.6 Implementation 212
12.7 Problems 213
13 Geometric Continuity II 215
13.1 Gamma splines 215
13.2 Local Basis Functions for G2 Splines 218
13.3 Beta splines 222
13.4 Higher Order Geometric Continuity 223
13.5 Implementation 226
13.6 Problems 227
14 Conic Sections 229
14.1 Projective Maps of the Real Line 229
14.2 Conies as Rational Quadratics 233
14.3 A de Casteljau Algorithm 238
14.4 Derivatives 239
14.5 The Implicit Form 240
14.6 Two Classic Problems 242
14.7 Classification 244
14.8 Control Vectors 246
14.9 Implementation 248
14.10 Problems 249
15 Rational Bezier and B spline Curves 251
15.1 Rational Bezier Curves 251
15.2 The de Casteljau Algorithm 252
15.3 Derivatives 255
15.4 Osculatory Interpolation 256
15.5 Reparametrization and Degree Elevation 257
CONTENTS xi
15.6 Control Vectors 260
15.7 Rational Cubic B spline Curves 261
15.8 Interpolation with Rational Cubics 263
15.9 Rational B splines of Arbitrary Degree 264
15.10 Implementation 265
15.11 Problems 266
16 Tensor Product Bezier Surfaces 267
16.1 Bilinear Interpolation 267
16.2 The Direct de Casteljau Algorithm 269
16.3 The Tensor Product Approach 271
16.4 Properties 277
16.5 Degree Elevation 278
16.6 Derivatives 279
16.7 Normal Vectors 281
16.8 Twists 284
16.9 The Matrix Form of a Bezier Patch 285
16.10 Nonparametric Patches 286
16.11 Implementation 288
16.12 Problems 288
17 Composite Surfaces and Spline Interpolation 291
17.1 Smoothness and Subdivision 291
17.2 Bicubic B spline Surfaces 294
17.3 Twist Estimation 296
17.4 Tensor Product Interpolants 301
17.5 The Parametrization 305
17.6 Bicubic Hermite Patches 307
17.7 Rational Bezier and B spline Surfaces 309
17.8 Surfaces of Revolution 311
17.9 Volume Deformations 313
17.10 Trimmed Surfaces 316
17.11 Implementation 317
17.12 Problems 319
18 Bezier Triangles 321
18.1 Barycentric Coordinates and Linear Interpolation 321
18.2 The de Casteljau Algorithm 324
18.3 Triangular Blossoms 328
xii CONTENTS
18.4 Bernstein Polynomials 329
18.5 Derivatives 331
18.6 Subdivision 335
18.7 Differentiability 338
18.8 Degree Elevation 339
18.9 Nonparametric Patches 340
18.10 Rational Bezier Triangles 343
18.11 Quadrics 346
18.12 Implementation 350
18.13 Problems 350
19 Geometric Continuity for Surfaces 353
19.1 Introduction 353
19.2 Triangle Triangle 354
19.3 Rectangle Rectangle 358
19.4 Rectangle Triangle 359
19.5 Filling in Rectangular Patches 360
19.6 Filling in Triangular Patches 361
19.7 Theoretical Aspects 362
19.8 Problems 362
20 Coons Patches 363
20.1 Ruled Surfaces 364
20.2 Coons Patches: Bilinearly Blended 365
20.3 Coons Patches: Partially Bicubically Blended 368
20.4 Coons Patches: Bicubically Blended 370
20.5 Piecewise Coons Surfaces 372
20.6 Problems 373
21 Coons Patches: Additional Material 375
21.1 Compatibility 375
21.2 Control Nets from Coons Patches 378
21.3 Translational Surfaces 380
21.4 Gordon Surfaces 381
21.5 Boolean Sums 383
21.6 Triangular Coons Patches 385
21.7 Implementation 388
21.8 Problems 388
CONTENTS xiii
22 W. Boehm: Differential Geometry II 389
22.1 Parametric Surfaces and Arc Element 389
22.2 The Local Frame 391
22.3 The Curvature of a Surface Curve 392
22.4 Meusnier s Theorem 394
22.5 Lines of Curvature 395
22.6 Gaussian and Mean Curvature 397
22.7 Euler s Theorem 398
22.8 Dupin s Indicatrix 399
22.9 Asymptotic Lines and Conjugate Directions 400
22.10 Ruled Surfaces and Developables 401
22.11 Nonparametric Surfaces 403
22.12 Composite Surfaces 404
23 Interrogation and Smoothing 407
23.1 Use of Curvature Plots 407
23.2 Curve and Surface Smoothing 408
23.3 Surface Interrogation 411
23.4 Implementation 414
23.5 Problems 416
24 Evaluation of Some Methods 417
24.1 Bezier Curves or B spline Curves? 417
24.2 Spline Curves or B spline Curves? 417
24.3 The Monomial or the Bezier Form? 418
24.4 The B spline or the Hermite Form? 421
24.5 Triangular or Rectangular Patches? 422
25 Quick Reference of Curve and Surface Terms 425
Appendix 1 List of Programs 431
Appendix 2 Notation 433
Bibliography 435
Index 465
|
| 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 | BV008278318 |
| classification_rvk | ST 320 |
| classification_tum | DAT 756f TEC 630f DAT 810f |
| ctrlnum | (OCoLC)633846982 (DE-599)BVBBV008278318 |
| discipline | Technik Informatik |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-09T17:17:38Z |
| institution | BVB |
| isbn | 0122490525 |
| language | English |
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| physical | XVII, 473 S. Ill., zahlr. graph. Darst. 1 Diskette, 5,25" |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Acad. 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 3. ed. Boston [u.a.] Acad. Press 1993 XVII, 473 S. Ill., zahlr. graph. Darst. 1 Diskette, 5,25" txt rdacontent n rdamedia nc rdacarrier Computer science and scientific computing Flächendarstellung (DE-588)4232296-0 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf CAD (DE-588)4069794-0 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Computergrafik (DE-588)4010450-3 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 Später u.d.T. Curves and surfaces for computer aided geometric design HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005469614&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 Flächendarstellung (DE-588)4232296-0 gnd Kurve (DE-588)4033824-1 gnd Geometrische Modellierung (DE-588)4156717-1 gnd CAD (DE-588)4069794-0 gnd Fläche (DE-588)4129864-0 gnd Computergrafik (DE-588)4010450-3 gnd |
| subject_GND | (DE-588)4232296-0 (DE-588)4033824-1 (DE-588)4156717-1 (DE-588)4069794-0 (DE-588)4129864-0 (DE-588)4010450-3 |
| 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_new | Curves and surfaces for computer aided geometric design |
| 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 | Flächendarstellung (DE-588)4232296-0 gnd Kurve (DE-588)4033824-1 gnd Geometrische Modellierung (DE-588)4156717-1 gnd CAD (DE-588)4069794-0 gnd Fläche (DE-588)4129864-0 gnd Computergrafik (DE-588)4010450-3 gnd |
| topic_facet | Flächendarstellung Kurve Geometrische Modellierung CAD Fläche Computergrafik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005469614&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT faringeralde curvesandsurfacesforcomputeraidedgeometricdesignapracticalguide |