Curves and surfaces for CAGD: a practical guide
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| Previous Title: | Farin, Gerald Curves and surfaces for computer aided geometric design |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
San Francisco [u.a.]
Morgan Kaufmann
2002
|
| Edition: | 5. ed. |
| Series: | The Morgan Kaufmann series in computer graphics and geometric modeling
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 499 S. Ill., graph. Darst. |
| ISBN: | 1558607374 9781558607378 |
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MARC
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| 250 | |a 5. ed. | ||
| 264 | 1 | |a San Francisco [u.a.] |b Morgan Kaufmann |c 2002 | |
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Record in the Search Index
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| adam_text | Contents
Preface xv
Chapter 1 P. Bezier: How a Simple System Was Born 1
Chapter 2 Introductory Material 13
2.1 Points and Vectors 13
2.2 Affine Maps 17
2.3 Constructing Affine Maps 20
2.4 Function Spaces 22
2.5 Problems 24
Chapter 3 Linear Interpolation 25
3.1 Linear Interpolation 25
3.2 Piecewise Linear Interpolation 29
3.3 Menelaos Theorem 30
3.4 Blossoms 31
3.5 Barycentric Coordinates in the Plane 34
3.6 Tessellations 37
3.7 Triangulations 39
3.8 Problems 41
Chapter 4 The de Casteljau Algorithm 43
4.1 Parabolas 43
4.2 The de Casteljau Algorithm 45
4.3 Some Properties of Bezier Curves 47
vii
vlii Contents
4.4 The Blossom 50
4.5 Implementation 53
4.6 Problems 54
Chapter 5 The Bernstein Form of a Bezier Curve 57
5.1 Bernstein Polynomials 57
5.2 Properties of Bezier Curves 60
5.3 The Derivatives of a Bezier Curve 62
5.4 Domain Changes and Subdivision 68
5.5 Composite Bezier Curves 71
5.6 Blossom and Polar 73
5.7 The Matrix Form of a Bezier Curve 74
5.8 Implementation 75
5.9 Problems 78
Chapter 6 Bezier Curve Topics 81
6.1 Degree Elevation 81
6.2 Repeated Degree Elevation 83
6.3 The Variation Diminishing Property 84
6.4 Degree Reduction 85
6.5 Nonparametric Curves 86
6.6 Cross Plots 87
6.7 Integrals 88
6.8 The Bezier Form of a Bezier Curve 89
6.9 The Weierstrass Approximation Theorem 90
6.10 Formulas for Bernstein Polynomials 91
6.11 Implementation 92
6.12 Problems 93
Chapter 7 Polynomial Curve Constructions 95
7.1 Aitken s Algorithm 95
7.2 Lagrange Polynomials 98
7.3 The Vandermonde Approach 99
7.4 Limits of Lagrange Interpolation 101
7.5 Cubic Hermite Interpolation 102
7.6 Quintic Hermite Interpolation 106
7.7 Point Normal Interpolation 107
Contents ix
7.8 Least Squares Approximation 108
7.9 Smoothing Equations 110
7.10 Designing with Bezier Curves 112
7.11 The Newton Form and Forward Differencing 114
7.12 Implementation 116
7.13 Problems 117
Chapter 8 B Spline Curves 119
8.1 Motivation 120
8.2 B Spline Segments 122
8.3 B Spline Curves 126
8.4 Knot Insertion 130
8.5 Degree Elevation 133
8.6 Greville Abscissae 134
8.7 Smoothness 135
8.8 B Splines 140
8.9 B Spline Basics 143
8.10 Implementation 144
8.11 Problems 146
Chapter 9 Constructing Spline Curves 147
9.1 Greville Interpolation 147
9.2 Least Squares Approximation 149
9.3 Modifying B Spline Curves 153
9.4 C2 Cubic Spline Interpolation 154
9.5 More End Conditions 157
9.6 Finding a Knot Sequence 161
9.7 The Minimum Property 167
9.8 C1 Piecewise Cubic Interpolation 169
9.9 Implementation 174
9.10 Problems 176
Chapter 10 W. Boehm: Differential Geometry I 179
10.1 Parametric Curves and Arc Length 179
10.2 The Frenet Frame 181
10.3 Moving the Frame 182
10.4 The Osculating Circle 184
X Contents
10.5 Nonparametric Curves 187
10.6 Composite Curves 188
Chapter 11 Geometric Continuity 191
11.1 Motivation 191
11.2 The Direct Formulation 192
11.3 The y, v, and £ Formulations 194
11.4 C2 Cubic Splines 195
11.5 Interpolating C2 Cubic Splines 199
11.6 Higher Order Geometric Continuity 200
11.7 Implementation 203
11.8 Problems 203
Chapter 1 2 Conic Sections 205
12.1 Projective Maps of the Real Line 205
1 2.2 Conies as Rational Quadratics 209
12.3 A de Casteljau Algorithm 214
12.4 Derivatives 215
12.5 The Implicit Form 216
12.6 Two Classic Problems 219
12.7 Classification 220
12.8 Control Vectors 223
12.9 Implementation 224
12.10 Problems 225
Chapter 13 Rational Bezier and B Spline Curves 227
13.1 Rational Bezier Curves 227
1 3.2 The de Casteljau Algorithm 230
13.3 Derivatives 233
1 3.4 Osculatory Interpolation 234
13.5 Reparametrization and Degree Elevation 235
1 3.6 Control Vectors 238
1 3.7 Rational Cubic B Spline Curves 238
13.8 Interpolation with Rational Cubics 240
13.9 Rational B Splines of Arbitrary Degree 241
13.10 Implementation 242
13.11 Problems 243
Contents xi
Chapter 14 Tensor Product Patches 245
14.1 Bilinear Interpolation 245
1 4.2 The Direct de Casteljau Algorithm 247
14.3 The Tensor Product Approach 250
14.4 Properties 253
14.5 Degree Elevation 254
14.6 Derivatives 255
14.7 Blossoms 258
1 4.8 Curves on a Surface 260
14.9 Normal Vectors 261
14.10 Twists 264
14.11 The Matrix Form of a Bezier Patch 265
14.12 Nonparametric Patches 266
14.13 Problems 267
Chapter 15 Constructing Polynomial Patches 269
15.1 Ruled Surfaces 269
15.2 Coons Patches 270
1 5.3 Translational Surfaces 272
1 5.4 Tensor Product Interpolation 274
1 5.5 Bicubic Hermite Patches 276
1 5.6 Least Squares 278
15.7 Finding Parameter Values 281
1 5.8 Shape Equations 282
1 5.9 A Problem with Unstructured Data 282
15.10 Implementation 283
15.11 Problems 284
Chapter 16 Composite Surfaces 285
16.1 Smoothness and Subdivision 285
16.2 Tensor Product B Spline Surfaces 288
1 6.3 Twist Estimation 290
1 6.4 Bicubic Spline Interpolation 293
1 6.5 Finding Knot Sequences 295
1 6.6 Rational Bezier and B Spline Surfaces 297
1 6.7 Surfaces of Revolution 299
xii Contents
16.8 Volume Deformations 301
1 6.9 CONS and Trimmed Surfaces 304
16.10 Implementation 306
16.11 Problems 308
Chapter 17 Bezier Triangles 309
17.1 The de Casteljau Algorithm 309
17.2 Triangular Blossoms 313
17.3 Bernstein Polynomials 315
17.4 Derivatives 316
17.5 Subdivision 320
17.6 Differentiability 323
17.7 Degree Elevation 326
17.8 Nonparametric Patches 326
17.9 The Multivariate Case 328
17.10 S Patches 330
17.11 Implementation 331
17.12 Problems 332
Chapter 18 Practical Aspects of Bezier Triangles 335
18.1 Rational Bezier Triangles 335
18.2 Quadrics 337
18.3 Interpolation 341
18.4 Cubic and Quintic Interpolants 341
18.5 The Clough Tocher Interpolant 343
18.6 The Powell Sabin Interpolant 345
18.7 Least Squares 346
18.8 Problems 347
Chapter 19 W. Boehm: Differential Geometry II 349
19.1 Parametric Surfaces and Arc Element 349
19.2 The Local Frame 352
19.3 The Curvature of a Surface Curve 352
19.4 Meusnier s Theorem 354
1 9.5 Lines of Curvature 355
19.6 Gaussian and Mean Curvature 357
19.7 Euler s Theorem 358
Contents xiii
1 9.8 Dupin s Indicatrix 359
1 9.9 Asymptotic Lines and Conjugate Directions 360
19.10 Ruled Surfaces and Developables 361
19.11 Nonparametric Surfaces 363
19.12 Composite Surfaces 364
Chapter 20 Geometric Continuity for Surfaces 367
20.1 Introduction 367
20.2 Triangle Triangle 368
20.3 Rectangle Rectangle 372
20.4 Rectangle Triangle 373
20.5 Filling in Rectangular Patches 374
20.6 Filling in Triangular Patches 375
20.7 Theoretical Aspects 375
20.8 Problems 376
Chapter 21 Surfaces with Arbitrary Topology 377
21.1 Recursive Subdivision Curves 377
21.2 Doo Sabin Surfaces 380
21.3 Catmull Clark Subdivision 383
21.4 Midpoint Subdivision 386
21.5 Loop Subdivision 387
21.6 V3 Subdivision 389
21.7 Interpolating Subdivision Surfaces 389
21.8 Surface Splines 392
21.9 Triangular Meshes 394
21.10 Decimation 395
21.11 Problems 398
Chapter 22 Coons Patches 399
22.1 Coons Patches: Bilinearly Blended 400
22.2 Coons Patches: Partially Bicubically Blended 402
22.3 Coons Patches: Bicubically Blended 404
22.4 Piecewise Coons Surfaces 406
22.5 Two Properties 407
22.6 Compatibility 408
22.7 Gordon Surfaces 410
xiv Contents
22.8 Boolean Sums 412
22.9 Triangular Coons Patches 414
22.10 Problems 417
Chapter 23 Shape 419
23.1 Use of Curvature Plots 419
23.2 Curve and Surface Smoothing 421
23.3 Surface Interrogation 425
23.4 Implementation 427
23.5 Problems 429
Chapter 24 Evaluation of Some Methods 431
24.1 Bezier Curves or B Spline Curves? 431
24.2 Spline Curves or B Spline Curves? 431
24.3 The Monomial or the Bezier Form? 432
24.4 The B Spline or the Hermite Form? 435
24.5 Triangular or Rectangular Patches? 435
Appendix A Quick Reference of Curve and Surface Terms 437
Appendix B List of Programs 445
Appendix C Notation 447
References 449
Index 491
|
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| dewey-ones | 516 - Geometry |
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| dewey-search | 516.3520285 |
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| discipline | Technik Informatik Mathematik |
| edition | 5. ed. |
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| indexdate | 2024-07-09T18:56:02Z |
| institution | BVB |
| isbn | 1558607374 9781558607378 |
| language | English |
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| spelling | Farin, Gerald E. 1953- Verfasser (DE-588)109438760 aut Curves and surfaces for CAGD a practical guide Gerald Farin 5. ed. San Francisco [u.a.] Morgan Kaufmann 2002 XVII, 499 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Morgan Kaufmann series in computer graphics and geometric modeling Computer graphics Computer-aided design Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 s DE-604 4. Auflage Farin, Gerald 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=009591234&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farin, Gerald E. 1953- Curves and surfaces for CAGD a practical guide Computer graphics Computer-aided design Geometrische Modellierung (DE-588)4156717-1 gnd |
| subject_GND | (DE-588)4156717-1 |
| title | Curves and surfaces for CAGD a practical guide |
| title_auth | Curves and surfaces for CAGD a practical guide |
| title_exact_search | Curves and surfaces for CAGD a practical guide |
| title_full | Curves and surfaces for CAGD a practical guide Gerald Farin |
| title_fullStr | Curves and surfaces for CAGD a practical guide Gerald Farin |
| title_full_unstemmed | Curves and surfaces for CAGD a practical guide Gerald Farin |
| title_old | Farin, Gerald Curves and surfaces for computer aided geometric design |
| title_short | Curves and surfaces for CAGD |
| title_sort | curves and surfaces for cagd a practical guide |
| title_sub | a practical guide |
| topic | Computer graphics Computer-aided design Geometrische Modellierung (DE-588)4156717-1 gnd |
| topic_facet | Computer graphics Computer-aided design Geometrische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009591234&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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