Interpolating cubic splines
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston ; Basel ; Berlin
Birkhäuser
2000
|
| Schriftenreihe: | Progress in computer science and applied logic
18 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Knott, Gary D. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Interpolating cubic splines |c Gary D. Knott |
| 264 | 1 | |a Boston ; Basel ; Berlin |b Birkhäuser |c 2000 | |
| 300 | |a XII, 244 S. |b graph. Darst. |c 24 cm | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in computer science and applied logic |v 18 | |
| 500 | |a Literaturverz. S. 233 - 236 | ||
| 650 | 4 | |a Interpolation | |
| 650 | 4 | |a Spline theory | |
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Datensatz im Suchindex
| _version_ | 1819604983460397056 |
|---|---|
| adam_text | Contents
Preface ix
1 Mathematical Preliminaries 1
1.1 The Pythagorean Theorem 1
1.2 Vectors 3
1.3 Subspaces and Linear Independence 6
1.4 Vector Space Bases 8
1.5 Euclidean Length 11
1.6 The Euclidean Inner Product 12
1.7 Projection onto a Line 16
1.8 Planes in 3 Space 20
1.9 Coordinate System Orientation 24
1.10 The Cross Product 26
2 Curves 31
2.1 The Tangent Curve 32
2.2 Curve Parameterization 34
2.3 The Normal Curve 36
2.4 Envelope Curves 37
vi Contents
2.5 Arc Length Parameterization 38
2.6 Curvature 39
2.7 The Frenet Equations 41
2.8 Involutes and Evolutes 43
2.9 Helices 45
2.10 Signed Curvature 46
2.11 Inflection Points 47
3 Surfaces 51
3.1 The Gradient of a Function 52
3.2 The Tangent Space and Normal Vector 54
3.3 Derivatives 55
4 Function and Space Curve Interpolation 59
5 2D Function Interpolation 63
5.1 Lagrange Interpolating Polynomials 63
5.2 Whittaker s Interpolation Formula 65
5.3 Cubic Splines for 2D Function Interpolation 65
5.4 Estimating Slopes 68
5.5 Monotone 2D Cubic Spline Functions 69
5.6 Error in 2D Cubic Spline Interpolation Functions 72
6 A Spline Curves With Range Dimension d 75
7 Cubic Polynomial Space Curve Splines 77
7.1 Choosing the Segment Parameter Limits 81
7.2 Estimating Tangent Vectors 85
7.3 Bezier Polynomials 90
8 Double Tangent Cubic Splines 95
8.1 Kochanek Bartels Tangents 96
8.2 Fletcher McAllister Tangent Magnitudes 97
9 Global Cubic Space Curve Splines 101
9.1 Second Derivatives of Global Cubic Splines 108
9.2 Third Derivatives of Global Cubic Splines 112
9.3 A Variational Characterization of Natural Splines 114
9.4 Weighted v Splines 116
Contents vii
10 Smoothing Splines 123
10.1 Computing an Optimal Smoothing Spline 124
10.2 Computing the Smoothing Parameter 127
10.3 Best Fit Smoothing Cubic Splines 129
10.4 Monotone Smoothing Splines 130
11 Geometrically Continuous Cubic Splines 133
11.1 Beta Splines 136
12 Quadratic Space Curve Based Cubic Splines 139
13 Cubic Spline Vector Space Basis Functions 143
13.1 Bases for C1 and C2 Space Curve Cubic Splines 144
13.2 Cardinal Bases for Cubic Spline Vector Spaces 148
13.3 The B Spline Basis for Global Cubic Splines 151
14 Rational Cubic Splines 157
15 Two Spline Programs 159
15.1 Interpolating Cubic Splines Program 159
15.2 Optimal Smoothing Spline Program 178
16 Tensor Product Surface Splines 193
16.1 Bicubic Tensor Product Surface Patch Splines 193
16.2 A Generalized Tensor Product Patch Spline 197
16.3 Regular Grid Multi Patch Surface Interpolation 199
16.4 Estimating Tangent and Twist Vectors 200
16.5 Tensor Product Cardinal Basis Representation 203
16.6 Bicubic Splines with Variable Parameter Limits 205
16.7 Triangular Patches 205
16.8 Parametric Grids 207
16.9 3D Function Interpolation 208
17 Boundary Curve Based Surface Splines 211
17.1 Boundary Curve Based Bilinear Interpolation 211
17.2 Boundary Curve Based Bicubic Interpolation 213
17.3 General Boundary Curve Based Spline Interpolation . . . 215
viii Contents
18 Physical Splines 217
18.1 Computing a Space Curve Physical Spline Segment .... 222
18.2 Computing a 2D Physical Spline Segment 230
References 233
Index 237
|
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| dewey-full | 511/.42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.42 |
| dewey-search | 511/.42 |
| dewey-sort | 3511 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV013075135 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:20:07Z |
| institution | BVB |
| isbn | 3764341009 0817641009 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008908394 |
| oclc_num | 42072291 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-20 DE-634 DE-11 |
| owner_facet | DE-824 DE-703 DE-20 DE-634 DE-11 |
| physical | XII, 244 S. graph. Darst. 24 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in computer science and applied logic |
| series2 | Progress in computer science and applied logic |
| spellingShingle | Knott, Gary D. Interpolating cubic splines Progress in computer science and applied logic Interpolation Spline theory Kubische Form (DE-588)4569782-6 gnd Spline-Interpolation (DE-588)4182396-5 gnd |
| subject_GND | (DE-588)4569782-6 (DE-588)4182396-5 |
| title | Interpolating cubic splines |
| title_auth | Interpolating cubic splines |
| title_exact_search | Interpolating cubic splines |
| title_full | Interpolating cubic splines Gary D. Knott |
| title_fullStr | Interpolating cubic splines Gary D. Knott |
| title_full_unstemmed | Interpolating cubic splines Gary D. Knott |
| title_short | Interpolating cubic splines |
| title_sort | interpolating cubic splines |
| topic | Interpolation Spline theory Kubische Form (DE-588)4569782-6 gnd Spline-Interpolation (DE-588)4182396-5 gnd |
| topic_facet | Interpolation Spline theory Kubische Form Spline-Interpolation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008908394&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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