NURB curves and surfaces: from projective geometry to practical use
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Wellesley, Mass.
Peters
1995
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 229 S. graph. Darst. |
| ISBN: | 1568810385 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface xi
1 The Projective Plane 1
1.1 Motivation 1
1.2 The Projective Plane 4
1.3 Points and Lines 5
1.4 Projective Line Coordinates 7
1.5 Projective Plane Coordinates 9
1.6 Ranges and Pencils 11
1.7 Pappus Theorem 12
1.8 Duality 15
1.9 The Extended Affine Plane 15
1.10 Topological Aspects 17
1.11 Projective Three space 20
1.12 Problems 21
2 Projective Maps 23
2.1 Perspectivities 23
2.2 Cross Ratios 25
2.3 Projectivities 27
2.4 Moebius Transformations 29
v
vi Contents
2.5 Collineations 30
2.6 Constructing Collineations 31
2.7 Affine Maps 33
2.8 Problems 36
3 Conies 37
3.1 Line Conies 37
3.2 Conic Constructions 40
3.3 Points and Lines 42
3.4 Pascal s Theorem 45
3.5 Affine Conies 49
3.6 Problems 51
4 Conies in Parametric Form 53
4.1 Parametric Curves in JP2 53
4.2 The Bernstein Form of a Conic 55
4.3 Parametric Point conies 58
4.4 Derivatives 59
4.5 The Implicit Form 61
4.6 Implicit Interpolating Conies 63
4.7 Parametric Interpolating Conies 64
4.8 Blossoms and Polars 65
4.9 Reparametrization 68
4.10 The Complementary Segment 70
4.11 Parametric Affine Conies 71
4.12 Problems 72
5 Rational Quadratic Conies 73
5.1 The Rational Quadratic Form 73
5.2 Conic Classification 74 :
5.3 Properties of Rational Quadratics 76
5.4 Derivatives 78
5.5 Control Vectors 78 !
5.6 The Parabola 80
5.7 The Circle 80 .
5.8 Circles and the Stereographic Projection 82 i
5.9 Problems 83
6 Conic Splines 85
6.1 C1 Conditions 85
6.2 Parametric Continuity for Rational Conic Splines 87
6.3 Conic B splines 88
I
i
Contents vii
6.4 Curvature Continuity 90
6.5 G2 Conic Splines 91
6.6 Interpolation with G2 Conic Splines 93
6.7 Higher Order Smoothness 95
6.8 Problems 96
7 Rational Bezier Curves 97
7.1 The Bernstein Form 98
7.2 The de Casteljau Algorithm 100
7.3 Degree Elevation 104
7.4 Degree Reduction 105
7.5 Reparametrization 107
7.6 Nonparametric Curves 109
7.7 Base Points 110
7.8 Derivatives 112
7.9 Blossoms 113
7.10 Control Vectors 115
7.11 Duality 116
7.12 Hybrid Bezier Curves 119
7.13 Problems 122
8 Rational Cubics 123
8.1 Straight Line Cubics 123
8.2 Rational Cubic Conies 124
8.3 Embedding Cones 127
8.4 The Embedding Bilinear Patch 129
8.5 Asymptotes 130
8.6 The Hermite Form 133
8.7 Cubic Lagrange Interpolation 134
8.8 Osculatory Interpolation 135
8.9 Problems 136
9 Projective Splines 137
9.1 Osculants and Smoothness 137
9.2 Reparametrization 140
9.3 Projective Cubic Splines 141
9.4 Problems 142
10 Rational B splines 143
10.1 Definitions 143
10.2 Knot Insertion and the de Boor Algorithm 146
10.3 Derivatives 147
viii Contents
10.4 Properties 149
10.5 Conversion to Rational Bezier Form 149
10.6 Problems 151
11 Rectangular Patches 153
11.1 Bilinear Patches 153
11.2 Bezier Patches 156
11.3 De Casteljau Algorithms, Blossoms, and Derivatives .... 157
11.4 The Weight Points 163
11.5 Reparametrization 164
11.6 Rectangular NURBS Surfaces 164
11.7 Surfaces of Revolution 167
11.8 Developable Surfaces 169
11.9 Problems 173
12 Rational Bezier Triangles 175
12.1 Projective Bezier Triangles 175
12.2 Degree Elevation 178
12.3 Blossoms and Derivatives 179
12.4 Barycentric Coordinates 182
12.5 Rational Bezier Triangles 183
12.6 Problems 185
13 Quadrics 187 !
13.1 Quadrics 187 I
13.2 Quadric Classification 188
13.3 The Stereographic projection 190
13.4 Quartics on Quadrics 193
13.5 Problems 196 i
14 Gregory Patches 197
14.1 Bicubic Gregory Patches 198 |
14.2 The Rational Bezier Form 200 !
14.3 RBG Patches 201
14.4 Gregory Triangles 202 I
14.5 Base Points and Multisided Patches 204 !
14.6 Problems 204
I
15 Examples and Standards 205
15.1 IGES 205
15.2 A Semicircle 209
15.3 A Hyperbolic Paraboloid 209
Contents ix
15.4 A Quarter of a Cylinder 210
15.5 A Rational Quadratic Patch on a Sphere 210
15.6 An Octant of a Sphere 211
15.7 A Sixth of a Sphere 212
15.8 A Sixteenth of a Torus 213
15.9 Problems 213
Notation 215
Bibliography 217
Index 224
|
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| id | DE-604.BV010113749 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:46:45Z |
| institution | BVB |
| isbn | 1568810385 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006715672 |
| oclc_num | 613294323 |
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| owner | DE-29T DE-634 DE-898 DE-BY-UBR |
| owner_facet | DE-29T DE-634 DE-898 DE-BY-UBR |
| physical | XII, 229 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Peters |
| record_format | marc |
| spelling | Farin, Gerald E. 1953- Verfasser (DE-588)109438760 aut NURB curves and surfaces from projective geometry to practical use Gerald E. Farin Wellesley, Mass. Peters 1995 XII, 229 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Datenverarbeitung Computer-aided design Spline theory Data processing Kurve (DE-588)4033824-1 gnd rswk-swf Fläche (DE-588)4129864-0 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Fläche (DE-588)4129864-0 s Geometrische Modellierung (DE-588)4156717-1 s DE-604 Kurve (DE-588)4033824-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006715672&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farin, Gerald E. 1953- NURB curves and surfaces from projective geometry to practical use Datenverarbeitung Computer-aided design Spline theory Data processing Kurve (DE-588)4033824-1 gnd Fläche (DE-588)4129864-0 gnd Geometrische Modellierung (DE-588)4156717-1 gnd |
| subject_GND | (DE-588)4033824-1 (DE-588)4129864-0 (DE-588)4156717-1 |
| title | NURB curves and surfaces from projective geometry to practical use |
| title_auth | NURB curves and surfaces from projective geometry to practical use |
| title_exact_search | NURB curves and surfaces from projective geometry to practical use |
| title_full | NURB curves and surfaces from projective geometry to practical use Gerald E. Farin |
| title_fullStr | NURB curves and surfaces from projective geometry to practical use Gerald E. Farin |
| title_full_unstemmed | NURB curves and surfaces from projective geometry to practical use Gerald E. Farin |
| title_short | NURB curves and surfaces |
| title_sort | nurb curves and surfaces from projective geometry to practical use |
| title_sub | from projective geometry to practical use |
| topic | Datenverarbeitung Computer-aided design Spline theory Data processing Kurve (DE-588)4033824-1 gnd Fläche (DE-588)4129864-0 gnd Geometrische Modellierung (DE-588)4156717-1 gnd |
| topic_facet | Datenverarbeitung Computer-aided design Spline theory Data processing Kurve Fläche Geometrische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006715672&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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