NURBS: from projective geometry to practical use
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Natick, Mass.
Peters
1999
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 267 S. graph. Darst. |
| ISBN: | 1568810849 |
Internformat
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| 245 | 1 | 0 | |a NURBS |b from projective geometry to practical use |c Gerald E. Farin |
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| 264 | 1 | |a Natick, Mass. |b Peters |c 1999 | |
| 300 | |a XV, 267 S. |b graph. Darst. | ||
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| 650 | 4 | |a Computer-aided design | |
| 650 | 4 | |a Spline theory |x Data processing | |
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Datensatz im Suchindex
| _version_ | 1804127770331054080 |
|---|---|
| adam_text | NURBS FROM PROJECTIVE GEOMETRY TO PRACTICAL USE SECOND EDITION GERALD E.
FARIN ARIZONA STATE UNIVERSITY TEMPE, ARIZONA AK PETERS NATICK,
MASSACHUSETTS CONTENTS PREFACE XIII 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 10 1.6
RANGES AND PENCILS 13 1.7 PAPPUS THEOREM 13 1.8 MENELAOS THEOREM 15
1.9 DUALITY 16 1.10 THE EXTENDED AFFINE PLANE 17 1.11 TOPOLOGICAL
ASPECTS 19 1.12 PARAMETRIC LINES 22 1.13 LINES AND LINE SEGMENTS 23 1.14
PROJECTIVE THREE-SPACE 25 1.15 PROBLEMS 26 2 PROJECTIVE MAPS 27 2.1
PERSPECTIVITIES 27 2.2 CROSS RATIOS 29 VII VUEI CONTENTS 2.3
PROJECTIVITIES 31 2.4 MOEBIUS TRANSFORMATIONS 33 2.5 COLLINEATIONS 34
2.6 CONSTRUCTING COLLINEATIONS 38 2.7 AFFINE MAPS 39 2.8 PROBLEMS 41 3
CONICS 43 3.1 LINE AND POINT CONICS 43 3.2 CONIC CONSTRUCTIONS 47 3.3
POINTS AND LINES 48 3.4 PASCAL S THEOREM 52 3.5 AFFINE CONICS 55 3.6
PROBLEMS 57 4 CONICS IN PARAMETRIC FORM 59 4.1 PARAMETRIC CURVES IN P 1
59 4.2 THE BERNSTEIN FORM OF A CONIC 62 4.3 THE DUAL FORM 64 4.4
DERIVATIVES 66 4.5 THE IMPLICIT FORM 68 4.6 IMPLICIT INTERPOLATING
CONICS 70 4.7 PARAMETRIC INTERPOLATING CONICS 72 4.8 BLOSSOMS AND POLARS
73 4.9 REPARAMETRIZATION 76 4.10 THE COMPLEMENTARY SEGMENT 77 4.11
PARAMETRIC AFFINE CONICS 79 4.12 PROBLEMS 79 5 RATIONAL QUADRATIC CONICS
81 5.1 THE RATIONAL QUADRATIC FORM 81 5.2 CONIC CLASSIFICATION 83 5.3
PROPERTIES OF RATIONAL QUADRATICS 85 5.4 DERIVATIVES 86 5.5 CONTROL
VECTORS 87 5.6 THEPARABOLA 88 5.7 THE CIRCLE 89 5.8 PROBLEMS 90 CONTENTS
IX 6 CONIC SPLINES 93 6.1 C 1 CONDITIONS 93 6.2 PARAMETRIC CONTINUITY
FOR RATIONAL CONIC SPLINES 96 6.3 CONIC B-SPLINES 97 6.4 CURVATURE
CONTINUITY 99 6.5 G 2 CONIC SPLINES 100 6.6 INTERPOLATION WITH G 2 CONIC
SPLINES 101 6.7 HIGHER ORDER SMOOTHNESS 103 6.8 PROBLEMS 105 7 RATIONAL
BEZIER CURVES 107 7.1 THE BERNSTEIN FORM 107 7.2 THE DE CASTELJAU
ALGORITHM 113 7.3 DEGREE ELEVATION 116 7.4 DEGREE REDUCTION 117 7.5
REPARAMETRIZATION 118 7.6 NONPARAMETRIC CURVES 121 7.7 BASE POINTS 122
7.8 DERIVATIVES 123 7.9 SMOOTHNESS 125 7.10 BLOSSOMS 125 7.11 CONTROL
VECTORS 129 7.12 DUALITY 130 7.13 HYBRID BEZIER CURVES 132 7.14 STRAIGHT
LINES AS BEZIER CURVES 136 7.15 PROBLEMS 137 8 RATIONAL CUBICS 139 8.1
RATIONAL CUBIC CONICS 139 8.2 EMBEDDING CONES 142 8.3 THE EMBEDDING
BILINEAR PATCH 144 8.4 ASYMPTOTES 146 8.5 THE HERMITE FORM 148 8.6 CUBIC
LAGRANGE INTERPOLATION 149 8.7 OSCULATORY INTERPOLATION 150 8.8 PROBLEMS
151 9 NURBS 153 9.1 KNOT INSERTION 154 9.2 THE DE BOOR ALGORITHM 156 9.3
PROPERTIES 159 9.4 THE B-SPLINE FORM 162 X CONTENTS 9.5 BLOSSOMS 163 9.6
DERIVATIVES 164 9.7 MORE NURB PROPERTIES 165 9.8 PROBLEMS 167 10
PYTHAGOREAN CURVES 169 10.1 CIRCLES AND THE STEREOGRAPHIC PROJECTION 169
10.2 PYTHAGOREAN HODOGRAPH CURVES 172 10.3 RATIONAL PH OFFSETS 175 10.4
RATIONAL OFFSETS 177 10.5 RATIONAL CURVES ON THE SPHERE 178 10.6
PROBLEMS 180 11 RECTANGULAR PATCHES 181 11.1 BILINEAR PATCHES 181 11.2
BEZIER PATCHES 184 11.3 DE CASTELJAU ALGORITHMS AND BLOSSOMS 187 11.4
THE WEIGHT POINTS 188 11.5 DERIVATIVES AND CONTINUITY 190 11.6
REPARAMETRIZATION 194 11.7 RECTANGULAR NURBS SURFACES 195 11.8 BLOSSOMS
198 11.9 SURFACES OF REVOLUTION 199 11.10 DEVELOPABLE SURFACES 201 11.11
PROBLEMS 205 12 RATIONAL BEZIER TRIANGLES 207 12.1 PROJECTIVE BEZIER
TRIANGLES 207 12.2 DEGREE ELEVATION 211 12.3 BLOSSOMS AND DERIVATIVES
212 12.4 BARYCENTRIC COORDINATES 214 12.5 RATIONAL BEZIER TRIANGLES 216
12.6 PROBLEMS 217 13 QUADRICS 219 13.1 QUADRICS 219 13.2 QUADRIC
CLASSIFICATION 220 13.3 THE STEREOGRAPHIC PROJECTION 223 13.4 QUARTICS
ON QUADRICS 227 13.5 PROBLEMS 232 CONTENTS XI 14 GREGORY PATCHES 233
14.1 BICUBIC GREGORY PATCHES 233 14.2 THE RATIONAL BEZIER FORM 235 14.3
RBG PATCHES 237 14.4 GREGORY TRIANGLES 238 14.5 BASE POINTS AND
MULTI-SIDED PATCHES 239 14.6 PROBLEMS 240 15 EXAMPLES AND STANDARDS 241
15.1 IGES 241 15.2 A SEMICIRCLE 245 15.3 A HYPERBOLIC PARABOLOID 246
15.4 A QUARTER OF A CYLINDER 246 15.5 A RATIONAL QUADRATIC PATCH ON A
SPHERE 247 15.6 AN OCTANT OF A SPHERE 247 15.7 A SIXTH OF A SPHERE 248
15.8 A SIXTEENTH OF A TORUS 249 15.9 PROBLEMS 250 16 NOTATION 251
BIBLIOGRAPHY 253 INDEX 263
|
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| author | Farin, Gerald E. 1953- |
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| dewey-sort | 3511 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T18:38:38Z |
| institution | BVB |
| isbn | 1568810849 |
| language | English |
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| physical | XV, 267 S. graph. Darst. |
| publishDate | 1999 |
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| spelling | Farin, Gerald E. 1953- Verfasser (DE-588)109438760 aut NURBS from projective geometry to practical use Gerald E. Farin 2. ed. Natick, Mass. Peters 1999 XV, 267 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Datenverarbeitung Computer-aided design Spline theory Data processing Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Spline-Funktion (DE-588)4056332-7 gnd rswk-swf CAD (DE-588)4069794-0 gnd rswk-swf CAD (DE-588)4069794-0 s DE-604 Spline-Funktion (DE-588)4056332-7 s Datenverarbeitung (DE-588)4011152-0 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008906566&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Farin, Gerald E. 1953- NURBS from projective geometry to practical use Datenverarbeitung Computer-aided design Spline theory Data processing Datenverarbeitung (DE-588)4011152-0 gnd Spline-Funktion (DE-588)4056332-7 gnd CAD (DE-588)4069794-0 gnd |
| subject_GND | (DE-588)4011152-0 (DE-588)4056332-7 (DE-588)4069794-0 |
| title | NURBS from projective geometry to practical use |
| title_auth | NURBS from projective geometry to practical use |
| title_exact_search | NURBS from projective geometry to practical use |
| title_full | NURBS from projective geometry to practical use Gerald E. Farin |
| title_fullStr | NURBS from projective geometry to practical use Gerald E. Farin |
| title_full_unstemmed | NURBS from projective geometry to practical use Gerald E. Farin |
| title_short | NURBS |
| title_sort | nurbs from projective geometry to practical use |
| title_sub | from projective geometry to practical use |
| topic | Datenverarbeitung Computer-aided design Spline theory Data processing Datenverarbeitung (DE-588)4011152-0 gnd Spline-Funktion (DE-588)4056332-7 gnd CAD (DE-588)4069794-0 gnd |
| topic_facet | Datenverarbeitung Computer-aided design Spline theory Data processing Spline-Funktion CAD |
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