Curves and surfaces in computer aided geometric design:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1988
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Japan. übers. |
| Beschreibung: | X, 378 S. Ill |
| ISBN: | 3540174494 0387174494 |
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Datensatz im Suchindex
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| adam_text | FUJIO YAMAGUCHI CURVES AND SURFACES IN COMPUTER AIDED GEOMETRIC DESIGN
WITH 244 FIGURES AND 9 TABLES SPRINGER-VERLAG BERLIN HEIDELBERG NEWYORK
LONDON PARIS TOKYO CONTENTS ON THE SYMBOLS USED IN THIS BOOK XI 0.
MATHEMATICAL DESCRIPTION OF SHAPE INFORMATION 1 0.1 DESCRIPTION AND
TRANSMISSION OF SHAPE INFORMATION 1 0.2 PROCESSING AND ANALYSIS OF
SHAPES 2 0.3 MATHEMATICAL DESCRIPTION OF FREE FORM SHAPES 3 0.4 THE
DEVELOPMENT OF MATHEMATICAL DESCRIPTIONS OF FREE FORM CURVES AND
SURFACES 4 REFERENCES 10 1. BASIC THEORY OF CURVES AND SURFACES 11 1.1
GENERAL 11 1.1.1 PROPERTIES OF OBJECT SHAPES AND THEIR MATHEMATICAL
REPRESENTATION 11 1.1.2 DESIGN AND MATHEMATICAL REPRESENTATIONS 14 1.1.3
INVARIANCE OF A SHAPE UNDER COORDINATE TRANSFORMATION .... 18 1.2 CURVE
THEORY 20 1.2.1 PARAMETRIC REPRESENTATION OF CURVES; TANGENT LINES AND
OSCULATING PLANES 20 1.2.2 CURVATURE AND TORSION 24 1.2.3 FRENET FRAMES
AND THE FRENET-SERRET EQUATIONS 29 1.2.4 CALCULATION OF A POINT ON A
CURVE 31 1.2.5 CONNECTION OF CURVE SEGMENTS 33 1.2.6 PARAMETER
TRANSFORMATION 35 1.2.7 PARTITIONING OF A CURVE SEGMENT 39 1.2.8
PARAMETRIC CUBIC CURVES 39 1.2.9 LENGTH AND AREA OF A CURVE 42 1.2.10
INTERSECTION OF A CURVE WITH A PLANE 43 1.2.11 INTERSECTION OF TWO
CURVES 43 1.3 THEORY OF SURFACES 44 1.3.1 PARAMETRIC REPRESENTATION OF
SURFACES 44 1.3.2 THE FIRST FUNDAMENTAL MATRIX OF A SURFACE 46 1.3.3
DETERMINING CONDITIONS FOR A TANGENT VECTOR TO A CURVE ON A SURFACE 48
1.3.4 CURVATURE OF A SURFACE 49 1.3.5 CALCULATION OF A POINT ON A
SURFACE 51 1.3.6 SUBDIVISION OF SURFACE PATCHES 55 1.3.7 CONNECTION OF
SURFACE PATCHES 57 VIII CONTENTS * 1.3.8 DEGENERATION OF A SURFACE PATCH
59 1.3.9 CALCULATION OF A NORMAL VECTOR ON A SURFACE 60 1.3.10
CALCULATION OF SURFACE AREA AND VOLUME OF A SURFACE 61 1.3.11 OFFSET
SURFACES 63 REFERENCES 63 2. LAGRANGE INTERPOLATION 64 2.1 LAGRANGE
INTERPOLATION CURVES 64 2.2 EXPRESSION IN TERMS OF DIVIDED DIFFERENCES
67 REFERENCES 71 3. HERMITE INTERPOLATION 72 3.1 HERMITE INTERPOLATION
72 3.2 CURVES 73 3.2.1 DERIVATION OF A FERGUSON CURVE SEGMENT 73 3.2.2
APPROXIMATE REPRESENTATION OF A CIRCULAR ARC BY A FERGUSON CURVE SEGMENT
78 3.2.3 HERMITE INTERPOLATION CURVES 80 3.2.4 PARTITIONING OF FERGUSON
CURVE SEGMENTS 84 3.2.5 INCREASE OF DEGREE OF A FERGUSON CURVE SEGMENT
85 3.3 SURFACES 87 3.3.1 FERGUSON SURFACE PATCH 87 3.3.2 THE COONS
SURFACE PATCHES (1964) 91 3.3.3 THE COONS SURFACE PATCHES (1967) 102
3.3.4 TWIST VECTORS AND SURFACE SHAPES 112 3.3.5 METHODS OF DETERMINING
TWIST VECTORS 117 3.3.6 PARTIAL SURFACE REPRESENTATION OF THE COONS
BI-CUBIC SURFACE PATCH 122 3.3.7 CONNECTION OF THE COONS BI-CUBIC
SURFACE PATCHES 123 3.3.8 SHAPE CONTROL OF THE COONS BI-CUBIC SURFACE
PATCH 126 3.3.9 TRIANGULAR PATCHES FORMED BY DEGENERATION 131 3.3.10
DECOMPOSITION OF COONS SURFACE PATCHES AND 3 TYPES IN CONSTRUCTING
SURFACES 132 3.3.11 SOME CONSIDERATIONS ON HERMITE INTERPOLATION CURVES
AND SURFACES 133 REFERENCES 134 4. SPLINE INTERPOLATION 135 4.1 SPLINES
135 4.2 SPLINE FUNCTIONS 136 4.3 MATHEMATICAL REPRESENTATION OF SPLINE
FUNCTIONS 137 4.4 NATURAL SPLINES 138 4.5 NATURAL SPLINES AND THE
MINIMUM INTERPOLATION PROPERTY 140 4.6 SMOOTHING SPLINES 144 4.7
PARAMETRIC SPLINE CURVES 145 .CONTENTS IX 4.8 END CONDITIONS ON A SPLINE
CURVE 151 4.9 CUBIC SPLINE CURVES USING CIRCULAR ARC LENGTH C 3 . 159
4.10 B-SPLINES 160 4.11 GENERATION OF SPLINE SURFACES 163 REFERENCES 168
5. THE BERNSTEIN APPROXIMATION 1 69 5.1 CURVES 169 5.1.1 MODIFICATION OF
FERGUSON CURVE SEGMENTS 169 5.1.2 CUBIC BEZIER CURVE SEGMENTS 173 5.1.3
BEZIER CURVE SEGMENTS 182 5.1.4 PROPERTIES OF THE BERNSTEIN BASIS
FUNCTION AND BERNSTEIN POLYNOMIAL : 189 5.1.5 VARIOUS REPRESENTATIONS
FOR BEZIER CURVE SEGMENTS 193 5.1.6 DERIVATIVE VECTORS OF BEZIER CURVE
SEGMENTS 198 5.1.7 DETERMINATION OF A POINT ON A CURVE SEGMENT BY LINEAR
OPERATIONS 199 5.1.8 INCREASE OF THE DEGREE OF A BEZIER CURVE SEGMENT
204 5.1.9 PARTITIONING OF A BEZIER CURVE SEGMENT 209 5.1.10 CONNECTION
OF BEZIER CURVE SEGMENTS . 213 5.1.11 CREATION OF A SPLINE CURVE WITH
CUBIC BEZIER CURVE SEGMENTS 214 5.2 SURFACES 216 5.2.1 BEZIER SURFACE
PATCHES 216 5.2.2 THE RELATION BETWEEN A BI-CUBIC BEZIER SURFACE PATCH
AND A BI-CUBIC COONS SURFACE PATCH 218 5.2.3 CONNECTION OF BEZIER
SURFACE PATCHES 221 5.2.4 TRIANGULAR PATCHES FORMED BY DEGENERATION 226
5.2.5 TRIANGULAR PATCHES 228 5.2.6 SOME CONSIDERATIONS ON BEZIER CURVES
AND SURFACES 231 REFERENCES 232 6. THE B-SPLINE APPROXIMATION 233 6.1
UNIFORM CUBIC B-SPLINE CURVES 233 6.1.1 DERIVATION OF THE CURVE FORMULA
233 6.1.2 PROPERTIES OF CURVES 240 6.1.3 DETERMINATION OF A POINT ON A
CURVE BY FINITE DIFFERENCE OPERATIONS 246 6.1.4 INVERSE TRANSFORMATION
OF A CURVE 247 6.1.5 CHANGE OF POLYGON VERTICES 250 6.2 UNIFORM BI-CUBIC
B-SPLINE SURFACES 251 6.2.1 SURFACE PATCH FORMULAS 251 6.2.2
DETERMINATION OF A POINT ON A SURFACE BY FINITE DIFFERENCE OPERATIONS
259 6.2.3 INVERSE TRANSFORMATION OF A SURFACE 262 6.2.4 SURFACES OF
REVOLUTION 265 X CONTENTS 6.3 B-SPLINE FUNCTIONS AND THEIR PROPERTIES
(1) 270 6.4 B-SPLINE FUNCTIONS AND THEIR PROPERTIES (2) 272 6.5
DERIVATION OF B-SPLINE FUNCTIONS 274 6.6 B-SPLINE CURVE TYPE (1) 281 6.7
B-SPLINE CURVE TYPE (2) 283 6.8 RECURSIVE CALCULATION OF B-SPLINE
FUNCTIONS 285 6.9 B-SPLINE FUNCTIONS AND THEIR PROPERTIES (3) 291 6.10
B-SPLINE CURVE TYPE (3) 294 6.11 DIFFERENTIATION OF B-SPLINE CURVES 309
6.12 GEOMETRICAL PROPERTIES OF B-SPLINE CURVES 311 6.13 DETERMINATION OF
A POINT ON A CURVE BY LINEAR OPERATIONS 312 6.14 INSERTION OF KNOTS 316
6.15 CURVE GENERATION BY GEOMETRICAL PROCESSING 320 6.16 INTERPOLATION
OF A SEQUENCE OF POINTS WITH A B-SPLINE CURVE 325 6.17 MATRIX EXPRESSION
OF B-SPLINE CURVES 327 6.18 EXPRESSION OF THE FUNCTIONS C 00 (T), C 0L
(T), C L0 (T) AND C UL (T) BY B-SPLINE FUNCTIONS 329 6.19 GENERAL
B-SPLINE SURFACES 334 REFERENCES 336 7. THE RATIONAL POLYNOMIAL CURVES
337 7.1 DERIVATION OF PARAMETRIC CONIC SECTION CURVES 337 7.2
CLASSIFICATION OF CONIC SECTION CURVES 340 7.3 PARABOLAS 342 7.4
CIRCULAR ARC FORMULAS 343 7.5 CUBIC/CUBIC RATIONAL POLYNOMIAL CURVES 346
7.6 T-CONIC CURVES 347 REFERENCES 350 APPENDIX A: VECTOR EXPRESSION OF
SIMPLE GEOMETRICAL RELATIONS 351 APPENDIX B: PROOFS OF FORMULAS RELATING
TO B-SPLINE FUNCTIONS 356 APPENDIX C: EFFECT OF MULTIPLE KNOTS ON
B-SPLINE FUNCTIONS 360 BIBLIOGRAPHY 366 SUBJECT INDEX 375
|
| any_adam_object | 1 |
| author | Yamaguchi, Fujio |
| author_facet | Yamaguchi, Fujio |
| author_role | aut |
| author_sort | Yamaguchi, Fujio |
| author_variant | f y fy |
| building | Verbundindex |
| bvnumber | BV001310152 |
| classification_rvk | ST 300 ST 320 |
| classification_tum | MAS 045f DAT 756f |
| ctrlnum | (OCoLC)242719239 (DE-599)BVBBV001310152 |
| discipline | Informatik Maschinenbau |
| format | Book |
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| id | DE-604.BV001310152 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:27:02Z |
| institution | BVB |
| isbn | 3540174494 0387174494 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000790948 |
| oclc_num | 242719239 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-739 DE-29T DE-706 DE-634 DE-83 DE-11 |
| physical | X, 378 S. Ill |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Springer |
| record_format | marc |
| spelling | Yamaguchi, Fujio Verfasser aut Konpyūta dispurei ni yoru kejiō shori kōgaku Curves and surfaces in computer aided geometric design Fujio Yamaguchi Berlin u.a. Springer 1988 X, 378 S. Ill txt rdacontent n rdamedia nc rdacarrier Aus dem Japan. übers. Fläche (DE-588)4129864-0 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf CAD (DE-588)4069794-0 gnd rswk-swf Kurve (DE-588)4033824-1 gnd rswk-swf Computergrafik (DE-588)4010450-3 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Computergrafik (DE-588)4010450-3 s Geometrie (DE-588)4020236-7 s DE-604 Fläche (DE-588)4129864-0 s Kurve (DE-588)4033824-1 s Geometrische Modellierung (DE-588)4156717-1 s CAD (DE-588)4069794-0 s HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000790948&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yamaguchi, Fujio Curves and surfaces in computer aided geometric design Fläche (DE-588)4129864-0 gnd Geometrie (DE-588)4020236-7 gnd CAD (DE-588)4069794-0 gnd Kurve (DE-588)4033824-1 gnd Computergrafik (DE-588)4010450-3 gnd Geometrische Modellierung (DE-588)4156717-1 gnd |
| subject_GND | (DE-588)4129864-0 (DE-588)4020236-7 (DE-588)4069794-0 (DE-588)4033824-1 (DE-588)4010450-3 (DE-588)4156717-1 |
| title | Curves and surfaces in computer aided geometric design |
| title_alt | Konpyūta dispurei ni yoru kejiō shori kōgaku |
| title_auth | Curves and surfaces in computer aided geometric design |
| title_exact_search | Curves and surfaces in computer aided geometric design |
| title_full | Curves and surfaces in computer aided geometric design Fujio Yamaguchi |
| title_fullStr | Curves and surfaces in computer aided geometric design Fujio Yamaguchi |
| title_full_unstemmed | Curves and surfaces in computer aided geometric design Fujio Yamaguchi |
| title_short | Curves and surfaces in computer aided geometric design |
| title_sort | curves and surfaces in computer aided geometric design |
| topic | Fläche (DE-588)4129864-0 gnd Geometrie (DE-588)4020236-7 gnd CAD (DE-588)4069794-0 gnd Kurve (DE-588)4033824-1 gnd Computergrafik (DE-588)4010450-3 gnd Geometrische Modellierung (DE-588)4156717-1 gnd |
| topic_facet | Fläche Geometrie CAD Kurve Computergrafik Geometrische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000790948&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT yamaguchifujio konpyutadispureiniyorukejioshorikogaku AT yamaguchifujio curvesandsurfacesincomputeraidedgeometricdesign |