Geometric concepts for geometric design:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Wellesley, Mass.
Peters
1994
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [389] - 393 |
| Beschreibung: | XVII, 393 S. zahlr. graph. Darst. |
| ISBN: | 1568810040 |
Internformat
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| 100 | 1 | |a Böhm, Wolfgang |d 1928-2018 |e Verfasser |0 (DE-588)119040956 |4 aut | |
| 245 | 1 | 0 | |a Geometric concepts for geometric design |c Wolfgang Boehm ; Hartmut Prautzsch |
| 264 | 1 | |a Wellesley, Mass. |b Peters |c 1994 | |
| 300 | |a XVII, 393 S. |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1807591447892852736 |
|---|---|
| adam_text |
GEOMETRIC CONCEPTS FOR GEOMETRIC DESIGN WOLFGANG BOEHM TECHNISCHE
UNIVERSITAT BRAUNSCHWEIG BRAUNSCHWEIG, GERMANY HARTMUT PRAUTZSCH
UNIVERSITAT KARLSRUHE KARLSRUHE, GERMANY A K PETERS WELLESLEY,
MASSACHUSETTS CONTENTS PREFACE XV NOTATION XVII I SOME LINEAR ALGEBRA
LINEAR SYSTEMS 1.1 MATRIX NOTATION 3 5 6 7 9 10 11 13 14 16 17 18 20 21
23 24 25 1.2 1.3 1.4 1.5 1.6 1.7 MATRIX MULTIPLICATION GAUSSIAN
ELIMINATION GAUSS-JORDAN ALGORITHM LU-FACTORIZATION CRAMER'S RULE NOTES
AND PROBLEMS LINEAR SPACES 2.1 2.2 2.3 2.4 2.5 2.6 BASIS AND DIMENSION
CHANGE OF BASES LINEAR MAPS KERNEL AND FIBERS POINT SPACES NOTES AND
PROBLEMS LEAST SQUARES 3.1 3.2 3.3 3.4 OVERDETERMINED SYSTEMS
HOMOGENEOUS SYSTEMS CONSTRAINED LEAST SQUARES LINEARIZATION VI CONTENTS
3.5 UNDERDETERMINED SYSTEMS 26 3.6 NOTES AND PROBLEMS 27 II IMAGES AND
PROJECTIONS 29 31 35 37 39 39 41 43 45 46 47 6 PERSPECTIVE DRAWINGS 6.1
HOMOGENEOUS COORDINATES 48 6.2 CENTRAL PROJECTION 49 6.3 MOVING THE
OBJECT 51 6.4 VANISHING POINTS 52 6.5 COMPLETING A PERSPECTIVE DRAWING
54 6.6 MOVING THE CAMERA 55 6.7 SPATIAL PERSPECTIVE MAPS 56 6.8 NOTES
AND PROBLEMS 57 7 THE MAPPING MATRIX 7.1 MAIN THEOREM O , 59 7.2 CAMERA
DATA 61 7.3 THE SPATIAL PERSPECTIVE 62 7.4 VANISHING POINTS OF THE
SYSTEM 62 7.5 STEREO PAIRS 67 7.6 NOTES AND PROBLEMS 68 PARALLEL
PROJECTIONS 4.1 4.2 4.3 4.4 4.5 POHLKE'S THEOREM ORTHOGONAL PROJECTIONS
COMPUTING A PARALLEL PROJECTION PROJECTING RAYS NOTES AND PROBLEMS
MOVING THE OBJECT 5.1 5.2 5.3 5.4 5.5 EUCLIDEAN MOTIONS COMPOSITE
MOTIONS EULER ANGLES COORDINATE EXTENSION NOTES AND PROBLEMS CONTENTS
RECONSTRUCTION 8.1 KNOWING THE OBJECT 71 8.2 STRAIGHT LINES IN THE IMAGE
PLANE 72 8.3 SEVERAL IMAGES 73 8.4 CAMERA CALIBRATION 75 8.5 NOTES AND
PROBLEMS ,-* 76 III AFFINE GEOMETRY 77 9 AFFINE SPACE 9.1 AFFINE
COORDINATES 9.2 AFFINE SUBSPACES 9.3 HYPERPLANES 9.4 INTERSECTION 9.5
PARALLEL BUNDLES 9.6 NOTES AND PROBLEMS 10 THE BARYCENTRIC CALCULUS 10.1
BARYCENTRIC COORDINATES 10.2 SUBSPACES 10.3 AFFINE INDEPENDENCE _ 10.4
HYPERPLANES 10.5 JOIN 10.6 VOLUMES , 10.7 A GENERALIZATION OF
BARYCENTRIC COORDINATES 10.8 NOTES AND PROBLEMS 11 AFFINE MAPS 11.1
BARYCENTRIC REPRESENTATION 11.2 AFFINE REPRESENTATION 11.3 PARALLELISM
AND RATIO 11.4 FIBERS * 11.5 AFFINITIES 11.6 CORRESPONDENCE OF
HYPERPLANES 11.7 NOTES AND PROBLEMS 79 80 82 83 84 85 86 88 89 91 92 93
95 96 99 101 102 102 104 104 105 VIII CONTENTS 12 AFFINE FIGURES 12.1
TRIANGLES 107 12.2 QUADRANGLES 109 12.3 POLYGONS AND CURVES 110 12.4
CONIC SECTIONS . 112 12.5 AXIAL AFFINITIES 114 12.6 DILATATION 117 12.7
NOTES AND PROBLEMS 118 13 QUADRICS IN AFFINE SPACES 13.1 THE EQUATION OF
A QUADRIC 120 13.2 MIDPOINTS 122 13.3 SINGULAR POINTS 124 13.4 TANGENTS
125 13.5 TANGENT PLANES 126 13.6 POLAR PLANES 127 13.7 NOTES AND
PROBLEMS 129 14 MORE ON AFFINE QUADRICS 14.1 DIAMETRIC PLANES 131 14.2
CONJUGATE DIRECTIONS 133 14.3 SPECIAL AFFINE COORDINATES 134 14.4 AFFINE
NORMAL FORMS 136 14.5 THE TYPES OF QUADRICS IN THE PLANE 138 14.6 THE
TYPES OF QUADRICS IN SPACE 139 14.7 NOTES AND PROBLEMS 141 15 HOMOTHETIC
PENCILS 15.1 THE EQUATION 143 15.2 ASYMPTOTIC CONES 144 15.3 HOMOTHETIC
PARABOLOIDS 145 15.4 INTERSECTION WITH A SUBSPACE 146 15.5 PARALLEL
INTERSECTIONS & 148 15.6 NOTES AND PROBLEMS 150 CONTENTS IX IV EUCLIDEAN
GEOMETRY 153 16 THE EUCLIDEAN SPACE 16.1 THE DISTANCE OF POINTS 155 16.2
THE DOT PRODUCT ^ 156 16.3 GRAM-SCHMIDT ORTHOGONALIZATION 158 16.4
CARTESIAN COORDINATES 159 16.5 THE ALTERNATING PRODUCT 160 16.6
EUCLIDEAN MOTIONS 161 16.7 SHORTEST DISTANCES 162 16.8 THE STEINER
SURFACE IN EUCLIDEAN SPACE 163 16.9 NOTES AND PROBLEMS 166 17 SOME
EUCLIDEAN FIGURES 17.1 THE ORTHOCENTER 168 17.2 THE INCIRCLE 169 17.3
THE CIRCUMCIRCLE 170 17.4 POWER OF A POINT 172 17.5 RADICAL CENTER 173
17.6 ORTHOGONAL SPHERES 174 17.7 CENTERS OF SIMILITUDE 175 17.8 NOTES
AND PROBLEMS 177 18 QUADRICS IN EUCLIDEAN SPACE 18.1 NORMALS 179 18.2
PRINCIPAL AXES 180 18.3 REAL AND SYMMETRIC MATRICES 181 18.4 PRINCIPAL
AXIS TRANSFORMATION 182 18.5 NORMAL FORMS OF EUCLIDEAN QUADRICS 183 18.6
NOTES AND PROBLEMS 186 19 FOCAL PROPERTIES 19.1 THE ELLIPSE " . 188
19.2 THE HYPERBOLA 190 19.3 THE PARABOLA 192 19.4 CONFOCAL CONIC
SECTIONS 193 19.5 FOCAL CONIES 195 19.6 FOCAL DISTANCES 198 CONTENTS
19.7 DUPIN'S CYCLIDE 199 19.8 NOTES AND PROBLEMS 202 V SOME PROJECTIVE
GEOMETRY 205 20 THE PROJECTIVE SPACE 20.1 HOMOGENEOUS COORDINATES 207
20.2 PROJECTIVE COORDINATES 209 20.3 THE EQUATIONS OF PLANES AND
SUBSPACES 211 20.4 THE EQUATION OF A POINT 212 20.5 PENCILS AND BUNDLES
214 20.6 DUALITY 216 20.7 NOTES AND PROBLEMS 219 21 PROJECTIVE MAPS 21.1
MATRIX NOTATION 221 21.2 EXCEPTIONAL SPACES 223 21.3 THE DUAL MAP 224
21.4 COLLINEATIONS AND CORRELATIONS 225 21.5 THE CROSSRATIO 227 21.6
HARMONIC POSITION ' 229 21.7 NOTES AND PROBLEMS 230 22 SOME PROJECTIVE 1
FIGURES 22.1 COMPLETE QUADRUPLES IN THE PLANE 231 22.2 DESARGUES'
CONFIGURATION 234 22.3 PAPPUS' CONFIGURATION 235 22.4 CONIC SECTIONS 237
22.5 PASCAL'S THEOREM 238 22.6 BRIANCHON'S THEOREM 240 22.7 RATIONAL
BEZIER CURVES * 242 22.8 RATIONAL BEZIER SURFACES 244 22.9 NOTES AND
PROBLEMS 245 23 PROJECTIVE QUADRICS 23.1 PROJECTIVE QUADRICS 247 23.2
TANGENT PLANES 248 CONTENTS XI 23.3 THE ROLE OF THE IDEAL PLANE 250 23.4
HARMONIC POINTS AND POLARITY 252 23.5 PENCILS OF QUADRICS 253 23.6
RANGES OF QUADRICS 255 23.7 THE IMAGINARY IN PROJECTIVE GEOMETRY 257
23.8 THE STEINER SURFACE ^ 260 23.9 NOTES AND PROBLEMS 262 VI SOME
DESCRIPTIVE GEOMETRY 265 24 ASSOCIATED PROJECTIONS 24.1 PLAN AND
ELEVATION 267 24.2 SIDE ELEVATION 269 24.3 SPECIAL SIDE ELEVATIONS 271
24.4 CROSS ELEVATION 273 24.5 CURVES ON SURFACES 276 24.6 CANAL SURFACE
278 24.7 THE FOUR-DIMENSIONAL SPACE 280 24.8 NOTES AND PROBLEMS 282 25
PENETRATIONS 25.1 INTERSECTIONS 284 25.2 DISTINGUISHED POINTS 286 25.3
DOUBLE POINTS ( 287 25.4 THE ORDER ' 289 25.5 BEZOUT'S THEOREM 291 25.6
DECOMPOSITIONS 292 25.7 PROJECTIONS 294 25.8 NOTES AND PROBLEMS 295 VII
BASIC ALGEBRAIC GEOMETRY 297 26 IMPLICIT CURVES AND SURFACES 26.1 PLANE
ALGEBRAIC CURVES 299 26.2 MULTIPLE POINTS 300 XII CONTENTS 26.3 EULER'S
IDENTITY 302 26.4 POLAR FORMS OF CURVES 303 26.5 ALGEBRAIC SURFACES 305
26.6 POLAR FORMS OF SURFACES 307 26.7 NOTES AND PROBLEMS 309 27
PARAMETRIC CURVES AND SURFACES 27.1 RATIONAL CURVES 310 27.2 CHANGING
THE PARAMETER 312 27.3 OSCULANTS OF A CURVE 314 27.4 BEZIER CURVES 317
27.5 SPLINES 319 27.6 OSCULANTS OF A SURFACE 321 27.7 NOTES AND PROBLEMS
324 28 SOME ELIMINATION METHODS 28.1 SYLVESTER'S METHOD 327 28.2
CAYLEY'S METHOD 329 28.3 COMPUTING CAYLEY'S MATRIX 330 28.4 DIXON'S
METHOD 331 28.5 COMPUTING DIXON'S MATRIX . 332 28.6 TRIANGULAR MATRICES
333 28.7 NOTES AND PROBLEMS 335 29 IMPLICITIZATION, INVERSION AND
INTERSECTION 29.1 PARAMETRIC CURVES IN THE PLANE 337 29.2 PARAMETRIC
SPACE CURVES 340 29.3 NORMAL CURVES 341 29.4 PARAMETRIC TENSOR PRODUCT
SURFACES 343 29.5 PARAMETRIC TRIANGULAR SURFACES 345 29.6 INTERSECTIONS
346 29.7 NOTES AND PROBLEMS 348 CONTENTS XIII VIII DIFFERENTIAL GEOMETRY
351 30 CURVES 30.1 PARAMETRIC CURVES AND ARC LENGTH 353 30.2 THE FRENET
FRAME 354 30.3 MOVING THE FRAME "' 356 30.4 THE SPHERICAL IMAGE 357 30.5
OSCULATING PLANE AND SPHERE 358 30.6 OSCULATING CURVES 361 30.7 NOTES
AND PROBLEMS 362 31 CURVES ON SURFACES 31.1 PARAMETRIC SURFACES AND ARC
ELEMENT 366 31.2 THE LOCAL FRAME 369 31.3 THE CURVATURE OF A CURVE 370
31.4 MEUSNIER'S THEOREM 371 31.5 THE DARBOUX FRAME 373 31.6 NOTES AND
PROBLEMS 374 32 SURFACES 32.1 DUPIN'S INDICATRIX AND EULER'S THEOREM 376
32.2 GAUSSIAN CURVATURE AND MEAN CURVATURE 379 32.3 CONJUGATE DIRECTIONS
AND ASYMPTOTIC LINES 381 32.4 RULED SURFACES AND DEVELOPABLES 382 32.5
CONTACT OF ORDER R 385 32.6 NOTES AND PROBLEMS 386 BIBLIOGRAPHY 389
INDEX 395 |
| any_adam_object | 1 |
| author | Böhm, Wolfgang 1928-2018 Prautzsch, Hartmut |
| author_GND | (DE-588)119040956 |
| author_facet | Böhm, Wolfgang 1928-2018 Prautzsch, Hartmut |
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| isbn | 1568810040 |
| language | English |
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| spelling | Böhm, Wolfgang 1928-2018 Verfasser (DE-588)119040956 aut Geometric concepts for geometric design Wolfgang Boehm ; Hartmut Prautzsch Wellesley, Mass. Peters 1994 XVII, 393 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. [389] - 393 Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 s DE-604 Prautzsch, Hartmut Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006373866&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Böhm, Wolfgang 1928-2018 Prautzsch, Hartmut Geometric concepts for geometric design Geometrische Modellierung (DE-588)4156717-1 gnd |
| subject_GND | (DE-588)4156717-1 |
| title | Geometric concepts for geometric design |
| title_auth | Geometric concepts for geometric design |
| title_exact_search | Geometric concepts for geometric design |
| title_full | Geometric concepts for geometric design Wolfgang Boehm ; Hartmut Prautzsch |
| title_fullStr | Geometric concepts for geometric design Wolfgang Boehm ; Hartmut Prautzsch |
| title_full_unstemmed | Geometric concepts for geometric design Wolfgang Boehm ; Hartmut Prautzsch |
| title_short | Geometric concepts for geometric design |
| title_sort | geometric concepts for geometric design |
| topic | Geometrische Modellierung (DE-588)4156717-1 gnd |
| topic_facet | Geometrische Modellierung |
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