Handbook of computer aided geometric design:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2002
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXVIII, 820 S. Ill., graph. Darst. |
| ISBN: | 0444511040 |
Internformat
MARC
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| 245 | 1 | 0 | |a Handbook of computer aided geometric design |c edited by Gerald Farin, Josef Hoschek, Myung-Soo Kim |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2002 | |
| 300 | |a XXVIII, 820 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a CAD |2 gtt | |
| 650 | 7 | |a Computergraphics |2 gtt | |
| 650 | 4 | |a Conception assistée par ordinateur | |
| 650 | 7 | |a Geometrische methoden |2 gtt | |
| 650 | 4 | |a Infographie | |
| 650 | 4 | |a Computer graphics | |
| 650 | 4 | |a Computer-aided design | |
| 650 | 0 | 7 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Farin, Gerald E. |d 1953- |e Sonstige |0 (DE-588)109438760 |4 oth | |
| 700 | 1 | |a Hoschek, Josef |d 1935-2002 |e Sonstige |0 (DE-588)138372896 |4 oth | |
| 700 | 1 | |a Kim, Myung-Soo |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009883320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-009883320 | |
Datensatz im Suchindex
| _version_ | 1807591448470618112 |
|---|---|
| adam_text |
Contents
Preface v
Contributors xxiii
1 A History of Curves and Surfaces in CAGD (G. Farin) 1
1.1 INTRODUCTION 1
1.2 EARLY DEVELOPMENTS 2
1.3 DE CASTELJAU AND BEZIER 4
1.4 PARAMETRIC CURVES 6
1.5 RECTANGULAR SURFACES 8
1.6 B SPLINE CURVES AND NURBS 9
1.7 TRIANGULAR PATCHES 10
1.8 SUBDIVISION SURFACES 11
1.9 SCIENTIFIC APPLICATIONS 12
1.10 SHAPE 13
1.11 INFLUENCES AND APPLICATIONS 14
2 Geometric Fundamentals (W. Boehm and H. Prautzsch) 23
2.1 AFFINE FUNDAMENTALS 23
2.1.1 Points and vectors 23
2.1.2 Affine systems 23
2.1.3 Barycentric coordinates 24
2.1.4 Affine subspaces and parallelism 24
2.1.5 Affine maps and axonometric images 25
2.1.6 Affine combinations and A frame 26
2.2 CONIC SECTIONS AND QUADRICS 27
2.2.1 Quadrics in affine space 27
2.2.2 Tangents and polar planes 28
2.2.3 Pascal's and Brianchon's theorems 29
2.3 THE EUCLIDEAN SPACE 30
2.3.1 Cartesian coordinates 30
2.3.2 Gram Schmidt orthogonalization 30
2.3.3 Euclidean motions and orthogonal projections 31
2.3.4 Quadrics in Euclidean space 32
2.4 PROJECTIVE FUNDAMENTALS 32
vii
viii
2.4.1 Homogeneous coordinates 32
2.4.2 Projective coordinates 33
2.4.3 Projective maps 33
2.4.4 The procedure of inhomogeneizing 34
2.4.5 Repeated projective combinations 34
2.4.6 Quadrics in projective space 34
2.4.7 Parametrizing a quadric and its equation 35
2.5 DUALITY 35
2.6 OSCULATING CURVES AND SURFACES 36
2.6.1 Curve and surface 36
2.6.2 Curve and curve 37
2.6.3 Surface and surface 37
2.6.4 Contur lines, reflection lines and isophotes 37
2.7 DIFFERENTIAL FUNDAMENTALS 38
2.7.1 Arc length and osculating plane 38
2.7.2 Curvature and torsion 39
2.7.3 The Frenet frame 39
2.7.4 Curves on surfaces 39
2.7.5 Meusnier's sphere and Dupin's indicatrix 40
2.7.6 The curvatures of a surface 41
3 Geometries for CAGD (H. Pottmann and S. Leopoldseder) 43
3.1 CURVES AND SURFACES IN PROJECTIVE GEOMETRY 44
3.1.1 Bezier curves and surfaces as images of normal curves and surfaces 44
3.1.2 NURBS curves and surfaces in projective geometry 46
3.1.3 Duality and dual representation 47
3.1.4 Developable surfaces as dual curves 49
3.2 SPHERE GEOMETRIES 50
3.2.1 Models of Laguerre geometry 50
3.2.2 Mobius geometry 53
3.2.3 Applications of the cyclographic image of a curve in 3 space . 54
3.2.4 The medial axis transform in a sphere geometric approach 55
3.2.5 Canal surfaces (in Laguerre and Mobius geometry) 56
3.2.6 Rational curves and surfaces with rational offsets 58
3.3 LINE GEOMETRY 60
3.3.1 Basics of line geometry . . . ." 60
3.3.2 Linear complexes in kinematics and reverse engineering 61
3.3.3 Ruled surfaces 62
3.3.4 Other applications of line geometry in geometric computing . 63
3.4 APPROXIMATION IN SPACES OF GEOMETRIC OBJECTS 63
3.4.1 Approximation in the space of spheres 64
3.4.2 Approximation in the space of planes 64
3.4.3 Approximation in line space 64
3.5 NON EUCLIDEAN GEOMETRIES 65
3.5.1 Hyperbolic geometry and geometric topology 65
ix
3.5.2 Elliptic geometry and kinematics 66
3.5.3 Isotropic geometry and analysis of functions and images 66
4 Bezier Techniques (D. Hansford ) 75
4.1 WHY BEZIER TECHNIQUES? 75
4.2 BEZIER CURVES 76
4.2.1 Parametric curves 76
4.2.2 Properties of Bezier curves 77
4.2.3 The de Casteljau algorithm for Bezier curves 80
4.2.4 Bernstein polynomials 81
4.2.5 Derivatives of Bezier curves 83
4.2.6 Degree elevation of Bezier curves 85
4.2.7 Interrogation techniques for Bezier curves 85
4.2.8 Basis conversion 86
4.2.9 Piecewise Bezier curves 87
4.3 RECTANGULAR BEZIER PATCHES 88
4.3.1 Bilinear patches 89
4.3.2 Bezier patches 90
4.3.3 Properties of Bezier patches 91
4.3.4 Evaluation of Bezier patches 93
4.3.5 Derivatives of Bezier patches 93
4.3.6 Working with Bezier patches 95
4.3.7 C1 Bezier patches 96
4.4 TRIANGULAR BEZIER PATCHES 97
4.4.1 Bezier triangles introduced 97
4.4.2 Properties of Bezier triangles 98
4.4.3 The de Casteljau algorithm for Bezier triangles 100
4.4.4 Bivariate Bernstein polynomials 100
4.4.5 Derivatives of Bezier triangles 102
4.4.6 Working with Bezier triangles 103
4.4.7 C1 Bezier triangles 104
5 Rational Techniques (H.J. Wolters) 111
5.1 INTRODUCTION Ill
5.2 RATIONAL BEZIER CURVES 112
5.2.1 Basic definitions 112
5.2.2 Derivatives 114
5.2.3 Fundamental algorithms 115
5.2.4 Conies 117
5.3 RATIONAL B SPLINE CURVES 118
5.3.1 Basic definitions 119
5.3.2 Derivatives 120
5.3.3 Fundamental algorithms 121
5.4 GEOMETRIC CONTINUITY FOR RATIONAL CURVES 122
5.5 RATIONAL CURVE APPROXIMATION AND INTERPOLATION . 123
X
5.5.1 Rational curve interpolation 124
5.5.2 Rational curve approximation 126
5.6 RATIONAL BEZIER SURFACES 127
5.6.1 Basic definitions 127
5.6.2 Derivatives 129
5.6.3 Algorithms 130
5.7 RATIONAL B SPLINE SURFACES 131
5.7.1 Basic definitions 131
5.7.2 Derivatives 131
5.7.3 Algorithms 133
5.8 GEOMETRIC CONTINUITY FOR RATIONAL PATCHES 133
5.9 INTERPOLATION AND APPROXIMATION ALGORITHMS 134
5.10 RATIONAL SURFACE CONSTRUCTIONS 136
5.10.1 Surfaces of revolution 136
5.10.2 Canal and pipe surfaces 136
5.11 CONCLUDING REMARKS 137
6 Spline Basics (C. de Boor) 141
6.1 PIECEWISE POLYNOMIALS 141
6.2 B SPLINES DEFINED 141
6.3 SUPPORT AND POSITIVITY 143
6.4 SPLIINE SPACES DEFINED 144
6.5 SPECIFIC KNOT SEQUENCES 145
6.6 THE POLYNOMIALS IN THE SPLINE SPACE: MARSDEN'S IDENTITY147
6.7 THE PIECEWISE POLYNOMIALS IN THE SPLINE SPACE 148
6.8 DUAL FUNCTIONALS AND BLOSSOMS 151
6.9 GOOD CONDITION 152
6.10 CONVEX HULL 152
6.11 DIFFERENTIATION AND INTEGRATION 153
6.12 EVALUATION 154
6.13 SPLINE FUNCTIONS VS SPLINE CURVES 155
6.14 KNOT INSERTION 156
6.15 VARIATION DIMINUTION AND SHAPE PRESERVATION: SCHOEN
BERG'S OPERATOR 158
6.16 ZEROS OF A SPLINE, COUNTING MULTIPLICITY 159
6.17 SPLINE INTERPOLATION: SCHOENBERG WHITNEY 159
6.18 SMOOTHING SPLINE 161
6.19 LEAST SQUARES SPLINE APPROXIMATION 161
6.20 BACKGROUND 162
7 Curve and Surface Constructions (D. Hansford and G. Farin) 165
7.1 INTRODUCTION 165
7.2 POLYNOMIAL CURVE METHODS 165
7.2.1 Point Data Interpolation 166
7.2.2 Point Data Approximation 170
xi
7.2.3 Point and Tangent Data Interpolation 173
7.3 C2 CUBIC SPLINE INTERPOLATION 175
7.3.1 End Conditions 177
7.3.2 Defining a Knot Sequence 178
7.3.3 The Minimum Property 179
7.4 POLYNOMIAL SURFACE METHODS 179
7.4.1 Discrete Coons Patches 179
7.4.2 Tensor Product Interpolation 181
7.4.3 Approximation with Tensor Product Patches 182
7.4.4 Bicubic Hermite Patches 185
7.5 C2 BICUBIC SPLINE INTERPOLATION 186
7.5.1 Finding Knot Sequences 187
7.6 VOLUME DEFORMATIONS 188
8 Geometric Continuity (J. Peters) 193
8.1 MOTIVATING EXAMPLES 193
8.1.1 Differentiation and evaluation 197
8.2 GEOMETRIC CONTINUITY OF PARAMETRIC CURVES/SURFACES 198
8.2.1 Joining parametric curve pieces 199
8.2.2 Geometric continuity of edge adjacent patches 200
8.2.3 Geometric continuity at a vertex 202
8.2.4 Free form surface splines 209
8.3 EQUIVALENT AND ALTERNATIVE DEFINITIONS 210
8.3.1 Matching intrinsic curve properties 210
8.3.2 Ck manifolds 212
8.3.3 Tangent and normal continuity 212
8.3.4 Global and regional reparametrization 214
8.3.5 Implicit representation 217
8.3.6 Generalized subdivision 217
8.4 CONSTRUCTIONS 218
8.4.1 Free form surface splines of low degree 220
8.5 ADDITIONAL LITERATURE 220
9 Splines on Surfaces (M. Neamtu) 229
9.1 INTRODUCTION 229
9.2 SCALAR SPLINES ON SMOOTH SURFACES 236
9.3 ALTERNATIVE METHODS FOR FUNCTIONS ON SURFACES 246
9.3.1 Discrete surfaces 246
9.3.2 Radial basis functions 246
9.3.3 Variational methods 247
9.3.4 Distance weighting methods 247
9.3.5 Transfmite methods 247
9.3.6 Implicit methods 248
9.3.7 Other types of splines 248
9.3.8 Multiresolution methods 248
xii
9.3.9 Visualization of surfaces on surfaces 248
10 Box Splines (H. Prautzsch and W. Boehm) 255
10.1 BOX SPLINES 255
10.1.1 Inductive definition 255
10.1.2 Geometric definition 256
10.1.3 Further definitions of Box splines 257
10.1.4 Basic properties of Box splines 258
10.1.5 Derivatives 259
10.2 BOX SPLINE SURFACES 260
10.2.1 Translates of Box splines 260
10.2.2 Derivatives and polynomial properties 262
10.2.3 Convexity 262
10.2.4 Subdivision 263
10.2.5 General subdivision 264
10.2.6 Convergence under subdivision 265
10.2.7 Bezier representation 266
10.2.8 Bezier representation of symmetric Box splines 268
10.2.9 Generalized Box spline surfaces 269
10.3 HALF BOX SPLINES 272
10.3.1 Inductive definition 272
10.3.2 Basic properties 273
10.3.3 Derivatives and polynomial structure 274
10.4 HALF BOX SPLINE SURFACES 275
10.4.1 Translates of Half Box splines 275
10.4.2 Derivatives and polynomial properties 276
10.4.3 Subdivision 276
10.4.4 Bezier representation 278
10.4.5 Generalized Half Box spline surfaces 278
11 Finite Element Approximation with Splines (K. Hollig) 283
11.1 INTRODUCTION 283
11.2 SPLINES ON UNIFORM GRIDS 285
11.2.1 Uniform B splines 285
11.2.2 Splines on bounded domains 286
11.2.3 Hierarchical bases 287
11.3 FINITE ELEMENT BASES 289
11.3.1 Mesh based elements 289
11.3.2 WEB basis 290
11.3.3 R functions 293
11.3.4 Stability 295
11.4 APPROXIMATION OF BOUNDARY VALUE PROBLEMS 296
11.4.1 Essential boundary conditions 296
11.4.2 Natural boundary conditions 298
11.4.3 Mixed and higher order boundary conditions 299
xiii
11.4.4 Error estimates 301
11.4.5 Implementation 302
11.5 SUMMARY 304
12 Subdivision Surfaces (M. Sabin) 309
12.1 SUBDIVISION SURFACE DEFINITIONS 309
12.2 INTRODUCTION SUBDIVISION CURVES 309
12.2.1 The Chaikin construction 309
12.2.2 Higher degree splines 310
12.2.3 The 4 point interpolatory scheme 312
12.3 BOX SPLINES 312
12.4 GENERALIZATIONS TO ARBITRARY TOPOLOGY 313
12.5 SOME SPECIFIC SCHEMES 313
12.5.1 The Doo Sabin quadratic scheme 313
12.5.2 The Catmull Clark cubic scheme 314
12.5.3 The Loop triangular mesh scheme 314
12.5.4 The Butterfly interpolatory scheme 314
12.6 ANALYSIS OF CONTINUITY AT THE SINGULARITIES 315
12.6.1 Support 315
12.6.2 Regular regions 315
12.6.3 Neighbourhoods of singularities 316
12.6.4 Limit point 317
12.6.5 Natural configuration and characteristic map 318
12.6.6 Curvatures 318
12.6.7 Tuning subdivisions for better behaviour 319
12.6.8 Jordan blocks 319
12.6.9 Discontinuities of curvature 320
12.6.10 Higher derivatives 320
12.6.11 Precision set 320
12.7 FIRST STEP ARTIFACTS 320
12.8 CURRENT RESEARCH DIRECTIONS 321
12.8.1 Square root of 3 scheme 321
12.8.2 Subdivision over semiregular lattices 321
12.8.3 Dual schemes and contact elements 321
12.8.4 Unequal intervals 322
12.8.5 Artifact analysis 323
12.9 CONCLUSIONS 323
13 Interrogation of Subdivision Surfaces (M. Sabin) 327
13.1 SUBDIVISION SURFACE INTERROGATIONS 327
13.2 HISTORICAL BACKGROUND 328
13.3 THE CONVEX HULL PROPERTY 329
13.3.1 Other hulls 329
13.3.2 Hulls of non positive bases 331
13.3.3 Normal hulls 331
xiv
13.3.4 Offset subdivision surfaces 332
13.4 AN API FOR SUBDIVISION SURFACES 332
13.5 EXAMPLE INTERROGATIONS 333
13.5.1 Z buffer imaging 333
13.5.2 Raycast 333
13.5.3 Plane section 335
13.5.4 Surface surface intersection 336
13.5.5 Silhouette 337
13.6 PERFORMANCE ISSUES 338
13.7 CONCLUSIONS 340
14 Multiresolution Techniques (L.P. Kobbelt) 343
14.1 INTRODUCTION 343
14.2 MULTIRESOLUTION REPRESENTATIONS FOR CURVES 344
14.3 LIFTING 347
14.4 GEOMETRIC SETTING 349
14.5 MULTIRESOLUTION REPRESENTATIONS FOR SURFACES 350
14.5.1 Coarse to fine hierarchies 350
14.5.2 Fine to coarse hierarchies 353
14.6 APPLICATIONS 357
14.6.1 Multiresolution editing 357
14.6.2 Geometry compression 358
15 Algebraic Methods for Computer Aided Geometric Design
(T. W. Sederberg and J. Zheng) 363
15.1 INTRODUCTION 363
15.2 POLYNOMIALS, IDEALS, AND VARIETIES 364
15.2.1 Notation and terminology 364
15.2.2 Ideals and varieties 366
15.2.3 Grobner bases 366
15.3 RESULTANTS 367
15.3.1 Sylvester's resultant 367
15.3.2 Bezout's resultant 368
15.3.3 Dixon's resultant 369
15.4 CURVE IMPLICITIZATION AND INVERSION 370
15.4.1 Resultant based method 370
15.4.2 Grobner basis technique 371
15.4.3 Moving curve technique 372
15.5 CURVE PARAMETRIZATION 373
15.5.1 Planar algebraic curves 373
15.5.2 Genus and rationality 374
15.5.3 Parametrizing curves 374
15.6 INTERSECTION COMPUTATIONS 377
15.6.1 Parametric curve and implicit curve 377
15.6.2 Implicit curve and implicit curve 378
XV
15.6.3 Parametric curve and parametric curve 379
15.7 SURFACES 380
15.7.1 Implicit degree of a rational parametric surface 381
15.7.2 Surface intersection curves 382
15.7.3 Implicitization 382
15.7.4 Parametrizaion 383
15.8 OTHER ISSUES 384
16 Scattered Data Interpolation: Radial Basis and Other Methods
(S.K. Lodha and R. Franke) 389
16.1 INTRODUCTION 389
16.2 RADIAL INTERPOLATION 390
16.2.1 Existence and uniqueness 392
16.2.2 Computation of the interpolant 393
16.2.3 Evaluation 396
16.2.4 Applications 397
16.3 OTHER LOCAL METHODS 399
16.4 CONCLUSIONS 401
17 Pythagorean Hodograph Curves (R.T. Farouki) 405
17.1 PREAMBLE 405
17.2 POLYNOMIAL PH CURVES 406
17.2.1 Planar PH curves 407
17.2.2 Complex representation 408
17.2.3 PH space curves 410
17.3 CONSTRUCTION ALGORITHMS 412
17.3.1 PH quintic Hermite interpolants 412
17.3.2 Shape properties of PH quintics 414
17.3.3 C2 PH quintic splines 414
17.3.4 Spatial PH quintic Hermite interpolants 416
17.3.5 Geometric Hermite interpolants 417
17.3.6 Further constructions 417
17.4 REAL TIME CNC INTERPOLATORS 417
17.5 RATIONAL CURVES WITH RATIONAL OFFSETS 419
17.5.1 Rational PH curves 419
17.5.2 Improper parameterizations 421
17.6 MINKOWSKI PH CURVES 421
17.6.1 Minkowski metric of special relativity 421
17.6.2 Minkowski metric defined by convex indicatrix 422
17.7 CLOSURE 423
18 Voronoi Diagrams (K. Sugihara) 429
18.1 ORDINARY VORONOI DIAGRAM 429
18.2 DELAUNAY DIAGRAM 431
18.3 BASIC PROPERTIES OF THE VORONOI AND DELAUNAY DIAGRAMS432
xvi
18.4 ALGORITHMS 433
18.5 APPLICATIONS 435
18.5.1 Site retrieval 435
18.5.2 Medial axis 435
18.5.3 Offset curves and surfaces 436
18.5.4 Interpolation 437
18.6 EXTENSIONS 441
18.6.1 Voronoi diagrams for general distances 441
18.6.2 Additively weighted Voronoi diagram 441
18.6.3 Multiplicatively weighted Voronoi diagram 441
18.6.4 Power diagram 442
18.6.5 Voronoi diagram based on Lp distance 444
18.6.6 Voronoi diagram based on elliptic distance 444
18.6.7 Obstacle avoidance Voronoi diagram 445
18.6.8 Voronoi diagram in a river 446
18.6.9 Crystal Voronoi diagram 446
18.6.10 Voronoi diagram for lines and polygons 446
18.6.11 Voronoi diagram for general figures 448
18.7 CONCLUSION 448
19 The Medial Axis Transform (H.I. Choi and C.Y. Han) 451
19.1 INTRODUCTION 451
19.2 MATHEMATICAL THEORY OF THE MEDIAL AXIS TRANSFORM . . 453
19.2.1 Assumptions on the domain 453
19.2.2 Medial axis transform 455
19.2.3 Finiteness results 457
19.2.4 Graph structure of medial axis transform 458
19.2.5 Domain decomposition lemma 458
19.3 ALGORITHMS 460
19.3.1 Piecewise linear and circular arc boundary 460
19.3.2 Domains with free form boundaries 461
19.3.3 Global decomposition algorithm 462
19.4 CONCLUDING REMARKS 464
20 Solid Modeling (V. Shapiro) 473
20.1 INTRODUCTION 473
20.1.1 A premise of informational completeness 473
20.1.2 Outline 474
20.2 MATHEMATICAL MODELS 475
20.2.1 First postulates 475
20.2.2 Continuum point set model of solidity 476
20.2.3 Combinatorial model of solidity 477
20.2.4 Generalizations 480
20.3 COMPUTER REPRESENTATIONS 480
20.3.1 Implicit and constructive 481
xvii
20.3.2 Enumerative and combinatorial 485
20.3.3 Boundary representation: a compromise 488
20.3.4 Unification of representation schemes 490
20.4 ALGORITHMS 491
20.4.1 Fundamental computations 491
20.4.2 Enabling algorithms 494
20.5 APPLICATIONS 497
20.5.1 Geometric design 498
20.5.2 Analysis and simulation 498
20.5.3 Dynamic analysis and lumped parameter systems 500
20.5.4 Planning and generation 500
20.5.5 Manufacturing 501
20.6 SYSTEMS 502
20.6.1 Classical systems 502
20.6.2 Parametric interaction 503
20.6.3 Standards and interfaces 505
20.7 CONCLUSIONS 506
20.7.1 Unsolved problems and promising directions 506
20.7.2 Summary 510
21 Parametric Modeling (CM. Hoffmann and R. Joan Arinyo) 519
21.1 INTRODUCTION 519
21.2 PARAMETRIC MODELS 520
21.3 VARIANT MODELING 521
21.4 CONSTRAINT BASED MODELING 522
21.4.1 Constraints 522
21.4.2 Modeling with constraints 522
21.4.3 Solving geometric and equational constraints 523
21.4.4 Degrees of freedom analysis 526
21.5 FEATURE BASED MODELING 527
21.5.1 Features and the feature model 527
21.5.2 A brief feature taxonomy 528
21.5.3 Feature model construction 528
21.5.4 Feature representation 530
21.5.5 Features and constraints 531
21.6 TRENDS 531
21.6.1 Feature libraries 532
21.6.2 Multiple views 532
21.6.3 Semantic features 533
21.6.4 Persistent naming 534
21.7 OPEN PROBLEMS 535
21.7.1 Constraint solving 535
21.7.2 Features 535
21.7.3 Semantics of parametric design 535
21.7.4 Assembly centric design 536
xviii
22 Sculptured Surface NC Machining
(B.K. Choi, B.H. Kim, and KB. Jerard) 543
22.1 INTRODUCTION 543
22.1.1 Overview of the sculptured surface machining process 543
22.1.2 Information processing issues 545
22.2 UNIT MACHINING OPERATIONS 547
22.2.1 Tool path topology and milling strategy options 548
22.2.2 Ball endmill UMOs 548
22.2.3 Flat endmill UMOs 549
22.3 INTERFERENCE HANDLING 550
22.3.1 CL point interference 551
22.3.2 CL line interference 551
22.3.3 Collisions 552
22.4 TOOL PATH GENERATION METHODS 552
22.4.1 The conventional approach and the C space approach 552
22.4.2 Geometric issues in conventional approach 555
22.4.3 Geometric issues in the C space approach 557
22.5 GEOMETRIC ALGORITHMS 558
22.5.1 CL surface construction 558
22.5.2 2D PS curve offsetting 561
22.5.3 Area scan algorithm 564
22.5.4 Point sequence curve fairing 567
22.5.5 Collision detection algorithms 572
22.6 CONCLUSION 572
23 Cyclides (W. Degen) 575
23.1 INTRODUCTION 575
23.2 THE GEOMETRY OF DUPIN CYCLIDES 576
23.2.1 Dupin cyclides in classical differential geometry 576
23.2.2 The three main types of Dupin cyclides and their parameter repre¬
sentations 578
23.2.3 Implicit equations 582
23.3 SUPERCYCLIDES 583
23.3.1 Curves and surfaces in the projective space 583
23.3.2 Basic properties of supercyclides 583
23.4 CYCLIDES IN CAGD 586
23.4.1 Bezier representation of cyclides 586
23.4.2 Using cyclides as blendings 588
23.4.3 Blending with supercyclides 591
23.5 APPENDIX: STUDYING DUPIN CYCLIDES WITH LIE GEOMETRY . 593
24 Geometry Processing (T.A. Grandine) 603
24.1 INTRODUCTION 603
24.2 ROOT FINDING 604
24.3 INTEGRATION 613
xix
24.4 COMPUTING MASS PROPERTIES 618
25 Intersection Problems (N.M. Patrikalakis and T. Maekawa) 623
25.1 INTRODUCTION 623
25.2 CLASSIFICATION OF INTERSECTION PROBLEMS 624
25.2.1 Classification by dimension 624
25.2.2 Classification by type of geometric specification 624
25.2.3 Classification by number system 625
25.3 OVERVIEW OF NONLINEAR SOLVERS 625
25.3.1 Brief review of local and global methods 625
25.3.2 IPP algorithm 627
25.4 CURVE/SURFACE INTERSECTION 632
25.4.1 RPP curve/IA surface intersection 632
25.4.2 RPP curve/RPP surface intersection 633
25.4.3 IA curve/IA surface intersection 633
25.4.4 IA curve/RPP surface intersection 634
25.5 SURFACE/SURFACE INTERSECTIONS 634
25.5.1 RPP/IA surface intersection 634
25.5.2 RPP/RPP surface intersection 639
25.5.3 IA/IA surface intersection 642
25.6 CONCLUSION 642
26 Reverse Engineering (T. Varady and R. Martin) 651
26.1 INTRODUCTION 651
26.2 THE BASIC PHASES OF REVERSE ENGINEERING 652
26.3 DATA CAPTURE 653
26.3.1 Laser scanners 654
26.3.2 Multiple view registration 654
26.4 TRIANGULATION AND DECIMATION 654
26.4.1 Triangulation overview 655
26.4.2 Kos's method 655
26.5 RECONSTRUCTING FREE FORM OBJECTS 656
26.5.1 Segmentation strategies 656
26.5.2 Fitting free form surfaces 659
26.5.3 Fitting feature surfaces 662
26.6 RECONSTRUCTING CONVENTIONAL ENGINEERING OBJECTS . . 663
26.6.1 Segmentation 663
26.6.2 Fitting analytic surfaces 665
26.6.3 Fitting extruded and rotational surfaces 667
26.6.4 Constrained fitting for multiple curves and surfaces 668
26.6.5 Reconstructing blend surfaces 672
26.6.6 Building solid models 673
26.6.7 Beautifying solid models 675
26.7 CONCLUSION 676
XX
27 Vector and Tensor Field Visualization (G. Scheuermann and H. Hagen) 683
27.1 INTRODUCTION 683
27.2 VISUALIZATION PROCESS 684
27.3 DATA SET TYPES AND INTERPOLATION METHODS 685
27.4 DIRECT MAPPINGS TO GEOMETRIC PRIMITIVES 686
27.4.1 Point based methods 686
27.4.2 Line based methods 687
27.4.3 Surface and volume based methods 690
27.5 ATTRIBUTE MAPPINGS 691
27.6 STRUCTURE AND FEATURE BASED MAPPINGS 692
27.6.1 Vector field topology 692
27.6.2 Tensor field topology 694
27.6.3 Feature detection algorithms 695
28 Splines over Triangulations (F. Zeilfelder and H. P. Seidel) 701
28.1 INTRODUCTION 701
28.2 BERNSTEIN BEZIER TECHNIQUES 702
28.3 DIMENSION 704
28.4 FINITE AND MACRO ELEMENTS 708
28.5 INTERPOLATION 710
28.6 TRIANGULAR B SPLINES 714
29 Kinematics and Animation (B. Jiittler and M.G. Wagner) 723
29.1 INTRODUCTION 723
29.2 THE KINEMATICAL MAPPING 724
29.2.1 Coordinates 724
29.2.2 Motions of a rigid body 724
29.2.3 Euler parameters 726
29.2.4 The kinematical mapping 727
29.3 QUATERNIONS 727
29.3.1 Fundamentals 727
29.3.2 Homogeneous quaternions and the kinematical mapping 728
29.3.3 Summary: homogeneous quaternion coordinates for 3D rotations . . 729
29.4 MOTION DESIGN USING CURVES ON S3 729
29.4.1 Slerping 730
29.4.2 Problems of slerping 731
29.4.3 Other approaches 731
29.4.4 Motion design desired features 731
29.5 SPHERICAL RATIONAL MOTIONS 732
29.6 SPATIAL RATIONAL MOTIONS 735
29.6.1 Construction 735
29.6.2 Special cases 737
29.6.3 Affine control structure 737
29.6.4 Some properties 739
29.6.5 Interpolation schemes and applications 741
xxi
29.6.6 Rational frames and sweeping surfaces 744
29.7 CLOSURE 745
30 Direct Rendering of Freeform Surfaces (G. Elber) 749
30.1 INTRODUCTION 749
30.2 SCAN CONVERSION OF CURVES 751
30.2.1 Forward differencing 751
30.2.2 Adaptive forward differencing 752
30.3 SURFACE COVERAGE AND RENDERING USING CURVES 753
30.3.1 Coverage based on adaptive isoparametric curves 756
30.3.2 Rendering using adaptive isoparametric curves 757
30.4 RAY TRACING 759
30.4.1 Bezier clipping 759
30.4.2 Ruled tracing 761
30.5 EXTENSIONS 765
30.5.1 Isometric texture mapping 765
30.5.2 Machining using adaptive isoparametric curves 770
30.5.3 Line art rendering 770
30.6 CONCLUSION 773
31 Modeling and Processing with Quadric Surfaces (W. Wang) 777
31.1 DEFINITION AND CLASSIFICATIONS 777
31.1.1 Definition 777
31.1.2 Euclidean classification 778
31.1.3 Affine classification 779
31.1.4 Projective classification 779
31.2 PARAMETRIC REPRESENTATION 780
31.2.1 Global rational parameterization 780
31.2.2 Generalized stereographic projection 782
31.2.3 Surface patches on quadrics 784
31.3 FITTING, BLENDING, AND OFFSETTING 785
31.3.1 Fitting 785
31.3.2 Blending 786
31.3.3 Offsetting 788
31.4 INTERSECTION AND INTERFERENCE 789
31.4.1 Computation of intersection curves 789
31.4.2 Detecting interference 792
31.5 ACKNOWLEDGMENTS 792
Index 797 |
| any_adam_object | 1 |
| author_GND | (DE-588)109438760 (DE-588)138372896 |
| building | Verbundindex |
| bvnumber | BV014497553 |
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| dewey-full | 006.6 |
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| dewey-sort | 16.6 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Technik Architektur Informatik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV014497553 |
| illustrated | Illustrated |
| indexdate | 2024-08-17T00:12:18Z |
| institution | BVB |
| isbn | 0444511040 |
| language | English |
| lccn | 2002069649 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009883320 |
| oclc_num | 49719297 |
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| owner_facet | DE-703 DE-522 DE-91 DE-BY-TUM DE-634 DE-188 DE-739 DE-B1550 |
| physical | XXVIII, 820 S. Ill., graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Elsevier |
| record_format | marc |
| spelling | Handbook of computer aided geometric design edited by Gerald Farin, Josef Hoschek, Myung-Soo Kim 1. ed. Amsterdam [u.a.] Elsevier 2002 XXVIII, 820 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index CAD gtt Computergraphics gtt Conception assistée par ordinateur Geometrische methoden gtt Infographie Computer graphics Computer-aided design Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 s DE-604 Farin, Gerald E. 1953- Sonstige (DE-588)109438760 oth Hoschek, Josef 1935-2002 Sonstige (DE-588)138372896 oth Kim, Myung-Soo Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009883320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Handbook of computer aided geometric design CAD gtt Computergraphics gtt Conception assistée par ordinateur Geometrische methoden gtt Infographie Computer graphics Computer-aided design Geometrische Modellierung (DE-588)4156717-1 gnd |
| subject_GND | (DE-588)4156717-1 |
| title | Handbook of computer aided geometric design |
| title_auth | Handbook of computer aided geometric design |
| title_exact_search | Handbook of computer aided geometric design |
| title_full | Handbook of computer aided geometric design edited by Gerald Farin, Josef Hoschek, Myung-Soo Kim |
| title_fullStr | Handbook of computer aided geometric design edited by Gerald Farin, Josef Hoschek, Myung-Soo Kim |
| title_full_unstemmed | Handbook of computer aided geometric design edited by Gerald Farin, Josef Hoschek, Myung-Soo Kim |
| title_short | Handbook of computer aided geometric design |
| title_sort | handbook of computer aided geometric design |
| topic | CAD gtt Computergraphics gtt Conception assistée par ordinateur Geometrische methoden gtt Infographie Computer graphics Computer-aided design Geometrische Modellierung (DE-588)4156717-1 gnd |
| topic_facet | CAD Computergraphics Conception assistée par ordinateur Geometrische methoden Infographie Computer graphics Computer-aided design Geometrische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009883320&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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