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Farin G. — Curves and surfaces for computer aided geometric design
Farin G. — Curves and surfaces for computer aided geometric design

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Название: Curves and surfaces for computer aided geometric design

Автор: Farin G.

Аннотация:

This unified treatment of curve and surface design concepts is the Fourth Edition of the popular text, Curves and Surfaces for Computer-Aided Geometric Design, Third Edition (Academic Press, 1992). Assuming only a background in calculus and basic linear algebra, this revised and updated classic is highly accessible and should be of interest to a wide audience; from computer graphics hobbyists to software developers for CAD/CAM systems. The author's informal style makes this book very reader-friendly, and the IBM disk included in the back of the book will allow the user to gain first-hand experience with the concepts as they are explained.
This book focuses on Bezier and B-spline methods for curves, rational Bezier and B-spline curves, geometric continuity, spline interpolation, and Coons methods. In this Fourth Edition, the content has been thoroughly revised and updated to include a new chapter on recursive subdivision, new material on nonrectangular topology, surface faceting, stereo lithography, and new sections on triangulations and scattered data interpolants. The disk provided in the back of the book has also been updated to include all of the data sets and the C code used in the book.

Features:
- Covers tensor product Bezier surfaces
- Includes a chapter on recursive subdivisions
- Incorporates new material on surface faceting, stereo lithography, and nonrectangular topology
- Provides many C programs and data sets on the IBM disk included with the book


Язык: en

Рубрика: Computer science/Вычислительная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: fourth edition

Год издания: 1997

Количество страниц: 429

Добавлена в каталог: 16.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abi — Ezzi, S.      94
Absolute curvature      367
Ackland, T.      119
Adaptive forward differencing      94
Adini’s twist      262
Affine, combination      13
Affine, domain transformation      90
Affine, geometry      196
Affine, invariance      21 24 34 47 83 104 109 117
Affine, invariance of Bezier curves      36
Affine, invariance of Bezier patches      239
Affine, invariance of Bezier triangles      281
Affine, map      16 31
Affine, pair      292 308
Affine, parameter transformation      132 133
Affine, reparametrization      72
Affine, space      12
Aitken, A.      81
Aitken’s algorithm      83 230
Akima, H.      119
Akima’s interpolant      121
Albrecht, G.      298
Alfeld, P.      295 303
Andersson, R.      369
Approximation      163
Arc length      129 172 181 192 371
Arc length of surface curve      349
Arc length, parametrization      211
Area of triangle      24
Area, element      349
Area, under a curve      73
Asymptotic line      358
B-spline      326 372
B-spline curve      104
B-spline curve, containing straight line      106
B-spline curve, nonpar ametric      141
B-spline curve, parametric      157
B-spline interpolation, iterative      125
B-spline polygon      103 141 260 363 372
B-spline polygon, check      101
Baer, g.      185
Barnhill, R.      262 279 295 326 336 344 346
Barry, P.      168
Barsky, B.      159 184 192 194
Bartels, R.      94 192 317
Bary centric form, of Bezier patch      244
Bary centric, combinations      13 32 83 213
Bary centric, coordinates      19 24 74 345
Basis      30
Basis transformation      59 248
BBG interpolant      344
Beatty, J.      192
Beck, J.      367
Bedard, C.      346
Bernstein polynomials      9 44
Bernstein, S.      44
Bessel, end condition      133
Bessel, tangent      119 121
Bessel, twist      263
Bezier, abscissa      249
Bezier, curves, composite      96
Bezier, function      71
Bezier, net      234
Bezier, ordinates      71 249
Bezier, P.      49 74 185 271 274
Bezier, patch, trivariate      272
Bezier, points      35
Bezier, polygon      35
Bezier, surface      234
Bezier, tetrahedron      295 307
Biaffine      233
Bias      184
Bicubic Hermite interpolant      333
Bicubic splines      340
Bilinear interpolant      263 329
Bilinear interpolation      231
Bilinearly blended Coons patch      262 329 336 339 340
Binomial coefficient      44
Binormal      173
Birkhoff, G.      344 364
Blaschke, W.      35
Blending function      329 343
Blossom      40 58 76 159 282 286
Blossom for triangular patches      282
Blossom of tensor product surface      243
Bobrow, J.      276
Boehm, W      33 40 108 141 150 154 180 184 185 194 283 300 308 316 362
Bol, G.      180
Bonneau, G.      276
Boolean sum      343 345
Boundary point      28
Braun, J.      29 69 262
Breakpoint      96 122
Brianchon, C.      197
Brunet, P.      264 276 308
Brunnett, G.      276
Canonical coordinates      173
Canonical form      175
Cardinal      84 88 92
Carlson, R.      113
Casale, M.      276
Catmull — Rom spline      118
Catmull, E.      320
Centroid      14 16
Ceva’s theorem      24
Chaikin, G.      157
Chain rule      97
Chang, G      59
Chang, S.      94 276
Charrot, P.      308 321 346
Chebychev, economization      70
Chebychev, polynomials      69 326
Chiyokura, H.      338
Chord length      172
Chord length, parametrization      110 116
Chou, J.      224
Chrysler      69 326
circle      2 5 129 211 226 270
Circle, osculating      175
Clark, J.      320
Clay model      5
Closed curve      107 124
Cobb, J.      300
Cohen, E.      54 133 158
Cohn — Vossen, S.      367
Collinear      19
Comer      100 102 116
Comer of a curve      132
Comer, twist      261
Comer-cutting      157
Compatibility      336
Complementary segment of a conic      209
Computation count      255
Computational fluid dynamics      326
Conic precision      227
Conic section      34 196 199 298 357 361
Conjugate direction      358
Connection matrix      194
Cons      274
Control, net      234
Control, point, infinite      213
Control, points      35
Control, polygon      35
Control, polygon of a conic      202
Control, vectors      224
Conversion of B-spline surfaces      260
Conversion, B-spline to Bezier      162
Convex combination      14 340 341
Convex hull      15 28 31 38
Convex hull property      38 47 84 104 105 108 213 296
Convex hull property for rational Bezier curves      216
Convex hull property of Bezier patches      240
Convex hull property of Bezier triangles      281
Convex set      15
Convexity      31 67 328
Convexity of surfaces      248
Convexity, preservation      146
Coons patch, bilinearly blended      262 329
Coons, S.      2 196 215 326
Coordinate system      12
Coordinate-free      12
Correction surface      343
Cox, M      141 155
Coxeter, H.      14
Cramer’s Rule      24
Cross plot      72 91 191
Cross ratio      197 202 208 218
Cross-boundary derivative      242 287 332
Cross-boundary normal derivative      304
Cross-ratio theorem      197
Crouch, P.      137
Cubic B-spline curve      108
Cubic Hermite interpolant      346
Cubic Hermite interpolation      114 332 344 345
Cubic Hermite polynomial      89 126 189 332
Cubic precision      140 227
Curvature      137 174 363
Curvature of a nonparametric curve      178
Curvature of a rational Bezier curve      176 177 220
Curvature, derivative of      179 364
Curvature, plot      129 133 363
Curvature, signed      221 230
Curve on surface      274
Curve, composite      98
Cusp      100 133
Cylinder      270
Dahmen, W.      54
Daniel, M.      373
Data transfer      65
Daubisse, J.      373
Davis, P.      30 44 77 279
de Boor, algorithm for rational B-splines      228
de Boor, C      30 122 124 141 155 157 221 256 279 307
de Boor, ordinates      144
de Boor, polygon      103
de Casteljau algorithm      34 52 53 99 150 233
De Casteljau, P.      2 22 33 40 54 141 231 279
Degen, W.      194
Degenerate patch      245
Degree elevation      224 293
Degree elevation for B-splines      163 168
Degree elevation for Bernstein polynomials      79
Degree elevation for Bezier curves      64 157
Degree elevation for Bezier patches      240
Degree elevation for rational Bezier curves      222
Degree reduction      67
Degree reduction for Bezier triangles      307
Delaunay triangulation      28
Depth, of an S-patch      322
deRham, G.      158
Derivative of a B-spline      167
Derivative of a conic      205
Derivative of a rational Bezier curve      220
DeRose, T.      16 40 194 244 272 308 320 321 375
Design      39
Developable surface      356
Difference operator      49 241
Dill, J.      364 367
Dimension of B-spline spaces      151
Directional derivative      75 285
Directrix      10
Dirichlet tessellation      26
Discriminant      349
Divided differences      141
Do Carmo, M.      194
Domain      53 232
Domain knot      143
Doo — Sabin surfaces      317 323
Doo, D.      317
Double knot      145
Duck      136
Dupin’s indicatrix      316 357 361
Dyn, N      29 158 194
Eck, M      69
ellipse      209 357
Elliptic point      355
End condition      375
End condition, Bessel      127 277
End condition, clamped      126
End condition, natural      128
End condition, not-a-knot      127
End condition, quadratic      127
Endpoint interpolation      47 105 109
Endpoint interpolation of Bezier curves      39
Epstein, M.      132
Equidistant parametrization      124
Euclidean map      18
Euclidean space      12
Euler, L.      16 76 171 356
Extrapolation      54 69
Fairness of a curve      364
Farin, G.      67 194 279 293 295 307 339 365
Farouki, R.      211 276 367 373
Faux, I.      59
Fayard, L.      368
Ferguson, J.      1 122 256 262
Fine tune      187
Fiorot, J.      215
First fundamental form      349
Flat point      355
Flat spot      332
Floater, M.      220 228
FMILL      118
Foley, T.      113 132 133
Font design      18 106 120
Ford      326
Ford, H.      11
Forrest, A.      49 67 69 196 202 215 364 367
Forsey, D.      317
Forward difference      49
Forward differencing      92
Four tangent theorem      202
Fractals      63
Frederickson, L.      279
Frenet frame      173
Frenet frame, continuity      194
Frenet — Serret formulas      174
Fritsch, F.      113
Functional curve      71
Gauss — Seidel iteration      125
Gauss, C.      171 355
Gaussian curvature      355 367
Geise, G.      185 194
General Motors      326
Generalized Vandermonde matrix      86
Generatrix      270 359
Geodesic      360
Geometric continuity      180 181 211
Geometric programming      16
Geometry matrix      248
Goldman, R      12 16 40 168 180 194 283 307
Gonska, H.      44
Goodman, T.      194 221
Gordon surface      341
Gordon surface, spline-blended      343
Gordon, W      2 150 326 341 344
Gradient, of implicit conic      206
Grassmann, H.      32
Gregory, J.      158 194 308 321 336 346 377
Gregory’s square      337
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