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Farin G. — Curves and surfaces for computer aided geometric design
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Название: Curves and surfaces for computer aided geometric designАвтор: 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.
Язык: Рубрика: Computer science /Вычислительная геометрия /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: fourth editionГод издания: 1997Количество страниц: 429Добавлена в каталог: 16.11.2005Операции: Положить на полку |
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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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