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| Авторизация |
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| Barrels R.H., Beatty J.C. — An Introduction to Splines for use in Computer Graphics and Geometric Modeling |
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| Предметный указатель |
Endpoint interpolation 199 450
Endpoint match 332
Endpoint-interpolating cubic 200 204 206 208
Equality 75 88 98 105
Equation system for Beta-spline representation 376
Equation system for explicit Beta-splines 347
EQUIVALENCE 75
Euclidean knot spacing 16 450 451
Evaluation by subdivision 226
Evaluation of Beta-splines 305 332 365
Explicit Beta-spline 319 320 343 346 347
Faux I. D. 37
Faux, I. D. 3
Finite interval 13
Flamingo 422
Flatness 218 232
Foley, J. D. 2
Forsythe — Malcolm — Moler 15 437
Forsythe, G. E. 15 436 448 450
Forward differencing 305 333 400 403 404
Forward elimination 14 17 444
Fotrest, A. R. 211 213 412
Fournier, A. 215
Fractal 414
Free-form surface 1
Gap 62
Geometric construction of Bezier curve 226
Geometric continuity 215 293 294 299 301 302 303 307 311 312 313 315 317 318 319 321 324 331 334 371
Geometric continuity constraint 304 305 338 357 359 364
Geometrically-continuous splines 360
Global control 215
Goldman, R. N. 218
Goodman, T. N. T. 318 319 346 348 365
Gordon, W. J. 2
Greenberg, D. P. 438 440
Half-open interval 25 111 146
Hat function 22 24
Height fields 417
Hermite cardinal basis 422 425 435 436
Hermite interpolation 9 11 12 19 243 324 424
Hermite representation 243 245
Hoellig, K. 319 371
Homer’s rule 333 365 400
Hosaka, M. 218
Hou, H. S. 446
Hump 47
Identical splines 98
Identity element 75
IMSL 3
Inbetween 422
Incremental technique 414
INDEX 47 5
Index of continuity 89
Initialization of forward differencing 406
Interpolating cardinal spline 446
Interpolation at a knot position 441
Interpolation constraint 11 14 322
Interpolation equation system 12
Interpolation of control vertex 40 44 59 195 196 198 213 329 330
Interpolation of derivative 434
Interpolation of endpoints 450
Interpolation of points 1 7 331 434
Interpolation of shape parameters 321 323 324 327 332 334
Intersection 417
Intersection testing 415
interval 27 28
Invertible 81
Joe, B. 218
Joint 2 6 8 12 42 222 247 293 295 302 306 307 310 315 317 319 321 324 325 327 329 331 332 351 352
Joy, K. I. 418
Kajiya, J. T. 414 417 418
key frames 422
key points 423
Key-frame inbetweening 422
Kimura, F. 218
Kink 325 327
Klassen, R. V. 446
Knapp, L. C. 217
Knot 6 8 25 29 69 71 87 89 102 103 104 109 110 152 195 209 238 247 269 307 323 345 358
Knot confluence 143
Knot insertion 86 218 248 249 250 254 257 280
Knot interval 6
Knot multiplicity 146 450
Knot position 438
Knot sequence 6 47 67 89 95 106 133 162 168 198 199 204 238 248 254 441
Knot spacing 16 172 201 319 343 346 348 361 368 450
Knot vector 6
Kochanek, D. H. U. 11 422
Koparkar, P. A. 218
Lack of local control 114 361
Lagrange polynomial 434 448
Lane, J. M. 218 222 223 224 414
Least-squares approximation 421 448 453
Lee, E. T. Y. 218 263
Left-handed derivative 136
Leibniz rule 173 174 175 179
LIMIT 142
Limits on multiplicity 195
Line as spline segment 197 198
Line segment approximation to curve 1
Linear B-spline 20 152
Linear blending functions 435
linear combination 24 26 86 87 118 132 133 157 161 251 253 257 263 329 359 363 388
Linear factor 183 386
Linear independence 79 88 112 115 154 259 263 283 365 435
Linear interpolation 422
Linear operator 143
Local control 19 24 114 173 215 325 333 367 412
Local parametrization 6 10 32 49
Local support 27 47 114 128 162 311 362 365 446
Locality of control vertex refinement 284
Locality of refinement 280 282
Locality of shape parameters 321 327 338 343
Lyche, T. 247 248 409
M 9
Mach band 1
Macsyma 304 324 338 365
Magnification of raster image 445
Malcolm, M. A. 15
Manning, J. R. 2 294 313
Mapping 139
Matrix and geometric continuity 318
Matrix representation 242 244 383 408
Matrix system 443
Micchelli, C. A. 318
Midpoint subdivision/refinement 217 223 287 290
Minor of a matrix 319
Moler, C. B. 15
Mortenson, M. E. 3
Motion dynamics 424
Mudur, S. P. 218
Multiple control vertices 39 42 59 197 198 331
Multiple knot 6 109 133 152 161 162 165 166 168 195 198
Multiplicity 92 94 195 197 198 201 209 238 249 269
Multiplicity index 94
Multivariate B-splines 46 2 248
Natural cubic spline 12 439
Natural end condition 440
Nested bounding boxes 415
Newman, W. M. 2
Newton iteration 414 417 418 419 420
Nielson, G. M. 313
Nonnegativity 34 280 284 319 328 365
Nonsingular 81
Nonuniform 67 133
Nonzero 27 28 268
Normal vector 294 412
Normalizing condition 29
Not-a-knot 15
Numerical accuracy 158 162 189 365 404 405 422
| Numerical cancellation 114 162 361 365
Numerical instability 114
NURB 3
Nydegger, R. W. 218
One-sided basis 112 114 148 149 154 358 361
One-sided basis function 104
One-sided function 72
One-sided power function 73 103 104 106 110 111 112 118 131 133 134 136 142 154 161 162 357
One-sided representation 105 108 150 151 154
Open curve/surface 45 332
Open on the left 136
Open on the right 111 134 146
Order and maximal continuity 71
Order of B-spline 145
Order of spline 68
Ordering of differencing/differentiation 144
Osculating circle 37 294
Osculating plane 37
Oslo algorithm 86 218 263 407 408 410 415
Parameter range 6 28 73 86 87 88 105 112 148 149 150 153 154 158 168 249 263 407
Parameter space 248
Parameter value 449
Parametric continuity 2 293
Parametric curve/surface 2 5
Parametric derivative 2 30 293 294 296 303 321 322 331
Parametric mesh 47
Parametric partition 217
Parametric polynomial 27
Parametric region 47
Parametric representation 299
Parametrization of segment 294
Partitioning 216
Patch 52 54 56 311
Patterson, R. R. 3
Penna, M. A. 3
Perspective transformation 56
Phantom vertex 39 43 44 45 61 331
Physical continuity 301
Picture processing 445
Piecewise curve/surface 1
Piecewise linear approximation 218 226
Piecewise linear curve 24 156
Piecewise linear factor 348
Piecewise linear function 146 147
Piecewise linear interpolation 20
Piecewise polynomial 6 131
Piecewise polynomial representation 104 398
Piegl, L. 218
Planarity 412
Plass, M. 448 453
Polygonal approximation to surface 1 217 411
Polynomial 102 104
Polynomial basis 101 212
Polynomial segment 304
Polynomial subspace 85 99
Polynomial vector space 73 77
Positivity of B-spline 145 173 189 191
Positivity of Beta-splines 365
Positivity of difference 132
Powers basis 78
Powers representation 102 104 243 245 246 365 385 398
Pratt M. J. 37
Pratt, M. J. 3
Prautzsch, H. 218 247 257 263
Product rule 135
Product rule for differentiation 174
Product rule for divided difference 174
Quadratic B-spline 159 160
Quadratic spline 112
Quadruple knot 166
Quintic Hermite interpolation 324
Radius of curvature 37
Ramer, U. 218
Rational polynomial 56
Rational spline 3
Ray tracing 414 415
Rectangular surface patches 46
Recurrence relation 182
Recurrence table 188
Recursive Bezier evaluation 218
Recursive definition 123
Refined B-splines 251 253 254 255 262 282
Refined control vertices 262 407
Refinement of a knot sequence 250 257
Refinement of a surface 288
Regular data 444
Relabeling 249 250
Rendering 216 222 244 333 400 413 414
Reparametrization 301 315 316 317 318 344
Representation with respect to a basis 78
Residual 453
Riesenfeld, R. F. 2 218 222 223 247 248
Right-handed derivative 134
Rogers, D. F. 2
Rom, R. J. 446
Rotation invariance 35 56
Row ordering 244
Running average 35
Sabin, M. A. 218
Scalar multiplication 75 88
Scaled sum 26 104 254 310
Scaling 22
Scaling invariance 36 56
Scan-line rendering 414
Scattered data 443
Schmitt, F. J. M. 217 453
Schoenberg and Whitney theorem 442 445
Schoenberg, I. 67
Schumaker, L. L. 2 3 68 106 142 249 257 395 399
Schweikert, D. G. 313
Schweitzer, D. 414
Second difference 123
Segment interval 87 319
Segment polynomial 27 28 68 86 96 163 164 166 199 200 206 304 345 346 372 385 398 435 436
Separability 55 311
Shading 1 411
SHAPE 2 14 16 35 56 114 166 172 193 198 213 214 216 218 222 301 306 307 309 310 351 352
Shape parameters 321 338 367 448
Shifted power 73 101 102 105
Silhouette 1
Silhouette edge 414
Single knot 95 159
Smith, A. R. 244
Solution approximation 419
Source chord 427
Spline basis 161
Spline segment 111
Spline subspace 257 263
Spline vector space 73 85 87 249 257 263
Sproull, R. F. 2
Step function 110 147 148 149 150 151
Stone, M. 422 448 453
Subdivision/refinement 86 211 217 218 222 228 237 247 254 289 333 371 415
Subdivision/refinement tree 218 232 239
subspace 85 253
Subspace basis 86
Summation to one 29 34 35 173 191 319 365 377 446
Support 29
Support of B-spline 31 145
Support of Beta-spline 307 319 325
Support of discrete B-spline 268
Surface interpolation 442
Surface intersection 414
Surface patch 1 334 337 414
Sweeney, M. A. J. 414 415 416
Symbolic cancellation 115 117 121 124 128 131 162 180
Symmetric endpoint-interpolating cubics 201 208
Symmetric matrix 244
Tangent vector 2 199 214 293 302 303 315
Tangent vector continuity 294 337
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