Barrels R.H., Beatty J.C. — An Introduction to Splines for use in Computer Graphics and Geometric Modeling :: Электронная библиотека попечительского совета мехмата МГУ

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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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Название: An Introduction to Splines for use in Computer Graphics and Geometric Modeling

Авторы: Barrels R.H., Beatty J.C.

Аннотация:

An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities.

Язык:

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 476

Добавлена в каталог: 14.11.2009

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Предметный указатель

$(-1)^{k}(\overline{u}_{i+\lambda}-\overline{u}_{i})[\overline{u}_{i}(k):t](\overline{u}-t)^{k-1}_{+}$       146
$(\frac{\textit{l}}{r})$       174
$(\overline{u}-t)^{r}$       73
$(\overline{u}-t)^{r}_{+}$       134 136
$b_{-0}(u)$       28
$b_{-1}(u)$       28
$b_{-2}(u)$       28
$b_{-3}(u)$       28
$b_{i, k}(\overline{u})$       146
$b_{i}(\overline{u})$       23
$c(\overline{u})$       37
$C^{-1}$       71
$C^{d}$       6
$D_{\overline{u}}^{(l)}$       134
$G^{1}$       302
$G^{2}$       294 304
$G^{n}$       318
$G_{i, k}$       306
$G_{i}(u)$       305
$H(\beta_{i-1}, \beta_{i}; u)$       322
$k^{th}$ -order polynomials      74
$N_{j, k}(\overline{u})$       248
$P_{i, d}$       211
$P_{left}(\overline{u})$       69 96
$P_{right}(\overline{u})$       69 96
$s(\overline{u})$       96
$s_{i+1, -2}(\overline{u})$       346
$s_{i+2, -1}(\overline{u})$       346
$s_{i+3, -0}(\overline{u})$       346
$s_{i, -3}(\overline{u})$       346
$V_{i}$       20
$X\overline{u}$       5
$x_{i}$       10
$X_{i}(\overline{u})$       10
$Y\overline{u}$       10
$y_{i}$       10
$Y_{i}(\overline{u})$       10
$Z(\overline{u})$       10
$Zero^{th}$ degree      110
$Z_{i}(\overline{u})$       10
$[z_{i}(r):x]$       142
$[\overline{u}_{i}(r):t]$       142
$[\overline{u}_{i}, \overline{u}_{i+1})$       24 6
$[\overline{u}_{\delta}, \overline{u}_{\delta+1}]$       96
$\alpha_{i, \lambda}(j)$       253
$\beta(u)$       321
$\beta_{1, i}$       321
$\beta_{1}$       2 302 317
$\beta_{1}(u)$       321
$\beta_{2, i}$       321
$\beta_{2}$       2 302 318
$\beta_{2}(u)$       321
$\beta_{3}$       318
$\Delta$       95
$\Delta(\overline{u})$       72
$\Delta_{+}(\overline{u})$       72
$\eta(i)$       251
$\hat{\textbf{N}}(\overline{u})$       5 294
$\kappa(\overline{u})$       37
$\mu_{i}$       89 94
$\nu$ -spline      313
$\nu_{j}$       249
$\overline{u}$       5
$\overline{u}_{i+k}>\overline{u}_{i}$       146
$\overline{u}_{i}$       69
$\overline{u}_{max}$       6
$\overline{u}_{min}$       6
$\overline{u}_{\delta}\leq\overline{u}<\overline{u}_{\delta+1}$       96
$\overline{u}_{\delta}\leq\overline{w}_{j}<\overline{u}_{\delta+1}$       251
$\overline{w}_{j}$       249
$\overline{w}_{\delta}\leq\overline{u}<\overline{w}_{\delta+1}$       250
$\overline{\nu}$       46
$\rho(i)$       281
$\rho(\overline{u})$       37
$\textbf{B}$       257
$\textbf{K}(\overline{u})$       37
$\textbf{N}$       257
$\textbf{P}^{k}$       74
$\textbf{P}_{i}$       9
$\textbf{Q}(\overline{u})$       5
$\textbf{Q}(\overline{u}, \overline{\nu})$       46
$\textbf{Q}_{d}(\textbf{V}_{0}, \textbf{V}_{1}, ..., \textbf{V}_{d}; 0, 1; u)$       224
$\textbf{Q}_{d}(\textbf{V}_{0}, \textbf{V}_{1}, ..., \textbf{V}_{d}; a)$       228
$\textbf{Q}_{i, j}(\overline{u}, \overline{\nu})$       52
$\textbf{Q}_{i}(\overline{u})$       10
$\textbf{S}(\textbf{P}^{k}, \{\overline{u}_{i}\}_{0}^{m+k})$       97 99 105 133 146 158
$\textbf{S}(\textbf{P}^{k}, \{\overline{w}_{j}\}_{0}^{m+n+k})$       257
$\textbf{V}_{i, j}$       46
$\textbf{V}_{i}^{[r]}$       226 285
$\textbf{W}_{j}$       248
$\{\overline{u}_{i}\}^{m+k}_{0}$       94
$\{\overline{w}_{j}\}^{m+n+k}_{0}$       250
$“ \bullet ”$ notation in figures      7
Adams, J. A.      2
Adaptive subdivision      217 222
Aho, A. V.      400
Algebraic properties      143
Alternative basis      84
Andrews H. C.      446
Animation      422
Approximation of a cylinder      62
Approximation of points      1 7
Approximation to a circle      61
Approximation to a cylinder      62
Approximation to a torus      63
Arbitrary subdivision/refinement      223 228 261
Arc-length parametrization      317
Associativity      75
B-spline      2 36 52 67 68 73 86 87 88 108 114 133 146 147 150 151 152 154 156 157 158 160 164 165 166 170 172 179 195 197 199 209 211 238 239 246 254 304 305 329 330 348 361 373 421 436 445
B-spline as basis      80
B-spline curve/surface      42 45 46 47 50 55 56 86 195 197 217 303 310 383 442
B-spline derivative      90
B-spline equation system      29 30
B-spline evaluation      162 173 187 189 385 388 398 400
B-spline interpolation      438 439
B-spline order      193
B-spline properties      19 22 29 34 35 46 56 145 173 189 191
B-spline recurrence      173 182 183 185 187 189 259 264 385 386
B-spline representation      115 146 151 215 244 245 246 251 253 254 255 262 264 282 319 398
B-spline subdivision/refinement      247 248 261 286
B-spline surface interpolation      443 444
B-spline-sum derivative recurrence      396
B-spline-sum recurrence      389 391
B-spline-value recurrence      386
B-spline/Bezier representation for Beta-splines      371 422
Backward substitution      14 17 444
Barsky, B. A.      2 37 45 61 162 193 198 215 218 223 232 244 293 294 301 305 313 315 317 318 321 324 325 330 332 333 365 422 438 440 446 448
Bartels, R. H.      11 315 365 414 422 446
Basis      30 73 80 87 357 360
Basis function      24 26 28 29 30 32 46 52 104 118 132 133 200 254 303 304 306 307 310 318 326 365
Basis polynomial      73 77 86
Basis segment      28 32 52 67 209 304 307 319 321 328 332 334 343 347 365 398 413
Basis spline      421 434 446
Basis transformation      244
Basis vector      80
Beatty, J. C.      162 193 321 365
Benesh Dance Notation      448
Bernstein polynomial      84 212 224 238 239 245 246 247 319 371
Bernstein — Bezier      211
Beta 2—splines      218 365 367
Beta-spline curve/surface      2 346 364
Beta-spline properties      304 319 325 343 351 365 377
Beta-spline recurrence      320 346 348
Beta-spline representation      346
Beta-spline subdivision/refinement      218
Beta-splines      302 303 319
Bezier      214 232
Bezier basis      212
Bezier curve/surface      84 199 211 213 214 226 237 246
Bezier properties      212 215 222

Bezier representation      244 319
Bezier subdivision/refinement      216 217 219 220 222 223 247
Bezier, P. E.      2 211
Bhetanabhotla, M. N.      418
Bias      2 306 309 310 317 319 325 327 334 352
Bilinearity      218
Blending functions      435
Boehm, W.      46 218 247 438
Bogen, R.      304 324 365
Boundary      334 414
Boundary condition      57 439 441 445
Boundary vertex      59
Bounding box      414
Bounding-box tree      415
Breakpoint      94 106 109 121 156 165 166 195
Breakpoint interval      95 96 111 250
Breakpoint value      95
Canonical basis      78
Cardinal basis      421 434 436
Cardinal basis spline      427 435 436
Cardinal spline      427
Carpenter, L. C.      218
Catmull — Rom      446
Catmull — Rom spline      19 427 446
Catmull — Rom splines      421 447
Catmull, E. E.      218 289 446
Center of curvature      37
Chaiken, G. M.      218
Chain rule      220 315 317 318 319 337 345
Change of basis      84
Change of basis matrix      82 385
Change of representation      422
Clark, J. H.      218 223
Closed Beta-spline curve      332
Closed curve/surface      17 45 61 62 332
Closed on the left      25
Cobb, E. S.      414
Coefficient      11 28 30 31 67 69 71 74 76 79 81 86 102 114 161 224 239 244 253 258 262 266 283 311 333 347 348 361 362 365 375 379 385 391 393 398 405
Cohen, E.      68 218 247 248 249 263 280 414
Collinear/co-planar      38 42 56 59 61 197 214 215 296 301 330
Column ordering      243
Comer      42 48 57 60 330 331 332 334
Commutativity      75
Compact support      161 162 173
Composite Bezier      214 215
Composite curve/surface      46 52 216 217 246 248
Compression of raster image      445
Computational problems      114
Computer signature      422
Confluent knots      143
Constant polynomial      74
Constant spline      110
Constrained discontinuity      2
Constraint      43
Continuity      6 11 25 26 29 30 42 45 56 67 69 71 89 90 92 102 110 134 136 162 165 196 198 214 215 222 295 296 334
Continuity constraint      6 29 67 215 216 246
Continuity index      89 92
Continuity loss      89 92
Continuously-shaped Beta-spline      319
Continuously-shaped Beta-spline curve/surface      325 334
Continuously-shaped Beta-splines      321 327 328 329 330 332
Control      2 80
Control graph      19 39 46 59 60 61 62 193 197 217 218 222 226 232 237 248 289 307 310 311 325 327 412 422
Control graph subdivision/refinement      286
Control mesh      46
Control polygon      19
Control vertex      2 19 20 24 31 34 35 36 45 52 54 55 56 63 80 115 168 191 196 197 212 214 216 217 220 222 228 242 247 253 269 270 304 307 311 312 325 326 327 329 331 367 413 415 420 437 442 448
Control vertex constraint      371
Control vertex conversion      244 246
Control vertex influence      21 23 193 333
Control vertex subdivision/refinement      280 284
Control-graph approximation      60
Control-vertex approximation      19 445 447
Control-vertex interpolation      447
Control-vertex-refinement recurrence      410
Convergence      217 218 222 289 307 309 310 326 327 354
Conversion of B-splines to segment polynomials      399
Conversion of Beta-splines      351
Conversion of representation      244 245
Convex combination      32 34 198 224
Convex hull      32 34 36 56 193 198 212 280 327 329 368 416
Convex hull property      34 43 145 173 191 197 212 222 284 304 327 368
Coons, S. A.      2
Coordinate      5 10 14 26 46 51 52 54 286 311 326 333 388 413 415 443
Coordinate system      63 77
Cox, M.      67
Cox, M. G.      173 438 439
Cross product      302
Cubic      168
Cubic spline      105
Cubic spline interpolation      9 17
Cup and ball      110
Curry and Schoenberg      158
Curvature      37 38 39 43 197 198 294 302 303 331
Curvature continuity      198 332 337
Curvature vector      2 37 294 301 315
Curvature vector continuity      293 296 302
Curve      10
Curve rendering      334
Curve segment      1 6 8 9 20 25 32 36 39 40 43 45 87 197 198 215 246 254 294 302 309 312 315 317 325 327 330 331 333 413
Curve segment tangent to line      330
Curve tangent to line      39
Curve/surface      54
Curve/surface approximation      1 217 218 222 226 289 411
Curve/surface updating      334 413
Data fitting      217
de Boor, C.      2 3 15 67 68 106 158 173 395 438 442
De Casteljau, P.      218
Degree      211 333
Degree of continuity      2
Degree of polynomial      67
Degree raising      213
Derivative      25 29 91 97 99 103 133 134 136 138 162 164 214 303 315 316 317 357 393 424 434
Derivative continuity      6 11 26 45 48 70 164 198 307 357 371
Derivative of B-spline sums      395
Derivative of B-splines      383 393
Derivative of Beta-splines      324 334 345 347 348 365
Derivative vector      11 15 25 37 38 39 42 43 45 61 293 294 295 296 301 331 427
Derivative vector continuity      294
DeRose, T. D.      215 218 315 317 318 333 446 448
Destination chord      427
Determinant      83 319
Difference of product      179
Differencing      117 121 131 361
Differentiability      119
Differentiation      135 144
Differentiation operator      139 143
DIMENSION      80 158 168 365
Discontinuity      111 156 157 195 319 332 358 423
Discrete B-spline evaluation      407
Discrete B-spline properties      280
Discrete B-spline recurrence      259 262 264 407
Discrete B-spline support      280
Discrete B-splines      268 269 270 284
Discrete — B-spline-value recurrence      409
Discretely-shaped Beta-splines      319 357 364
Display      217
Distributivity      75
Divided difference      88 117 118 123 128 133 138 139 142 143 144 147 160 162 180 319 357 393
Divided difference operator      139 141 143
Divided difference table      159 160
Doo, D. W. H.      218
Double knot      92 95 157 160 164 169
Double vertex      39 57 330
Dransch, D.      448 450
Du, W — H.      433
Dual functional      263
Dyn, N.      318
End condition      12 14 36 38 39 40 43 45 63 198 330 331 437 439
Endpoint      213 329

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