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Barrels R.H., Beatty J.C. — An Introduction to Splines for use in Computer Graphics and Geometric Modeling
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: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
1 2 3
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