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Piegl L.A.,, Tiller W. — The NURBS Book (Monographs in Visual Communication)
Piegl L.A.,, Tiller W. — The NURBS Book (Monographs in Visual Communication)



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Название: The NURBS Book (Monographs in Visual Communication)

Авторы: Piegl L.A.,, Tiller W.

Аннотация:

The second, revised edition of this book covers all aspects of non-uniform rational B-splines necessary to design geometry in a computer-aided environment. Basic B-spline features, curve and surface algorithms, and state-of-the-art geometry tools are all discussed. Detailed code for design algorithms and computational tricks are covered, too, in a lucid, easy-to-understand style, with a minimum of mathematics and using numerous worked examples. The book is a must for students, researchers, and implementors whose work involves the use of splines.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 646

Добавлена в каталог: 03.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Affine transformation      83 105 118 130
Algorithm, Bezier to power basis conversion matrix      269
Algorithm, bicubically blended Coons surface      502
Algorithm, compute knot removal error bound curve      428
Algorithm, constraint-based surface modification      564
Algorithm, control points of B-spline derivative curves      98
Algorithm, conversion from NURBS to other spline forms      590
Algorithm, curve approximation, global, to points and derivatives      417
Algorithm, curve approximation, global, to points, error bounded      431
Algorithm, curve approximation, local, error bounded cubic      448
Algorithm, curve approximation, local, error bounded quadratic      440
Algorithm, curve global interpolation, cubic spline to points      373
Algorithm, curve global interpolation, to points      369
Algorithm, decompose B-spline, curve into piecewise Bezier segments      173
Algorithm, decompose B-spline, surface into piecewise Bezier patches      177
Algorithm, degree elevation, curve      206 223
Algorithm, degree elevation, surface      209
Algorithm, derivatives of rational B-spline, curve      127
Algorithm, derivatives of rational B-spline, surface      137
Algorithm, find knot span      68
Algorithm, Gordon surface      494
Algorithm, knot insertion, curve      151
Algorithm, knot insertion, surface      155
Algorithm, knot refinement, curve      164
Algorithm, knot refinement, surface      167
Algorithm, knot removal curve      185
Algorithm, NURBS, circle      308
Algorithm, NURBS, open conic arc      317
Algorithm, NURBS, surface of revolution      346
Algorithm, NURBS, three-sided patch on sphere      359
Algorithm, point and derivatives of B-spline, curve      93 99
Algorithm, point and derivatives of B-spline, surface      111 115
Algorithm, point on B-spline curve      82
Algorithm, point on B-spline surface      103
Algorithm, point on Bezier curve      22 24
Algorithm, point on Bezier surface      39
Algorithm, point on power basis curve      7
Algorithm, point on power basis surface      36
Algorithm, point on rational B-spline curve      124 153
Algorithm, point on rational B-spline surface      134
Algorithm, power basis to Bezier conversion matrix      275
Algorithm, quadratic rational Bezier arc      314
Algorithm, remove knots from curve, error bounded      429
Algorithm, surface approximation global to points      422
Algorithm, surface fitting parameter values      377
Algorithm, surface interpolation, global to points      380
Algorithm, surface interpolation, local to points      404
Algorithm, surfaces      114
Algorithm, swept surface, trajectory interpolated      475
Algorithm, swept surface, trajectory not interpolated      477
Algorithm, unclamp a B-spline curve      577
Algorithm, value of Bernstein polynomial      20
Algorithm, value of one B-spline basis function      74
Algorithm, value of one B-spline basis function and derivatives      76
Algorithm, values of nonzero B-spline basis functions      70
Algorithm, values of nonzero B-spline basis functions and derivatives      72
Algorithm, values of nth-degree Bernstein polynomials      20 21
Approximation      361
B-spline basis functions      50. See also Basis functions
B-spline curve      81. See also Curve B-spline
B-spline programming      593. See also Software
B-spline surface      100. See also Surface B-spline
Barycentric coordinates      528
Basis functions, B-spline, computational algorithms      67—78
Basis functions, B-spline, continuity      57 58
Basis functions, B-spline, definition and examples      50—55
Basis functions, B-spline, derivatives      57—63 78
Basis functions, B-spline, properties      55—58 63—67
Basis functions, curve, Bezier      10 15—17
Basis functions, curve, power basis      6
Basis functions, curve, rational B-spline      118
Basis functions, curve, rational Bezier      27
Basis functions, products of B-splines      102 104
Basis functions, surface, Bezier      37
Basis functions, surface, power basis      35
Basis functions, surface, rational B-spline      128—130
Basis functions, surface, rational Bezier      40
Bending      547
Bending, circular      550
Bending, cylindrical      551
Bending, parabolic      550
Bernstein polynomials      10 52 104
Bezier comparison with power basis form      24 25
Bezier curve      9 382
Bezier curve, definition      9
Bezier curve, degree elevation      202—205
Bezier curve, degree reduction      214 219—221
Bezier curve, derivatives      22
Bezier curve, properties      12—14
Bezier surface, definition      37
Bezier surface, properties      38
Blending functions      6. See also Basis functions
Breakpoint      47 51 588
circle      1 26 28 32 45 244 254 279 295 296
Circle, construction of      298—309
Circle, higher degree rational Bezier      326—330
Circle, undamped      578
Clamped curves      576
Clamped knots      571
Composite B-spline curve      181 192
Conic form, conversion and type classification      320—325
Conic form, implicit equation      282 320
Conic form, implicit equation, standard position      283
Conic form, maximum inscribed area      289 320
Conic form, NURBS      321
Conic form, rational Bezier      291 321
Conic form, rational power basis      288 321
Conic form, shape factor      261. See also Shape factor
Conic form, shoulder point      294 394 439
Conic, construction of      310—320
Conic, eccentricity      281
Constraint-based modification, curves      555
Constraint-based modification, surfaces      562
Constraints      361
Continuity in skinning      469
Continuity of B-spline basis functions      57 58
Continuity of B-spline curves      88
Continuity of B-spline surfaces      109
Continuity of closed B-spline curves      575
Continuity of piecewise polynomial and rational curves      47
Continuity, order of      47 588
Continuity, parametric (C) vs geometric (G)      382 588
Control net, Bezier      37
Control net, data structure      600
Control point, B-spline      81
Control point, Bezier      10
Control point, data structure      597
Control point, infinite      295. See also Infinite control point
Control point, multiple      90
Control point, rational B-spline      117
Control point, repositioning      84 108 511 516 533 555 562
Control point, repositioning, minimum length solution      557
Control point, weighted      30 120
Control polygon, B-spline      82
Control polygon, Bezier      11
Control polygon, data structure      598
Control polygon, rational B-spline      117
Conversion, B-spline to/from piecewise power basis polynomials      180 265—278
Conversion, Bezier to/from power basis polynomials      265 272
Conversion, of conies      320
Convex hull property      229
Convex hull property, B-spline      83 105
Convex hull property, Bezier      12 38
Convex hull property, rational B-spline      118 130
Coons surface, bicubically blended      497
Coons surface, bilinearly blended      496
Cross ratio      524 547
Cross-boundary derivatives      497
Curve, B-spline, definition and properties      81—91
Curve, B-spline, derivatives and continuity      88 180
Curve, Bezier      9 82 119
Curve, Bezier, degree elevation      202—205
Curve, Bezier, degree reduction      214 219—221
Curve, clamped      576
Curve, cubic      8 12
Curve, data structure      596 599
Curve, derivative of      2 6
Curve, evaluation of points and derivatives by knot insertion      151
Curve, fitting approximation      410 413 427 438 441
Curve, fitting interpolation      364 370 371 373 388 392 395
Curve, implicit form      1
Curve, parametric form      1
Curve, piecewise, Bezier      47 48
Curve, piecewise, polynomial      47—49 82
Curve, piecewise, rational      47 50
Curve, power basis form      6
Curve, rational B-spline, definition and properties      117—120
Curve, rational B-spline, derivatives      125—127
Curve, rational Bezier, definition      27
Curve, rational Bezier, homogeneous form      30
Curve, rational Bezier, properties      27
Curve, reversal      263
Curve, splitting / subdivision by knot insertion      151
Curve, unclamped      576
Cusp      8 13
Cylinder      40
Data exchange      571 580 583 586
deCasteljau Algorithm      24 32 38 145 314 396 446
Decomposition of B-splines into piecewise, Bezier      169—179
Decomposition of B-splines into piecewise, polynomials      162 168
Degree elevation      188—212 326
Degree reduction      212—227
Derivatives of B-spline basis functions      57—63
Derivatives of B-spline curves      88 91—100
Derivatives of B-spline curves, with respect to the weights      520
Derivatives of B-spline surfaces      109—115
Derivatives of Bernstein polynomials      17
Derivatives of Bezier curves      22
Derivatives of composition of two functions      247
Derivatives of parametric curves      2
Derivatives of parametric surfaces      4
Derivatives of power basis curves      6
Derivatives of power basis surfaces      36
Derivatives of rational B-spline curves      125—127
Derivatives of rational B-spline surfaces      136—138
Derivatives of rational basis functions      555
ellipse      26 282 290 293
Ellipse, construction of full      320
Fitting, choosing knots      365 370 371 374 389 398 412
Fitting, choosing parameters      364 365 376 386 389 398
Flattening      542
Frenet frame      479
Global fitting algorithms      363 405
Gordon surface      485
Homogeneous coordinates      29
Homogeneous representation of circular arc      33
Homogeneous representation of NURBS curve      120
Homogeneous representation of NURBS surface      132
Horner's method, curve      6 9
Horner's method, surface      36
Hyperbola      26 282 290 293
IGES      580
IGES, parametric splines      270 277
Implicit equation, compared with parametric form      4 5
Implicit equation, of curve      1
Implicit equation, of surface      2
Infinite control point      295 298 309 312
Inflection point      8
Interpolation      361
Inverse knot insertion      154 512 525 532
Isoparametric curve      35
Isoparametric curve on B-spline surface      109
Isoparametric curve on Bezier surface      37
Isoparametric curve on rational B-spline surface      135
Isoparametric curve, extraction by knot insertion      161
Knot insertion      141—161 309 326
Knot refinement      162—179 265 533
Knot removal      179—188 272 427 533 576
Knots, clamped open (nonperiodic)      66 572
Knots, clamped vs undamped      571
Knots, data structure      598
Knots, definition      50 51
Knots, merging      162
Knots, multiplicity      57 58 64
Knots, nonperiodic (clamped open)      66 572
Knots, partitioning of the control polygon      147
Knots, periodic vs nonperiodic      574
Knots, span      51
Knots, uniform and nonuniform      66 571
Least squares approximation      410
Line      7 10
Local fitting algorithms      363 382 437
Local support      49 55 118 128
Lofted surface      457. See also Skinned surface
Loop      8 13
Newton iteration      230
Node, B-spline      512 516 530
NURBS representation of bilinear surface      333
NURBS representation of Coons surface      496
NURBS representation of ellipsoid      349
NURBS representation of elliptic paraboloid      349
NURBS representation of general cone      338
NURBS representation of general cylinder      334
NURBS representation of Gordon surface      485
NURBS representation of hyperbolic paraboloid      334
NURBS representation of planar surface      334
NURBS representation of ruled surface      337
NURBS representation of skinned surface      457
NURBS representation of sphere      344
NURBS representation of surface of revolution      340
NURBS representation of swept surface      472
NURBS representation of swung surface      455
NURBS representation of three-sided patch on sphere      351
NURBS representation of torus      344
Offsetting      475 479 552 588
Order      50
parabola      7 11 26 282 290 293
Parametric error      221
Parametric form      1 4
Parametric form of curve      1
Parametric form of surface      2
Parametric form, comparison with implicit equation form      4 5
Parametric form, derivative of      2 4
Parametric form, surface normal vector      4
Partition of unity      16 27 38 57 118 128
Periodic vs nonperiodic curves      575
Perspective map      30 121
PHIGS      585
Point inversion      229. See also Point projection)
Point projection to curve      229—232
Point projection to surface      232—234
Polynomial      6
Power basis form      5 9 24
Power basis form of curve      5
Power basis form of surface      35
Power basis form, derivative of      6
Programming, B-spline      593. See also Software
Projections of curves and surfaces, parallel      236
Projections of curves and surfaces, perspective      237
Rational B-spline curve      117. See also Curve rational
Rational B-spline surface      128. See also Surface rational
Rational B-spline, basis functions      118 534.
Rational Bezier curve definition      27
Rational Bezier surface definition      40
Rational functions      26 *
Reparameterization      44 241—263 265 269 271 589
Reparameterization with a linear function      250 263
Reparameterization with a linear rational function      255
Reparameterization with a piecewise polynomial function      250
Reparameterization with a piecewise rational function      251
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