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Sapidis N.S. — Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Sapidis N.S. — Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design

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Название: Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design

Автор: Sapidis N.S.

Аннотация:

The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. A valuable resource for engineers working in CAD, CAM, or computer-aided engineering.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 318

Добавлена в каталог: 27.10.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Airfoil curve, leading edge      37 38
Airfoil curve, smoothing the curvature of      38 43
Almost rational spline      32
Automatic fairing, of spline curves      45
Automatic fairing, point sets in      45
Automatic fairing, problem      86
Automotive design, exterior      3 17 26 232
Averaging, Doo Sabin algorithm for      279
Averaging, mask      282
Bezier curves      79 87 90 93 94
Bezier patch      110 119
Bezier patch, convex combination of      297 300
Bezier patch, rational      297
Blend, extended      240
Blend, PDE      210
Blend, ratio      278 291
boundary conditions      233 237 211
Boundary conditions, derivative      212
Boundary conditions, function      242
Boundary-value technique      232
Circular splines, basic facts of      21
Circular splines, computation of      22—24
Circular splines, discretization using      18—21
Computer-aided design      29
Constrained optimization      79 89
Constrained optimization as a basis for curve smoothing      32 34—36
Constrained optimization, geometrical and smoothness constraints in      30
Continuity by penalty      142
Continuity, tangent      142
Continuity, tangent plane      242 283
contour      306 310
Control matrices, for positional patches      298
Control patterns, planar      296 298 299 300 308
Control patterns, planar, construction of      306—307
Control polygon      61
Convex combination, of Bezier patches      297 300
Convex hull      61 62 64 67 300
Convex hull, of spheres      163 172
Convex set, extreme points of      62—63 67 70
Convexity      162 201—207
Convexity, local      202
Convexity, proof of      205 207
Convexity-preserving spline      257
Convolution kernel      296 297
Convolution surface      296 297
Corner-cutting      277
Corner-cutting control pattern      306
Cornu spiral      31
Cubic spline      76—77
Cubic spline, $\nu$-spline      77—78
Cubic spline, minimum property of      77—79
Curvature      129 161 207 209 see
Curvature, constrained optimization problem of      62 68
Curvature, constraints on area under curve      79
Curvature, constraints, computing circular splines with      18—27
Curvature, continuity at a vertex      146
Curvature, continuum methods of      143
Curvature, control problem      255
Curvature, convexity      32
Curvature, convexity, alpha convexity      16—18
Curvature, convexity, conditions of      12 13 17
Curvature, convexity, intrinsic parameters of      14—15
Curvature, empirical properties of      12
Curvature, empirical properties of, maxima and minima of      4 8
Curvature, Gaussian      146 149 150
Curvature, maximum absolute      291
Curvature, mean      146 253
Curvature, monotonicity of      8—11
Curvature, numerical      21 24
Curvature, optimization of      10 18 62 68
Curvature, principal      124
Curvature, principal, least squares fit of      136—138
Curvature, principal, lines of      140
Curvature, tensor      141
Curve fitting, aesthetic constraints of      3—27
Curve fitting, aesthetic constraints of, analysis using parametric representations      5
Curve fitting, intrinsic equation of      4 7—8
Curve fitting, problem      4
Curve fitting, smoothing      26—27
Curve fitting, use of styling radius for      11
Cusp-free surfaces      202—203
Cyclide      162 163f 175 178f 185 186f
Cyclide, Dupin      175—177
Cyclide, edge      184—185
Design, concept      231
Design, engineering      231
Design, free-form      236
Design, interactive      234 239—246
Design, interactive free-form      246—248
Design, real-time      241
Designer's intuition      161 209
Difference geometry of polygons      46—50
Difference geometry of polygons, arc length      46
Difference geometry of polygons, chord length parameterization      46
Difference geometry of polygons, closed      46
Difference geometry of polygons, derivatives of      49
Difference geometry of polygons, discrete curvature      46 47
Difference geometry of polygons, discrete Frenet frame      47
Difference geometry of polygons, discrete Frenet — Serret frame      47
Difference geometry of polygons, discrete torsion      47
Difference geometry of polygons, euclidean invariants      49
Difference geometry of polygons, inflection points      49
Difference geometry of polygons, open      46
Difference geometry of polygons, osculating planes      48
Difference geometry of polygons, rigid body motions      49
Discrete Curvature Method      53
Discrete Curvature-Torsion Method      56
Discrete Frenet frame      47
Discrete Frenet — Serret frame      47
Facet spheres      172—175
Facet spheres, bounds on the radii of      187—201
Faired curves      75—120
Faired curves, curvature plot      79
Faired curves, curvature plot, fairness metrics      80—86
Faired curves, fairness metrics and derived curves      82 83
Faired curves, fairness metrics and design curves      82 83
Faired curves, fairness metrics, algorithms for      86—87 95
Faired curves, fairness metrics, arc length      81 87 94 95
Faired curves, fairness metrics, centers of spherical curvature      84
Faired curves, fairness metrics, flattening      84
Faired curves, fairness metrics, Frenet — Serret formulas an      81 83 85
Faired curves, fairness metrics, geometric invariants      81 87
Faired curves, fairness metrics, implementation of      86—104
Faired curves, fairness metrics, planar evolute      90
Faired curves, fairness metrics, radius of spherical curvature      84
Faired curves, fairness metrics, rounding      84
Faired curves, fairness metrics, smoothing      84
Faired curves, fairness metrics, total variation      89
Faired curves, smoothness      83
Faired curves, variational methods      78
Fairing problem      253
Fairness criteria      254
Fairness criteria for curves      76 78
Fairness criteria for curves, discrete      50
Fairness criteria for curves, global      50
Fairness criteria for curves, local      50
Fairness criteria for curves, metrics      80—86
Fairness criteria for curves, metrics, implementation of      86—104
Fairness metrics for curves      80—86
Fairness metrics for curves, adaptive quadrature in      87
Fairness metrics for curves, algorithms for      86—87 95
Fairness metrics for curves, examples      95—104
Fairness metrics for curves, implementation of      86—104
Fairness metrics for curves, software engineering and      81—93
Fairness metrics for curves, total variation      89
Fairness metrics for curves, total variation, for monotone curvature      89—90 93
Fairness metrics for curves, typical problem in      87
Fairness metrics for surfaces      104—119
Fairness metrics for surfaces, algorithm for      109—110
Fairness metrics for surfaces, derived surface      105
Fairness metrics for surfaces, flattening      106 107 110—119
Fairness metrics for surfaces, Gaussian curvature      105 110—119
Fairness metrics for surfaces, geometric invariants      104 105
Fairness metrics for surfaces, mean curvature      105 110—119
Fairness metrics for surfaces, principal curvature      105
Fairness metrics for surfaces, rolling      106 108 110—119
Fairness metrics for surfaces, rounding      106 107—108 110—119
Fairness metrics for surfaces, surface area      105
Feasible polygon      63 65
Feasible polygon, inflection segment of      63 65 66 68
Finite element analysis, of smooth surfaces      128
Fresnel integral      31
Gauss map      205—206
Gaussian curvature      146
Gaussian curvature, functional offset surfaces in      150
Geometric primitive      296 297
Hermite curves      129
Highlight bands, application examples, discontinuity magnification      217 219f—220f
Highlight bands, application examples, irregularity detection      217 220 221f—223f
Highlight bands, application examples, real time manipulation      220
Highlight bands, computational algorithm, basic steps of      221 224
Highlight bands, computational algorithm, exhaustive search method      221
Highlight bands, computational algorithm, principles of      221
Highlight bands, computational algorithm, resolution, choices of      224
Highlight bands, defined      215
Highlight bands, graphical representation      215—216
Highlight bands, optimal performing code, code decomposition      226 227f
Highlight bands, optimal performing code, floating point operations, analysis of      225—226
Highlight bands, optimal performing code, global results      227—228 228f
Highlight bands, optimal performing code, vector and parallel processing      226—227
Highlight bands, properties, band shape, manifestation of      216—217 218f—219f
Highlight bands, properties, band width, manifestation of      215—216 217f
Highlight lines, defined      214—215
Highlight lines, model of      214
Interpolation, interpolation curves      132
Interpolation, inversion, of surfaces      177—183 185
Interpolation, of points      282
Interpolation, surfaces      161 193—399
Isophote patterns      307
Krein — Milman, theorem of      63
Linear curves, piecewise      61
Linear curves, rough and fine fairing of      62 66 69 70
Lines of principal curvature      140
Lines of reflection      149
Mesh, irregular      279
Mesh, of points      277
Mesh, refinement      279 283
Mesh, regular      277 279
Minimization, of fairness functionals      131
Minimum energy curve (MEC)      126
Minimum energy curve (MEC), comparison with MVC and natural splines      147
Minimum energy curve (MEC), definition      123
Minimum energy curve (MEC), space curves      149
Minimum norm networks      127
Minimum variation curve (MVC) and nonlinear splines      126—127
Minimum variation curve (MVC), calculation of      133
Minimum variation curve (MVC), comparison with natural spline and MEC      147
Minimum variation curve (MVC), computation of      128
Minimum variation curve (MVC), convexity preserving      123
Minimum variation curve (MVC), existence and uniqueness of      133
Minimum variation curve (MVC), functional of      130
Minimum variation curve (MVC), initialization for minimization      132
Minimum variation curve (MVC), previous work on      126—127
Minimum variation curve (MVC), space curves      149
Minimum variation curve (MVC), specification of      124 125f
Minimum variation networks (MVN), computation of      135
Minimum variation networks (MVN), continuity of      135
Minimum variation networks (MVN), initialization for minimization      136
Minimum variation networks (MVN), optional continuity constraints      138 139f
Minimum variation networks (MVN), previous work on      127
Minimum variation networks (MVN), representation of      135
Minimum variation surface (MVS), computation of      138
Minimum variation surface (MVS), continuity of penalty      142
Minimum variation surface (MVS), functional of      140
Minimum variation surface (MVS), initialization for minimization      144
Minimum variation surface (MVS), optimization of      153
Minimum variation surface (MVS), tangent continuity and      142
Mouse, use in interactive design      237 241
N-sided patches      297—300
N-sided patches, four-sided subpatch      296
N-sided patches, homogeneous      295
N-sided patches, normal continuity for      300—304
Natural spline, comparison with MVC and MEC      147
Nonlinear optimization      128
Nonlinear splines      127
Nonuniform degree, polynomial splines of      253 255—259
Norm, of a spline curve      32
Offending node      254
Optimization problem, constrained      62 68
Optimization, constrained      79 89
Optimization, constrained, as a basis for curve smoothing      32 34
Optimization, constrained, geometrical and smoothness constrain in      30
Optimization, constrained, nonlinear      128
Optimization, constrained, of smooth surfaces      128 248
Parallel processing, application of      see "Highlight bands"
Parametrization      235 242 248
Patch, bicubic      278 280 282 285 289
Patch, degenerate      295
Patch, N-sided      297—304
Patch, polynomial      297
Patch, positional      296 297 298
Patch, rational      282
Patch, weight      296 297 302
PDE blends      240
PDE method      232 233—236
Piecewise linear curves      61
Piecewise linear curves, rough and fine fairing of      62 66 68 70
Planar fairing algorithm      51—54
Planar fairing algorithm and distance tolerance      53
Planar fairing algorithm and shape preservation      59
Planar fairing algorithm and stability      59
Planar fairing algorithm, Discrete Curvature Method      53
Planar fairing algorithm, nonlinear optimization      53
Plane curves, differential geometry of      5
Plane curves, differential geometry of, analysis using parametric representations      5
Plane curves, differential geometry of, arc length      5
Plane curves, differential geometry of, curvature of      7
Plane curves, differential geometry of, curvature of, bulk distribution of      30 41
Plane curves, differential geometry of, curvature of, denominator of      33
Plane curves, differential geometry of, curvature of, high and low frequency features of      30
Plane curves, differential geometry of, curvature of, modification of      29
Plane curves, differential geometry of, curvature of, monotone      33 37 39
Plane curves, differential geometry of, curvature of, nonnegative      33
Plane curves, differential geometry of, curvature of, numerator of      33
Plane curves, differential geometry of, curvature of, profile      30 38f 43f
Plane curves, differential geometry of, curvature of, slope numerator of      34
Plane curves, differential geometry of, intrinsic condition      8
Plane curves, differential geometry of, intrinsic equation      7—8
Plane curves, differential geometry of, tangent angle of      6
Principal curvature, definition of      124
Principal curvature, least squares fit of      136—138
Principal curvature, lines of      140
Principal direction, definition of      124
Principal direction, least squares fit of      136—138
Principle of simplest shape      4
Reparametrization      278 283
Shape parameter      278
Shape-preserving interpolation problem      253
Space curve      149
Spatial fairing algorithm      54—58
Spatial fairing algorithm, Discrete Curvature — Torsion Method      56
Spline curve, $\nu$-spline      77—78
Spline curve, automatic fairing of      45
Spline curve, B-spline      79 91
Spline curve, Bezier      79 87 90
Spline curve, cubic interpolatory      76 79
Spline curve, fairness metrics and      91
Spline curve, natural      147
Spline curve, nonlinear      127
Spline curve, norm of      32
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