√лавна€    Ex Libris     ниги    ∆урналы    —татьи    —ерии     аталог    Wanted    «агрузка    ’удЋит    —правка    ѕоиск по индексам    ѕоиск    ‘орум   
blank
јвторизаци€

       
blank
ѕоиск по указател€м

blank
blank
blank
 расота
blank
Yamaguchi F. Ч Curves and surfaces in computer aided geometric design
Yamaguchi F. Ч Curves and surfaces in computer aided geometric design

„итать книгу
бесплатно

—качать книгу с нашего сайта нельз€

ќбсудите книгу на научном форуме



Ќашли опечатку?
¬ыделите ее мышкой и нажмите Ctrl+Enter


Ќазвание: Curves and surfaces in computer aided geometric design

јвтор: Yamaguchi F.

јннотаци€:

The material for the book started life as a set of notes for computer aided geometric design courses which I had at the graduate schools of both computer science, the university of Utah in U.S.A. and Kyushu Institute of Design in Japan. The book has been used extensively as a standard text book of curves and surfaces for students, practical engineers and researchers.


язык: en

–убрика: Computer science/¬ычислительна€ геометри€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1988

 оличество страниц: 379

ƒобавлена в каталог: 25.11.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
blank
ѕредметный указатель
Acceleration, normal      27
Acceleration, tangential      27
AdiniТs method      118 119
Approximation, B-spline-      233Ч336
Approximation, Bernstein-      169Ч232
APT system      3
Area of a surface      42 43 47 48
B-spline curve segment      233Ч334
B-spline curve segment, derivatives      309Ч311
B-spline curve segment, interpolation of a sequence of points      247 to 250 325Ч327
B-spline curve segment, matrix representation      327Ч329
B-spline curve segment, properties      311 312
B-spline curve type (1)      281 282
B-spline curve type (2)      283
B-spline curve type (3)      294Ч296
B-spline, B-spline function, approximation      233Ч336
B-spline, B-spline function, definition      270Ч273
B-spline, B-spline function, normalized      273
B-spline, B-spline function, properties      270Ч274 291Ч294
B-spline, B-spline function, recursive calculation      285Ч291
B-spline, B-spline function, relation to Bernstein basis      293 294
B-spline, B-spline function, variation diminishing property      294
Bernoulli Ч Euler law      135
Bernstein approximation      169Ч232
Bernstein approximation, derivatives      190
Bernstein approximation, properties      189Ч193
Bernstein approximation, smoothing effect      193
Bernstein basis function      183 189Ч193
Bernstein basis vector      195
Bernstein polynomial      174
Bezier curve segment      169Ч232
Bezier curve segment, connection      213 214
Bezier curve segment, derivatives      198 199
Bezier curve segment, finite difference representation      194 195
Bezier curve segment, increase of degree      204-209
Bezier curve segment, partitioning      209Ч212
Bezier curve segment, various representation      193Ч198
Bezier net      217
Bezier polygon      173
Bezier surface patch      216Ч232
Bezier surface patch, connection      221Ч226
Bilinear transformation      36
Binomial expansion      182 183
Binormal vector, unit-      28
Blending function      77
Boundary condition matrix      111
C-spline      139
Cartesian product surface patch      132 133
CauchyТs relation      19
ChaikinТs algorithm      320Ч325
Characteristic net      217
Characteristic polygon      173
Circular arc, circle, approximation      78Ч80 177 178 243Ч245
Circular arc, circle, approximation by Bezier curve segments      177 178
Circular arc, circle, approximation by cubic B-spline curve segments      243 to 245
Circular arc, circle, approximation by Ferguson curve segments      78Ч80
Circular arc, circle, approximation error      80 178
Circular arc, circle, approximation, passing through 3 points      354 355
Common perpendicular, length      352 353
Condition for determining a tangent vector to a curve on a surface      48
Conic section      337Ч346
Connection of Bezier curve segments      213 214
Connection of Bezier surface patches      221Ч226
Connection of Coons bi-cubic surface patches      96 97 107Ч109
Connection of curve segments      33Ч35
Connection of Ferguson surface patches      89Ч91
Connection of surface patches      57Ч59
Continuity, clss $C^r$-      20 44
Control point      16
Convex combination      171 241 274
Convex hull property      241 311
Crease      15
Cross partial derivative vector      98 112Ч122
Cubic spline curves      145Ч160
Cubic spline curves, using circular arc length      159 160
Curvature      24Ч27
Curvature of a surface      49Ч51
Curvature vector      24Ч27
Curvature, average(mean)      51
Curvature, Gauss-      51
Curvature, normal      50
Curvature, principal      51
Curvature, radius      25
Curvature, total      51
Curve defining polygon      173
Curve generation by geometric processing      320Ч325
Curve segment, B-spline      233Ч334
Curve segment, Bezier-      169Ч232
Curve segment, conic section      337Ч346
Curve segment, cubic B-spline      233Ч251
Curve segment, cubic B-spline, geometrical relations among derivatives      342 343
Curve segment, cubic Bezier      169Ч182
Curve segment, cubic/cubic rational polynomial      346 347
Curve segment, Ferguson-      73Ч80
Curve segment, Hermite-      72Ч86
Curve segment, increase of degree      85 86 204Ч209
Curve segment, Lagrange-      64Ч71
Curve segment, non-uniform B-spline-      296
Curve segment, rational polynomial      337Ч350
Curve segment, T-comc      347Ч350
Curve segment, uniform cubic B-spline      233Ч251
Cusp      15
Cusp by cubic B-spline curve segments      245
De BoorТs algorithm      312Ч315
Degeneration of a surface patch      44
Degeneration, formation of triangular surface patch      59 to 61
Derivatives of B-sphne curve segments      309Ч311
Derivatives of Bernstein polynomials      198 199
Derivatives of Bezier curve segments      198 199
DescartesТ sign rule      192
Determination of a point by linear operations      199Ч204
Determination of a point on a B-sphne curve segment by linear operations      312Ч315
Determination of a point on a cubic Bezier curve segment      178 179
Divided difference      67
Divided difference, interpolation formula with remainder (NewtonТs formula)      68
ellipse      340
Equation of a normal plane      23
Equation of a plane passing through 3 points      353
Equation of a straight line segment      351
Equation of a tangent plane      46
Equation of an osculating plane      23
Error in approximating a circle      80 178
Finite difference, computation      32 33
Finite difference, determination of a point, on a curve      32 33
Finite difference, determination of a point, on a surface      51Ч55
Finite difference, matrix      33 52Ч55
Finite difference, operator      32
Finite difference, representation of a Bezier curve segment      194 195
First fundamental matrix of a surface      46Ч48
FMILL      89
ForrestТs method      117
Frenet frame      29
Frenet Ч Serret formula      31
Function, B-spline-      236 237 270Ч273
Function, Bernstein basis-      182 183 189Ч193
Function, blending-      77
Function, Coons blending-      77
Function, full spline basis-      291
Function, Hermite-      72Ч83
Function, truncated power-      138
Function, uniform B-spline-      296
Functional determinant      44
Gauss curvature      51
Gauss quadrature      42
Hermite interpolation      72Ч134
Hermite polynomial      72 Ч134
Hyperbola      340
Increase of degree of a Bezier curve segment      204Ч209
Increase of degree of a Ferguson curve segment      85 86
Independence of coordinate axes      12Ч14
Interpolation, Hermite-      72Ч134
Interpolation, Lagrange-      64Ч71
Interpolation, of a sequence of points by a B-sphne curve      247Ч250 325Ч327
Interpolation, spline-      135Ч168
Intersection of 2 curves      43 44
Intersection of 3 planes      354
Intersection of a curve and a plane      43
Invariance of shape under coordinate transformation      18 19
Inverse transformation of a uniform cubic, B-sphne curve      247Ч250 325Ч327
Jacobian      44 60Ч62
Knot, additional      272
Knot, extended      272
Knot, insertion      316Ч320
Knot, interior      272
Knot, multiple      291
Knot, pseudo      292
Kronecker delta      92
LagrangeТs formula      65
LeibnitzТ formula      356
Length of a curve      42
Length of a curve, on a surface      47
Length of common perpendicular      352 353
Line segment by a Bezier curve segment      176 177
Line segment by a cubic B-spline curve segment      243
Line segment, perpendicular bisector      351
Local uniqueness      242
MarsdenТs identity      358 359
Mathematical model      3 4
Matrix representation of a B-spline curve segment      327Ч329
Matrix, boundary condition-      111
Matrix, finite difference-      33 52Ч55
Matrix, first fundamental- (of a surface)      46Ч48
Matrix, second fundamental- (of a surface)      50
Minimal interpolation property      140Ч144
Model, mathematical      3 4
Model, physical      3 4
Moving frame      29
Net, surface defining-      217
Normal plane      23
Normal plane, equation      23
Normal vector, unit-      46
Normal, principal-      23
Normalized B-spline      273
Offset surfaces      63
Order of spline      136
Ordinary point      20
Osculating plane      23
parabola      342
Parametric cubic curve      31
Parametric representation of a curve      20
Parametric representation of a surface      44
Partitioning of Coons bi-cubic surface patches      122 123
Partitioning of cubic Bezier curve segments      179Ч182
Partitioning of curve segments      39
Partitioning of Ferguson curve segments      84 85
Pentagonal surface      9 10
Perpendicular bisector of a line segment      351 352
Physical model      3 4
Plane curve, condition to be      29
Plane, normal      23
Plane, osculating      23
Plane, passing through 3 points      353
Plane, rectifying      24
Plane, tangent      46
Plane, vector representation      353
Point, control-      16
Point, inflection-      27
Point, knot-      240
Point, ordinary      20
Point, regular      20
Point, singular      20
Polynomial, Bernstein-      189
Polynomial, Lagrange-      65
Power basis vector      195
Principal normal, vector, unit-      46
Principle of minimizing total bending energy      136 140
Product of differences      64
Property, minimal interpolation-      140Ч144
Property, of B-spline curve segments      311 312
Property, of Bernstein polynomials      189Ч193
Property, of Bezier curve segments      189Ч193
Property, variation diminishing-      192 294 312
Rectifying plane      24
Regular      20
Second fundamental matrix of a surface      50
Shape control, global      16 17
Shape control, local      16 17
Shape control, of a Coons bi-cubic surface patch      126Ч131
Shift operator      193 194
Singular point      20
SKETCHPAD      3 4
Space curve      14
Space curve, condition to be      29
Spatial uniqueness      11
SPLINE      135Ч168
Spline curve      145Ч160
Spline Function      136 137
Spline interpolation      135Ч168
Spline surface      163Ч168
Spline, basis-      160Ч163 270Ч273
Spline, bending rigidity      136
Spline, by Bezier curve segments      214Ч216
Spline, C-spline      139
Spline, end conditions of parametric-      151Ч159
Spline, fundamental      163
Spline, mathematical      136
Spline, minimal interpolation property      140Ч144
Spline, natural      138Ч144
Spline, periodic      159
Spline, physical      136
Spline, smoothing      144
Spline, stored bending energy      136
Spline, under tension      7
Subsphne basis      291
Surface of revolution      264
Surface of revolution by cubic B-spline curve segments      264Ч270
Surface patch, B-sphne-      334 335
Surface patch, Bezier-      216Ч226
Surface patch, bicubic Coons-      111 112
Surface patch, bilinear      100
Surface patch, Boolean sum type      133
Surface patch, Cartesian product      132
Surface patch, Coons-(1964)      91Ч101
Surface patch, Coons-(1967)      102Ч112
Surface patch, Ferguson-      87Ч91
Surface patch, general B-spline surface      334 335
Surface patch, loft      132
Surface patch, tensor product      132
Surface patch, triangular      228Ч231
Tangent plane      46
Tangent plane, equation      46
Tangent vector, unit-      21
Tangent, equation of a tangent line      21
Torsion      28
Torsion of a cubic curve      41
Transformation, bilinear      36
Transformation, homographic      36
Transformation, invariance of shape under coordinate-      18 19
Transformation, inverse      247Ч250 262Ч264 325Ч327
Transformation, inverse, curve      247Ч250 325Ч327
Transformation, inverse, surface      262Ч264
Transformation, parameter      35Ч39
Transformation, rational formula      36
Triangular area coordinate      229
Triangular surface patch      228Ч231
Triangular surface patch by degeneration      59 60 131 226Ч228
Truncated power function      138
Twist vector      91 98 104 112Ч116
Twist vector, method of determination      117 Ч122
Types of surfaces      132Ч133
1 2
blank
–еклама
blank
blank
HR
@Mail.ru
       © Ёлектронна€ библиотека попечительского совета мехмата ћ√”, 2004-2017
Ёлектронна€ библиотека мехмата ћ√” | Valid HTML 4.01! | Valid CSS! ќ проекте