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Название: Curves and surfaces in computer aided geometric design

Автор: Yamaguchi F.

Аннотация:

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: Рубрика: Computer science/Вычислительная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 379

Добавлена в каталог: 25.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель
 Acceleration, normal      27 Acceleration, tangential      27 Adini’s method      118 119 Approximation, B-spline-      233—336 Approximation, Bernstein-      169—232 APT system      3 Area of a surface      42 43 47 48 B-spline curve segment      233—334 B-spline curve segment, derivatives      309—311 B-spline curve segment, interpolation of a sequence of points      247 to 250 325—327 B-spline curve segment, matrix representation      327—329 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)      294—296 B-spline, B-spline function, approximation      233—336 B-spline, B-spline function, definition      270—273 B-spline, B-spline function, normalized      273 B-spline, B-spline function, properties      270—274 291—294 B-spline, B-spline function, recursive calculation      285—291 B-spline, B-spline function, relation to Bernstein basis      293 294 B-spline, B-spline function, variation diminishing property      294 Bernoulli — Euler law      135 Bernstein approximation      169—232 Bernstein approximation, derivatives      190 Bernstein approximation, properties      189—193 Bernstein approximation, smoothing effect      193 Bernstein basis function      183 189—193 Bernstein basis vector      195 Bernstein polynomial      174 Bezier curve segment      169—232 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      209—212 Bezier curve segment, various representation      193—198 Bezier net      217 Bezier polygon      173 Bezier surface patch      216—232 Bezier surface patch, connection      221—226 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 Cauchy’s relation      19 Chaikin’s algorithm      320—325 Characteristic net      217 Characteristic polygon      173 Circular arc, circle, approximation      78—80 177 178 243—245 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      78—80 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      337—346 Connection of Bezier curve segments      213 214 Connection of Bezier surface patches      221—226 Connection of Coons bi-cubic surface patches      96 97 107—109 Connection of curve segments      33—35 Connection of Ferguson surface patches      89—91 Connection of surface patches      57—59 Continuity, clss -      20 44 Control point      16 Convex combination      171 241 274 Convex hull property      241 311 Crease      15 Cross partial derivative vector      98 112—122 Cubic spline curves      145—160 Cubic spline curves, using circular arc length      159 160 Curvature      24—27 Curvature of a surface      49—51 Curvature vector      24—27 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      320—325 Curve segment, B-spline      233—334 Curve segment, Bezier-      169—232 Curve segment, conic section      337—346 Curve segment, cubic B-spline      233—251 Curve segment, cubic B-spline, geometrical relations among derivatives      342 343 Curve segment, cubic Bezier      169—182 Curve segment, cubic/cubic rational polynomial      346 347 Curve segment, Ferguson-      73—80 Curve segment, Hermite-      72—86 Curve segment, increase of degree      85 86 204—209 Curve segment, Lagrange-      64—71 Curve segment, non-uniform B-spline-      296 Curve segment, rational polynomial      337—350 Curve segment, T-comc      347—350 Curve segment, uniform cubic B-spline      233—251 Cusp      15 Cusp by cubic B-spline curve segments      245 De Boor’s algorithm      312—315 Degeneration of a surface patch      44 Degeneration, formation of triangular surface patch      59 to 61 Derivatives of B-sphne curve segments      309—311 Derivatives of Bernstein polynomials      198 199 Derivatives of Bezier curve segments      198 199 Descartes’ sign rule      192 Determination of a point by linear operations      199—204 Determination of a point on a B-sphne curve segment by linear operations      312—315 Determination of a point on a cubic Bezier curve segment      178 179 Divided difference      67 Divided difference, interpolation formula with remainder (Newton’s 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      51—55 Finite difference, matrix      33 52—55 Finite difference, operator      32 Finite difference, representation of a Bezier curve segment      194 195 First fundamental matrix of a surface      46—48 FMILL      89 Forrest’s method      117 Frenet frame      29 Frenet — Serret formula      31 Function, B-spline-      236 237 270—273 Function, Bernstein basis-      182 183 189—193 Function, blending-      77 Function, Coons blending-      77 Function, full spline basis-      291 Function, Hermite-      72—83 Function, truncated power-      138 Function, uniform B-spline-      296 Functional determinant      44 Gauss curvature      51 Gauss quadrature      42 Hermite interpolation      72—134 Hermite polynomial      72 —134 Hyperbola      340 Increase of degree of a Bezier curve segment      204—209 Increase of degree of a Ferguson curve segment      85 86 Independence of coordinate axes      12—14 Interpolation, Hermite-      72—134 Interpolation, Lagrange-      64—71 Interpolation, of a sequence of points by a B-sphne curve      247—250 325—327 Interpolation, spline-      135—168 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      247—250 325—327 Jacobian      44 60—62 Knot, additional      272 Knot, extended      272 Knot, insertion      316—320 Knot, interior      272 Knot, multiple      291 Knot, pseudo      292 Kronecker delta      92 Lagrange’s formula      65 Leibnitz’ 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 Marsden’s identity      358 359 Mathematical model      3 4 Matrix representation of a B-spline curve segment      327—329 Matrix, boundary condition-      111 Matrix, finite difference-      33 52—55 Matrix, first fundamental- (of a surface)      46—48 Matrix, second fundamental- (of a surface)      50 Minimal interpolation property      140—144 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      179—182 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-      140—144 Property, of B-spline curve segments      311 312 Property, of Bernstein polynomials      189—193 Property, of Bezier curve segments      189—193 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      126—131 Shift operator      193 194 Singular point      20 SKETCHPAD      3 4 Space curve      14 Space curve, condition to be      29 Spatial uniqueness      11 SPLINE      135—168 Spline curve      145—160 Spline Function      136 137 Spline interpolation      135—168 Spline surface      163—168 Spline, basis-      160—163 270—273 Spline, bending rigidity      136 Spline, by Bezier curve segments      214—216 Spline, C-spline      139 Spline, end conditions of parametric-      151—159 Spline, fundamental      163 Spline, mathematical      136 Spline, minimal interpolation property      140—144 Spline, natural      138—144 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      264—270 Surface patch, B-sphne-      334 335 Surface patch, Bezier-      216—226 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)      91—101 Surface patch, Coons-(1967)      102—112 Surface patch, Ferguson-      87—91 Surface patch, general B-spline surface      334 335 Surface patch, loft      132 Surface patch, tensor product      132 Surface patch, triangular      228—231 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      247—250 262—264 325—327 Transformation, inverse, curve      247—250 325—327 Transformation, inverse, surface      262—264 Transformation, parameter      35—39 Transformation, rational formula      36 Triangular area coordinate      229 Triangular surface patch      228—231 Triangular surface patch by degeneration      59 60 131 226—228 Truncated power function      138 Twist vector      91 98 104 112—116 Twist vector, method of determination      117 —122 Types of surfaces      132—133
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