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Curves and surfaces in computer aided geometric design - Yamaguchi F.

Yamaguchi F. Curves and surfaces in computer aided geometric design - Tokyo, 1988. - 390 p.
Download (direct link): curvesandsurfacesincomputer1988.djvu
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normal 23
osculating 23 rectifying 24 tangent 46
passing through 3 points 353 vector representation 353 Point control- 16 inflection- 27 knot- 240 ordinary 20 regular 20 singular 20 Polynomial Bernstein- 189 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 variation diminishing- 192, 294, 312 of Bernstein polynomials 189 193 of Bezier curve segments 189-193 of B-spline curve segments 311, 312
Regular 20 Rectifying plane 24
Second fundamental matrix of a surface 50 Shape control global 16, 17 local 16, 17
of a Coons bi-cubic surface patch 126-131 Shift operator 193, 194 Sketchpad 3,4 Singular point 20 Space curve 14 condition to be 29 Spatial uniqueness 11 Spline 135-168 basis- 160-163,270-273 stored bending energy 136 bending rigidity 136 C-spline 139
end conditions of parametric- 151-159 fundamental 163 by Bezier curve segments 214-216 natural 138-144 mathematical 136
minimal interpolation property 140-144 periodic 159 physical 136 smoothing 144 under tension 7 Spline curve 145 160
378
Subject Index
Spline function 136,137 Spline interpolation 135-168 Spline surface 163 168 Subsplme basis 291 Surface of revolution 264 by cubic B-spline curve segments 264-270 Surface patch Bezier- 216-226 Boolean sum type 133 bilinear 100 bicubic Coons- 111,112 Cartesian product 132 Ferguson- 87-91 tensor product 132 Coons-(1964) 91 101 Coons-(1967) 102-112
loft 132
B-spline- 334, 335
general B-spline surface 334, 335
triangular 228-231
Tangent, equation of a tangent line 21 Tangent vector, unit- 21 Tangent plane 46 equation 46 Torsion 28
of a cubic curve 41
Transformation bilinear 36 homographic 36
invariance of shape under coordinate- 18, 19
inverse 247-250, 262-264, 325-327 curve 247-250, 325-327 surface 262-264 parameter 35-39 rational formula 36 Triangular area coordinate 229 Triangular surface patch 228-231 by degeneration 59, 60, 131, 226-228 Truncated power function 138 Twist vector 91, 98, 104, 112-116 method of determination 117-122 Types of surfaces 132-133
-curve 45 UNISURF 7
Variation diminishing property 192, 294,
312
Volume, enclosed by a surface 62 w-curve 45
This book contains various types of mathematical descriptions of curves and surfaces, such as Ferguson, Coons, Spline, Bezier and -spline curves and surfaces.
The materials are classifted and arranged in a unified way so that beginners can easily understand the whole spectrum of parametric curves and surfaces. This book will be useful to many researchers, designers, teachers, and students who are working on curves and surfaces.
The book can be used as a textbook in computer aided design classes.
ISBN 3-540-17449-4 ISBN 0-387-17449-4
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