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A survey of curve and surface methods in CAGD. (English) Zbl 0604.65005
CAGD - short for Computer Aided Geometric Design - is concerned with the approximation and representation of curves and surfaces that arise when these objects have to be processed by a computer. Designing curves and surfaces plays an important role in the construction of quite different products such as car bodies, ship hulls, airplane fuselages and wings, propeller blades, shoe insoles, bottles, etc, etc, but also in the description of geological, physical and even medical phenomena. In this survey we mainly present methods for the generation of curves and surfaces, not for subsequent operations such as viewing, intersections, etc. Also not covered are generation methods that construct curves and surfaces from other such objects, such as fillet curves/surfaces, offset curves/surfaces etc.

MSC:
65D05 Numerical interpolation
65D07 Numerical computation using splines
41A05 Interpolation in approximation theory
41A15 Spline approximation
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
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