Abstract
The Chebyshev economisation technique described in chapter 5 is restricted in its application to degree reduction of parametric polynomial curves and surfaces. In practice rational, trigonometric or procedurally defined parametric surfaces are frequently used in CAD systems, and some more general technique of polynomial approximation is needed for data exchange applications. In general the problem is to find a polynomial approximation of specified degree, according to the capabilities of the receiving system, which gives an acceptable fit to the original data. One well known criterion for ‘goodness of fit’ is the least squares criterion. This can be combined with appropriate orthogonal polynomials, in order to avoid the numerical instability problems commonly found in solving the normal equations associated with the simple least squares method.
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