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Intrinsic parametrization for approximation. (English) Zbl 0644.65011
Let \(P_ i\) \((i=1(1)n)\) be n given points. If this set of points is parametrized by a parameter \(t_ i\), the approximation curve \[ Y(t)=\sum^{n}_{i=0}b_ if_ i(t)\quad (t\in I,\quad I=[a,b])\quad (n+1<N) \] with prescribed basis functions \(f_ i\) is called optimal if the shortest distances between the points \(P_ i\) and the approximation curve Y(t) is minimized.
An iterative Newton-like approach of intrinsic parametrization for the optimal approximation is proposed. The method is extended to optimal approximation surface of a given set of points \(P_{ik}\) parametrized by parameter values \((u_ i,v_ k)\).
Reviewer: L.Gatteschi

MSC:
65D15 Algorithms for approximation of functions
53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
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