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


65D15 Algorithms for approximation of functions
53A04 Curves in Euclidean and related spaces
53A05 Surfaces in Euclidean and related spaces
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[1] Epstein, M.P., On the influence of parametrization in parametric interpolation, SIAM J. numer. anal., 13, 261-268, (1976) · Zbl 0319.41005
[2] Hoschek, J., Approximate conversion of spline curves, Computer aided geometric design, 4, 59-66, (1987) · Zbl 0645.65008
[3] Hoschek, J., Spline approximation of offset curves, Computer aided geometric design, 5, 33-40, (1988) · Zbl 0647.65007
[4] Lasser, D., Bernstein-Bézier darstellung trivariater splines, diss., (1987), TH Darmstadt
[5] Strauss, R.; Henning, H., Ein leistungsfähiges verfahren zur approximation von raumpunkten durch ein flächenstück, Angewandte informatik, 18, 401-406, (1976)
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