Intrinsic parametrization for approximation
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 \((u_ i,v_ k)\).
scientific article; zbMATH DE number 4050843