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Approximating surfaces by moving total least squares method. (English) Zbl 0943.65026
Summary: We suggest a method for generating a surface approximating the given data \((x_i,y_i,z_i)\) \(\in \mathbb{R}^3\), \(i= 1,\dots, m\), assuming that the errors can occur both in the independent variables \(x\) and \(y\), as well as in the dependent variable \(z\). Our approach is based on the moving total least squares method, where the local approximants (local planes) are determined in the sense of total least squares. The parameters of the local approximants arere obtained by finding the eigenvector, corresponding to the smallest eigenvalue of a certain symmetric matrix. To this end, we develop a procedure based on the inverse power method. The method is tested on several examples.

MSC:
65D17 Computer-aided design (modeling of curves and surfaces)
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F20 Numerical solutions to overdetermined systems, pseudoinverses
Software:
VanHuffel
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