Surface Fitting Using the Moving Total L_p Approximation
by
Tomislav Marošević
University of Osijek, Faculty of Electrical Engineering, Department of Mathematics
Coauthors: Rudolf Scitovski (University of Osijek, Department of Mathematics)

We look at the problem of generating a surface on the basis of the given data (x_i, y_i, z_i), i=1, ... , m. When the errors appear in all data variables, in general it is suitable to use the so-called moving total L_p approximation (1 <= p <= \infty). Particularly, if p=2 we have the moving total least squares method, and for p=1 the moving total least absolute deviations.

The surface can be locally approximated by planes such that the weighted L_p distances from the points to the plane are minimized in the sense of the total least L_p-norms. Then a global approximant is obtained by means of a certain combination of local approximants, with a possible use of appropriate weight functions. We also consider some examples.

Date received: March 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadz-69.