Title: Surface least squares approximation: a shape preserving approach

Authors: Francesca Feraudi

Addresses: Dipartimento di Matematica, Universita degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy

Abstract: A new approach for fitting surfaces to scattered data is presented. In particular, the desired values of an approximating surface evaluated at points on a rectangular grid are given. The aim of the work is to take into account more information than just positional values, namely the intrinsic geometric properties of the surfaces. A local polynomial least squares surface approximation is defined for each data point, in order to minimise an objective function; for this aim only the data points whose gaussian and mean curvatures are close (in a specified sense) to those at the point in question are taken into account, in order to obtain a shape preserving approximation of the surface. Finally a weighted mean of the values assumed at each grid point G_j, by the polynomials corresponding at suitable data points surrounding G_j, is assumed to be the value of the approximating surface at G_j.

Keywords: curvature; least squares approximation; local supports; partial derivatives; shape parameters; shape preserving; surface fitting; scattered data; surface approximation; geometric properties; surface properties; polynomial definition.

DOI: 10.1504/IJCAT.2005.006483

International Journal of Computer Applications in Technology, 2005 Vol.23 No.2/3/4, pp.219 - 228

Published online: 13 Mar 2005 *

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