Surface Fitting for Extremely Large Scattered Data Sets
by
Emanualle Galligani
Università di Mdena e Reggio Emilia
Coauthors: Maria Angela Magnani (Università di Padova)

In this paper a method for the construction of a smooth bivariate function z=S(x, y) is analysed: given a set of arbitrarily spaced three dimensional points { (x_i , y_i , z_i) , i=1, ..., N }, a surface S which has properties of regularity and S(x_i , y_i)=z_i  , i=1, ..., N is computed. The method consists of three separate steps: at the beginning a triangulation of the domain is executed; then a curve network is constructed on the subset consisting of the union of all edges of the triangulation and then, by means of a blending method which harmonizes the data on the edges of the triangulation, a C¹ surface S is determined.

In order to avoid possible oscillations of the surface, the main step is the computation of a suitable curve network. A well known approach to this problem, consists in minimizing a quadratic functional which considers not only a minimum condition on the curvature of the restricted function to each edges of the triangulation, but also of a tension term; the obtained quadratic form is proved to be positive definite. The sparsity of the hessian matrix of the quadratic form suggests to minimize the functional with the Coniugate Gradient Method. The implementation of the global method to compute the C¹ surface, has been carried out with Fortran codes on workstation Digital Alpha 500au.

Date received: January 26, 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 # caeb-21.