A hole filling method for surfaces by using C-1-Powell-Sabin splines. Estimation of the smoothing parameters
Let D subset of R-2 be a polygonal domain, H be a subdomain of D and f is an element of C-1((D) over bar - (H) over circle). In this paper we propose a method to reconstruct f over the whole (D) over bar using a technique based on the minimization of an energy functional J More precisely, we construct a new C-1-Powell-Sabin spline function f* over (D) over bar that approximates f outside H, and fills the hole off inside H. The resulting filling patch strongly depends on the values of two smoothing parameters involved in the functional J. We give a criteria to select optimum values of the parameters and we present some graphical and numerical examples. (C) 2010 IMACS. Published by Elsevier E.V. All rights reserved.
filling holes minimal energy optimum parameters powell-sabin