A hole filling method for surfaces by using C~1-Powell-Sabin splines. Estimation of the smoothing parameters

摘要

Let D is contained in R~2 be a polygonal domain, H be a subdomain of D and f εC~1(D — H). In this paper we propose a method to reconstruct f over the whole D 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 that approximates/outside H, and fills the hole of/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.