A hole filling method for surfaces by using C1-Powell–Sabin splines. Estimation of the smoothing parameters

Let D⊂R2 be a polygonal domain, H be a subdomain of D   and f∈C1(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 C1-Powell–Sabin spline function f∗ over D¯ that approximates f outside H, and fills the hole of f 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.