a hole filling method for surfaces by usingc1 -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.