A hole filling method for explicit and parametric surfaces by using C1-Powell Sabin splines

In this work we develop a method to fill a hole in a surface, either explicit or in parametric form, or just in a set of three dimensional scattered data. We will construct a new surface which is very close to the original one where it is known and that fills the hole in a homogeneous way, in such a way that the final reconstruction is of class C1. We give results which prove the existence and uniqueness of solution of the proposed method, and we present several graphical examples which show the efficiency of the theory developed.