Hole-filling techniques by using minimal energy surfaces

In the last few years, several techniques to fill holes of a given surface by means of minimal energy surfaces have been proposed. In all cases, the filling patches are obtained by minimizing an `energy functional' defined in a vector space of spline functions over the Powell-Sabin triangulation associated to a $Delta^1$-type triangulation of a given domain D. The energy functional and the space of spline functions are defined in order to the filling patch fulfills certain geometric features. In this work we present, for the first time, a general framework to include most of techniques above referred. Under this general new frame, we review the main filling-holes techniques developed until now, we give their main characteristics, the computation aspects as well as some graphical examples.