Filling holes with shape preserving conditions

Recently, several techniques have been developed to fill polygonal holes in a given surface by using C1C1-spline patches. Such techniques are based on the minimization of an energy functional which controls the fairness of the patch as well as its closeness to the original surface where it is known, that is, outside the hole. Nevertheless, the filling patch obtained tends to be flat due to the definition of the energy functional, so the used technique does not work properly in certain cases. Here we propose to generalize the filling method previously developed in other works in order to fill holes with some ‘shape’ conditions, i.e., in such a way that the filling patch ‘inherits’ as much as possible the shape of the original surface where it is known.