Custódio, A. L.Fortes, M. A.Sajo-Castelli, A. M.2023-09-222023-09-222023-032238-3603PURE: 72197200PURE UUID: c851d62b-135b-459a-81f4-bf2225ff0776Scopus: 85147545121WOS: 000928064000004http://hdl.handle.net/10362/158163Publisher Copyright: © 2023, The Author(s).In this paper we handle the problem of filling the hole in the graphic of a surface by means of a patch that joins the original surface with C1-smoothness and fulfills an additional non-linear geometrical constraint regarding its area or its mean curvature at some points. Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method.253042161engArea constraintCurvature constraintEnergy functionalFilling holesSurface reconstructionComputational MathematicsApplied Mathematicsjournal article10.1007/s40314-023-02210-3https://www.scopus.com/pages/publications/85147545121