Approximation methods for the Plateau-Bézier problem

The stretching energy functional and the bending energy functional are widely used for approximating the solution of the Plateau-Beacuteizer problem. This paper presents another two simple methods by using the extended stretching energy functional and the extended bending energy functional. The resulting surface obtained by the new methods will have a smaller area. Comparisons are made with both the area and the mean curvature of the resulting surfaces.