Quasi-area functional for the Plateau-Bezier problem

Area functional is an important concept in minimal surface design. However, it is highly nonlinear and hence rather difficult to handle in practice. Therefore various functionals are proposed instead to solve the Plateau-Bezier problem, including Dirichlet energy, quasi-harmonic functional, bending energy and the harmonic and biharmonic masks, etc. In this paper, we compare the differences between these methods with area functional, and propose a new energy functional called quasi-area functional to obtain the approximate minimal Bezier surface from given boundaries. This functional is constructed by a balanced sum among the quasiharmonic functional, Dirichlet functional and a functional which measures isothermality. It improves greatly the approximation efficiency of existing methods. Different parameters can be selected freely according to the needs of the actual situation in this method. Experimental comparisons of the quasi-area functional with existing methods are also performed which show that the quasi-area functional method is more flexible and effective.