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-Bézier 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 Bézier surface from given boundaries. This functional is constructed by a balanced sum among the quasi-harmonic 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.

区域功能是最小化表面设计中的重要概念。但是，它是高度非线性的，因此在实践中很难处理。因此，提出了各种函数来解决Plateau-Bézier问题，包括Dirichlet能量，准谐波函数，弯曲能量以及谐波和双谐波蒙版等。在本文中，我们将这些方法与面积函数的区别进行了比较，并且提出了一种新的称为拟面积函数的能量函数，以从给定边界获得近似最小的贝塞尔曲面。该函数是由准谐波函数，Dirichlet函数和测量等温性的函数之间的平衡总和构成的。它大大提高了现有方法的逼近效率。这种方法可以根据实际需要自由选择不同的参数。还对准区域功能方法和现有方法进行了实验比较，结果表明准区域功能方法更加灵活有效。