The quasi-Bézier surface is a kind of commonly used surfaces in CAGD/CAD systems. In this paper, we present a novel approach to construct quasi-Bézier surfaces from the boundary information based on a general second order functional. This functional includes many common functionals as special cases, such as the Dirichlet functional, the biharmonic functional and the quasi-harmonic functional etc. The problem turns into solving simple linear equations about inner control points, and finally the internal control points of the resulting quasi-Bézier surface can be obtained as linear combinations of the given boundary control points. Some representative examples show the effectiveness of the presented method.

准贝塞尔曲面是CAGD/CAD系统中常用的一种曲面。在本文中，我们提出了一种基于一般二阶泛函从边界信息构造准贝塞尔曲面的新方法。这个泛函包括许多常见的泛函作为特例，如狄利克雷泛函、双调和泛函和拟调和泛函等。问题变成求解关于内控制点的简单线性方程组，最后求解得到的拟内控制点- 贝塞尔曲面可以作为给定边界控制点的线性组合获得。一些有代表性的例子表明了所提出方法的有效性。