Construction of quasi-Bézier surfaces from boundary conditions

Abstract

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.