Minimal quasi-Bézier surface

The quasi-Bézier surface is a kind of commonly used surfaces in CAGD/CAD systems. In this paper, we study how to find the quasi-Bézier surface of minimal area among all the quasi-Bézier surfaces with prescribed borders, i.e., the Plateau-quasi-Bézier problem. The prescribed borders can not only be polynomial curves, but also catenaries and circular arcs. Moreover, the harmonic and biharmonic quasi-Bézier surfaces are investigated.