Construction of Minimal Catmull-Clark's Subdivision Surfaces with Given Boundaries

Minimal surface is an important class of surfaces. They are widely used in the areas such as architecture, art and natural science etc.. On the other hand, subdivision technology has always been active in computer aided design since its invention. The flexibility and high quality of the subdivision surface makes them a powerful tool in geometry modeling and surface designing. In this paper, we combine these two ingredients together aiming at constructing minimal subdivision surfaces. We use the mean curvature flow, a second order geometric partial differential equation, to construct minimal Catmull-Clark’s subdivision surfaces with specified B-spline boundary curves. The mean curvature flow is solved by a finite element method where the finite element space is spanned by the limit functions of the modified Catmull-Clark’s subdivision scheme.