Smooth surface extension with curvature bound

Abstract

For a given surface with a piecewise smooth boundary, a new method to extend the surface across its boundary is suggested. The extended surface is $C^2$-continuous along the old boundary, and some extra conditions can be imposed on the new boundary. Furthermore, it is shown that normal curvature of the extended part of the surface can be controlled by predetermined conditions. In order to test the effectiveness of our algorithm, it is shown that surfaces with rectangular and circular boundaries can be extended with all necessary conditions satisfied.