A rectangular Gm-continuous filling surface patch and some improvements at corners Original Research Article

We propose a method for filling a four-sided hole that interpolates four connected boundary curves in a net of patches. The surfaces defining these given boundary curves can be of different kinds with their suitable representations: Bézier–de Casteljau polynomial patches, (SBR) rational patches, or other parametric surfaces. Pole-functions are introduced as they extend the Gregory square-functions. The pole-functions result from appropriate combinations of derivatives up to order m (m⩾1) at points belonging to the boundary of [0,1]2 of functions that define the surfaces to be joined. The proposed filling surface is a combination of these pole-functions. It has the Gm geometric continuity join property and is in one piece. We shall improve the quality of the interior filling patch by requiring that the filling surface should become continuously differentiable at corners. This strategy turns out to be significant. Some examples of G1, G2 and G3-continuous filling surfaces illustrate this construction.