Filling n-sided regions with G1 triangular Coons B-spline patches

Filling n-sided regions is an essential operation in shape and surface modeling. Positional and tangential continuities are highly required in designing and manufacturing. We propose a method for filling n-sided regions with untrimmed triangular Coons B-spline patches, preserving G1 continuity exactly. The algorithm first computes a central point, a central normal, the central, and the corner derivative vectors. Then the region is split into n triangular areas by connecting the central point to each corner of the boundary. These inner curves and all cross-boundary derivatives are computed fulfilling G1 compatibility conditions. And finally, the triangular patches are generated in the Coons B-spline form, one boundary of which is regressed to the central vertex. Neither positional nor tangential error is introduced by this method. And only one degree elevation is needed.