G1 continuous conditions of biquartic B-spline surfaces

The necessary and sufficient conditions of G1 continuity between two biquartic B-spline patches with single interior knots are obtained, and the intrinsic conditions of the common boundary control points are also presented. Further, some remarkable difference on the conditions for G1 continuity of two adjacent Bézier patches and those of two adjacent B-spline patches are studied. As a result, the construction of local scheme by using biquartic B-spline surfaces with the single interior knots does not exist.