G1 continuity conditions of adjacent NURBS surfaces

For the special NURBS surfaces such as bicubic or biquartic B-spline surfaces with single interior knots, some results of the G1 continuity conditions for two adjacent surfaces appeared recently. But for the NURBS surfaces with arbitrary degrees and generally structured knots, the G1 continuity conditions are still unsolved. Therefore, this paper pays attention to studying this problem. In this paper, we obtain the necessary and sufficient conditions of G1 continuity, and present two kinds of sufficient conditions of G1 continuity for two adjacent NURBS surfaces with arbitrary degrees and generally structured knots. In particular, we obtain the intrinsic conditions for the control points and weights of the common boundary curve (so-called the uniform continuity conditions of G1 continuity). It should be pointed out that this case is unique in the discussion of G1 continuity of adjacent NURBS surfaces. At the end, we give the algorithm for constructing adjacent G1 NURBS surfaces.