G(1) 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 G(1) continuity conditions for two adjacent surfaces appeared recently. But for the NURBS surfaces with arbitrary degrees and generally structured knots, the G(1) 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 G(1) continuity, and present two kinds of sufficient conditions of G(1) 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 G(1) continuity). It should be pointed out that this case is unique in the discussion of G(1) continuity of adjacent NURBS surfaces. At the end, we give the algorithm for constructing adjacent G(1) NURBS surfaces. (c) 2005 Elsevier B.V. All rights reserved.
g(1) continuity nurbs surface uniform continuity conditions piecewise bezier curve knot removal piecewise polynomial function