GC1 continuity between two adjacent rational Bézier surface patches
Computer Aided Geometric Design
On the G1 continuity of piecewise Be´zier surfaces: a review with new results
Computer-Aided Design - Special Issue: Be´zier Techniques
The NURBS book
GCn continuity conditions for adjacent rational parametric surfaces
Computer Aided Geometric Design
G1 continuous conditions of biquartic B-spline surfaces
Journal of Computational and Applied Mathematics - Selected papers of the international symposium on applied mathematics, August 2000, Dalian, China
Geometric continuity between adjacent Bézier patches and their constructions
Computer Aided Geometric Design
Reconstruction of convergent G1 smooth B-spline surfaces
Computer Aided Geometric Design
Merging multiple B-spline surface patches in a virtual reality environment
Computer-Aided Design
G2 B-spline interpolation to a closed mesh
Computer-Aided Design
Technical Section: Real-time ray casting of algebraic B-spline surfaces
Computers and Graphics
Properties of g1 continuity conditions between two b-spline surfaces
CGI'06 Proceedings of the 24th international conference on Advances in Computer Graphics
The calculation of parametric NURBS surface interval values using neural networks
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Constructing G1 Bézier surfaces over a boundary curve network with T-junctions
Computer-Aided Design
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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.