Algorithms for G1 connection of multiple parametric bicubic NURBS surfaces

The objective of this paper is to introduce an innovative approach for constructing effective algorithms for removing gaps between parametric NURBS surfaces in three-space, while maintaining geometrical smoothness for the combined (or compound) surface. Similar to the degenerate case of tensor-product B-spline surfaces, if the underlying knot sequences along the connecting boundaries of two NURBS surfaces are proportional, then the parametric surfaces can be connected in a G¹ fashion. This approach can be easily extended to connecting three or four parametric NURBS surfaces. We will demonstrate the feasibility of our approach by focusing on the C¹ bicubic setting with knot sequences being equally-spaced and having double interior knots. This revised version was published online in June 2006 with corrections to the Cover Date.