Smooth connection of trimmed NURBS surfaces

An automatic smooth surface connection method that has the capability of tension control is presented. Given two trimmed NURBS surfaces, the new method constructs a smooth connection surface to connect the trimming regions of the trimmed surfaces at the trimming curves. The connection satisfies the pseudo-G¹ or pseudo-C¹ smoothness requirement, a condition not as strong as G¹ or C¹, but smooth enough for most industrial applications. The construction process consists of four major steps: connection curves construction and alignment, initial blends construction, setting up continuity constraints, and internal and external boundary smoothing. The advantages of the new method include: (1) providing the users with more flexibility in adjusting the shape of the connection surface, (2) the representation of the connection surface is compatible with most of the current data-exchange standards, (3) including the classical blending as a special case but with more flexib ility on the setting of the rail curves, and (4) smoother shape of the resulting connection surface through an energy optimization process. Test cases that cover important applications are included.