I use B-spline curve fitting to obtain one smooth curve. If I obtain two smooth B-spline , how can I connect then smoothly. For example, I have 59 points((x0,y0,z0),...,(x58, y58, z58)) and I have two fitted B spline. One B-spline is for the first 30 points, another is for the next 30 points and the two point set share one common point((x29,y29,z29)). The point (x29,y29,z29) will be modified twice due to curve fitting and will have two new positions. If I just connect the two new positions, the final curve will not be smooth at the point (x29,y29,z29). Currently I perform curve fitting for all data together but that will modify the smooth curve for the first 30 points entirely. I hope to only modify the connecting part of the first smooth curve. I know I need to impose derivatives need to be equal at the joint. I don't know how to do that.
Fitting together B-splines with a given continuity is a hard problem. This was actually the motivation behind developing a generalization of NURBS called T-splines. There are many articles on T-splines and T-NURCCs that could be helpful to you if you're interested in going that route.