It's a great question. No kidding. Of course, you can since you can build the first piece naturally, then get the second from a pair of points and a derivative of the first, and so on. But it would generally oscillate as hell. The trick is - if you're approximating a parametric curve, you don't want derivatives to actually match. You want the tangential continuity, which is a proportion of dx/dt and dy/dt derivatives and not the exact number. So if you just tame your derivatives a little, you would still keep the tangential continuity and not let the oscillations loose.