How can I generate the equation of a curve that matches all arbitrarily given (x,y) pairs? I would like a polynomial of nth degree, where n does not matter, as long as the curve passes thru all the given points.
I guess this problem is NP-complete. If so, how do I find the closest matching curve in a feasible amount of time?
Furthermore; how do I generate a piecewise polynomial, in case the given (x,y) pairs are discontinuous, or they draw the shape of a, say, circle?
Thanks in advance.