Maybe this will help: Spline interpolation - Wikipedia, the free encyclopedia
I have a question that sat on my mind for some time and i've always wondered this: is it possible to construct a function from scratch just by viewing a graph (and i'm not talking about simple functions like f(x) = x^2 + 2x +1) knowing some points on the graph, lets say 10 of them? If yes, what's the method called?
I hope you understood my question.
Maybe this will help: Spline interpolation - Wikipedia, the free encyclopedia
Note, however, that given any finite number of data points, there exist an infinite number of functions (or continuous functions or polynomial functions) passing through those points. The spline interpolation earboth gives a relatively simple, accurate method.