Is there a way to estimate the shape or curvature of a function given some data points?

Question

I have a series of measurements (data points), we can call them Ys for now, and two input variables m and n, such that f(m,n) = Y. Is there an easy way to compute the shape or curvature for function f that maps m,n into Ys - i.e., determining whether the function is polynomial or something else? Thanks!