Recent I try to work out a program that can judge how similar the two functions is. the form of the function is not known yet,but we can use cubic spline curve fit to obtain its form.the question is that dose there exist a criteria which can use to measure the similarity of those two datasets? Intuitively,I use the mean distance between two curves as a criteria.
One way to do this is to fit both datasets with the same function and then compare the fit results. This requires that you select a model/fitting function that best describes the data and then fit with that model to both datasets. In your case you could try something like a polynomial function.
In Origin versions 7.0 and higher, this can be done using the Fit Comparison tool under the Tools menu. The tool will fit both datasets and compute an F value from the fits and then a p-value which reports if the two datasets are significantly different or not.