Results of interpolation are different if I use:
Method -> "Spline", InterpolationOrder -> 3 in Mathematica
and cubic spline in C++
I believe this is due to difference in methods used by Mathematica and C++.
While the method spline interpolation is generated in C++ is known I have no idea what Mathematica calls a cubic spline (probably BSpline , but I am not sure as C++ doesn't seem to have implementation of BSpline, so I can't compare)
I thought of implementing C++ spline method in Mathematica to make one to one comparison to C++. Other option would be to learn what algorithm does Mathematica use for spline interpolation, but I believe it is not open source, or is it?