Interpolating 1D Gaussian into 2D Gaussian?

EDIT: based on your clarification, it's clear what's going on. You are trying to interpolate a function beyond the range of available data -- i.e. You are going from interpolation to extrapolation.

Splines are going to result in the overshoot that you are observing. The solution is simply to make sure that your 1D function has values in the interval min(r), max(r). Note that in the original data, max(r) is about 424, while the function you are interpolating is defined on the range -300,299.

Leo is right in his diagnosis. I'd like to suggest a simpler (I hope) remedy: to do what you want to do (which is basically rotate a Gaussian around its symmetry axis) and to get a reasonable answer in a 600x600 square you need a Gaussian 600*sqrt(2)=849 pixels long. If you can do that, then all further thttp://stackoverflow.com/questions/2443046/interpolating-1d-gaussian-into-2d-gaussianrickery is not necessary.

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