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Very general question, I never really covered this.

Say I have ten data points in 2D space and I need to find a curve which passes THROUGH these points, how do I go about this? I need it to be a curve because I need a function to operate on analytically, not a set of points.

Ordinarily I'd try some least squares fitting, but that won't do here because I really need the curve to cross all the points. Also, I can't use a polynomial fit because the function needs to go to 0 at infinity.

I have it in my head from reading somewhere that this can be done by fitting it to a set of basis functions, eg. a set of Gaussian distributions, and adding them together will make it a lot easier to fit to the points.

Does this have a proper name or something so I can research it further?

Thanks,

Ordinarily I'd go to the library for this sort of thing but my knowledge is so vague I don't have a starting point on this one.

Thanks,