Re: Interpolating in three dimensions

Hi all,

Apologies for the radio silence, I have been on vacation.

As suggested, I have compared the tricubic interpolator with some of SciPy's existing interpolators, namely RegularGridInterpolator and Rbf (I had some difficulties using the newer RBFInterpolator). I have put together a Jupyter notebook in the repository (https://github.com/fgittins/tricubic), which showcases these comparisons.

To summarise: for the simple functions I considered, the tricubic interpolator fares better than Rbf and RegularGridInterpolator with default options. It seems to have "outperformed" Rbf because it is a local interpolator and will always fit to the data, whereas Rbf forms a smooth function across the grid. With the cubic method for RegularGridInterpolator, the two approaches have similar accuracy. I have also briefly shown how tricubic can estimate derivatives and, for the one case I looked at, it was reasonably accurate.

I don't claim to have done an exhaustive (or particularly quantitative) set of comparisons, so please consider these tests as preliminary and illustrative.

I would appreciate your thoughts and suggestions. It sounds like there is scope and interest for such an interpolator in the SciPy library.

Best wishes,

Fabian
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