Re: Interpolating in three dimensions

Hi Fabian,

On Wed, Jul 5, 2023, at 11:28, Fabian Gittins via SciPy-Dev wrote:
> I came across this paper 
> (http://www.cds.caltech.edu/~marsden/bib/2005/08-LeMa2005/LeMa2005.pdf), 
> which describes (local) tricubic interpolation in three dimensions that 
> is continuous in the function and its first derivatives.

Thanks for your offer to contribute a new feature to SciPy!

It sounds useful to have higher accuracy interpolation derivatives available. Have you compared the results with those from SciPy on some synthetic data to see how they differ, both in result and derivative accuracy?  I'd also be curious to see what work has been done in this area since 2005.

Thanks to Trever Hines, our Radial Basis Function interpolation routines were much improved recently. I'm rusty, but I vaguely recall that it may be possible to calculate the derivative of those interpolations? See, e.g., [1].

Stéfan

[1] https://www.colorado.edu/amath/sites/default/files/attached-files/rbf_1.pdf
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