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MikaelSlevinsky / FastTransforms

:bullettrain_front: Fast orthogonal polynomial transforms :surfer:
MIT License
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Generalised Zernike polynomials? #51

Closed dlfivefifty closed 3 years ago

dlfivefifty commented 4 years ago

I remember there used to be docs on what the transforms actually do, but they seem to have disappeared from the docs page! Where's the Disk transform definition, for example??

MikaelSlevinsky commented 4 years ago

The doxygen layout is kinda strange in that any added pages are under the "Related Page" tab, so is this what you were remembering? https://mikaelslevinsky.github.io/FastTransforms/transforms.html

dlfivefifty commented 4 years ago

Thanks!! @tsgut here's the link

We actually want to do generalised Zernike polynomials. That is, orthogonal w.r.t. (1-r^2)^β. Is that possible?

MikaelSlevinsky commented 4 years ago

These are spin-weighted Zernike? or different?

dlfivefifty commented 4 years ago

Don't think so...

dlfivefifty commented 4 years ago

They are just like Zernike but with β in the Jacobi paramters somewhere

MikaelSlevinsky commented 4 years ago

It should be possible to support orthonormality with respect to r^a (1-r^2)^b on the disk.

MikaelSlevinsky commented 3 years ago

A pull request will soon appear for generalized Zernike polynomials, orthonormal w.r.t L^2(D^2, r^{2α+1}(1-r^2)^β dr dθ).