New appendix page: spherical harmonics #104
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| &space;=&space;\sqrt{\frac{(2l+1)}{4\pi}\frac{(l-m)!}{(l+m)!}}&space;P_l^m(\cos&space;\theta)&space;e^{im\phi}") | ||
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| for integer *order* *l*, *phase* *m*, associated Legendre polynomials *P*. |
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Consider "phase factor" instead of "phase"? See dipy/dipy#3086 (comment) and preceding discussing there.
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Lately I've tried to consistently use "degree" rather than "order" for l. Wikipedia uses "degree" and "order". "Phase factor" is at risk of erroneous conflation with specifically the Condon-Shortley phase factor. So I wonder if adopting "degree" and "order" here would be better?
(I'd likely modify the MRtrix3 online documentation accordingly)
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I would really prefer to use "order" here (rather than "degree") for the reasons mentioned in that PR discussion in DIPY (i.e., to be consistent with the dMRI literature). But I agree that "phase" is fine, even though it implies something continuous, it is easy to understand what it means.
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@jdtournier any strong opinions? I have some limited sense that we've tried to transition to "degree" for l, but our own SH docs page conflicts, other docs self-conflict, and I'm not able to find any discussions online.
PS. This terminology is not just for the appendix, there's also a metadata field specifying maximal l. Could call it "SphericalHarmonicLmax" or the like if there's too much contention.
Co-authored-by: Ariel Rokem <[email protected]>
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That's probably something I did 😄 |
Closes #100.
I'm not 100% happy with the structure: there's a section on "truncated spherical harmonics", and there there are tables relating maximal spherical harmonic degree to number of coefficients, yet the former don't reside in the latter. But they can't just be moved because of other order dependencies.