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[Draft] Calculate first order derivatives of SH using recurrence relations #194

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@jb-ye jb-ye commented May 30, 2024

This is the drafted implementation of calculating d f / d varphi and d f / d theta for spherical harmonics.

Some mathematical details:
https://www.ppsloan.org/publications/StupidSH36.pdf
https://jcgt.org/published/0002/02/06/
https://en.wikipedia.org/wiki/Associated_Legendre_polynomials#Reparameterization_in_terms_of_angles

I use recurrence relations below to compute derivatives of Associated Legendre polynomials.

Screenshot 2024-05-30 at 3 44 16 PM

@jb-ye jb-ye marked this pull request as draft May 30, 2024 17:12
@jb-ye jb-ye changed the title Calculate first order derivatives of SH using recurring relations Calculate first order derivatives of SH using recurrence relations May 30, 2024
@jb-ye jb-ye changed the title Calculate first order derivatives of SH using recurrence relations [Draft] Calculate first order derivatives of SH using recurrence relations May 30, 2024
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