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Questions tagged [spherical-harmonics]

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Algorithm for evaluation of spin-weighted spherical harmonics

Is there an algorithm to evaluate spin-weighted spherical harmonics (swSH) at arbitrary points on the sphere? In particular I am looking for, e.g. a recursion relation to evaluate the "spin weighted ...
48 views

Spherical Gradient along $z$-axis

Let us consider a function $f(r,\theta,\phi)$ that can only be efficiently computed in spherical coordinates. We need its Cartesian gradient. We can implement its analytical spherical derivatives, ...
2k views

Computing spherical harmonic coefficients using Scipy

The scipy.special.sph_harm function evaluates a spherical harmonic function at a point. Does Scipy provide any functions to compute the spherical harmonic ...
70 views

Spherical Harmonics: band-limited representations of a vector field on a sphere

I have used pyShtools in the past to expand scalar functions to spherical harmonics and to synthesize band-limited representations of them. However, I am not too sure how to achieve this for a vector ...
547 views

Generating harmonic polynomials in cartesian coordinates

TLDR: Are these polynomials really harmonic polynomials, and how can I generate them? Long version: I want to describe an electrostatic potential $\Phi(x,y,z)$ over a source-free volume, by using a ...
337 views

Discrete Spherical Harmonic Transform from Cartesian grid

I have a grid of data on a 3D Cartesian grid and I would like to find a routine that will allow me to input this data and output a spherical harmonic transform for specific values of radial distances. ...
I am trying to interpolate irregular data $f(\theta, \phi)$ on a sphere and I have so far tried a scipy approach using Kd-Trees and inverse distance weighting, which works ok - however I was wondering ...
I have a function $f(r,\theta,\phi)$ which I am expressing in terms of spherical harmonics $$f(r,\theta,\phi) = \sum_{l=0}^{\infty} \sum_{m=-l}^{l} g_{l,m}(r) d_{l,m}(\theta,\phi)$$ where $d_{l,m}$...