# Questions tagged [spherical-harmonics]

The tag has no usage guidance.

13 questions
Filter by
Sorted by
Tagged with
41 views

1 vote
80 views

### 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 ...
1 vote
69 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, ...
1 vote
4k 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 ...
1 vote
96 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 ...
2k 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 ...
537 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 $d_{l,m}$...