sphericalHarmonics: Compute spherical harmonic values at given points on the...

In frycast/rcosmo: Cosmic Microwave Background Data Analysis

Compute spherical harmonic values at given points on the sphere.

Description

The function sphericalHarmonics computes the spherical harmonic values for the given 3D Cartesian coordinates.

Usage

sphericalHarmonics(L, m, xyz)

Arguments

L	The degree of spherical harmonic (L=0,1,2,...)
m	The order number of the degree-L spherical harmonic (m=-L,-L+1,...,L-1,L)
xyz	Dataframe for given points in 3D cartesian coordinates

Value

values of spherical harmonics

References

See https://en.wikipedia.org/wiki/Table_of_spherical_harmonics

It uses equation (7) in Hesse, K., Sloan, I. H., & Womersley, R. S. (2010). Numerical integration on the sphere. In Handbook of Geomathematics (pp. 1185-1219). Springer Berlin Heidelberg,

but instead of the order k=1,...,2L+1 in the book we use m=k-L-1.

Examples

## Calculate spherical harmonic value at
## the point (0,1,0) with L=5, m=2
point<-data.frame(x=0,y=1,z=0)
sphericalHarmonics(5,2,point)

## Calculate spherical harmonic values at
## the point (1,0,0), (0,1,0), (0,0,1) with L=5, m=2
points<-data.frame(diag(3))
sphericalHarmonics(5,2,points)

frycast/rcosmo documentation built on Oct. 11, 2022, 5:21 p.m.