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

Description Usage Arguments Value References Examples

View source: R/MathHelpers.R

Description

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

Usage

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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

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## 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)

rcosmo documentation built on Feb. 14, 2020, 5:06 p.m.