Let us consider continuous functions that only depend on the orientation in space (θ,φ). The spherical harmonics are a basis of such functions.
The decomposition in spherical harmonics is used to represent these functions ; it is similar to the Fourier transform for periodic functions.
In the plane (circular harmonics)Edit
A function is decomposed as
where Yl is the circular harmonic. It is expressed as
where Pl is the Legendre polynomial
The circular harmonics are represented in three ways:
|Cartesian plot of||Polar plot of||Polar plot of|