a class representing a function on the sphere by its harmonic series
The function is stored by its coefficients fhat with respect to the spherical harmonics, ordered degree by degree. This is the default representation in MTEX, since convolution, rotation and quadrature are cheap on it.
Syntax
sF = S2FunHarmonic(fhat)
sF = S2FunHarmonic(fun)
sF = S2FunHarmonic(psi)
sF = S2FunHarmonic(fun,'bandwidth',N)Input
| fhat | harmonic coefficients, ordered by degree |
| fun | S2Fun or @function_handle to be approximated |
| psi | S2Kernel |
Output
| sF | S2FunHarmonic |
Options
| bandwidth | maximum harmonic degree |
| antipodal | the function fulfills f(v) = f(-v) |
Class Properties
| fhat | harmonic coefficients |
| bandwidth | maximum harmonic degree |
| antipodal | f(v) = f(-v) |
| isReal | the function takes only real values |
Example
sF = S2FunHarmonic.quadrature(@(v) dot(v,vector3d.Z).^2)sF = S2FunHarmonic (y↓→x)
bandwidth: 128
antipodal: true