Integrates an S2Fun on the region of all vector3d's that are close to a specified vector3d (center) by a tolerance (radius), i.e.
\[ \int_{\angle(g,c)<r} f(g) \, dg.\]
Description
The function 'volume' returns the ratio of the volume of an S2Fun on the region (of all vector3d's that are close to a specified vector3d (center) by a tolerance (radius)) to the volume of the entire spherical function.
Note that if the S2Fun \(f\) is 'antipodal' the volume in any center with radius 90° will return the mean value of the S2Fun, which is infact the volume of the whole sphere.
Syntax
v = volume(sF,center,radius)Input
| sF | S2FunHarmonic |
| center | vector3d |
| radius | double |