volume

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

Options

See also

S2FunHarmonic.volume S2Fun.sum S2Fun.mean