Spherical surface plot from custom function

I have a function where the input is a set of Euler angles (z, x', z') and a four tensor, C, and outputs scalers, lets call them E and G.

I wish to plot the value of this scaler for every possible direction as a surface plot.

For example, if the value of E is the same in every direction, then the surface plot is just a sphere.

If E varies, then E can be considered the radius of the distorted sphere in that direction.

I think I can use spherical co-ordinates as my Euler angles.

For example, the first Euler rotation around z is the azimuthal angle φ (phi) the second Euler rotation around xp is the polar angle θ (theta) there is no third Euler rotation? I think combinations of these first two rotations should point to every point in the sphere.

This is a very similar problem, solved by somebody in Mathematica. Here the scaler is young's modulus. I have more scalers, so will have several plots

https://mathematica.stackexchange.com/questions/143524/3d-plot-of-a-anisotropy-of-youngs-modulus