Obtain the maximum and minimum values of a plot's color map

[James Bowery]

Is there some way to obtain the maximum and minimum colormap function values from the resulting plot?

Colormap functions must return a value between 0 and 1.  Therefore, if one is trying to color map a function, one must know the maximum and minimum value of that function over the plotted domain.  For example, I've got a color-mapped plot:

theta,phi = var('theta phi')
cm = colormaps.coolwarm
def c(theta,phi): return ((2/3)*(1+sin(theta)*sin(phi))-(1/3)*(1+sin(theta)*cos(phi))-(1/3)*(1+cos(theta)));
spherical_plot3d(2,(theta,0,2*pi),(phi,0,pi),color=(c,cm))

Since sphereical_plot3d evaluates all of the colormap function values, it should be able to return the maximum and minimum.  That would enable me to offset and scale the colormap function.