Solved! SphericalRegion->True does the job. I think I did try it set to true in the sphere before I posted here, but maybe I was messing things elsewhere.
- N
Animate[Show[sphere, Axes -> False, SphericalRegion -> True,
ViewVertical -> {Sin[v], Cos[v], 0}], {v, 0, 2 Pi, Pi/36}]
Well this seems to be the feature, as the help specifies,
Parameters to ColorFunction are normally scaled to be between 0 and 1:
__________________________(by default)_________________________
So, the parameters are scaled, not the results.
- N