I am trying to create a graphic demonstrating the difference between an idealized perfect sphere and the Earth's reference ellipsoid. (I know this is also an approximation, but nevertheless.) To this end I want to also exaggerate the eccentricity of the ellipsoid.
Anyway, should I simply scale a sphere vertically such that the vertical axis is shorter than the horizontal axis? If I have a map of the Earth wrapped around the sphere, is squashing the sphere vertically sufficient? Or do I need to convert between geocentric and geodetic latitude first?
What's the proper way to handle this situation?