Help achieving 3D effect of color sweeping over surfaces

I had to do something like this in reverse once with real footage.  To understand the shape of the animation and timing I recreated the scene in very simple 3D and used a shrinking (in my case) sphere to show where the surfaces needed to change to create the circle shapes.  I'd suggest doing something similar here and using the sphere as the matte

Indeed just simple masks, though probably combined with 3D rendered mattes and possibly a few other techniques like exporting placeholder Nulls/ solids to get the perspective right. Overall simple enough, though. Could be done 100% in AE even without extra render passes. It would just be a bit more work to create extra masks to retain the illusion of 3D obscuration.

Mylenium