Hi Don, I was experimenting a bit with this, I think it will help if the flat base surface for the flow mapping is also a revolved surface with a pole in it as well like this:
That way the center of the object will map to the bottom pole of the sphere and the outer edge of the flat base surface will map to the top edge of the sphere, with this result using Transform > Deform > Flow:
If you use a plane surface (for the base surface in Flow) that only has 4 corner points instead of a radial control point layout it won't map well because an edge in the 4 corner point plane will map to the sphere pole and it will get squished down a lot.
For this case a revolved base surface matches up to a revolved sphere better.
One note - the revolve command replaces revolved horizontal lines with 4 point plane surfaces because those can get special treatment in booleans and fillets so to make a revolved flat disk you have to revolve angled line with no end cap to make an open cone first and then squish it flat.
- Michael
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