Dome Roof - Getting CA to literally bend to my will! HELP!

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I'm working on a refugee project where a client of mine has come up with a system for refugee camp to erect simple dome structures for habitation.  I'm frustratingly trying to get CA to create the shape of the structure to reflect what my clients system shows which is a oblate ellipsoid which provides better headroom and a lower ceiling at the peak.  I'm close but its not exact.  I've attached images of what I've done, which looks like a half a perfect sphere and what it's really supposed to look like. If anyone can get the dome of the roof to follow more of an oblate ellipsoid shape, I would greatly appreciate any insight on how to get the program to do this.  The best I can figured out how to do is a half sphere.

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