Create an ellipse dome surface (9.9 KB)

I want to create an ellipse dome structure and its surface. Can anyone please help? Many thanks!

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here a solution more similar to the images you put.
The idea is to make an ellipsoid using deformation of a sphere, then shifting this shape up, then searching intersection with planes, then lofting these intersections, then transforming to mesh to have quads. (15.5 KB)

There are other ways with more control of the shape that is not always ellipsoid.

Thanks a lot! (16.1 KB)
Another way…