From povray.newusers:

The question was asked about adding a smoothly rounded base to a conical
flask.
To me, the problem seemed quite complicated.  But after I drew it out, it
simplified itself quickly.

The description of the geometry is in an image on p.b.images under the same
name..

The working .pov file is here. The diagram changes as you change the
parameters.

Alan

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Download 'geometry.pov.txt' (3 KB)