I know that the desired shape here is quite specific: a more rounded domed center that morphs to more pinched corners.

With NURBS construction there are so many ways to achieve surface configurations, each having their own character.

Though, the examples I give are more rounded on the corners, some of the possible construction methods may hold just as viable:



http://moi3d.com/forum/index.php?webtag=MOI&msg=4388.107