Drawing arcs, or other methods that draws curves manually
May gives more freedom designing.
To have a surface linked between a square and a circle is much more long process to obtain the surface you want (or the profil curve that generates the surface).
as the circle and the square cant meet each other directly, you need intermediar shapes to make the gap between them.
For other purposes but different geometrical process
Polygons might be helpful ?
Imagine a circle inscribed in a square, then adding two points on this circle then it becomes an hexagon, the more you add points the more it will became a circle.
Thus this will affect your profil curvature but you will have more precision and information about it.