A bow front is the most expensive shape in furniture, because everything about it has to curve - and the doors are the reason.
A curved door has to swing without its outer edge striking the carcass it is set into. On a flat front that is trivial: the door simply opens. On a bow front the door's own curve means the leading edge sweeps outward as it turns, and if the hinge is placed where it would sit on a flat door, the edge fouls the frame within a few degrees.
So the hinge knuckle is set forward of the carcass face, out past the curve, and the door edge is then cut to a bevel that follows the arc it will actually travel through. That bevel is different on the left-hand door from the right-hand one, and different again if the bow is more pronounced.
Our artisans set it out full size on a board, swing a template through the arc, and cut the bevel to match. It is why the doors on a properly made bow front open sweetly through their whole travel, and why the ones on a poorly made bow front open forty degrees and stop.