The backs of most modern musical instruments have a slight arch to them, they are not flat. The slight arch makes the instrument stronger, and allows expansion and contraction with changes in humidity. As the back swells with increased humidity the arch gets a little higher. I use a pretty standard arch which is a circle with a radius of 15 feet. The back braces are also cut with this 15 foot radius arch so that when they are glued to the back, the back has the desired arch. The braces are glued to the back in a dish which has the same 15 foot radius cut into the surface. One can buy these radius dishes, but they are (in my mind) pretty expensive, so I have cut my own. As I build out the shop here in Florida, I need to cut some new dishes.
To cut a dish I made up a jig which is a channel just the width of a router base. The bottom of the channel is made with some thin plastic trim molding which is bent along a 15 foot radius line. Then as the router is run along, it cuts the 15 foot radius line. The dish has a center pin, so you just rotate the dish and re-run the router along the channel. A great project to do outside on a cool and breezy day because it makes a lot of sawdust cutting that dish out of a piece of plywood. When you are done with the router a quick sanding to take off any unevenness and fuzz, a coat of shellac to seal the surface, and you are good to go.
