Our full size guitars at Montana guitar shop are built with curved backs with a 15' radius running lengthwise and widthwise.  Rather than using the concave sanding discs that most shops use to trim the sides of the guitar before the back goes on we invented our own jig that trims very cleanly and accurately.  Backs fit very precisely which is another aspect of building stress free guitars.  Using a router the mechanism glides on ball bearings and is adjustable for different size guitars.  Note that head and tail blocks are also carved at the precise curve to match the sides.