Sorry Doug like most "customers" you have bought the sail maker BS,
most sails of the type we're talking about here, are cut lying staked
"flat" on the loft floor. (save the super new high tech materials &
laminates but they effectively mould the shape into them over a jig)

It's easy enough to confirm?? just lay the sail flat on a floor; or
measure the panels you'll find most "normal" sails have parallel panels.

The shape is induced when a curved edge (the luff or combination of
luff & foot) are stretched to varying degrees, in an essentially
straight line. (often along a forestay, mast, boom etc.)


K
Not! Each seam is cut on a curve and when sewn creates the sail shape,
unless you are sailing a sunfish or something. The most obvious example
is a spinnaker. Try laying that flat on the floor. None of my sails
lay flat except the storm jib.

Gaz