I saw a demonstration on one of the quilt shows, but don't remember which one, that was done like a peek-a-boo quilt. You make circles, with the outer border pieced on the back side. They will have to be sewn together and turned so you have no raw edges. When you sew the circles together, in a square, your curved edges should be on top of the quilt. Fold them out flat and the pieced arcs will show on top. Then just tack them down. I haven't tried it myself, as I'm a little frightened of curves. But they made it look really easy on TV (of course).