Pamela Boatright answered:
The plat will only lie flat if your wedges are accurately cut and sewn, so you need a good pattern to start with. Someone else had started this quilt, so I can't take credit for the pieces, but I did have to do a bit of adjusting to make them lie flat. One of the things I did was to sew in segments. There were 16 wedges in each circle, so I would sew 4 together, then make sure the outside seams made a 90 degree angle. Then I would sew two together and make sure each half was straight across the bottom. That way I could make minor adjustments as I progressed and when I sewed the halves the plates were nice and flat.