As others have recommended, I freezer paper piece NYB blocks.
I HATE conventional foundation piecing where you sew through the paper, but the freezer paper mothed is different and I love it.
Check out this tutorial for the basic method:
http://www.twiddletails.com/store/in...age=page&id=21
I piece the spiky arcs this way, for sharp clean points. Very easy.
Then to the curves:
For the solid arcs, I cut a piece of freezer paper for each, iron it onto the wrong side of the fabric, mark the curve on the fabric along the freezer paper with fadeaway marker, and pull the freezer paper off (keep it for next time, it reuses beautifully about half a dozen times).
I mark the curves on the spiky arc fabric the same way, pull the freezer paper off - then I pin the curves with tons of pins along the marked lines, and sew very slowly.
Done. 8-)