I'll be teaching a workshop for my guild in June on curved piecing, and spent today finishing up the samples--placemats made using two different methods. The first one, above, is done in a "quilt-as-you-go" method, using thin straight strips that are manipulated into curves as you sew. I learned this method from my friend Mary Beth; I think it must be the same method used by Ann Brauer, whose gorgeous work I saw in a show a few years ago. The fabric above is an assortment of Japanese Daiwabo fabric. The second placemat was done by laying wider strips of fabric on top of the other, right sides up, overlapping a bit, and cutting the curve one wants. This way one can get deeper "waves."
I've collected instructions for this second method from several sources. Brenda Gael Smith's instructions are especially clear--see any of her patterns that include curved piecing, available on her web site.