I have made quite a few irregular shaped pieces in the years since around 1992-3, many of which can be found in the gallery pages of my website, www.alisonschwabe.com
In the past couple of days, on the Quiltart list there have been questions about doing this, and various answers given, and since I sent the original questioner this jpg, I thought I should post my version for anyone else who is interested in trying irregular shapes but intimidated by the finishing.
There are lots of ways any shape can be finished, and even look ‘unfinished’ if that goes with the integrity of the work, but irregular shapes can be tricky if you are looking for a really neat ‘properly finished’ edge, as many who are currently entering pieces in the experimental areas of quilt shows are feeling they need to achieve. (the Quilt Police loom large here) If the outline of the quilt is not too convoluted a binding will probably work OK. But if you have lots of pointy bits this one really works well. Granted a bagged back is popular, and probably perfect for small things, but I have noticed that bag-backed large quilts are often just that – ‘baggy’. This method always works for me, and despite the several diagrams is not at all difficult; if you can face an armhole or neckline of a garment, you can do this easily. Note point #8 – faced pointy bits do tend to curl a little allowing the facing to roll forward and be seen from the front, even other less shaped areas will tend to do this too. Even if you use some of the same fabric as used on the front, this looks sloppy and incompetent. So use the instructions in point #7 around the whole, and #8 where you get to a tricky point shape. Then complete by sewing the edge of the facing down.
I teach workshops taking this all further, including how to get some seriously non-straight shaping along the top edge. Some steps need to be taken in the pre-quilting construction stages to ensure these hang easily and conventionally, also that they fold for transportation, if these things are an issue with your work. To me it sometimes feels disappointing to see exciting shapes along the sides and bottom of a quilt hanging from a straight edge along the top. I think that if that person had known how, he/she might have chosen to make the top shaped, too. .. or maybe not, of course.