As for most sewing projects where a pattern is not readily available, I’ll create a test piece (or six) before using my good fabrics.
I know a simple circle is not the correct answer, but I’ll start there. I cut out a circle a little larger than the circumference of my aventail fully stretched out (approx. 1"). Then I’ll cut a smaller circle out of the center, this being about the circumference of the bascinet.
I’ll have to add a second piece to account for the 2” rise under my vervelles. This rise is 4” for the length of the face opening. The total length of this piece will be the circumference of the bascinet (plus seam allowance). As always, add an extra inch for the fudge factor. You can always trim it off later.
To make the pieces match up, I had to cut a dart (triangle, about 4” on a side) out of the circular piece of fabric . For the final pattern I’ll have to remember to remove 4 darts of 1” length spaced equally around the circumference.
[edited for clarity]