I'm sure people all over the world are doing this, but it's the first time I've ever thought of it: I had thrifted embroidery in my hand that I wanted to make into a pillow cover, but the oval shape was throwing me off. Usually I piece strips around my crewelwork to frame it with color and make it the right size. But how to manage the curves?
1. Cut out the "mat" just like the frame store would do. Square corners on the outside, then the round opening in the middle, all out of fabric. If you're really picky about sizing, make the opening about 3/8 inch smaller than you want the finished mat to look. The rest of us will just not think about it.
2. Lay the mat over your embroidery, pin in place carefully (don't tug on those bias edges cause they'll stretch!). Machine-stitch in place about 1/4 inch from the raw edge of the mat.
3. Choose some good-looking bias binding, and pin in place with the wrong side up. The binding should be unfolded, and its raw edge should be just lined up with the raw edge of the mat, as in the picture. Make sure to deal intelligently with the ends. Fold one up, and plan to overlap the other on top of it, so that the raw edge will be enclosed later. Around curves, pin generously and try to pin in the tiniest bit of slack or ease to allow the outer edge to make it around the corner later.
4. Machine-stitch, using the fold in the bias tape as your stitching guide. Take your time around the curves, stopping with the needle down to lift the foot and swivel the fabric as needed.
5. Gently press the binding back over the raw edge of the mat, refolding the other edge underneath, so that everything is nice and tidy. Pin neatly in place.
6. Sewing by hand, slip-stitch the outer edge of the binding into place. You can gently press and steam if you have trouble getting it to lie flat around curves, but don't make yourself crazy. If you're making a pillow cover, like I always am, tell yourself that wrapping the cover around the pillow form will take all the bumps out of it.
7. Make up the pillow cover, put on Daisy's bed, and admire!