Mary is putting together a dogbone headrest pillow for a friend who will be spending a lot of time in a chair. It’ll be similar to this one from a while ago:

She used Bonnie Browning’s pattern and I offered to laser-cut it as practice for other projects I have in mind.
It eventually worked out well enough:

Fold a piece of fabric in half, align the pattern’s bottom edge with the fold, cut around the perimeter, make two more, and sew ’em together.
My first mistake was attempting to assemble the two halves of the pattern from the PDF document into a bitmap image using The GIMP:

That is both tedious and unnecessary, as I found out while trying to align the pieces.
The end goal is a simple and symmetric vector path defining the outline, including a line across the bottom, suitable for laser cutting. Rather than assembling an image, tracing it into a bunch of vectors, then cleaning up the mess, just lay a smooth spline vector path around half of it and invoke symmetry, much as happened with the Lip Balm Holder.
So import the slightly misaligned bitmap into LightBurn, draw a rectangle over just the left half, convert the rectangle to a path, then add a few nodes anchoring the splines to key points of the image:

Although it’s not visible, the top and bottom spline nodes defining the vertical line down the middle are not quite vertically aligned, even though I dragged them to the middle of the pattern. Unsurprisingly, the bitmap image is not exactly aligned with the axes, even though the conversion from PDF to bitmap is entirely digital; the original design may be off by an itsy that would never matter for its intended application.
Tweak the splines / control points, add a few more nodes, and in short order the vector path runs pretty nearly along the middle of the bitmap image:

Rather than trying to draw the second half just like the first half, duplicate the path and mirror the copy left-to-right to get the right half of the pattern. Grab the lower-left corner of the copy and snap it to the lower-right corner of the original, whereupon you will find the two points at the top of those lines don’t quite line up.
This is a grossly zoomed look at the top center, with the two red angles showing the two halves not quite meeting in the middle:

Now the magic happens.
In quick succession:
- Select the right-side path
- Invoke Arrange → Two-point Rotate / Scale
- Zoom way in on the bottom center
- Click on the center point to define the Rotate center
- Zoom way in on the top center
- Click-n-drag the right corner to snap it onto the left corner
- Done!
What just happened is that the right half now directly adjoins the left half, with the upper and lower center points overlapping.
Invoke the node editor and delete the center lines from both halves, leaving just the (overlaid) top and bottom nodes. Select both paths, then invoke Edit → Auto-join selected shapes to merge the two halves into one:

I missed the clip line in the middle of the top, but that’s why the first version is always a prototype.
This was easy, but it’s good to stay in practice …
The obvious next step: the laser cutter cuts the fabric pieces. – And in the second iteration, it can also add seam allowances and alignment marks, or for synthetics, spot-weld two pieces together, so you don’t need pins for alignment.
Oh, a resizing tool would also be nice. And maybe a 3d-program with a virtual adjustable mannequin that can be dressed and the output fed to a pattern making script for a laser cutter or a chalk-line fabric plotter… ;)
The painfully obvious problem with Step 1: the smell of charred fabric.
I suspect carefully tuning speed vs. power for a particular fabric will help, but there seems no way to completely avoid scorching. Apparently ozone knocks the smell down, perhaps while damaging the fabric or colors, and I should gimmick up something to test that notion.