I have a multi-colour project with ~100 pieces that I’ve been cutting out of plywood and staining separately, but I’d like to nest together like-coloured pieces then assemble it like a jigsaw.
My file is a collection of simple vectors that form many closed shapes. Is there a tool or function that allows me to “explode” apart those shapes, duplicating vectors that are shared between adjacent closed spaces?
Here is an example from the workpiece.
I haven’t found an easy way to do it. That task is pretty simple in CorelDraw (using their Smart Fill tool). It is also easy to do in a CAD program like Draftsight (using the Area Boundary command). A cost effective solution is the program Affinity Designer (using their Shape Builder tool)
There is almost certainly a problem with that artwork: the pieces appear closed to the eye, but are really lines & curves with abutting endpoints
The key fact: each node in a closed shape can join only two curves. Places where three curves meet at a T intersection have a single node parked atop the continuous line.
As a result, there are no closed shapes to pull apart, which you’ve probably already discovered. 
You can create closed shapes by taking advantage of LightBurn’s Image Trace tool. Export the layout as a PNG, import it back into LightBurn, then trace the image back into vectors. Because LightBurn lays a vector along each side of a black line, the original single vectors split in two and the shapes on either side of the line will be closed.
Most of the time, folks want “center line trace” to eliminate the splitting, but in this case it does what you need.
The result may need some cleanup at the intersections, but it’ll be much easier than re-drawing the whole thing by hand with paired lines.
Thanks for this - I actually bought a licence to Affinity a while ago, but haven’t committed to learning it, yet. Will report back later!
You are welcome. Look for the Shape Builder tool. It is in the current version of Affinity Designer.
If you want to do this in Lightburn, you can:
Offset all lines by a tiny amount (exaggerated in this example) in both directions
And then either:
A: Offset them outward with a corner-style corner, in batches (have to do this batches of things that don’t touch each other, else they weld back together).
B: use a kerf offset for the shapes equal to the offset, to make up for the gap.
If you use a really small offset value in the first step you might not even need to do the later compensation step, depending on the finished product.
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