How do I combine paths in Inkscape while preserving overlap?

Question

I'd like to CNC draw an image. The image is composed of many, many shapes that overlap with each other.

Say I'd like to draw this image:

Visually I can see the outline of the star, but part of the star's outline is occluded by the outline of the rectangle (because it's filled).

I'd like my CNC machine to draw the picture this way, but when I load it up it sees it like this instead:

What could I do to preserve the visual effect of the overlap? Essentially I'd like to select all fills, remove all paths behind those, and then get rid of the fills.

I'm having trouble understanding how the usual "break apart", "union", etc could work together to achieve this.

Answer 1

For CNC you probably don't want to have redundant path segments exactly on top of each other.

What you want to use is 'Path → Cut Path' with a duplicate of the rectangle (Ctrl+D), then deleting the slice of the path that should be hidden.

Answer 2

Try this.

1. Remove the fills from both shapes, although you don't have to do this, it will allow you to see what is going on under the rectangle

2. Select the rectangle and Copy it

3. Select both star and rectangle and do Path > Difference. This operation will consume the rectangle. This is normal, don't panic!

4. Do Edit > Paste in Place to get the rectangle back

This will create two separate paths that fit together exactly. If you need to combine them to one path, select both and do Path > Combine

For example

If you have multiple complex overlapping shapes, I posted an answer here with a possible solution that will probably work better, but I won't repeat it here.

If you need to delete redundant segments, select the segments using the Edit Paths by Nodes tool, and hit the Delete Segment button.

Answer 3

As I understood your question, you want to make the path below the square invisible and hide the part of the square, which reaches into the star, so you do as Billy Kerr shows in the upper animation, but instead of difference you select union.