How do I do this in Inkscape?
So you have 2 overlapping paths with a heavy black stroke, and want to remove the strokes and anything behind the strokes.
Let's call your 2 paths P1 and P2.
- Select them both and duplicate (ctrl-D), to produce duplicates P1d and P2d.
- Keep these duplicates selected and call Path -> Stroke to path. This will convert the strokes of P1d and P2d into black hollow paths.
- Select P2d and duplicate it; we'll need it twice. Now you have P1, P2, P1d, P2d and P2dd.
- We don't want strokes on the final figures, so select P1 and P2 and remove the stroke (stroke width 0, or no stroke paint).
- Select P1 and P1d, and call Path -> Difference (ctrl--). This will remove the area used by the black frame P1d from P1.
- Select P2 and P2d, call Path -> Difference. This will remove the area of the black frame from P2.
- Select P1 and P2dd, call Path -> Difference. This will remove P2's black frame from P1.
Now you are done. You may want to group or combine the 2 resulting paths into a group or a single path respectively.