What I meant is that if you use boxes, then there is no need to use Laurent’s approach as it deals with closed curves of all types, and you only need boxes, which simplifies the task a lot.

Boxes Axes_v01.gh (19.8 KB)

Here is a simple approach. The logic is to first generate longest center line of each rectangle. And then extend those to meet up the other curves, by projecting the end point to the closest curve. Naturally this creates some diagonal lines, which are culled. Then some exterior lines, which are also culled, and finally some pieces of the axes need to be trimmed, so they are also culled depending on their distance to the edge region.

Basically:

I tested for a couple of possible arrangements, and it seems to work. For now only rectangles, no squares.