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How could XYZ curve/mesh lines be created for each cubic area as defined by the object's edges?

enter image description here

It seems that this would be theoretically possible, assuming there is a way to connect the points created from the original edges, and then repeat that once more from the resulting edges to get the above pictured result.

enter image description here

This post seemed like a decent start, but the desired result was still out of reach.

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This setup here might be of interest to you:

enter image description here

Here I first capture the inverted normals so that they point inward.

Then I convert the faces into points and instantiate curves there.

At the same time, I move the positions of the faces a little inward, so that I can apply them to the original geometry as a starting position for a raycast to the opposite faces.

This Hit Position, which is then the position of the opposite face in this specific case, I transfer to the endpoint of the curve.

You can then process the curves further at the end and, for example, turn them into a mesh with Curve to Mesh.


(Blender 3.2+)

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