Tree branches in Join

New to Grasshopper, so this is probably a very basic question.
I’m trying to join sides of a square with its diagonals like this:

However, I can’t correctly align the two trees of curves for the join function. (10.3 KB)
I would like to get the diagonal to join with each of the two curve fragments resulting from Shatter.
What am I getting wrong?

Your approach is a bit complicated… I attached a file with two options (16.7 KB)

Thank you very much for the solution!
However, I was looking to extend this to a polygon where I am measuring all areas cut off by all chords between all vertices.
So I introduced a series to define the shift, but then the branches are off again: (12.0 KB)

Chords from each vertice to all other vertices?


Chords in between end points of two consecutive, joined edge segments?

Chords from each vertex to every other vertex.
To be joined with all the edges “subtended” by the chord.

I think a sketch of the desired result would be useful

Here is a sketch of areas I’m looking for (here for a single vertex, I’m looking to shoot chords from every vertex). Chord shown in yellow. The two areas resulting from a split shown in green and red.

(I am going to later use the area of the intersection as a convexity/concavity measure to use for fitting a plane.)

Intersection between what?

Intersection between the chord and the polygon. Area is the area clipped by the chord.

That’s what the image above shows (14.2 KB)

Wow, thanks so much, this is amazing!
Really appreciate your help and patience.

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