In this case,
I want to get the result like next png
ultimately,
I want to get a total of 4 curves (black, green, blue, red) from the first 6 curves (blacks)
First of all, thank you for your interest in my article.
My question is to make two overlapping lines into one line.
It is not spread out sideways.
well… this was just for the sake of trying 
if they intersect → and → the angle between them is multiple of Pi → melt them together (with a lot of suffer)
unique_lines.gh (21.6 KB)
[just waiting for someone to post a 3-component solution so I can finally drink the last gin tonic and contemplate poor life choices lol]
In your case this one seems to work:
unique_lines_RE.gh (24.8 KB)
I just saw, if you want them just in the same path you can skip the part behind List item:
