Clipper2 parallel lines concatenation

[MattJKF]

Ahoy!
I'm using Clipper2 for a hobby project about graphical representation.
Given a polygon shape, I would like to fill it with parallel segments (AB) and concatenate them in a zig-zag fancy (AB-BB-BA-AA-AB-...) :

To create the segments, I've used Clipper2Lib::Path64 segment; and I can see that it's working properly.
But when it comes to concatenate them... it's where the mess begins. I've made a sorting algorithm which works nicely 80% of the time, but the other 20% creates some diagonals:

So here comes my question: is there a method inside Clipper2 that makes it autonomously or do I have to improve my sorting algorithm?

[AngusJohnson]

Matt, I don't understand what you're trying to achieve. You question isn't making sense to me.