Self-Intersecting Polygons

I’m trying to manage the result of an offset polygon that self-intersects.

I can see a possible solution in this post, Geometry, join by intersection - #7 by JacobSmall, @JacobSmall talks about find the original surface with a 0.5, 0.5 UV point and I’m wondering how robust this is. How is the UV calculated and are there situations where that point wouldn’t land on the surface? If it’s essentially the centroid then I can see how it wouldn’t always work. What alternatives are there to this?

Before I fall down this rabbit-hole, does anyone have a solution they’d like to share? Ultimately I’d like to separate the self-intersecting polygon in to multiple polygons. I found quite a few solutions but nothing that are obvious enough for me to use yet.

…and the forum thinks I’m a new user cause it wouldn’t let me use my gmail account and will only let me post 2 links so, yeah, sorry about this.

www.researchgate DOT net/profile/Patrick-Glauner/publication/229158251_A_Simple_and_Correct_Even-Odd_Algorithm_for_the_Point-in-Polygon_Problem_for_Complex_Polygons/links/5a5a91f64585154502748c73/A-Simple-and-Correct-Even-Odd-Algorithm-for-the-Point-in-Polygon-Problem-for-Complex-Polygons.pdf?origin=publication_detail