Given the edges are represented by lines, line representation needs to be robust to any angle, including very vertical or very horizontal, and they are segments:

I expect the line segments are represented by their two end points.

This makes it easy to encode which side is fill vs. alpha, by ordering the two points. So that as you move from the first point to the second, fill is always on the right. (Or vice versa.)

Another benefit of ordering at both point and segment levels, is from one segment to the next, a turn to the fill side vs. the alpha side, can be used to inform clipping, either convex or concave, reflecting both segments.

No idea if any of this what is actually happening here, but this is one way to do it. The animation of segmentation did reflect ordered segments, and clockwise for the outside border, and counterclockwise for the cavity in R. Fill to the right.