I'll be referring to the definition of the offset bisector from the definitions section of CGAL's 2D Straight Skeleton and Polygon Offsetting module.
The halfplane to the bounded side of the line supporting a contour edge is called the offset zone of the contour edge.
The bounded side means the interior of the polygon built on the given contour.
Any two contour edges define an offset bisector, as follows: If the edges are non-parallel, their bisecting lines can be decomposed as 4 rays originating at the intersection of the supporting lines. Only one of these rays is contained in the combined offset zone of the edges (which one depends on the possible combinations of orientations).
There seems to be a problem with that definition: it's not always true that the bisector rays are contained in the offset zone as stated.
Here's a counterexample that doesn't match the definition: Take an equilateral triangle, and choose any two of its edges as the ones in question. The intersection point from which the bisector rays originate is the shared vertex of the two edges - as that vertex happens to be the intersection of the infinite lines that support the edges.
No matter how we understand the "combined offset zone of the edges", there is no single ray that is somehow special. Let's examine the possibilities:
The "combined" offset zone is the intersection of the offset zone half-planes on the two edges. No bisector rays are contained in such a zone:
The "combined" offset zone is the union of the offset zone half-planes. All bisector rays are contained in such a zone:
Even if we ignored the "intersection of the supporting lines", as a presumed slip of the keyboard, the bisectors will produce undistinguished rays, with no immediately apparent reason to favor one of.
So, the definition provided in CGAL's documentation seems wrong. How should it be fixed so that it makes sense? Or is my understanding of it somehow completely lopsided?