Before revision:  In this paper we prove that the polygons generated evacuating the triangles that intersect a constrained segment are such that all their convex vertices but two can be used to form triangles in an earcut fashion, without the need to check whether other polygon points are located within each ear.
After revision:  In this paper we prove that these polygons are such that all their convex vertices but two can be used to form triangles in an earcut fashion, without the need to check whether other polygon points are located within each ear.