Orientation, simplicity, and inclusion test for planar polygons

Closure: Every segment must be delimited by exactly two vertices, and every vertex must be at the intersection of exactly two segments. (Fig. la) No self-intersection: Any two segments can intersect only if they are adjacent, in this case the intersection point is the shared vertex (Fig. lb). Orientation: Every segment must have a direction, and the directions of all the segments must be consistent (Fig. Ic).