On the conditions for success of sklansky's convex hull algorithm

The convex hull algorithm for simple polygons, due to Sklansky, fails in some cases, but its extreme simplicity, compared to the later algorithms, revived an interest in this algorithm. A sufficient condition for its success was given recently by Toussaint and Avis. They have proved that the algorithm works for polygons known as weakly externally visible polygons.

In this paper a new notion called external left visibility is introduced and it is shown that this is a necessary and sufficient condition for the success of Sklansky's algorithm. Moreover, algorithms testing simple polygons for external left visibility and weak external visibility are given.