Method of orienting curves for determining the convex hull of a finite set of points in the plane

In this article, we present an efficient algorithm to determine the convex hull of a finite planar set using the idea of the Method of Orienting Curves (introduced by Phu in Zur Losung einer regularen Aufgabenklasse der optimalen Steuerung in Grossen mittels Orientierungskurven, Optimization, 18 (1987), pp. 65-81, for solving optimal control problems with state constraints). The convex hull is determined by parts of orienting lines and a final line. Two advantages of this algorithm over some variations of Graham's convex hull algorithm are presented.