A subset is convex if for any two points and in the set the line segment with endpoints and is contained in . The convex hull of a set is the smallest convex set containing . The convex hull of a set of points is a convex polygon with vertices in . A point in is an extreme point (with respect to ) if it is a vertex of the convex hull of .
CGAL provides functions for computing convex hulls in two dimensions as well as functions for testing if a given set of points is strongly convex or not. There are also a number of functions available for computing particular extreme points in 2D and subsequences of the hull points, such as the lower hull or upper hull of a set of points.