This stuff is confusing to me, please help me. My professor mentioned something about sharing a 'feature' or 'characteristic' in common? Is it just that points are on the edges? Do the position of the points mean something?

Convex Hull Problem eel nL Given: a set S of points in the plane or a higher dimensional space Convex hull of S: the smallest convex set that includes S Extreme points: points of S that are not middle points of any line segment with end points in S, e.g. P;, P. in the figure Problem: find the convex hull of S, which consists of the set of extreme points of S Pp ff Convex Hull Problem Observation: a line segment connecting two points P,; and P; of S is a part of the convex hull's boundary iff all the other points of S lie on the same side of the straight line through these two points Test: for each pair of points of 5, test if the line segment connecting them is on the boundary of the convex hull. first find the line equation ax + by +c =O Check each of other points using the line equation to see if the equation has the same sign. Efficiency: O(n) since there are O(n') pairs and for each pair test other O(n) points