Convex Hull

The convex hull of a set of points is the smallest convex set that contains all of them, equivalently the intersection of every convex set containing the points, or the set of every convex combination of those points. For a bounded set of points in the plane, it can be pictured as the shape a rubber band would take if stretched around every point and then allowed to contract until taut. The convex hull operator always contains the original set, respects subset relationships between sets, and produces no further change if applied a second time to its own result. Every compact convex set equals the convex hull of its own extreme points, a fact known as the Krein-Milman theorem.