What is "convex hull"

n. (context mathematics English) The smallest convex set of points in which a given set of points is contained.

In mathematics, the convex hull or convex envelope of a set X of points in the Euclidean plane or Euclidean space is the smallest convex set that contains X. For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around X.

Formally, the convex hull may be defined as the intersection of all convex sets containing X or as the set of all convex combinations of points in X. With the latter definition, convex hulls may be extended from Euclidean spaces to arbitrary real vector spaces; they may also be generalized further, to oriented matroids.

The algorithmic problem of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces is one of the fundamental problems of computational geometry.