Convex Hulls Of Simple Space Curves

Abstract

The convex hull of an arbitrary set M in real Euclidean n-space is known to consist of all the points within the r-simplexes with r + 1 vertices from M, r ≤ n. This note shows that if M is specialized to be a curve An of real order n, then its convex hull consists of all the points within the r-simplexes with r + 1 vertices on An, n = 2r + 1 or n = 2r.