Constructing Convex Hulls

Abstract

This chapter investigates the problem of constructing the convex hull of a finite set of points in E^d, that is, of producing a meaningful representation of the convex hull. If P is a finite set of points in E^d, then we write convP for the convex hull of P. By the definitions given in Appendix A, convP is the set of convex combinations of P. Equivalently, convP can be defined as

the smallest convex set that contains P, or the intersection of all convex sets that contain P, or the intersection of all half-spaces that contain P.