Convex Hulls

Years and Authors of Summarized Original Work

• 1972; Graham

• 1973; Jarvis

• 1977; Preparata, Hong

• 1996; Chan

Problem Definition

The convex hull of a set P of n points in $\mathbb{R}^{d}$ is the intersection of all convex regions that contain P. While convex hulls are defined for arbitrary d, the focus here is on d = 2 (and d = 3). For a more general overview, we recommend reading [7, 9] as well as [3].

A frequently used visual description for a convex hull in 2D is a rubber band: when we imagine the points in the plane to be nails and put a rubber band around them, the convex hull is exactly the structure we obtain by a tight rubber band; see Fig. 1.

Fig. 1

The convex hull of a set of points in $\mathbb{R}^{2}$