Living Reference Work Entry

Encyclopedia of Algorithms

pp 1-5

Date: Latest Version

Convex Hulls

  • Michael HemmerAffiliated withDepartment of Computer Science, TU Braunschweig Email author 
  • , Christiane SchmidtAffiliated withThe Selim and Rachel Benin School of Computer Science and Engineering, The Hebrew University of Jerusalem

Keywords

Computational geometry Point sets

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 ...

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