Navigation: Up, Table of Contents, Bibliography, Index, Title Page

Chapter 2
2D Convex Hulls and Extreme Points

Susan Hert and Stefan Schirra

A subset S ² is convex if for any two points p and q in the set the line segment with endpoints p and q is contained in S. The convex hull of a set S is the smallest convex set containing S. The convex hull of a set of points P is a convex polygon with vertices in P. A point in P is an extreme point (with respect to P) if it is a vertex of the convex hull of P.

CGAL provides functions for computing convex hulls in two dimensions as well as functions for testing if a given set of points is strongly convex or not. There are also a number of functions available for computing particular extreme points in 2D and subsequences of the hull points, such as the lower hull or upper hull of a set of points.

Assertions

The assertion flags for the convex hull and extreme point algorithms use CH in their names (e.g., CGAL_CH_NO_POSTCONDITIONS). For the convex hull algorithms, the postcondition check tests only convexity (if not disabled), but not containment of the input points in the polygon or polyhedron defined by the output points. The latter is considered an expensive checking and can be enabled by defining CGAL_CH_CHECK_EXPENSIVE .

Next chapter: 3D Convex Hulls

Navigation: Table of Contents, Bibliography, Index, Title Page

The CGAL Project . Tue, December 21, 2004 .

Chapter 22D Convex Hulls and Extreme Points

Assertions

Concepts

Traits Classes

Convex Hull Functions

Convexity Checking Functions

Hull Subsequence Functions

Extreme Point Functions

Alphabetical Listing of Reference Pages

Chapter 2
2D Convex Hulls and Extreme Points