Computing General Extremal Polygons

This section describes a general function to compute a maximal $$k-gon $$P_k that can be inscribed in a given convex polygon $$P. The criterion for maximality and some basic operations have to specified in an appropriate traits class as specified in section .

#include <CGAL/extremal_polygons_2.h>

template < class RandomAccessIC, class OutputIterator, class Traits >
OutputIterator	extremal_polygon ( RandomAccessIC points_begin, RandomAccessIC points_end, int k, OutputIterator o, Traits t)

computes a maximal (as specified by t) inscribed $$k-gon of the convex polygon described by [points_begin, points_end), writes its vertices to o and returns the past-the-end iterator of this sequence.

Precondition

1. Traits has to satisfy the requirements stated in section ,
2. Value type of RandomAccessIC must be Traits::Point_2,
3. OutputIterator accepts Traits::Point_2 as value type,
4. the - at least three - points denoted by the range [points_begin, points_end) form the boundary of a convex polygon (oriented clock- or counterclockwise) and
5. $$k t.min_k().

Implementation