CGAL::maximum_perimeter_inscribed_k_gon_2

Definition

• $$P_k is not unique in general, but it can be chosen in such a way that its vertices form a subset of the vertex set of $$P and
• the vertices of a maximum perimeter $$k-gon, where the $$k vertices are to be drawn from a planar point set $$S, lie on the convex hull of $$S i.e. a convex polygon.

#include <CGAL/extremal_polygon_2.h>

template < class RandomAccessIterator, class OutputIterator >
OutputIterator	maximum_perimeter_inscribed_k_gon_2 ( RandomAccessIterator points_begin, RandomAccessIterator points_end, int k, OutputIterator o)

computes a maximum perimeter 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. the - at least three - points denoted by the range [points_begin, points_end) form the boundary of a convex polygon (oriented clock- or counterclockwise).
2. $$k 2.

Requirement:

1. Value type of RandomAccessIterator is K::Point_2 where K is a model for Kernel.
2. There is a global function K::FT CGAL::sqrt(K::FT) defined that computes the squareroot of a number.
3. OutputIterator accepts the value type of RandomAccessIterator as value type.

See Also

Implementation

Example

#include <CGAL/Cartesian.h>
#include <CGAL/Polygon_2.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/random_convex_set_2.h>
#include <CGAL/extremal_polygon_2.h>
#include <iostream>
#include <vector>

typedef double                                    FT;

struct Kernel : public CGAL::Cartesian<FT> {};

typedef Kernel::Point_2                           Point;
typedef std::vector<int>                          Index_cont;
typedef CGAL::Polygon_2<Kernel>                   Polygon;
typedef CGAL::Random_points_in_square_2<Point>    Generator;

int main() {

  int n = 10;
  int k = 5;

  // generate random convex polygon:
  Polygon p;
  CGAL::random_convex_set_2(n, std::back_inserter(p), Generator(1));
  std::cout << "Generated Polygon:\n" << p << std::endl;

  // compute maximum perimeter incribed k-gon of p:
  Polygon k_gon;
  CGAL::maximum_perimeter_inscribed_k_gon_2(
    p.vertices_begin(), p.vertices_end(), k, std::back_inserter(k_gon));
  std::cout << "Maximum perimeter " << k << "-gon:\n"
            << k_gon << std::endl;

  return 0;
}