CGAL::min_parallelogram_2

Definition

#include <CGAL/min_quadrilateral_2.h>

computes a minimum area enclosing parallelogram of the point set described by [points_begin, points_end), writes its vertices (counterclockwise) to o and returns the past-the-end iterator of this sequence. If the input range is empty, o remains unchanged.
If the input range consists of one element only, this point is written to o four times.

Precondition

The geometric types and operations to be used for the computation are specified by the traits class parameter t. The parameter can be omitted, if ForwardIterator refers to a two-dimensional point type from one the CGAL kernels. In this case, a default traits class (Min_quadrilateral_default_traits_2<K>) is used.

Requirement

1. If Traits is specified, it is a model for MinQuadrilateralTraits_2 and the value type VT of ForwardIterator is Traits::Point_2. Otherwise VT is CGAL::Point_2<K> for some kernel K.
2. OutputIterator accepts VT as value type.

See Also

Implementation

Example

File: examples/Min_quadrilateral_2/minimum_enclosing_parallelogram_2.cpp

#include <CGAL/Cartesian.h>
#include <CGAL/Polygon_2.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/random_convex_set_2.h>
#include <CGAL/min_quadrilateral_2.h>
#include <iostream>

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

typedef Kernel::Point_2                           Point_2;
typedef Kernel::Line_2                            Line_2;
typedef CGAL::Polygon_2<Kernel>                   Polygon_2;
typedef CGAL::Random_points_in_square_2<Point_2>  Generator;

int main()
{
  // build a random convex 20-gon p
  Polygon_2 p;
  CGAL::random_convex_set_2(20, std::back_inserter(p), Generator(1.0));
  std::cout << p << std::endl;

  // compute the minimal enclosing parallelogram p_m of p
  Polygon_2 p_m;
  CGAL::min_parallelogram_2(
    p.vertices_begin(), p.vertices_end(), std::back_inserter(p_m));
  std::cout << p_m << std::endl;

  return 0;
}