The function random_polygon_2constructs a random simple polygon from points that are drawn from a specific domain. Though each simple polygon defined on this set of points has a non-zero probability of being constructed, some polygons may have higher probabilities than others. The overall distribution of the generated polygons is not known since it depends on the generated points.

#include <CGAL/random_polygon_2.h>

template < class OutputIterator, class PointGenerator, class Traits >
random_polygon_2 ( int n,
OutputIterator result,
PointGenerator pg,
Traits t = Default_traits)
computes a random simple polygon by writing its vertices (oriented counterclockwise) to result. The polygon generated will have a number of vertices equal to the number of unique points in the first n points generated by pg.


  1. Traits is a model of the concept RandomPolygonTraits_2
  2. PointGenerator::value_type is equivalent to Traits::Point_2 and OutputIterator::value_type.

The default traits class Default_traits is the kernel in which Traits::Point_2 is defined.

See Also

CGAL::Random_points_in_disc_2<Point_2, Creator>
CGAL::Random_points_in_square_2<Point_2, Creator>


The implementation is based on the method of eliminating self-intersections in a polygon by using so-called ``2-opt'' moves. Such a move eliminates an intersection between two edges by reversing the order of the vertices between the edges. No more than O(n3) such moves are required to simplify a polygon defined on n points [vLS82]. Intersecting edges are detected using a simple sweep through the vertices and then one intersection is chosen at random to eliminate after each sweep. The worse-case running time is therefore O(n4 logn).


The following program displays a random simple polygon with up to 50 vertices, where the vertex coordinates are drawn uniformly from the unit square centered at the origin.

// file: examples/Generator/random_poly_example.C

#include <CGAL/Cartesian.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/random_polygon_2.h>
#include <CGAL/Polygon_2.h>

typedef CGAL::Cartesian< double >                  K;
typedef K::Point_2                                 Point_2;
typedef std::list<Point_2>                         Container;
typedef CGAL::Polygon_2<K, Container>              Polygon_2;
typedef CGAL::Random_points_in_square_2< Point_2 > Point_generator;

int main() {
  Polygon_2 polygon;
  // create 50-gon and write it into a window:
  CGAL::random_polygon_2(50, std::back_inserter(polygon), 
  std::cout << polygon;
  return 0;