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 nonzero 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>
 

 
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. 
The default traits class Default_traits is the kernel in which Traits::Point_2 is defined.
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 50gon and write it into a window: CGAL::random_polygon_2(50, std::back_inserter(polygon), Point_generator(0.5)); std::cout << polygon; return 0; }