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 100 vertices, where the vertex coordinates are drawn uniformly from the unit square centered at the origin.
File: examples/Generator/random_polygon.cpp
#include <CGAL/Cartesian.h> #include <CGAL/Polygon_2.h> #include <CGAL/point_generators_2.h> #include <CGAL/random_polygon_2.h> #include <CGAL/Random.h> #include <CGAL/copy_n.h> #ifdef CGAL_USE_GMP #include <CGAL/Gmpz.h> typedef CGAL::Gmpz RT; #else // NOTE: the choice of double here for a number type may cause problems // for degenerate point sets #include <CGAL/double.h> typedef double RT; #endif #include <fstream> #include <list> typedef CGAL::Cartesian<RT> K; typedef K::Point_2 Point_2; typedef std::list<Point_2> Container; typedef CGAL::Polygon_2<K, Container> Polygon_2; typedef CGAL::Creator_uniform_2<int, Point_2> Creator; typedef CGAL::Random_points_in_square_2<Point_2, Creator> Point_generator; const double RADIUS = 100; const int MAX_POLY_SIZE = 100; int main( ) { Polygon_2 polygon; std::list<Point_2> point_set; CGAL::Random rand; int size = rand.get_int(4, MAX_POLY_SIZE); // copy size points from the generator, eliminating duplicates, so the // polygon will have <= size vertices CGAL::copy_n_unique(Point_generator(RADIUS), size, std::back_inserter(point_set)); std::ostream_iterator< Point_2 > out( std::cout, " " ); std::cout << "From the following " << point_set.size() << " points " << std::endl; std::copy(point_set.begin(), point_set.end(), out); std::cout << std::endl; CGAL::random_polygon_2(point_set.size(), std::back_inserter(polygon), point_set.begin()); std::cout << "The following simple polygon was made: " << std::endl; std::cout << polygon << std::endl; return 0; }