#include <iostream>
#include <CGAL/point_generators_3.h>
#include <CGAL/Random.h>
#include <CGAL/algorithm.h>
#include <CGAL/double.h>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <cassert>

typedef double RT;

typedef CGAL::Exact_predicates_inexact_constructions_kernel                 K;
typedef K::Point_3                                                         Point_3;
typedef K::Vector_3                                                         Vector_3;
typedef K::Triangle_3                                                         Triangle_3;
typedef K::Plane_3                                                         Plane_3;
typedef std::vector<Point_3>                                                Container;
typedef CGAL::Random_points_in_triangle_3<Point_3>                         Point_generator;

const double EPS = 1e-20;

template<class InputIterator>
bool inside_or_close_to_triangle(const Triangle_3& tri,InputIterator begin, InputIterator end) {
        Plane_3 plane = tri.supporting_plane();
        while(begin!=end) {
                K::FT dist = squared_distance(plane,*begin);
                if(dist>EPS) {
                        return false;
                }
                Triangle_3 OAB = Triangle_3(*begin,tri[0],tri[1]);
                Triangle_3 OAC = Triangle_3(*begin,tri[0],tri[2]);
                Triangle_3 OBC = Triangle_3(*begin,tri[1],tri[2]);
                K::FT OAB_area = sqrt(OAB.squared_area());
                K::FT OAC_area = sqrt(OAC.squared_area());
                K::FT OBC_area = sqrt(OBC.squared_area());
                K::FT tri_area = sqrt(tri.squared_area());
                if(fabs(OAB_area+OAC_area+OBC_area-tri_area)>1e-15) {
                        return false;
                }
                ++begin;
        }
        return true;
}

int main() {
        CGAL::Random rand;
        Container point_set;
        const int number_triangles = 10;
        const int number_points = 1000;
        for(int i = 0; i < number_triangles; ++i) {
                Point_3 pts[3];
                for(int j = 0; j < 3; ++j) {
                        pts[j]=Point_3(rand.get_double(),rand.get_double(),rand.get_double());
                }
                Triangle_3 tri(pts[0],pts[1],pts[2]);
                Point_generator g1( pts[0], pts[1], pts[2] );
                Point_generator g2( tri );
                Point_generator g3( g1 );

                point_set.clear();
                std::copy_n( g1, number_points,
                               std::back_inserter(point_set));
                assert(inside_or_close_to_triangle(tri,point_set.begin(),point_set.end()));

                point_set.clear();
                std::copy_n( g2, number_points,
                               std::back_inserter(point_set));
                assert(inside_or_close_to_triangle(tri,point_set.begin(),point_set.end()));

                point_set.clear();
                std::copy_n( g3, number_points,
                               std::back_inserter(point_set));
                assert(inside_or_close_to_triangle(tri,point_set.begin(),point_set.end()));
        }

        return 0;
}
