// Copyright (c) 1997
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.4/Generator/include/CGAL/point_generators_3.h $
// $Id: point_generators_3.h 98e4718 2021-08-26T11:33:39+02:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Lutz Kettner  <kettner@inf.ethz.ch>
//                 Pedro Machado Manhaes de Castro  <pmmc@cin.ufpe.br>
//                 Alexandru Tifrea
//                 Maxime Gimeno

#ifndef CGAL_POINT_GENERATORS_3_H
#define CGAL_POINT_GENERATORS_3_H 1

#include <CGAL/disable_warnings.h>

#include <CGAL/generators.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/number_type_basic.h>
#include <CGAL/Generator/internal/Generic_random_point_generator.h>
#include <CGAL/boost/graph/property_maps.h>

namespace CGAL {

template < class P, class Creator =
                   Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_in_sphere_3 : public Random_generator_base<P> {
    void generate_point();
public:
    typedef Random_points_in_sphere_3<P,Creator> This;
    Random_points_in_sphere_3( double r = 1, Random& rnd = CGAL::get_default_random())
        // g is an input iterator creating points of type `P' uniformly
        // distributed in the open sphere with radius r, i.e. |`*g'| < r .
        // Three random numbers are needed from `rnd' for each point
    : Random_generator_base<P>( r, rnd) { generate_point(); }
    This& operator++()    {
        generate_point();
        return *this;
    }
    This  operator++(int) {
        This tmp = *this;
        ++(*this);
        return tmp;
    }
};

template < class P, class Creator >
void
Random_points_in_sphere_3<P,Creator>::
generate_point() {
  // A strip between z and z+dz has an area independent of z
    typedef typename Creator::argument_type T;
    double alpha = this->_rnd.get_double() * 2.0 * CGAL_PI;
    double z     = 2 * this->_rnd.get_double() - 1.0;
    double r     = std::sqrt( 1 - z * z);
    r *= std::pow( this->_rnd.get_double() , 1.0/3.0 );
    Creator creator;
    this->d_item = creator( T(this->d_range * r * std::cos(alpha)),
                            T(this->d_range * r * std::sin(alpha)),
                            T(this->d_range * z));
}


template < class P, class Creator =
                   Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_on_sphere_3 : public Random_generator_base<P> {
    void generate_point();
public:
    typedef Random_points_on_sphere_3<P,Creator> This;
    Random_points_on_sphere_3( double r = 1, Random& rnd = CGAL::get_default_random())
        // g is an input iterator creating points of type `P' uniformly
        // distributed on the sphere with radius r, i.e. |`*g'| == r . A
        // two random numbers are needed from `rnd' for each point.
    : Random_generator_base<P>( r, rnd) { generate_point(); }
    This& operator++()    {
        generate_point();
        return *this;
    }
    This  operator++(int) {
        This tmp = *this;
        ++(*this);
        return tmp;
    }
};

template < class P, class Creator >
void
Random_points_on_sphere_3<P,Creator>::
generate_point() {
  // A strip between z and z+dz has an area independent of z
    typedef typename Creator::argument_type T;
    double alpha = this->_rnd.get_double() * 2.0 * CGAL_PI;
    double z     = 2 * this->_rnd.get_double() - 1.0;
    double r     = std::sqrt( 1 - z * z);
    Creator creator;
    this->d_item = creator( T(this->d_range * r * std::cos(alpha)),
                            T(this->d_range * r * std::sin(alpha)),
                            T(this->d_range * z));
}


template < class P, class Creator =
                   Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_in_cube_3 : public Random_generator_base<P>{
    void generate_point();
public:
    typedef Random_points_in_cube_3<P,Creator> This;
    Random_points_in_cube_3( double a = 1, Random& rnd = CGAL::get_default_random())
    : Random_generator_base<P>( a, rnd) { generate_point(); }
    This& operator++()    {
        generate_point();
        return *this;
    }
    This  operator++(int) {
        This tmp = *this;
        ++(*this);
        return tmp;
    }
};

template < class P, class Creator >
void
Random_points_in_cube_3<P,Creator>::
generate_point() {
    typedef typename Creator::argument_type T;
    Creator creator;
    this->d_item =
             creator( T(this->d_range * ( 2 * this->_rnd.get_double() - 1.0)),
                      T(this->d_range * ( 2 * this->_rnd.get_double() - 1.0)),
                      T(this->d_range * ( 2 * this->_rnd.get_double() - 1.0)));
}


template <class OutputIterator, class Creator>
OutputIterator
points_on_cube_grid_3( double a, std::size_t n,
                         OutputIterator o, Creator creator)
{
    if  (n == 0)
        return o;

    int m = int(std::ceil(
                  std::sqrt(std::sqrt(static_cast<double>(n)))));

    while (m*m*m < int(n)) m++;

    double base = -a;  // Left and bottom boundary.
    double step = 2*a/(m-1);
    int j = 0;
    int k = 0;
    double px = base;
    double py = base;
    double pz = base;
    *o++ = creator( px, py, pz);
    for (std::size_t i = 1; i < n; i++) {
        j++;
        if ( j == m) {
           k++;
           if ( k == m) {
              py = base;
              px = base;
              pz = pz + step;
              k = 0;
           }
           else {
              px = base;
              py = py + step;
           }
           j = 0;
        } else {
           px = px + step;
        }
        *o++ = creator( px, py, pz);
    }
    return o;
}

template <class OutputIterator>
OutputIterator
points_on_cube_grid_3( double a, std::size_t n, OutputIterator o)
{
    typedef std::iterator_traits<OutputIterator> ITraits;
    typedef typename ITraits::value_type         P;
    return points_on_square_grid_3(a, n, o,
                 Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P>());
}

template < class P, class Creator =
Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_in_triangle_3 : public Random_generator_base<P> {
        P _p,_q,_r;
        void generate_point();
public:
        typedef P result_type;
        typedef Random_points_in_triangle_3<P, Creator> This;
        typedef typename Kernel_traits<P>::Kernel::Triangle_3 Triangle_3;
        Random_points_in_triangle_3() {}
        Random_points_in_triangle_3( const This& x,Random& rnd)
        : Random_generator_base<P>( 1, rnd ),_p(x._p),_q(x._q),_r(x._r) {
                generate_point();
        }
        Random_points_in_triangle_3( const P& p, const P& q, const P& r, Random& rnd = get_default_random())
        : Random_generator_base<P>( 1, rnd ),_p(p),_q(q),_r(r) {
                generate_point();
        }
        Random_points_in_triangle_3( const Triangle_3& triangle,Random& rnd = get_default_random())
        : Random_generator_base<P>( 1,
                        rnd),_p(triangle[0]),_q(triangle[1]),_r(triangle[2]) {
                generate_point();
        }
        This& operator++() {
                generate_point();
                return *this;
        }
        This operator++(int) {
                This tmp = *this;
                ++(*this);
                return tmp;
        }
};


template<class P, class Creator >
void Random_points_in_triangle_3<P, Creator>::generate_point() {
        typedef typename Creator::argument_type T;
        Creator creator;
        double a1 = this->_rnd.get_double(0,1);
        double a2 = this->_rnd.get_double(0,1);
        if(a1>a2) std::swap(a1,a2);
        double b1 = a1;
        double b2 = a2-a1;
        double b3 = 1.0-a2;
        T ret[3];
        for(int i = 0; i < 3; ++i) {
            ret[i] = T(to_double(_p[i])*b1+to_double(_q[i])*b2+to_double(_r[i])*b3);
        }
        this->d_item = creator(ret[0],ret[1],ret[2]);
}

template < class P, class Creator =
                   Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_on_segment_3 : public Random_generator_base<P> {
    P _p;
    P _q;
    void generate_point();
public:
    typedef Random_points_on_segment_3<P,Creator> This;
    Random_points_on_segment_3() {}
    Random_points_on_segment_3( const P& p,
                                const P& q,
                                Random& rnd = CGAL::get_default_random())
        // g is an input iterator creating points of type `P' uniformly
        // distributed on the segment from p to q except q, i.e. `*g' ==
        // \lambda p + (1-\lambda)\, q where 0 <= \lambda < 1 . A single
        // random number is needed from `rnd' for each point.
      : Random_generator_base<P>( (std::max)( (std::max)( (std::max)(to_double(p.x()), to_double(q.x())),
                                                         (std::max)(to_double(p.y()), to_double(q.y()))),
                                                         (std::max)(to_double(p.z()), to_double(q.z()))),
                                  rnd) , _p(p), _q(q)
    {
      generate_point();
    }

    template <class Segment_3>
    Random_points_on_segment_3( const Segment_3& s,
                                Random& rnd = CGAL::get_default_random())
        // g is an input iterator creating points of type `P' uniformly
        // distributed on the segment from p to q except q, i.e. `*g' ==
        // \lambda p + (1-\lambda)\, q where 0 <= \lambda < 1 . A single
        // random number is needed from `rnd' for each point.
      : Random_generator_base<P>( (std::max)( (std::max)( (std::max)(to_double(s[0].x()), to_double(s[1].x())),
                                                         (std::max)(to_double(s[0].y()), to_double(s[1].y()))),
                                                         (std::max)(to_double(s[0].z()), to_double(s[1].z()))),
                                  rnd) , _p(s[0]), _q(s[1])
    {
      generate_point();
    }

    const P&  source() const { return _p; }
    const P&  target() const { return _q; }
    This& operator++()    {
        generate_point();
        return *this;
    }
    This  operator++(int) {
        This tmp = *this;
        ++(*this);
        return tmp;
    }
};

template < class P, class Creator >
void
Random_points_on_segment_3<P,Creator>::
generate_point() {
    typedef typename Creator::argument_type  T;
    double la = this->_rnd.get_double();
    double mu = 1.0 - la;
    Creator creator;
    this->d_item = creator(T(mu * to_double(_p.x()) + la * to_double(_q.x())),
                           T(mu * to_double(_p.y()) + la * to_double(_q.y())),
                           T(mu * to_double(_p.z()) + la * to_double(_q.z())));
}

template < class P, class Creator =
Creator_uniform_3<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_in_tetrahedron_3 : public Random_generator_base<P> {
        P _p,_q,_r,_s;
        void generate_point();
public:
        typedef P result_type;
        typedef Random_points_in_tetrahedron_3<P, Creator> This;
        typedef typename Kernel_traits<P>::Kernel::Tetrahedron_3 Tetrahedron_3;
        Random_points_in_tetrahedron_3() {}
        Random_points_in_tetrahedron_3( const This& x,Random& rnd)
        : Random_generator_base<P>( 1, rnd ),_p(x._p),_q(x._q),_r(x._r),_s(x._s) {
                generate_point();
        }
        Random_points_in_tetrahedron_3( const P& p, const P& q, const P& r, const P& s,Random& rnd = get_default_random())
        : Random_generator_base<P>( 1, rnd ),_p(p),_q(q),_r(r),_s(s) {
                generate_point();
        }
        Random_points_in_tetrahedron_3( const Tetrahedron_3& tetrahedron,Random& rnd = get_default_random())
        : Random_generator_base<P>( 1, rnd),_p(tetrahedron[0]),_q(tetrahedron[1]),_r(tetrahedron[2]),_s(tetrahedron[3]) {
                generate_point();
        }
        This& operator++() {
                generate_point();
                return *this;
        }
        This operator++(int) {
                This tmp = *this;
                ++(*this);
                return tmp;
        }
};

template<class P, class Creator >
void Random_points_in_tetrahedron_3<P, Creator>::generate_point() {
        typedef typename Creator::argument_type T;
        Creator creator;
        double a[3];
        for(int i = 0; i < 3; ++i) {
                a[i]=this->_rnd.get_double(0,1);
        }
        std::sort(a,a+3);
        double b[4];
        b[0]=a[0];
        b[1]=a[1]-a[0];
        b[2]=a[2]-a[1];
        b[3]=1.0-a[2];
        T ret[3];
        for(int i = 0; i < 3; ++i) {
            ret[i] = T(to_double(_p[i])*b[0]+to_double(_q[i])*b[1]+to_double(_r[i])*b[2]+to_double(_s[i])*b[3]);
        }
        this->d_item = creator(ret[0],ret[1],ret[2]);
}



template <class TriangleMesh,
          class VertexPointMap = typename boost::property_map<TriangleMesh,
                                                              CGAL::vertex_point_t>::const_type,
          class Creator = Creator_uniform_3<
                            typename Kernel_traits< typename boost::property_traits<VertexPointMap>::value_type >::Kernel::RT,
                            typename boost::property_traits<VertexPointMap>::value_type >
>
struct Random_points_in_triangle_mesh_3
  : public Generic_random_point_generator<
             typename boost::graph_traits <TriangleMesh>::face_descriptor ,
             CGAL::Property_map_to_unary_function<CGAL::Triangle_from_face_descriptor_map<
                                                    TriangleMesh, VertexPointMap > >,
             Random_points_in_triangle_3<typename boost::property_traits<VertexPointMap>::value_type, Creator>,
             typename boost::property_traits<VertexPointMap>::value_type>
{
  typedef typename boost::property_traits<VertexPointMap>::value_type  P;
  typedef Generic_random_point_generator<
            typename boost::graph_traits <TriangleMesh>::face_descriptor ,
            CGAL::Property_map_to_unary_function<CGAL::Triangle_from_face_descriptor_map<
            TriangleMesh,VertexPointMap> >,
            Random_points_in_triangle_3<P, Creator> , P>                   Base;
  typedef typename CGAL::Triangle_from_face_descriptor_map<
                     TriangleMesh,VertexPointMap>                          Object_from_id;
  typedef typename boost::graph_traits<TriangleMesh>::face_descriptor      Id;
  typedef P result_type;
  typedef Random_points_in_triangle_mesh_3< TriangleMesh, VertexPointMap, Creator>  This;


  Random_points_in_triangle_mesh_3( const TriangleMesh& mesh,Random& rnd = get_default_random())
    : Base( faces(mesh),
            CGAL::Property_map_to_unary_function<Object_from_id>(Object_from_id(&mesh, get(vertex_point, mesh))),
            internal::Apply_approx_sqrt<typename Kernel_traits<P>::Kernel::Compute_squared_area_3>(),
            rnd )
  {
  }
  Random_points_in_triangle_mesh_3( const TriangleMesh& mesh, VertexPointMap vpm, Random& rnd = get_default_random())
    : Base( faces(mesh),
            CGAL::Property_map_to_unary_function<Object_from_id>(Object_from_id(&mesh, vpm)),
            internal::Apply_approx_sqrt<typename Kernel_traits<P>::Kernel::Compute_squared_area_3>(),
            rnd )
  {
  }
  This& operator++() {
    Base::generate_point();
    return *this;
  }
  This operator++(int) {
    This tmp = *this;
    ++(*this);
    return tmp;
  }
  double mesh_area() const
  {
    return this->sum_of_weights();
  }
};

template <class EdgeListGraph,
          class VertexPointMap = typename boost::property_map<EdgeListGraph,
                                                              CGAL::vertex_point_t>::const_type,
          class Creator = Creator_uniform_3<
                            typename Kernel_traits< typename boost::property_traits<VertexPointMap>::value_type >::Kernel::RT,
                            typename boost::property_traits<VertexPointMap>::value_type >
>
struct Random_points_on_edge_list_graph_3
  : public Generic_random_point_generator<
             typename boost::graph_traits <EdgeListGraph>::edge_descriptor,
             CGAL::Property_map_to_unary_function<CGAL::Segment_from_edge_descriptor_map<
                                                  EdgeListGraph, VertexPointMap > >,
             Random_points_on_segment_3<typename boost::property_traits<VertexPointMap>::value_type, Creator>,
             typename boost::property_traits<VertexPointMap>::value_type>
{
  typedef typename boost::property_traits<VertexPointMap>::value_type  P;
  typedef Generic_random_point_generator<
            typename boost::graph_traits <EdgeListGraph>::edge_descriptor,
            CGAL::Property_map_to_unary_function<CGAL::Segment_from_edge_descriptor_map<
                                                 EdgeListGraph, VertexPointMap > >,
            Random_points_on_segment_3<P, Creator> , P>                    Base;
  typedef typename CGAL::Segment_from_edge_descriptor_map<
                     EdgeListGraph,VertexPointMap>                          Object_from_id;
  typedef typename boost::graph_traits<EdgeListGraph>::edge_descriptor      Id;
  typedef P result_type;
  typedef Random_points_on_edge_list_graph_3< EdgeListGraph, VertexPointMap, Creator>  This;

  Random_points_on_edge_list_graph_3( const EdgeListGraph& mesh,Random& rnd = get_default_random())
    : Base( edges(mesh),
            CGAL::Property_map_to_unary_function<Object_from_id>(Object_from_id(&mesh, get(vertex_point, mesh))),
            internal::Apply_approx_sqrt<typename Kernel_traits<P>::Kernel::Compute_squared_length_3>(),
            rnd )
  {
  }
  Random_points_on_edge_list_graph_3( const EdgeListGraph& mesh, VertexPointMap vpm, Random& rnd = get_default_random())
    : Base( edges(mesh),
            CGAL::Property_map_to_unary_function<Object_from_id>(Object_from_id(&mesh, vpm)),
            internal::Apply_approx_sqrt<typename Kernel_traits<P>::Kernel::Compute_squared_length_3>(),
            rnd )
  {
  }
  This& operator++() {
    Base::generate_point();
    return *this;
  }
  This operator++(int) {
    This tmp = *this;
    ++(*this);
    return tmp;
  }
  double mesh_length() const
  {
    return this->sum_of_weights();
  }
};

namespace internal
{

template<class C3T3>
class Triangle_from_c3t3_facet
{
  typedef typename C3T3::Triangulation                    Tr;
  typedef typename Tr::Bare_point                         Bare_point;
  typedef typename Tr::Triangle                           Triangle;
  typedef typename Tr::Facet                              Facet;
  typedef typename Tr::Cell_handle                        Cell_handle;

public:
  typedef Triangle                                        result_type;

  Triangle_from_c3t3_facet(const C3T3& c3t3) : tr(c3t3.triangulation()) { }

  Triangle operator()(const Facet& facet)const
  {
    Cell_handle cell = facet.first;
    int index = facet.second;
    typename Tr::Geom_traits::Construct_point_3 wp2p =
        tr.geom_traits().construct_point_3_object();

    const Bare_point& pa = wp2p(tr.point(cell, (index+1)&3));
    const Bare_point& pb = wp2p(tr.point(cell, (index+2)&3));
    const Bare_point& pc = wp2p(tr.point(cell, (index+3)&3));
    return Triangle(pa, pb, pc);
  }

  const Tr& tr;
};

template<class C3T3>
class Tetrahedron_from_c3t3_cell
{
  typedef typename C3T3::Triangulation                    Tr;
  typedef typename Tr::Cell_handle                        Cell;
  typedef typename Tr::Bare_point                         Bare_point;
  typedef typename Tr::Tetrahedron                        Tetrahedron;

public:
  typedef Tetrahedron                                     result_type;

  Tetrahedron_from_c3t3_cell(const C3T3& c3t3) : tr(c3t3.triangulation()) { }

  Tetrahedron operator()(const Cell cell)const
  {
    typename Tr::Geom_traits::Construct_point_3 wp2p =
        tr.geom_traits().construct_point_3_object();

    const Bare_point& p0 = wp2p(tr.point(cell, 0));
    const Bare_point& p1 = wp2p(tr.point(cell, 1));
    const Bare_point& p2 = wp2p(tr.point(cell, 2));
    const Bare_point& p3 = wp2p(tr.point(cell, 3));
    return Tetrahedron(p0, p1, p2, p3);
  }

  const Tr& tr;
};

template<typename Triangle, typename PointRange>
class Triangle_3_from_soup
{
  typedef typename boost::range_value<PointRange>::type  Point_3;
  typedef typename Kernel_traits<Point_3>::Kernel        Kernel;
public:
  typedef typename Kernel::Triangle_3                    result_type;

  Triangle_3_from_soup(const PointRange& pts) : points(pts) { }

  result_type operator()(const Triangle& t) const
  {
    return result_type(points[t[0]], points[t[1]], points[t[2]]);
  }

private:
  const PointRange& points;
};

}//end namespace internal

template <class C3t3,
          class Creator = Creator_uniform_3<
                            typename Kernel_traits<
                              typename C3t3::Triangulation::Point_3 >::Kernel::RT,
                            typename C3t3::Triangulation::Point_3 >
>
class Random_points_in_tetrahedral_mesh_boundary_3
  : public Generic_random_point_generator<
             typename C3t3::Triangulation::Facet,
             internal::Triangle_from_c3t3_facet<C3t3>,
             Random_points_in_triangle_3<typename C3t3::Triangulation::Point_3>,
             typename C3t3::Triangulation::Point_3>
{
  typedef Random_points_in_tetrahedral_mesh_boundary_3<C3t3, Creator> This;

public:
  typedef typename C3t3::Triangulation                               Tr;
  typedef typename Tr::Point_3                                       Point_3;
  typedef typename Tr::Facet                                         Facet;
  typedef typename Tr::Cell_handle                                   Cell_handle;

  typedef Generic_random_point_generator<
            Facet, internal::Triangle_from_c3t3_facet<C3t3>,
            Random_points_in_triangle_3<Point_3, Creator>,
            Point_3>                                                 Base;

  typedef Facet                                                      Id;
  typedef Point_3                                                    result_type;

  typedef typename Kernel_traits<Point_3>::Kernel  K;
  typedef typename K::Compute_squared_area_3       Compute_squared_area_3;
  typedef typename internal::Apply_approx_sqrt<Compute_squared_area_3>
                                                   Compute_squared_area_3_with_approx_sqrt;

  Random_points_in_tetrahedral_mesh_boundary_3(const C3t3& c3t3,
                                               Random& rnd = get_default_random())
    : Base( make_range( c3t3.facets_in_complex_begin(),
                        c3t3.facets_in_complex_end() ),
            internal::Triangle_from_c3t3_facet<C3t3>(c3t3),
            Compute_squared_area_3_with_approx_sqrt(),
            rnd )
  {
  }
  This& operator++() {
    Base::generate_point();
    return *this;
  }
  This operator++(int) {
    This tmp = *this;
    ++(*this);
    return tmp;
  }
};

template <class C3t3,
          class Creator = Creator_uniform_3<
                            typename Kernel_traits<
                              typename C3t3::Triangulation::Point_3 >::Kernel::RT,
                            typename C3t3::Triangulation::Point_3 >
>
class Random_points_in_tetrahedral_mesh_3
  : public Generic_random_point_generator<
             typename C3t3::Triangulation::Cell_handle,
             internal::Tetrahedron_from_c3t3_cell<C3t3>,
             Random_points_in_tetrahedron_3<
               typename C3t3::Triangulation::Point_3>,
             typename C3t3::Triangulation::Point_3>
{
  typedef Random_points_in_tetrahedral_mesh_3<C3t3, Creator>         This;

public:
  typedef typename C3t3::Triangulation                               Tr;
  typedef typename Tr::Point_3                                       Point_3;
  typedef typename Tr::Cell_handle                                   Cell_handle;

  typedef Generic_random_point_generator<Cell_handle,
            internal::Tetrahedron_from_c3t3_cell<C3t3>,
            Random_points_in_tetrahedron_3<Point_3, Creator>,
            Point_3>                                                 Base;

  typedef Cell_handle                                                Id;
  typedef Point_3                                                    result_type;

  typedef typename Kernel_traits<Point_3>::Kernel                    K;
  typedef typename K::Compute_volume_3                               Compute_volume_3;

  Random_points_in_tetrahedral_mesh_3(const C3t3& c3t3,
                                      Random& rnd = get_default_random())
    : Base( CGAL::make_prevent_deref_range(c3t3.cells_in_complex_begin(),
                                           c3t3.cells_in_complex_end() ),
            internal::Tetrahedron_from_c3t3_cell<C3t3>(c3t3),
            Compute_volume_3(),
            rnd )
  {
  }
  This& operator++() {
    Base::generate_point();
    return *this;
  }
  This operator++(int) {
    This tmp = *this;
    ++(*this);
    return tmp;
  }
};


template <class Point_3,
          class Triangle_3=typename Kernel_traits<Point_3>::Kernel::Triangle_3,
          class Creator = Creator_uniform_3<
                            typename Kernel_traits< Point_3 >::Kernel::RT,
                            Point_3 >
         >
struct Random_points_in_triangles_3
    : public Generic_random_point_generator<const Triangle_3*,
                                            internal::Deref<Triangle_3>,
                                            Random_points_in_triangle_3<Point_3>,
                                            Point_3>
{
  typedef Generic_random_point_generator<const Triangle_3*,
                                         internal::Deref<Triangle_3>,
                                         Random_points_in_triangle_3<Point_3, Creator>,
                                         Point_3>            Base;
  typedef const Triangle_3*                                         Id;
  typedef Point_3                                                   result_type;
  typedef Random_points_in_triangles_3<Point_3, Triangle_3, Creator>  This;

  template<typename TriangleRange>
  Random_points_in_triangles_3( const TriangleRange& triangles, Random& rnd = get_default_random())
    : Base(make_range( boost::make_transform_iterator(triangles.begin(), internal::Address_of<Triangle_3>()),
                       boost::make_transform_iterator(triangles.end(), internal::Address_of<Triangle_3>()) ),
           internal::Deref<Triangle_3>(),
           internal::Apply_approx_sqrt<typename Kernel_traits<Point_3>::Kernel::Compute_squared_area_3>()
           ,rnd )
  {
  }
  This& operator++() {
    Base::generate_point();
    return *this;
  }
  This operator++(int) {
    This tmp = *this;
    ++(*this);
    return tmp;
  }
};


template <class PointRange,
          class Triangle = std::vector<std::size_t>,
          class Creator = Creator_uniform_3<
                            typename Kernel_traits< typename PointRange::value_type >::Kernel::RT,
                            typename PointRange::value_type> >
struct Random_points_in_triangle_soup
    : public Generic_random_point_generator<Triangle,
                                            internal::Triangle_3_from_soup<Triangle, PointRange>,
                                            Random_points_in_triangle_3<typename PointRange::value_type>,
                                            typename PointRange::value_type>
{
  typedef Generic_random_point_generator<Triangle,
                                         internal::Triangle_3_from_soup<Triangle, PointRange>,
                                         Random_points_in_triangle_3<typename PointRange::value_type>,
                                         typename PointRange::value_type> Base;
  typedef typename PointRange::value_type                                 Point_3;
  typedef typename Kernel_traits<Point_3>::Kernel                         Kernel;
  typedef Triangle                                                        Id;
  typedef Point_3                                                         result_type;
  typedef Random_points_in_triangle_soup<PointRange, Triangle, Creator>   This;

  template<typename TriangleRange>
  Random_points_in_triangle_soup(const TriangleRange& triangles,
                                 const PointRange& points,
                                 Random& rnd = get_default_random())
    : Base(triangles,
           internal::Triangle_3_from_soup<Triangle, PointRange>(points),
           internal::Apply_approx_sqrt<typename Kernel_traits<Point_3>::Kernel::Compute_squared_area_3>(),
           rnd)
  { }

  This& operator++()
  {
    Base::generate_point();
    return *this;
  }

  This operator++(int)
  {
    This tmp = *this;
    ++(*this);
    return tmp;
  }
};

} //namespace CGAL

#include <CGAL/enable_warnings.h>

#endif // CGAL_POINT_GENERATORS_3_H //
// EOF //
