// 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); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: https://github.com/CGAL/cgal/blob/releases/CGAL-4.14.3/Generator/include/CGAL/point_generators_2.h $
// $Id: point_generators_2.h 07b720c 2019-02-20T09:59:21+01:00 Maxime Gimeno
// SPDX-License-Identifier: LGPL-3.0+
// 
//
// 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_2_H
#define CGAL_POINT_GENERATORS_2_H 1

#include <CGAL/disable_warnings.h>

#include <CGAL/generators.h>
#include <CGAL/number_type_basic.h>
#include <CGAL/internal/Generic_random_point_generator.h>
#include <CGAL/iterator.h>

#include <iterator>

namespace CGAL {

template < class P, class Creator = 
                  Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_in_disc_2 : public Random_generator_base<P>{
    void generate_point();
public:
    typedef Random_points_in_disc_2<P,Creator> This;
    Random_points_in_disc_2( double r = 1, Random& rnd = CGAL::get_default_random())
        // g is an input iterator creating points of type `P' uniformly
        // distributed in the open disc with radius r, i.e. |`*g'| < r .
        // 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_in_disc_2<P,Creator>::
generate_point() {
    typedef typename Creator::argument_type T;
    double alpha = this->_rnd.get_double() * 2.0 * CGAL_PI;
    double r = this->d_range * std::sqrt( this->_rnd.get_double());
    Creator creator;
    this->d_item = creator( T(r * std::cos(alpha)), 
                            T(r * std::sin(alpha)));
}


template < class P, class Creator = 
                  Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT, P> >
class Random_points_on_circle_2 : public Random_generator_base<P> {
    void generate_point();
public:
    typedef Random_points_on_circle_2<P,Creator> This;
    Random_points_on_circle_2( double r = 1, Random& rnd = CGAL::get_default_random())
        // g is an input iterator creating points of type `P' uniformly
        // distributed on the circle with radius r, i.e. |`*g'| == r . A
        // single random number is 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_circle_2<P,Creator>::
generate_point() {
    typedef typename Creator::argument_type T;
    double a = this->_rnd.get_double() * 2.0 * CGAL_PI;
    Creator creator;
    this->d_item = creator( T(this->d_range * std::cos(a)), 
                            T(this->d_range * std::sin(a)));
}


template < class P, class Creator = 
                   Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_in_square_2 : public Random_generator_base<P> {
    void generate_point();
public:
    typedef Random_points_in_square_2<P,Creator> This;
    Random_points_in_square_2( double a = 1, Random& rnd = CGAL::get_default_random())
        // g is an input iterator creating points of type `P' uniformly
        // distributed in the half-open square with side length a,
        // centered around the origin, i.e. \forall p = `*g': -\frac{a}{2}
        // <= p.x() < \frac{a}{2} and -\frac{a}{2} <= p.y() < \frac{a}{2}
        // . Two random numbers are needed from `rnd' for each point.
    : 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_square_2<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)));
}


template < class P, class Creator = 
                   Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_on_square_2 : public Random_generator_base<P> {
    void generate_point();
public:
    typedef Random_points_on_square_2<P,Creator> This;
    Random_points_on_square_2( double a = 1, Random& rnd = CGAL::get_default_random())
        // g is an input iterator creating points of type `P' uniformly
        // distributed on the boundary of the square with side length a,
        // centered around the origin, i.e. \forall p = `*g': one
        // coordinate is either \frac{a}{2} or -\frac{a}{2} and for the
        // other coordinate c holds -\frac{a}{2} <= c < \frac{a}{2} . A
        // single random number is needed from `rnd' for each point.
    : 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_on_square_2<P,Creator>::
generate_point() {
    typedef typename Creator::argument_type  T;
    double d = this->_rnd.get_double() * 4.0;
    int    k = int(d);
    d = this->d_range * (2 * (d - k) - 1.0);
    CGAL_assertion( - this->d_range <= d && d < this->d_range);
    Creator creator;
    switch (k) {
    case 0:
        this->d_item = creator(              T(d), T(-this->d_range));
        break;
    case 1:
        this->d_item = creator(              T(d),  T(this->d_range));
        break;
    case 2:
        this->d_item = creator( T(-this->d_range),        T(d));
        break;
    case 3:
        this->d_item = creator( T( this->d_range),        T(d));
        break;
    default:
        CGAL_assume(false);
    }
}


template < class P, class Creator = 
                   Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_in_iso_rectangle_2 : public Random_generator_base<P> {
  double left, right, top, bottom;
    void generate_point();
public:
    typedef Random_points_in_iso_rectangle_2<P,Creator> This;
    Random_points_in_iso_rectangle_2( const P&p, const P& q, Random& rnd = CGAL::get_default_random())
      : Random_generator_base<P>( 1.0 , rnd)
  {
    left = (std::min)(to_double(p.x()), to_double(q.x()));
    right = (std::max)(to_double(p.x()), to_double(q.x()));
    top = (std::min)(to_double(p.y()), to_double(q.y()));
    bottom = (std::max)(to_double(p.y()), to_double(q.y()));
    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_iso_rectangle_2<P,Creator>::
generate_point() {
    typedef typename Creator::argument_type  T;
    Creator creator;
    this->d_item =
	    creator( T(this->_rnd.get_double(left,right)),
                     T(this->_rnd.get_double(top,bottom)));
}



template < class P, class Creator = 
                   Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_on_segment_2 : public Random_generator_base<P> {
    P _p;
    P _q;
    void generate_point();
public:
    typedef Random_points_on_segment_2<P,Creator> This;
    Random_points_on_segment_2( const P& p = P( -1, 0),
                                const P& q = P(  1, 0),
                                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)( to_double(p.x()), to_double(q.x())),
                                              (std::max)( to_double(p.y()),
                                                          to_double(q.y()))),
                                  rnd) , _p(p), _q(q)
    {
        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_2<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())));
}

template < class P >
class Points_on_segment_2 : public Generator_base<P> {
    P _p;
    P _q;
    std::size_t  d_i;
    std::size_t  d_mx;
    void generate_point();
public:
    typedef Points_on_segment_2<P> This;
    Points_on_segment_2() {}
    Points_on_segment_2( const P& p, const P& q,
                         std::size_t mx, std::size_t i = 0)
      : Generator_base<P>( (std::max)( (std::max)( to_double(p.x()), to_double(q.x())),
                                       (std::max)( to_double(p.y()), to_double(q.y())))),
        _p(p), _q(q), d_i(i), d_mx(mx) 
    {
        generate_point();
    }
    const P&  source() const { return _p; }
    const P&  target() const { return _q; }
    // Sufficient equality test.
    bool operator==( const This& base) const { return ( d_i == base.d_i); }
    bool operator!=( const This& base) const { return ! operator==(base); }
    This& operator++()    {
        d_i++;
        generate_point();
        return *this;
    }
    This  operator++(int) {
        This tmp = *this;
        ++(*this);
        return tmp;
    }
};

template < class P >
void
Points_on_segment_2<P>::
generate_point() { this->d_item = _p + (_q-_p) * static_cast<double>(d_i) / (static_cast<double>(d_mx)-1); }

template <class OutputIterator, class Creator>
OutputIterator
points_on_square_grid_2( double a, std::size_t n, OutputIterator o,
                         Creator creator)
{
    typedef typename Creator::argument_type T;
    if  (n == 0)
        return o;
    int m = int(std::ceil(std::sqrt(static_cast<double>(n))));
    double base = -a;  // Left and bottom boundary.
    double step = (2*a)/(m - 1);
    int j = 0;
    double px = base;
    double py = base;
    *o++ = creator( T(px), T(py));
    for (std::size_t i = 1; i < n; i++) {
        j++;
        if ( j == m) {
            px = base;
            py = py + step;
            j = 0;
        } else {
            px = px + step;
        }
        *o++ = creator( T(px), T(py));
    }
    return o;
}

template <class OutputIterator>
OutputIterator
points_on_square_grid_2( 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_2(a, n, o, 
                Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P>());
}

template <class P, class OutputIterator>
OutputIterator
points_on_segment_2( const P& p, const P& q, std::size_t n,
                     OutputIterator o)
    // creates n points regular spaced on the segment from p to q, i.e.
    // \forall i: 0 <= i < n: o[i] := \frac{n-i-1}{n-1} p + \frac{i}{n-1
    // } q.
{
    for (std::size_t i = 0; i < n; i++) {
      *o++ = p + (q-p) * static_cast<typename Kernel_traits<P>::Kernel::FT>(static_cast<double>(i) / (static_cast<double>(n)-1));
    }
    return o;
}

template <class ForwardIterator, class Creator>
void perturb_points_2( ForwardIterator first,
                       ForwardIterator last,
                       double xeps,
                       double yeps,
                       Random& rnd,
                       Creator creator)
    // perturbs the points in the range [`first',`last') by replacing
    // each point with a random point from the rectangle `xeps' \times
    // `yeps' centered around the original point. Two random numbers are
    // needed from `rnd' for each point. Precondition:
    // The expression `to_double((*first).x())' and `to_double((
    // *begin).y())' must be legal.
{
    typedef typename Creator::argument_type T;
    xeps *= 2.0;
    yeps *= 2.0;
    for ( ; first != last; ++first) {
        double x = to_double( (*first).x());
        double y = to_double( (*first).y());
        x += xeps * (rnd.get_double() - 0.5);
        y += yeps * (rnd.get_double() - 0.5);
        *first = creator( T(x), T(y));
    }
}

template <class ForwardIterator>
void perturb_points_2( ForwardIterator first,
                       ForwardIterator last,
                       double xeps,
                       double yeps,
                       Random& rnd)
{
    typedef std::iterator_traits<ForwardIterator> ITraits;
    typedef typename ITraits::value_type          P;
    perturb_points_2( first, last, xeps, yeps, rnd,
                 Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P>());
}

template <class ForwardIterator>
inline
void perturb_points_2( ForwardIterator first,
                       ForwardIterator last,
                       double xeps,
                       Random& rnd)
{
    perturb_points_2( first, last, xeps, xeps, rnd);
}

template <class ForwardIterator>
void perturb_points_2( ForwardIterator first,
                       ForwardIterator last,
                       double xeps,
                       double yeps)
{
    perturb_points_2( first, last, xeps, yeps, CGAL::get_default_random());
}

template <class ForwardIterator>
void perturb_points_2( ForwardIterator first,
                       ForwardIterator last,
                       double xeps)
{
    perturb_points_2( first, last, xeps, xeps, CGAL::get_default_random());
}
template <class RandomAccessIterator, class OutputIterator, class Creator>
OutputIterator random_collinear_points_2(
                       RandomAccessIterator first,
                       RandomAccessIterator last,
                       std::size_t n,
                       OutputIterator first2,
                       Random& rnd,
                       Creator creator)
{
    typedef typename Creator::result_type   Point;
    typedef typename Creator::argument_type T;

    std::ptrdiff_t m = last - first;
    for ( std::size_t i = 0; i < n; i++) {
      const Point& p = first[ rnd.uniform_int<std::ptrdiff_t>( 0, m-1)];
        const Point& q = first[ rnd.uniform_int<std::ptrdiff_t>( 0, m-1)];
        double la = rnd.get_double();
        double mu = 1.0 - la;
        *first2++ = creator(T(mu * to_double(p.x()) +
                              la * to_double(q.x())),
                            T(mu * to_double(p.y()) +
                              la * to_double(q.y())));
    }
    return first2;
}

template <class RandomAccessIterator, class OutputIterator>
OutputIterator random_collinear_points_2(
                       RandomAccessIterator first,
                       RandomAccessIterator last,
                       std::size_t n,
                       OutputIterator first2,
                       Random& rnd)
    // choose two random points from the range [`first',`last'), create a
    // random third point on the segment connecting this two points, and
    // write it to `first2'. Repeat this n times, thus writing n points to
    // `first2' that are collinear with points in the range [`first',
    // `last'). Three random numbers are needed from `rnd' for each point.
    // Returns the value of `first2' after inserting the n points.
    // Precondition: The expression `to_double((*first).x()
    // )' and `to_double((*first).y())' must be legal.
{
    typedef std::iterator_traits<RandomAccessIterator> ITraits;
    typedef typename ITraits::value_type               P;
    return random_collinear_points_2( first, last, n, first2, rnd,
                 Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P>());
}

template <class RandomAccessIterator, class OutputIterator>
OutputIterator random_collinear_points_2(
                       RandomAccessIterator first,
                       RandomAccessIterator last,
                       std::size_t n,
                       OutputIterator first2)
{
    return  random_collinear_points_2( first, last, n, first2,
                                       CGAL::get_default_random());
}

template < class P, class Creator = 
Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT,P> >
class Random_points_in_triangle_2 : public Random_generator_base<P> {
	P _p,_q,_r;
	void generate_point();
public:
	typedef P result_type;
	typedef Random_points_in_triangle_2<P, Creator> This;
	typedef typename Kernel_traits<P>::Kernel::Triangle_2 Triangle_2;
	Random_points_in_triangle_2() {}
	Random_points_in_triangle_2( 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_2( 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_2( const Triangle_2& 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_2<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;
	this->d_item = creator(T(to_double(_p.x())*b1+to_double(_q.x())*b2+to_double(_r.x())*b3),
							T(to_double(_p.y())*b1+to_double(_q.y())*b2+to_double(_r.y())*b3));
}

namespace internal {

//Functor returning Triangle_2 from Triangulation_2 Faces
template <class T>
class Triangle_from_face_2
{
  typedef typename T::Triangle Triangle;
public:
  typedef Triangle result_type;
  Triangle_from_face_2() {}

  Triangle operator()(typename T::Finite_faces_iterator face) const {
    return Triangle(face->vertex(0)->point(), face->vertex(1)->point(), face->vertex(2)->point());
  }
};

struct Is_not_in_domain
{
  typedef bool                                   result_type;

  template <class FH>
  result_type operator()(const FH fh) const {
    return (!fh->is_in_domain());
  }
};

template <class T>
class In_domain_finite_faces_iterator
  : public Filter_iterator<typename T::Finite_faces_iterator, Is_not_in_domain>
{
  typedef CGAL::Filter_iterator<typename T::Finite_faces_iterator, Is_not_in_domain>     Base;
  typedef In_domain_finite_faces_iterator<T>                                             Self;

  typedef typename T::Face_handle                                                        Face_handle;
  typedef typename T::Finite_faces_iterator                                              Finite_faces_iterator;

public:
  In_domain_finite_faces_iterator() : Base() {}
  In_domain_finite_faces_iterator(const Base &b) : Base(b) {}
  Self & operator++() { Base::operator++(); return *this; }
  Self & operator--() { Base::operator--(); return *this; }
  Self operator++(int) { Self tmp(*this); ++(*this); return tmp; }
  Self operator--(int) { Self tmp(*this); --(*this); return tmp; }
  operator Finite_faces_iterator() const { return Base::base(); }
  operator Face_handle() const { return Face_handle(Base::base()); }
};

}//end namespace internal

template <class P,
          class T,
          class Creator = Creator_uniform_2<typename Kernel_traits<P>::Kernel::RT, P> >
class Random_points_in_triangle_mesh_2
  : public Generic_random_point_generator<internal::In_domain_finite_faces_iterator<T>,
                                          internal::Triangle_from_face_2<T>,
                                          Random_points_in_triangle_2<P, Creator>,
                                          P>
{
public:
  typedef Generic_random_point_generator<internal::In_domain_finite_faces_iterator<T>,
                                         internal::Triangle_from_face_2<T>,
                                         Random_points_in_triangle_2<P, Creator>,
                                         P>                           Base;
  typedef typename T::Face_handle                                     Id;
  typedef P                                                           result_type;
  typedef Random_points_in_triangle_mesh_2<P, T, Creator>             This;

  Random_points_in_triangle_mesh_2(const T& triangulation, Random& rnd = get_default_random())
    : Base(CGAL::make_prevent_deref_range(
             CGAL::filter_iterator(triangulation.finite_faces_end(),
                                   internal::Is_not_in_domain(),
                                   triangulation.finite_faces_begin()),
             CGAL::filter_iterator(triangulation.finite_faces_end(),
                                   internal::Is_not_in_domain())),
           internal::Triangle_from_face_2<T>(),
           typename Kernel_traits<P>::Kernel::Compute_area_2(),
           rnd)
  {
  }

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

namespace internal
{

template<class T>
class Deref
{
public:
  typedef const T& result_type;
  const T& operator()(const T* triangle) const
  {
    return *triangle;
  }
};

template<class A>
struct Address_of {
  typedef const A* result_type;
  const A* operator()(const A& a) const
  {
    return &a;
  }
};

}//namesapce internal

template <class Point_2,
          class Triangle_2=typename Kernel_traits<Point_2>::Kernel::Triangle_2,
          class Creator =
            Creator_uniform_2<typename Kernel_traits<Point_2>::Kernel::RT,Point_2> >
struct Random_points_in_triangles_2
  : public Generic_random_point_generator<const Triangle_2*,
                                          internal::Deref<Triangle_2>,
                                          Random_points_in_triangle_2<Point_2>,
                                          Point_2>
{
  typedef Generic_random_point_generator<const Triangle_2*,
                                         internal::Deref<Triangle_2>,
                                         Random_points_in_triangle_2<Point_2, Creator>,
                                         Point_2>                   Base;
  typedef const Triangle_2*                                         Id;
  typedef Point_2                                                   result_type;
  typedef Random_points_in_triangles_2<Point_2, Triangle_2, Creator>  This;

  template<typename TriangleRange>
  Random_points_in_triangles_2( const TriangleRange& triangles, Random& rnd = get_default_random())
    : Base(make_range( boost::make_transform_iterator(triangles.begin(), internal::Address_of<Triangle_2>()),
                       boost::make_transform_iterator(triangles.end(), internal::Address_of<Triangle_2>()) ),
           internal::Deref<Triangle_2>(),
           typename Kernel_traits<Point_2>::Kernel::Compute_area_2(),
           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_2_H //
// EOF //
