// Copyright (c) 2010 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.6.1/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_intersection.h $
// $Id: Triangle_3_Triangle_3_intersection.h c17c14f 2023-01-24T10:55:29+01:00 Mael Rouxel-Labbé
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Sebastien Loriot
//

#ifndef CGAL_INTERNAL_INTERSECTIONS_TRIANGLE_3_TRIANGLE_3_INTERSECTION_H
#define CGAL_INTERNAL_INTERSECTIONS_TRIANGLE_3_TRIANGLE_3_INTERSECTION_H

#include <CGAL/Intersection_traits_3.h>
#include <CGAL/Intersections_3/internal/Line_3_Triangle_3_intersection.h>
#include <CGAL/Intersections_3/internal/Line_3_Line_3_intersection.h>
#include <CGAL/Intersections_3/internal/Plane_3_Plane_3_intersection.h>

#include <CGAL/kernel_assertions.h>

#include <boost/next_prior.hpp>

#include <list>
#include <map>
#include <vector>

namespace CGAL {
namespace Intersections {
namespace internal{

template <class Kernel>
void intersection_coplanar_triangles_cutoff(const typename Kernel::Point_3& p,
                                            const typename Kernel::Point_3& q,
                                            const typename Kernel::Point_3& r,
                                            const Kernel& k,
                                            std::list<typename Kernel::Point_3>& inter_pts)
{
  typedef typename std::list<typename Kernel::Point_3>::iterator Iterator;

  if(inter_pts.empty())
    return;

  typename Kernel::Coplanar_orientation_3 orient = k.coplanar_orientation_3_object();
  typename Kernel::Construct_line_3 line = k.construct_line_3_object();

  //orient(p,q,r,r) is POSITIVE
  std::map<const typename Kernel::Point_3*,Orientation> orientations;
  for (Iterator it=inter_pts.begin();it!=inter_pts.end();++it)
    orientations[ &(*it) ]=orient(p,q,r,*it);

  CGAL_kernel_assertion_code(int pt_added = 0;)

  const typename Kernel::Point_3* prev = &(*boost::prior(inter_pts.end()));
  Iterator stop = inter_pts.size() > 2 ? inter_pts.end() : boost::prior(inter_pts.end());
  for(Iterator it=inter_pts.begin(); it!=stop; ++it)
  {
    const typename Kernel::Point_3& curr = *it;
    Orientation or_prev = orientations[prev],
                or_curr = orientations[&curr];

    if((or_prev == POSITIVE && or_curr == NEGATIVE) ||
       (or_prev == NEGATIVE && or_curr == POSITIVE))
    {
      typename Intersection_traits<Kernel, typename Kernel::Line_3, typename Kernel::Line_3>::result_type
        obj = intersection(line(p,q), line(*prev,curr), k);

      // assert "not empty"
      CGAL_kernel_assertion(bool(obj));

      const typename Kernel::Point_3* inter = intersect_get<typename Kernel::Point_3>(obj);
      CGAL_kernel_assertion(inter != nullptr);

      prev = &(*inter_pts.insert(it,*inter));
      orientations[prev] = COLLINEAR;
      CGAL_kernel_assertion_code(++pt_added;)
    }

    prev = &(*it);
  }

  CGAL_kernel_assertion(pt_added<3);
  Iterator it = inter_pts.begin();
  while(it!=inter_pts.end())
  {
    if(orientations[&(*it)] == NEGATIVE)
      inter_pts.erase(it++);
    else
      ++it;
  }
}

template <class K>
typename Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3>::result_type
intersection_coplanar_triangles(const typename K::Triangle_3& t1,
                                const typename K::Triangle_3& t2,
                                const K& k)
{
  const typename K::Point_3& p = t1.vertex(0),
                             q = t1.vertex(1),
                             r = t1.vertex(2);

  std::list<typename K::Point_3> inter_pts;
  inter_pts.push_back(t2.vertex(0));
  inter_pts.push_back(t2.vertex(1));
  inter_pts.push_back(t2.vertex(2));

  //intersect t2 with the three half planes which intersection defines t1
  intersection_coplanar_triangles_cutoff(p,q,r,k,inter_pts); //line pq
  intersection_coplanar_triangles_cutoff(q,r,p,k,inter_pts); //line qr
  intersection_coplanar_triangles_cutoff(r,p,q,k,inter_pts); //line rp

  switch(inter_pts.size())
  {
    case 0:
      return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>();
    case 1:
      return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>(*inter_pts.begin());
    case 2:
      return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>(
            k.construct_segment_3_object()(*inter_pts.begin(), *boost::next(inter_pts.begin())) );
    case 3:
      return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>(
            k.construct_triangle_3_object()(*inter_pts.begin(), *boost::next(inter_pts.begin()), *boost::prior(inter_pts.end())) );
    default:
      return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>(
            std::vector<typename K::Point_3>(inter_pts.begin(),inter_pts.end()));
  }
}

template<typename K>
struct Triangle_Line_visitor
{
  typedef typename Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3 >::result_type result_type;

  result_type operator()(const typename K::Point_3& p, const typename K::Segment_3& s) const
  {
    if(typename K::Has_on_3()(s, p))
      return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>(p);
    else
      return result_type();
  }

  result_type operator()(const typename K::Segment_3& s, const typename K::Point_3& p) const
  {
    return operator()(p,s);
  }

  result_type operator()(const typename K::Point_3& p1, const typename K::Point_3& p2) const
  {
    if(p1 == p2)
      return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>(p1);
    else
      return result_type();
  }

  result_type operator()(const typename K::Segment_3& s1, const typename K::Segment_3& s2) const
  {
    typename Intersection_traits<K, typename K::Segment_3, typename K::Segment_3>::result_type
      v = intersection_collinear_segments(s1,s2,K());

    if(v)
    {
      if(const typename K::Segment_3* s = intersect_get<typename K::Segment_3>(v))
        return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>(*s);
      if(const typename K::Point_3* p = intersect_get<typename K::Point_3>(v))
        return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>(*p);
    }

    return result_type();
  }
};

template <class K>
typename Intersection_traits<K, typename K::Triangle_3, typename K::Triangle_3>::result_type
intersection(const typename K::Triangle_3& t1,
             const typename K::Triangle_3& t2,
             const K& k)
{
  CGAL_precondition(!t1.is_degenerate() && !t2.is_degenerate());

  typename Intersection_traits<K, typename K::Plane_3, typename K::Plane_3>::result_type
    v = internal::intersection(t1.supporting_plane(), t2.supporting_plane(), k);

  if(!v)
  {
    // empty plane plane intersection
    return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>();
  }

  if(intersect_get<typename K::Plane_3>(v))
  {
    //coplanar triangles
    return intersection_coplanar_triangles(t1,t2,k);
  }

  if(const typename K::Line_3* line=intersect_get<typename K::Line_3>(v))
  {
    //The supporting planes of the triangles intersect along a line.
    typedef typename Intersection_traits<K, typename K::Triangle_3, typename K::Line_3>::result_type Triangle_Line_Inter;

    Triangle_Line_Inter inter1 = intersection_coplanar(t1,*line,k);
    Triangle_Line_Inter inter2 = intersection_coplanar(t2,*line,k);
    if(!inter1 || !inter2)
    {
      // one of the intersection is empty
      return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>();
    }

    return boost::apply_visitor(Triangle_Line_visitor<K>(), *inter1, *inter2);
  }

  return intersection_return<typename K::Intersect_3, typename K::Triangle_3, typename K::Triangle_3>();
}

} // namespace internal
} // namespace Intersections
} // namespace CGAL

#endif // CGAL_INTERNAL_INTERSECTIONS_TRIANGLE_3_TRIANGLE_3_INTERSECTION_H

