// Copyright (c) 2010 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1.1/Intersections_3/include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_intersection.h $
// $Id: include/CGAL/Intersections_3/internal/Triangle_3_Triangle_3_intersection.h 08b27d3db14 $
// 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

//#define CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION

#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 <boost/container/flat_set.hpp>

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

namespace CGAL {
namespace Intersections {
namespace internal{

template <class Kernel>
struct Point_on_triangle
{
  // triangle points are not stored in this class but are expected
  // to always be passed in the same order. For a triangle pqr,
  // edge 1 is pq, edge 2 qr and edge 3 rp. Point -1 is p, -2 is q and -3 is r.
  //
  //  (0,-) vertex of t2 inside t1
  //  (-,-) common point of t1 and t2
  //  (-,0) vertex of t1 inside t2
  //  (-,+) vertex of t1 on an edge of t2
  //  (+,+) edge of t1 intersecting edge of t2
  //  (+,-) vertex of t2 on an edge of t1
  //
  std::pair<int, int> t1_t2_ids;
  boost::container::flat_set<int> extra_t1; // store other ids of edges containing the point
  typename Kernel::FT alpha; //

//////

  static
  inline
  const typename Kernel::Point_3&
  point_from_id(const typename Kernel::Point_3& p,
                const typename Kernel::Point_3& q,
                const typename Kernel::Point_3& r,
                int id)
  {
    switch(id)
    {
      case -1:
        return p;
      case -2:
        return q;
      default:
        return r;
    }
  }

  Point_on_triangle(int i1, int i2, typename Kernel::FT alpha = 0.) // TODO add global zero()?
    : t1_t2_ids(i1,i2)
    , alpha(alpha)
  {}

  // orientation of the current point wrt to edge id1 (p1q1)
  Orientation
  orientation (const typename Kernel::Point_3& p1, // source of edge edge_id1
               const typename Kernel::Point_3& q1, // target of edge edge_id1
               const typename Kernel::Point_3& r1,
               int edge_id1,
               const typename Kernel::Point_3& p2,
               const typename Kernel::Point_3& q2,
               const typename Kernel::Point_3& r2,
               const Kernel& k) const
  {
    if (t1_t2_ids.first!=0 && t1_t2_ids.second >=0)
    {
      if (t1_t2_ids.first<0)
        return (edge_id1==t1_t2_ids.first || (edge_id1+1)%3==t1_t2_ids.first) ? ZERO:POSITIVE; // it is a point on t1
      // this is an intersection point

      if (t1_t2_ids.first==edge_id1)
        return ZERO;
      if (t1_t2_ids.first-1==(edge_id1)%3)
      {
        if (alpha==0) return ZERO;
        return alpha>=0 ? POSITIVE:NEGATIVE;
      }
      CGAL_assertion((t1_t2_ids.first)%3==edge_id1-1);
      if (alpha==1) return ZERO;
      return alpha<=1?POSITIVE:NEGATIVE;
    }
    else
    {
      //this is an input point of t2
      typename Kernel::Coplanar_orientation_3 orient = k.coplanar_orientation_3_object();
      const typename Kernel::Point_3& query = point_from_id(p2,q2,r2,t1_t2_ids.second);
      return orient(p1,q1,r1,query);
    }
  }


  int id1() const { return t1_t2_ids.first; }
  int id2() const { return t1_t2_ids.second; }

  void set_id1(int i) { t1_t2_ids.first=i; }
  void set_id2(int i) { t1_t2_ids.second=i; }

  // construct the intersection point from the info stored
  typename Kernel::Point_3
  point(const typename Kernel::Point_3& p1,
        const typename Kernel::Point_3& q1,
        const typename Kernel::Point_3& r1,
        const typename Kernel::Point_3& p2,
        const typename Kernel::Point_3& q2,
        const typename Kernel::Point_3& r2,
        const Kernel& k) const
  {
    if (t1_t2_ids.second<0)
      return point_from_id(p2,q2,r2,t1_t2_ids.second);
    if (t1_t2_ids.first<0)
      return point_from_id(p1,q1,r1,t1_t2_ids.first);

    return k.construct_barycenter_3_object()(point_from_id(p1,q1,r1,-(t1_t2_ids.first)%3-1), alpha,
                                             point_from_id(p1,q1,r1,-t1_t2_ids.first)) ;
  }
};

// the intersection of two triangles is computed by iteratively intersection t2
// with halfspaces defined by edges of t1. The following function is called
// for each each on t1 on edge of the current intersection.
// pq is such an edge and p1q1 from t1 defines the halfspace intersection
// we are currently interseted in. We return the intersection point of
// pq with p1q1
template <class Kernel>
Point_on_triangle<Kernel>
intersection(const Point_on_triangle<Kernel>& p,
             const Point_on_triangle<Kernel>& q,
             int edge_id_t1,
             const typename Kernel::Point_3& p1,
             const typename Kernel::Point_3& q1,
//             const typename Kernel::Point_3& r1,
             const typename Kernel::Point_3& p2,
             const typename Kernel::Point_3& q2,
             const typename Kernel::Point_3& r2,
             const Kernel& k)
{
#ifdef CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION
  std::cout << "    calling intersection: ";
  std::cout << " (" << p.id1() << "," << p.id2() << ",[" << p.alpha << "]) -";
  std::cout << " (" << q.id1() << "," << q.id2() << ",[" << q.alpha << "]) || e" << edge_id_t1 << "\n";
#endif
  typename Kernel::Compute_alpha_for_coplanar_triangle_intersection_3 compute_alpha
    = k.compute_alpha_for_coplanar_triangle_intersection_3_object();
  typedef Point_on_triangle<Kernel> Pot;

  auto common_edge_id = [](int pid, int qid)
  {
    if (pid==0 || qid==0) return 0;
    if (pid<0)
    {
      if (qid<0)
      {
        return (-pid)%3==-qid-1 ? -pid:-qid;
      }
      else
      {
        return (-pid==qid || (qid)%3==-pid-1) ? qid : 0;
      }
    }
    else
    {
      if (qid<0)
      {
        return (-qid==pid || (pid)%3==-qid-1) ? pid : 0;
      }
      else
      {
        return pid==qid ? pid : 0;
      }
    }
  };

  int common_eid1 = common_edge_id(p.id1(), q.id1());
  int common_eid2 = common_edge_id(p.id2(), q.id2());

  if (common_eid1!=0)
  {
    CGAL_assertion( (common_eid1)%3==edge_id_t1-1 || (edge_id_t1)%3==common_eid1-1 );
    int pid1 = (common_eid1)%3==edge_id_t1-1? -edge_id_t1:-common_eid1;
    return Point_on_triangle<Kernel>(pid1, common_eid2);
  }
  else
  {
    CGAL_assertion(common_eid2!=0);
    typename Kernel::FT alpha = compute_alpha(p1, q1,
                                              Pot::point_from_id(p2, q2, r2, -common_eid2),
                                              Pot::point_from_id(p2, q2, r2, -(common_eid2)%3-1));
    return Point_on_triangle<Kernel>(edge_id_t1, common_eid2, alpha);
  }
}

template <class Kernel>
void intersection_coplanar_triangles_cutoff(const typename Kernel::Point_3& p1,
                                            const typename Kernel::Point_3& q1,
                                            const typename Kernel::Point_3& r1,
                                            int edge_id,
                                            const typename Kernel::Point_3& p2,
                                            const typename Kernel::Point_3& q2,
                                            const typename Kernel::Point_3& r2,
                                            const Kernel& k,
                                            std::list<Point_on_triangle<Kernel>>& inter_pts)
{
#ifdef CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION
  std::cout << "  cutoff using e" << edge_id << ": "
            << to_double(p1.x()) << " " << to_double(p1.y()) << " " << to_double(p1.z()) << " "
            << to_double(q1.x()) << " " << to_double(q1.y()) << " " << to_double(q1.z()) << "\n";
#endif
  typedef typename std::list<Point_on_triangle<Kernel>>::iterator Iterator;

  if(inter_pts.empty())
    return;

  //orient(p1,q1,r1,r1) is POSITIVE
  std::map<const Point_on_triangle<Kernel>*,Orientation> orientations; // TODO skip map
  for (Point_on_triangle<Kernel>& pot : inter_pts)
  {
    orientations[ &pot ]=pot.orientation(p1,q1,r1,edge_id,p2,q2,r2,k);
    if (orientations[ &pot ]==COLLINEAR)
    {
      if (pot.id1()==0)
        pot.set_id1(edge_id);
      else
      {
        CGAL_assertion(pot.id1()>0);
        CGAL_assertion((edge_id)%3==pot.id1()-1 || (pot.id1())%3==edge_id-1);
        pot.set_id1( (edge_id)%3==pot.id1()-1 ? -pot.id1(): -edge_id );
      }
    }
  }

#ifdef CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION
  std::cout << "    Orientations:";
  for (const Point_on_triangle<Kernel>& pot : inter_pts)
    std::cout << " " << orientations[ &pot ];
  std::cout << "\n";
#endif
  CGAL_kernel_assertion_code(int pt_added = 0);

  Iterator prev = std::prev(inter_pts.end());

  Iterator stop = inter_pts.size() > 2 ? inter_pts.end() : std::prev(inter_pts.end());
  for(Iterator it=inter_pts.begin(); it!=stop; ++it)
  {
    Orientation or_prev = orientations[&(*prev)],
                or_curr = orientations[&(*it)];

    if((or_prev == POSITIVE && or_curr == NEGATIVE) ||
       (or_prev == NEGATIVE && or_curr == POSITIVE))
    {
      Point_on_triangle<Kernel> new_pt = intersection(*prev, *it, edge_id, p1, q1, p2, q2, r2, k);

      prev = inter_pts.insert(it,new_pt);
      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)
{
#ifdef CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION
  auto to_string = [](const typename K::Triangle_3& t)
  {
    std::stringstream sstr;
    sstr << "4 "
         << to_double(t[0].x()) << " "  << to_double(t[0].y()) << " "  << to_double(t[0].z()) << " "
         << to_double(t[1].x()) << " "  << to_double(t[1].y()) << " "  << to_double(t[1].z()) << " "
         << to_double(t[2].x()) << " "  << to_double(t[2].y()) << " "  << to_double(t[2].z()) << " "
         << to_double(t[0].x()) << " "  << to_double(t[0].y()) << " "  << to_double(t[0].z()) << "\n";
    return sstr.str();
  };

  std::cout << "intersection_coplanar_triangles\n";
  std::ofstream("/tmp/t1.polylines.txt") << std::setprecision(17) << to_string(t1) << "\n";
  std::ofstream("/tmp/t2.polylines.txt") << std::setprecision(17) << to_string(t2) << "\n";
#endif
  const typename K::Point_3& p1 = t1.vertex(0),
                             q1 = t1.vertex(1),
                             r1 = t1.vertex(2);

  const typename K::Point_3& p2 = t2.vertex(0),
                             q2 = t2.vertex(1),
                             r2 = t2.vertex(2);

  std::list<Point_on_triangle<K>> inter_pts;
  inter_pts.push_back(Point_on_triangle<K>(0,-1));
  inter_pts.push_back(Point_on_triangle<K>(0,-2));
  inter_pts.push_back(Point_on_triangle<K>(0,-3));

#ifdef CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION
  auto print_points = [&]()
  {
    std::cout << "  ipts size: " << inter_pts.size() << "\n";
    for(auto p : inter_pts) {std::cout << "  (" << p.id1() << "," << p.id2() << ",[" << p.alpha << "]) ";} std::cout <<"\n";
  };
  print_points();
#endif
  //intersect t2 with the three half planes which intersection defines t1
  intersection_coplanar_triangles_cutoff(p1,q1,r1,1,p2,q2,r2,k,inter_pts); //line pq
#ifdef CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION
  print_points();
#endif
  intersection_coplanar_triangles_cutoff(q1,r1,p1,2,p2,q2,r2,k,inter_pts); //line qr
#ifdef CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION
  print_points();
#endif
  intersection_coplanar_triangles_cutoff(r1,p1,q1,3,p2,q2,r2,k,inter_pts); //line rp
#ifdef CGAL_DEBUG_COPLANAR_T3_T3_INTERSECTION
  print_points();
#endif

  auto point = [&](const Point_on_triangle<K>& pot){ return pot.point(p1,q1,r1,p2,q2,r2,k); };
  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>(point(*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()(point(*inter_pts.begin()), point(*std::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()(point(*inter_pts.begin()), point(*std::next(inter_pts.begin())), point(*std::prev(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>(boost::make_transform_iterator(inter_pts.begin(), point),
                                             boost::make_transform_iterator(inter_pts.end(), point)));
  }
}

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 std::visit(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
