// Copyright (c) 2007-09  INRIA Sophia-Antipolis (France).
// Copyright (c) 2017 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v5.6.2/Surface_mesher/include/CGAL/IO/facets_in_complex_2_to_triangle_mesh.h $
// $Id: facets_in_complex_2_to_triangle_mesh.h e7bf5b661b6 2022-02-04T10:22:26+01:00 Sébastien Loriot
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Maxime Gimeno, Pierre Alliez

#ifndef CGAL_FACETS_IN_COMPLEX_2_TO_TRIANGLE_MESH_H
#define CGAL_FACETS_IN_COMPLEX_2_TO_TRIANGLE_MESH_H

#include <CGAL/license/Surface_mesher.h>

#include <CGAL/disable_warnings.h>

#include <CGAL/boost/graph/Euler_operations.h>
#include <unordered_map>
#include <set>
#include <stack>

namespace CGAL{
/*!
\ingroup PkgSurfaceMesher3FunctionsIO

 \brief converts a manifold surface reconstructed by `make_surface_mesh()` to a `TriangleMesh`.

 This function exports the surface as a `TriangleMesh` and appends it to `graph`.
 It must be manifold. For this purpose, you may call
 `make_surface_mesh()` with `Manifold_tag` or
 `Manifold_with_boundary_tag` parameter.

 @tparam C2T3 a model of `SurfaceMeshComplex_2InTriangulation_3`.
 @tparam TriangleMesh a model of `MutableFaceGraph` with an internal point property map. The point type should be compatible with the one used in `C2T3`.

 @param c2t3 a manifold instance of `C2T3`.
 @param graph an instance of `TriangleMesh`.

\sa `CGAL::output_surface_facets_to_off()`
*/
template<class C2T3, class TriangleMesh>
void facets_in_complex_2_to_triangle_mesh(const C2T3& c2t3, TriangleMesh& graph)
{
  typedef typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type VertexPointMap;
  typedef typename boost::property_traits<VertexPointMap>::value_type Point_3;
  typedef typename C2T3::Triangulation Tr;
  typedef typename Tr::Vertex_handle Vertex_handle;
  typedef typename Tr::Finite_vertices_iterator Vertex_iterator;
  typedef typename Tr::Geom_traits::Vector_3 Vector;
  typedef typename Tr::Edge Edge;
  typedef typename Tr::Facet Facet;
  typedef typename Tr::Finite_facets_iterator Finite_facets_iterator;

  const Tr& tr = c2t3.triangulation();
  VertexPointMap vpmap = get(boost::vertex_point, graph);
  const typename Tr::size_type number_of_facets = c2t3.number_of_facets();
  {
    //used to set indices of vertices
    std::unordered_map<Vertex_handle, int> V;

    // Finite vertices coordinates.
    Finite_facets_iterator fit = tr.finite_facets_begin();
    std::set<Facet> oriented_set;
    std::stack<Facet> stack;

    CGAL_assertion_code(typename Tr::size_type nb_facets = 0; )

    while (oriented_set.size() != number_of_facets) {
      while ( fit->first->is_facet_on_surface(fit->second) == false ||
              oriented_set.find(*fit) != oriented_set.end() ||

              oriented_set.find(c2t3.opposite_facet(*fit)) !=
              oriented_set.end() ) {
        ++fit;
      }
      oriented_set.insert(*fit);
      stack.push(*fit);
      while(! stack.empty() ) {
        Facet f = stack.top();
        stack.pop();
        for(int ih = 0 ; ih < 3 ; ++ih) {
          const int i1  = tr.vertex_triple_index(f.second, tr. cw(ih));
          const int i2  = tr.vertex_triple_index(f.second, tr.ccw(ih));
          if( c2t3.face_status(Edge(f.first, i1, i2)) == C2T3::REGULAR ) {
            Facet fn = c2t3.neighbor(f, ih);
            if (oriented_set.find(fn) == oriented_set.end() &&
                oriented_set.find(c2t3.opposite_facet(fn)) == oriented_set.end())
            {
              oriented_set.insert(fn);
              stack.push(fn);
            }
          } // end "if the edge is regular"
        } // end "for each neighbor of f"
      } // end "stack non empty"
    } // end "oriented_set not full"

    // Orients the whole mesh towards outside:
    // - find the facet with max z
    typename std::set<Facet>::const_iterator top_facet = oriented_set.begin();
    for(typename std::set<Facet>::const_iterator fit = oriented_set.begin();
        fit != oriented_set.end();
        ++fit)
    {
      double top_z =
          (top_facet->first->vertex(tr.vertex_triple_index(top_facet->second, 0))->point().z()
           + top_facet->first->vertex(tr.vertex_triple_index(top_facet->second, 1))->point().z()
           + top_facet->first->vertex(tr.vertex_triple_index(top_facet->second, 2))->point().z())/3.;
      Vertex_handle v0 = fit->first->vertex(tr.vertex_triple_index(fit->second, 0));
      Vertex_handle v1 = fit->first->vertex(tr.vertex_triple_index(fit->second, 1));
      Vertex_handle v2 = fit->first->vertex(tr.vertex_triple_index(fit->second, 2));
      double z = (v0->point().z() + v1->point().z() + v2->point().z())/3.;
      if (top_z < z){
        top_facet = fit;
      }
      // we just put them in the map and index them later
      V[v0] = 0;
      V[v1] = 0;
      V[v2] = 0;
    }
    // - orient the facet with max z towards +Z axis
    Vertex_handle v0 = top_facet->first->vertex(tr.vertex_triple_index(top_facet->second, 0));
    Vertex_handle v1 = top_facet->first->vertex(tr.vertex_triple_index(top_facet->second, 1));
    Vertex_handle v2 = top_facet->first->vertex(tr.vertex_triple_index(top_facet->second, 2));
    Vector normal = cross_product(v1->point()-v0->point(), v2->point()-v1->point());
    const Vector Z(0, 0, 1);
    bool regular_orientation = (Z * normal >= 0);

    int inum = 0;
    //add vertices
    std::vector<typename boost::graph_traits<TriangleMesh>::vertex_descriptor> vertices;
    for(Vertex_iterator vit = tr.finite_vertices_begin();
        vit != tr.finite_vertices_end();
        ++vit)
    {
      auto it = V.find(vit);
      if(it != V.end()){
        typename boost::graph_traits<TriangleMesh>::vertex_descriptor v = add_vertex(graph);
        vertices.push_back(v);
        put(vpmap,
            v,
            Point_3(
                    vit->point().x(),
                    vit->point().y(),
                    vit->point().z())
            );
        it->second = inum++;
      }
    }
    //add faces
    for(typename std::set<Facet>::const_iterator fit =
        oriented_set.begin();
        fit != oriented_set.end();
        ++fit)
    {
      int id0(V[fit->first->vertex(tr.vertex_triple_index(fit->second, 0))]),
          id1(regular_orientation ? V[fit->first->vertex(tr.vertex_triple_index(fit->second, 1))]
              : V[fit->first->vertex(tr.vertex_triple_index(fit->second, 2))]),
          id2(regular_orientation ? V[fit->first->vertex(tr.vertex_triple_index(fit->second, 2))]
              : V[fit->first->vertex(tr.vertex_triple_index(fit->second, 1))]);
      std::vector<typename boost::graph_traits<TriangleMesh>::vertex_descriptor> face;
      face.resize(3);
      face[0] = vertices[id0];
      face[1] = vertices[id1];
      face[2] = vertices[id2];
      CGAL::Euler::add_face(face, graph);
      CGAL_assertion_code(++nb_facets);
    }
    CGAL_assertion(nb_facets == number_of_facets);
  }
}

}// end CGAL

#include <CGAL/enable_warnings.h>

#endif // CGAL_FACETS_IN_COMPLEX_2_TO_TRIANGLE_MESH_H
