#ifndef CGAL_APPROXIMATION_L2_TRAITS_H
#define CGAL_APPROXIMATION_L2_TRAITS_H

#include <CGAL/license/Surface_mesh_approximation.h>

#include <CGAL/Kernel/global_functions.h>
#include <CGAL/squared_distance_3.h>
#include <CGAL/linear_least_squares_fitting_3.h>

#include <boost/graph/graph_traits.hpp>
#include <boost/unordered_map.hpp>

#include <list>

namespace CGAL {

/*!
 * \ingroup PkgTSMA
 * @brief Approximation traits for L2 metric.
 *
 * \cgalModels`Approximation_traits`
 *
 * @tparam TriangleMesh a triangle `FaceListGraph`
 * @tparam VertexPointMap a property map with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
    as key type, GeomTraits::Point_3 as value type
 * @tparam GeomTraits geometric traits
 */
template <typename TriangleMesh,
  typename VertexPointMap
    = typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
  typename GeomTraits
    = typename TriangleMesh::Traits>
class Approximation_l2_traits {
  typedef typename GeomTraits::FT FT;
  typedef typename GeomTraits::Point_3 Point_3;

  typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;

  typedef CGAL::internal::face_property_t<FT> Face_area_tag;
  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type Face_area_map;

public:
  // type required by the `Approximation_traits` concept
  typedef typename GeomTraits::Plane_3 Proxy;

  // constructor
  Approximation_l2_traits(const TriangleMesh &tm, const VertexPointMap &vpmap)
    : m_tm(&tm), m_vpmap(vpmap){
    m_famap = CGAL::internal::add_property(
      Face_area_tag("VSA-face_area"), const_cast<TriangleMesh &>(*m_tm));

    BOOST_FOREACH(face_descriptor f, faces(*m_tm)) {
      const halfedge_descriptor he = halfedge(f, *m_tm);
      const Point_3 &p0 = m_vpmap[source(he, *m_tm)];
      const Point_3 &p1 = m_vpmap[target(he, *m_tm)];
      const Point_3 &p2 = m_vpmap[target(next(he, *m_tm), *m_tm)];
      put(m_famap, f, std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
    }
  }

  // member function required by the `Approximation_traits` concept
  // It is a function that takes a facet and a proxy, returns the L21 error between them.
  FT compute_error(const face_descriptor &f, const Proxy &px) const {
    halfedge_descriptor he = halfedge(f, *m_tm);
    const Point_3 &p0 = m_vpmap[source(he, *m_tm)];
    const Point_3 &p1 = m_vpmap[target(he, *m_tm)];
    const Point_3 &p2 = m_vpmap[target(next(he, *m_tm), *m_tm)];
    const FT sq_d0 = CGAL::squared_distance(p0, px.fit_plane);
    const FT sq_d1 = CGAL::squared_distance(p1, px.fit_plane);
    const FT sq_d2 = CGAL::squared_distance(p2, px.fit_plane);
    const FT d0(std::sqrt(CGAL::to_double(sq_d0)));
    const FT d1(std::sqrt(CGAL::to_double(sq_d1)));
    const FT d2(std::sqrt(CGAL::to_double(sq_d2)));

    return (sq_d0 + sq_d1 + sq_d2 + d0 * d1 + d1 * d2 + d2 * d0) * get(m_famap, f) / FT(6.0);
  }

  // member function required by the `Approximation_traits` concept
  // It returns the proxy fitted from the facets from beg to end.
  template <typename FacetIterator>
  Proxy fit_proxy(const FacetIterator beg, const FacetIterator end) const {
    CGAL_assertion(beg != end);

    std::list<Triangle_3> tris;
    for (FacetIterator fitr = beg; fitr != end; ++fitr) {
      halfedge_descriptor he = halfedge(*fitr, *m_tm);
      const Point_3 &p0 = m_vpmap[source(he, *m_tm)];
      const Point_3 &p1 = m_vpmap[target(he, *m_tm)];
      const Point_3 &p2 = m_vpmap[target(next(he, *m_tm), *m_tm)];
      tris.push_back(Triangle_3(p0, p1, p2));
    }

    // construct and fit proxy plane
    Proxy px;
    CGAL::linear_least_squares_fitting_3(
      tris.begin(),
      tris.end(),
      px,
      CGAL::Dimension_tag<2>());

    // TODO: check and flip plane normal

    return px;
  }

private:
  const TriangleMesh *m_tm;
  const VertexPointMap m_vpmap;
  Face_area_map m_famap;
};

// specializaiton for point map
template <typename TriangleMesh, typename GeomTraits>
class Approximation_l2_traits<TriangleMesh,
  typename boost::property_map<TriangleMesh, boost::vertex_point_t>::type,
  GeomTraits> {
  typedef typename GeomTraits::FT FT;
  typedef typename GeomTraits::Point_3 Point_3;

  typedef typename boost::graph_traits<TriangleMesh>::face_descriptor face_descriptor;
  typedef typename boost::graph_traits<TriangleMesh>::halfedge_descriptor halfedge_descriptor;

  typedef CGAL::internal::face_property_t<FT> Face_area_tag;
  typedef typename CGAL::internal::dynamic_property_map<TriangleMesh, Face_area_tag >::type Face_area_map;

public:
  // type required by the `Approximation_traits` concept
  typedef typename GeomTraits::Plane_3 Proxy;

  // constructor
  Approximation_l2_traits(const TriangleMesh &tm)
    : m_tm(&tm), m_vpmap(get(boost::vertex_point, const_cast<TriangleMesh &>(tm))){
    m_famap = CGAL::internal::add_property(
      Face_area_tag("VSA-face_area"), const_cast<TriangleMesh &>(*m_tm));

    BOOST_FOREACH(face_descriptor f, faces(*m_tm)) {
      const halfedge_descriptor he = halfedge(f, *m_tm);
      const Point_3 &p0 = m_vpmap[source(he, *m_tm)];
      const Point_3 &p1 = m_vpmap[target(he, *m_tm)];
      const Point_3 &p2 = m_vpmap[target(next(he, *m_tm), *m_tm)];
      put(m_famap, f, std::sqrt(CGAL::to_double(CGAL::squared_area(p0, p1, p2))));
    }
  }

  // member function required by the `Approximation_traits` concept
  // It is a function that takes a facet and a proxy, returns the L21 error between them.
  FT compute_error(const face_descriptor &f, const Proxy &px) const {
    halfedge_descriptor he = halfedge(f, *m_tm);
    const Point_3 &p0 = m_vpmap[source(he, *m_tm)];
    const Point_3 &p1 = m_vpmap[target(he, *m_tm)];
    const Point_3 &p2 = m_vpmap[target(next(he, *m_tm), *m_tm)];
    const FT sq_d0 = CGAL::squared_distance(p0, px.fit_plane);
    const FT sq_d1 = CGAL::squared_distance(p1, px.fit_plane);
    const FT sq_d2 = CGAL::squared_distance(p2, px.fit_plane);
    const FT d0(std::sqrt(CGAL::to_double(sq_d0)));
    const FT d1(std::sqrt(CGAL::to_double(sq_d1)));
    const FT d2(std::sqrt(CGAL::to_double(sq_d2)));

    return (sq_d0 + sq_d1 + sq_d2 + d0 * d1 + d1 * d2 + d2 * d0) * get(m_famap, f) / FT(6.0);
  }

  // member function required by the `Approximation_traits` concept
  // It returns the proxy fitted from the facets from beg to end.
  template <typename FacetIterator>
  Proxy fit_proxy(const FacetIterator beg, const FacetIterator end) const {
    CGAL_assertion(beg != end);

    std::list<Triangle_3> tris;
    for (FacetIterator fitr = beg; fitr != end; ++fitr) {
      halfedge_descriptor he = halfedge(*fitr, *m_tm);
      const Point_3 &p0 = m_vpmap[source(he, *m_tm)];
      const Point_3 &p1 = m_vpmap[target(he, *m_tm)];
      const Point_3 &p2 = m_vpmap[target(next(he, *m_tm), *m_tm)];
      tris.push_back(Triangle_3(p0, p1, p2));
    }

    // construct and fit proxy plane
    Proxy px;
    CGAL::linear_least_squares_fitting_3(
      tris.begin(),
      tris.end(),
      px,
      CGAL::Dimension_tag<2>());

    // TODO: check and flip plane normal

    return px;
  }

private:
  const TriangleMesh *m_tm;
  const VertexPointMap m_vpmap;
  Face_area_map m_famap;
};

} // namespace CGAL

#endif // CGAL_APPROXIMATION_L2_TRAITS_H