// Copyright (c) 2005 Rijksuniversiteit Groningen (Netherlands)
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Skin_surface_3/include/CGAL/Triangulated_mixed_complex_observer_3.h $
// $Id: include/CGAL/Triangulated_mixed_complex_observer_3.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Nico Kruithof <Nico@cs.rug.nl>

#ifndef CGAL_TRIANGULATED_MIXED_COMPLEX_OBSERVER_3
#define CGAL_TRIANGULATED_MIXED_COMPLEX_OBSERVER_3

#include <CGAL/license/Skin_surface_3.h>

#include <CGAL/Skin_surface_quadratic_surface_3.h>
#include <CGAL/Triangulation_simplex_3.h>

#include <memory>

namespace CGAL {

template <class T>
struct SS_Dereference_type {
  typedef T value_type;
};
template <class T>
struct SS_Dereference_type<T *> {
  typedef T value_type;
};

template <class TriangulatedMixedComplex_3, class SkinSurface_3>
class Triangulated_mixed_complex_observer_3
{
public:
  typedef SkinSurface_3                              Skin_surface;
  typedef TriangulatedMixedComplex_3                 Triangulated_mixed_complex;

  typedef typename SkinSurface_3::Regular            Regular;
  typedef typename Regular::Geom_traits              Regular_traits;
  typedef typename Triangulated_mixed_complex::Geom_traits
                                                     Triangulated_mixed_complex_traits;
  typedef typename Triangulated_mixed_complex::Triangulation_data_structure
                                                     TMC_TDS;
  typedef typename SkinSurface_3::Quadratic_surface  Quadratic_surface;

  typedef typename Regular_traits::FT                FT;

  typedef typename Regular::Vertex_handle            Rt_Vertex_handle;
  typedef typename Regular::Edge                     Rt_Edge;
  typedef typename Regular::Facet                    Rt_Facet;
  typedef typename Regular::Cell_handle              Rt_Cell_handle;
  typedef Triangulation_simplex_3<Regular>           Rt_Simplex;

  typedef typename Regular::Bare_point               Rt_Bare_point;
  typedef typename Regular::Geom_traits              Rt_Geom_traits;
  typedef typename Rt_Geom_traits::RT                Rt_RT;
  typedef typename Regular::Weighted_point           Rt_Weighted_point;

  typedef typename Triangulated_mixed_complex::Vertex_handle TMC_Vertex_handle;
  typedef typename Triangulated_mixed_complex::Cell_handle   TMC_Cell_handle;

  typedef typename Quadratic_surface::K               Surface_traits;
  typedef typename Surface_traits::RT                 Surface_RT;
  typedef typename Quadratic_surface::Point           Surface_point;
  typedef typename Quadratic_surface::Vector          Surface_vector;
  typedef typename Surface_traits::Weighted_point_3   Surface_weighted_point;

  typedef
  Cartesian_converter < typename Rt_Bare_point::R,
                        typename Quadratic_surface::K >  R2S_converter;
  Triangulated_mixed_complex_observer_3(FT shrink) :
  shrink(shrink) {}

  void after_vertex_insertion(Rt_Simplex const &sDel,
                              Rt_Simplex const &sVor,
                              TMC_Vertex_handle &vh) {
    vh->info() = typename SkinSurface_3::Vertex_info(sDel, sVor);
  }

  void after_cell_insertion(Rt_Simplex const &s, TMC_Cell_handle &ch)
  {
    if (!(s == prev_s)) {
      prev_s = s;
      Rt_Vertex_handle vh;
      Rt_Edge          e;
      Rt_Facet         f;
      Rt_Cell_handle   ch;

      typename Surface_traits::Construct_point_3 wp2p;

      switch (s.dimension()) {
        case 0: {
          vh = s;
          Surface_weighted_point wp = r2s_converter(vh->point());
          create_sphere(wp.point(),
                        -wp.weight(),
                        r2s_converter(shrink), 1);
          break;
        }
        case 1: {
          e = s;
          Surface_weighted_point p0 =
            r2s_converter(e.first->vertex(e.second)->point());
          Surface_weighted_point p1 =
            r2s_converter(e.first->vertex(e.third)->point());

          create_hyperboloid(typename Surface_traits::
                             Construct_weighted_circumcenter_3()(p0,p1),
                             typename Surface_traits::
                             Compute_squared_radius_smallest_orthogonal_sphere_3()(p0,p1),
                             typename Surface_traits::
                             Construct_vector_3()(wp2p(p1),
                                                  wp2p(p0)),
                             r2s_converter(shrink),
                             1);
          break;
        }
        case 2: {
          f = Rt_Facet(s);
          Surface_weighted_point p0 =
            r2s_converter(f.first->vertex((f.second+1)&3)->point());
          Surface_weighted_point p1 =
            r2s_converter(f.first->vertex((f.second+2)&3)->point());
          Surface_weighted_point p2 =
            r2s_converter(f.first->vertex((f.second+3)&3)->point());

          create_hyperboloid(typename Surface_traits::
                             Construct_weighted_circumcenter_3()(p0,p1,p2),
                             typename Surface_traits::
                             Compute_squared_radius_smallest_orthogonal_sphere_3()(p0,p1,p2),
                             typename Surface_traits::
                             Construct_orthogonal_vector_3()(wp2p(p0),wp2p(p1),wp2p(p2)),
                             r2s_converter(1-shrink),
                             -1);
          break;
        }
        case 3: {
          ch = s;
          const Surface_weighted_point pts[4] =
            {
              r2s_converter(ch->vertex(0)->point()),
              r2s_converter(ch->vertex(1)->point()),
              r2s_converter(ch->vertex(2)->point()),
              r2s_converter(ch->vertex(3)->point())
            };

          create_sphere(typename Surface_traits::
                        Construct_weighted_circumcenter_3()
                        (pts[0],pts[1],pts[2],pts[3]),
                        typename Surface_traits::
                        Compute_squared_radius_smallest_orthogonal_sphere_3()
                        (pts[0],pts[1],pts[2],pts[3]),
                        r2s_converter(1-shrink),
                        -1);
        }
      }
    }
    ch->info() = typename SkinSurface_3::Cell_info(s,surf);
  }

  FT shrink;
  Rt_Simplex prev_s;
  std::shared_ptr<Quadratic_surface> surf;

  // c is the center of the orthogonal sphere
  // w is the weight of the orthogonal sphere
  // s is the shrink factor
  // orient is the orientation of the sphere
  void create_sphere(const Surface_point &c,
                     const Surface_RT &w,
                     const Surface_RT &s,
                     const int orient)
  {
    if (s == 1) {
      // Don't multiply by (1-s) as this will zero the equation
      Q[1] = Q[3] = Q[4] = 0;
      Q[0] = Q[2] = Q[5] = orient;

      surf = std::shared_ptr<Quadratic_surface>(new Quadratic_surface(Q, c, s*w, (orient==1? 0 : 3)));
    } else {
      // Multiply with 1-s to make the function defining the
      // skin surface implicitly continuous
      Q[1] = Q[3] = Q[4] = 0;
      Q[0] = Q[2] = Q[5] = orient*(1-s);

      surf = std::shared_ptr<Quadratic_surface>(new Quadratic_surface(Q, c, s*(1-s)*w, (orient==1? 0 : 3)));
    }
  }

  void create_hyperboloid(const Surface_point &c,
                          const Surface_RT &w,
                          const Surface_vector &t,
                          const Surface_RT &s,
                          const int orient)
  {
    Surface_RT den = t*t;

    Q[0] = orient*(-  t.x()*t.x()/den + (1-s));

    Q[1] = orient*(-2*t.y()*t.x()/den);
    Q[2] = orient*(-  t.y()*t.y()/den + (1-s));

    Q[3] = orient*(-2*t.z()*t.x()/den);
    Q[4] = orient*(-2*t.z()*t.y()/den);
    Q[5] = orient*(-  t.z()*t.z()/den + (1-s));

    surf = std::shared_ptr<Quadratic_surface>(new Quadratic_surface(Q, c, s*(1-s)*w, (orient==1? 1 : 2)));
  }

  Surface_RT Q[6];
  R2S_converter r2s_converter;
};

} //namespace CGAL

#endif // CGAL_TRIANGULATED_MIXED_COMPLEX_OBSERVER_3

