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/** \file LoopT.hh

 */

//=============================================================================
//
//  CLASS LoopT
//
//=============================================================================

#ifndef OPENMESH_SUBDIVIDER_UNIFORM_LOOPT_HH
#define OPENMESH_SUBDIVIDER_UNIFORM_LOOPT_HH


//== INCLUDES =================================================================

#include <OpenMesh/Core/System/config.hh>
#include <OpenMesh/Tools/Subdivider/Uniform/SubdividerT.hh>
#include <OpenMesh/Core/Utils/vector_cast.hh>
#include <OpenMesh/Core/Utils/Property.hh>
// -------------------- STL
#include <vector>
#if defined(OM_CC_MIPS)
#  include <math.h>
#else
#  include <cmath>
#endif


//== NAMESPACE ================================================================

namespace OpenMesh   { // BEGIN_NS_OPENMESH
namespace Subdivider { // BEGIN_NS_DECIMATER
namespace Uniform    { // BEGIN_NS_DECIMATER


//== CLASS DEFINITION =========================================================

/** %Uniform Loop subdivision algorithm.
 *
 *  Implementation as described in
 *
 *  C. T. Loop, "Smooth Subdivision Surfaces Based on Triangles",
 *  M.S. Thesis, Department of Mathematics, University of Utah, August 1987.
 *
 */
template <typename MeshType, typename RealType = double>
class LoopT : public SubdividerT<MeshType, RealType>
{
public:

  typedef RealType                                real_t;
  typedef MeshType                                mesh_t;
  typedef SubdividerT< mesh_t, real_t >           parent_t;

  typedef std::pair< real_t, real_t >             weight_t;
  typedef std::vector< std::pair<real_t,real_t> > weights_t;

public:


  LoopT(void) : parent_t(), _1over8( 1.0/8.0 ), _3over8( 3.0/8.0 )
  { init_weights(); }


  explicit LoopT( mesh_t& _m ) : parent_t(_m), _1over8( 1.0/8.0 ), _3over8( 3.0/8.0 )
  { init_weights(); }


  ~LoopT() {}


public:


  const char *name() const override { return "Uniform Loop"; }


  /// Pre-compute weights
  void init_weights(size_t _max_valence=50)
  {
    weights_.resize(_max_valence);
    std::generate(weights_.begin(), weights_.end(), compute_weight());
  }


protected:


  bool prepare( mesh_t& _m ) override
  {
    _m.add_property( vp_pos_ );
    _m.add_property( ep_pos_ );
    return true;
  }


  bool cleanup( mesh_t& _m ) override
  {
    _m.remove_property( vp_pos_ );
    _m.remove_property( ep_pos_ );
    return true;
  }


  bool subdivide( mesh_t& _m, size_t _n, const bool _update_points = true) override
  {

    ///TODO:Implement fixed positions

    typename mesh_t::FaceIter   fit, f_end;
    typename mesh_t::EdgeIter   eit, e_end;
    typename mesh_t::VertexIter vit;

    // Do _n subdivisions
    for (size_t i=0; i < _n; ++i)
    {

      if(_update_points) {
        // compute new positions for old vertices
        for (vit = _m.vertices_begin(); vit != _m.vertices_end(); ++vit) {
          smooth(_m, *vit);
        }
      }

      // Compute position for new vertices and store them in the edge property
      for (eit=_m.edges_begin(); eit != _m.edges_end(); ++eit)
        compute_midpoint( _m, *eit );

      // Split each edge at midpoint and store precomputed positions (stored in
      // edge property ep_pos_) in the vertex property vp_pos_;

      // Attention! Creating new edges, hence make sure the loop ends correctly.
      for (auto eh : _m.edges())
        split_edge(_m, eh );


      // Commit changes in topology and reconsitute consistency

      // Attention! Creating new faces, hence make sure the loop ends correctly.
      for (auto fh : _m.faces())
        split_face(_m, fh );

      if(_update_points) {
        // Commit changes in geometry
        for ( vit  = _m.vertices_begin();
            vit != _m.vertices_end(); ++vit) {
            _m.set_point(*vit, _m.property( vp_pos_, *vit ) );
        }
      }


#if defined(_DEBUG) || defined(DEBUG)
      // Now we have an consistent mesh!
      assert( OpenMesh::Utils::MeshCheckerT<mesh_t>(_m).check() );
#endif
    }

    return true;
  }

private:

  /// Helper functor to compute weights for Loop-subdivision
  /// \internal
  struct compute_weight
  {
    compute_weight() : valence(-1) { }
    weight_t operator() (void)
    {
#if !defined(OM_CC_MIPS)
      using std::cos;
#endif
      //              1
      // alpha(n) = ---- * (40 - ( 3 + 2 cos( 2 Pi / n ) )� )
      //             64

      if (++valence)
      {
        double   inv_v  = 1.0/double(valence);
        double   t      = (3.0 + 2.0 * cos( 2.0 * M_PI * inv_v) );
        double   alpha  = (40.0 - t * t)/64.0;

        return weight_t( static_cast<real_t>(1.0-alpha), static_cast<real_t>(inv_v*alpha) );
      }
      return weight_t(static_cast<real_t>(0.0), static_cast<real_t>(0.0));
    }
    int valence;
  };

private: // topological modifiers

  void split_face(mesh_t& _m, const typename mesh_t::FaceHandle& _fh)
  {
    typename mesh_t::HalfedgeHandle
      heh1(_m.halfedge_handle(_fh)),
      heh2(_m.next_halfedge_handle(_m.next_halfedge_handle(heh1))),
      heh3(_m.next_halfedge_handle(_m.next_halfedge_handle(heh2)));

    // Cutting off every corner of the 6_gon
    corner_cutting( _m, heh1 );
    corner_cutting( _m, heh2 );
    corner_cutting( _m, heh3 );
  }


  void corner_cutting(mesh_t& _m, const typename mesh_t::HalfedgeHandle& _he)
  {
    // Define Halfedge Handles
    typename mesh_t::HalfedgeHandle
      heh1(_he),
      heh5(heh1),
      heh6(_m.next_halfedge_handle(heh1));

    // Cycle around the polygon to find correct Halfedge
    for (; _m.next_halfedge_handle(_m.next_halfedge_handle(heh5)) != heh1;
         heh5 = _m.next_halfedge_handle(heh5))
    {}

    typename mesh_t::VertexHandle
      vh1 = _m.to_vertex_handle(heh1),
      vh2 = _m.to_vertex_handle(heh5);

    typename mesh_t::HalfedgeHandle
      heh2(_m.next_halfedge_handle(heh5)),
      heh3(_m.new_edge( vh1, vh2)),
      heh4(_m.opposite_halfedge_handle(heh3));

    /* Intermediate result
     *
     *            *
     *         5 /|\
     *          /_  \
     *    vh2> *     *
     *        /|\3   |\
     *       /_  \|4   \
     *      *----\*----\*
     *          1 ^   6
     *            vh1 (adjust_outgoing halfedge!)
     */

    // Old and new Face
    typename mesh_t::FaceHandle     fh_old(_m.face_handle(heh6));
    typename mesh_t::FaceHandle     fh_new(_m.new_face());


    // Re-Set Handles around old Face
    _m.set_next_halfedge_handle(heh4, heh6);
    _m.set_next_halfedge_handle(heh5, heh4);

    _m.set_face_handle(heh4, fh_old);
    _m.set_face_handle(heh5, fh_old);
    _m.set_face_handle(heh6, fh_old);
    _m.set_halfedge_handle(fh_old, heh4);

    // Re-Set Handles around new Face
    _m.set_next_halfedge_handle(heh1, heh3);
    _m.set_next_halfedge_handle(heh3, heh2);

    _m.set_face_handle(heh1, fh_new);
    _m.set_face_handle(heh2, fh_new);
    _m.set_face_handle(heh3, fh_new);

    _m.set_halfedge_handle(fh_new, heh1);
  }


  void split_edge(mesh_t& _m, const typename mesh_t::EdgeHandle& _eh)
  {
    typename mesh_t::HalfedgeHandle
      heh     = _m.halfedge_handle(_eh, 0),
      opp_heh = _m.halfedge_handle(_eh, 1);

    typename mesh_t::HalfedgeHandle new_heh, opp_new_heh, t_heh;
    typename mesh_t::VertexHandle   vh;
    typename mesh_t::VertexHandle   vh1(_m.to_vertex_handle(heh));
    typename mesh_t::Point          midP(_m.point(_m.to_vertex_handle(heh)));
    midP += _m.point(_m.to_vertex_handle(opp_heh));
    midP *= static_cast<RealType>(0.5);

    // new vertex
    vh                = _m.new_vertex( midP );

    // memorize position, will be set later
    _m.property( vp_pos_, vh ) = _m.property( ep_pos_, _eh );


    // Re-link mesh entities
    if (_m.is_boundary(_eh))
    {
      for (t_heh = heh;
           _m.next_halfedge_handle(t_heh) != opp_heh;
           t_heh = _m.opposite_halfedge_handle(_m.next_halfedge_handle(t_heh)))
      {}
    }
    else
    {
      for (t_heh = _m.next_halfedge_handle(opp_heh);
           _m.next_halfedge_handle(t_heh) != opp_heh;
           t_heh = _m.next_halfedge_handle(t_heh) )
      {}
    }

    new_heh     = _m.new_edge(vh, vh1);
    opp_new_heh = _m.opposite_halfedge_handle(new_heh);
    _m.set_vertex_handle( heh, vh );

    _m.set_next_halfedge_handle(t_heh, opp_new_heh);
    _m.set_next_halfedge_handle(new_heh, _m.next_halfedge_handle(heh));
    _m.set_next_halfedge_handle(heh, new_heh);
    _m.set_next_halfedge_handle(opp_new_heh, opp_heh);

    if (_m.face_handle(opp_heh).is_valid())
    {
      _m.set_face_handle(opp_new_heh, _m.face_handle(opp_heh));
      _m.set_halfedge_handle(_m.face_handle(opp_new_heh), opp_new_heh);
    }

    _m.set_face_handle( new_heh, _m.face_handle(heh) );
    _m.set_halfedge_handle( vh, new_heh);

    // We cant reconnect a non existing face, so we skip this here if necessary
    if ( !_m.is_boundary(heh) )
      _m.set_halfedge_handle( _m.face_handle(heh), heh );

    _m.set_halfedge_handle( vh1, opp_new_heh );

    // Never forget this, when playing with the topology
    _m.adjust_outgoing_halfedge( vh );
    _m.adjust_outgoing_halfedge( vh1 );
  }

private: // geometry helper

  void compute_midpoint(mesh_t& _m, const typename mesh_t::EdgeHandle& _eh)
  {
#define V( X ) vector_cast< typename mesh_t::Normal >( X )
    typename mesh_t::HalfedgeHandle heh, opp_heh;

    heh      = _m.halfedge_handle( _eh, 0);
    opp_heh  = _m.halfedge_handle( _eh, 1);

    typename mesh_t::Point
      pos(_m.point(_m.to_vertex_handle(heh)));

    pos += V( _m.point(_m.to_vertex_handle(opp_heh)) );

    // boundary edge: just average vertex positions
    if (_m.is_boundary(_eh) )
    {
      pos *= static_cast<RealType>(0.5);
    }
    else // inner edge: add neighbouring Vertices to sum
    {
      pos *= real_t(3.0);
      pos += V(_m.point(_m.to_vertex_handle(_m.next_halfedge_handle(heh))));
      pos += V(_m.point(_m.to_vertex_handle(_m.next_halfedge_handle(opp_heh))));
      pos *= _1over8;
    }
    _m.property( ep_pos_, _eh ) = pos;
#undef V
  }

  void smooth(mesh_t& _m, const typename mesh_t::VertexHandle& _vh)
  {
    typename mesh_t::Point            pos(0.0,0.0,0.0);

    if (_m.is_boundary(_vh) ) // if boundary: Point 1-6-1
    {
      typename mesh_t::HalfedgeHandle heh, prev_heh;
      heh      = _m.halfedge_handle( _vh );

      if ( heh.is_valid() )
      {
        assert( _m.is_boundary( _m.edge_handle( heh ) ) );

        prev_heh = _m.prev_halfedge_handle( heh );

        typename mesh_t::VertexHandle
          to_vh   = _m.to_vertex_handle( heh ),
          from_vh = _m.from_vertex_handle( prev_heh );

        // ( v_l + 6 v + v_r ) / 8
        pos  = _m.point( _vh );
        pos *= real_t(6.0);
        pos += vector_cast< typename mesh_t::Normal >( _m.point( to_vh ) );
        pos += vector_cast< typename mesh_t::Normal >( _m.point( from_vh ) );
        pos *= _1over8;

      }
      else
        return;
    }
    else // inner vertex: (1-a) * p + a/n * Sum q, q in one-ring of p
    {
      typedef typename mesh_t::Normal   Vec;
      typename mesh_t::VertexVertexIter vvit;
      size_t                            valence(0);

      // Calculate Valence and sum up neighbour points
      for (vvit=_m.vv_iter(_vh); vvit.is_valid(); ++vvit) {
        ++valence;
        pos += vector_cast< Vec >( _m.point(*vvit) );
      }
      pos *= weights_[valence].second; // alpha(n)/n * Sum q, q in one-ring of p
      pos += weights_[valence].first
          * vector_cast<Vec>(_m.point(_vh)); // + (1-a)*p
    }

    _m.property( vp_pos_, _vh ) = pos;
  }

private: // data

  OpenMesh::VPropHandleT< typename mesh_t::Point > vp_pos_;
  OpenMesh::EPropHandleT< typename mesh_t::Point > ep_pos_;

  weights_t     weights_;

  const real_t _1over8;
  const real_t _3over8;

};


//=============================================================================
} // END_NS_UNIFORM
} // END_NS_SUBDIVIDER
} // END_NS_OPENMESH
//=============================================================================
#endif // OPENMESH_SUBDIVIDER_UNIFORM_COMPOSITELOOPT_HH defined
//=============================================================================
