smesh/src/StdMeshers/StdMeshers_QuadFromMedialAxis_1D2D.cxx

// Copyright (C) 2007-2015  CEA/DEN, EDF R&D, OPEN CASCADE
//
// Copyright (C) 2003-2007  OPEN CASCADE, EADS/CCR, LIP6, CEA/DEN,
// CEDRAT, EDF R&D, LEG, PRINCIPIA R&D, BUREAU VERITAS
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
//
// See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
//
// File      : StdMeshers_QuadFromMedialAxis_1D2D.cxx
// Created   : Wed Jun  3 17:33:45 2015
// Author    : Edward AGAPOV (eap)

#include "StdMeshers_QuadFromMedialAxis_1D2D.hxx"

#include "SMESH_Block.hxx"
#include "SMESH_Gen.hxx"
#include "SMESH_MAT2d.hxx"
#include "SMESH_Mesh.hxx"
#include "SMESH_MeshEditor.hxx"
#include "SMESH_MesherHelper.hxx"
#include "SMESH_ProxyMesh.hxx"
#include "SMESH_subMesh.hxx"
#include "StdMeshers_FaceSide.hxx"
#include "StdMeshers_Regular_1D.hxx"
#include "StdMeshers_ViscousLayers2D.hxx"

#include <BRepBuilderAPI_MakeEdge.hxx>
#include <BRepTools.hxx>
#include <BRep_Tool.hxx>
#include <GeomAPI_Interpolate.hxx>
#include <Geom_Surface.hxx>
#include <Precision.hxx>
#include <TColgp_HArray1OfPnt.hxx>
#include <TopExp.hxx>
#include <TopLoc_Location.hxx>
#include <TopTools_MapOfShape.hxx>
#include <TopoDS.hxx>
#include <TopoDS_Edge.hxx>
#include <TopoDS_Face.hxx>
#include <TopoDS_Vertex.hxx>
#include <gp_Pnt.hxx>

#include <list>
#include <vector>

//================================================================================
/*!
 * \brief 1D algo
 */
class StdMeshers_QuadFromMedialAxis_1D2D::Algo1D : public StdMeshers_Regular_1D
{
public:
  Algo1D(int studyId, SMESH_Gen* gen):
    StdMeshers_Regular_1D( gen->GetANewId(), studyId, gen )
  {
  }
  void SetSegmentLength( double len )
  {
    _value[ BEG_LENGTH_IND ] = len;
    _value[ PRECISION_IND ] = 1e-7;
    _hypType = LOCAL_LENGTH;
  }
};
 
//================================================================================
/*!
 * \brief Constructor sets algo features
 */
//================================================================================

StdMeshers_QuadFromMedialAxis_1D2D::StdMeshers_QuadFromMedialAxis_1D2D(int        hypId,
                                                                       int        studyId,
                                                                       SMESH_Gen* gen)
  : StdMeshers_Quadrangle_2D(hypId, studyId, gen),
    _regular1D( 0 )
{
  _name = "QuadFromMedialAxis_1D2D";
  _shapeType = (1 << TopAbs_FACE);
  _onlyUnaryInput          = true;  // FACE by FACE so far
  _requireDiscreteBoundary = false; // make 1D by myself
  _supportSubmeshes        = true; // make 1D by myself
  _neededLowerHyps[ 1 ]    = true;  // suppress warning on hiding a global 1D algo
  _neededLowerHyps[ 2 ]    = true;  // suppress warning on hiding a global 2D algo
  _compatibleHypothesis.clear();
  //_compatibleHypothesis.push_back("ViscousLayers2D");
}

//================================================================================
/*!
 * \brief Destructor
 */
//================================================================================

StdMeshers_QuadFromMedialAxis_1D2D::~StdMeshers_QuadFromMedialAxis_1D2D()
{
  delete _regular1D;
  _regular1D = 0;
}

//================================================================================
/*!
 * \brief Check if needed hypotheses are present
 */
//================================================================================

bool StdMeshers_QuadFromMedialAxis_1D2D::CheckHypothesis(SMESH_Mesh&         aMesh,
                                                         const TopoDS_Shape& aShape,
                                                         Hypothesis_Status&  aStatus)
{
  return true; // does not require hypothesis
}

namespace
{
  typedef map< const SMDS_MeshNode*, list< const SMDS_MeshNode* > > TMergeMap;
  
  //================================================================================
  /*!
   * \brief Sinuous face
   */
  struct SinuousFace
  {
    FaceQuadStruct::Ptr   _quad;
    vector< TopoDS_Edge > _edges;
    vector< TopoDS_Edge > _sinuSide[2], _shortSide[2];
    vector< TopoDS_Edge > _sinuEdges;
    int                   _nbWires;
    list< int >           _nbEdgesInWire;
    TMergeMap             _nodesToMerge;

    SinuousFace( const TopoDS_Face& f ): _quad( new FaceQuadStruct )
    {
      list< TopoDS_Edge > edges;
      _nbWires = SMESH_Block::GetOrderedEdges (f, edges, _nbEdgesInWire);
      _edges.assign( edges.begin(), edges.end() );

      _quad->side.resize( 4 );
      _quad->face = f;
    }
    const TopoDS_Face& Face() const { return _quad->face; }
  };

  //================================================================================
  /*!
   * \brief Temporary mesh
   */
  struct TmpMesh : public SMESH_Mesh
  {
    TmpMesh()
    {
      _myMeshDS = new SMESHDS_Mesh(/*id=*/0, /*isEmbeddedMode=*/true);
    }
  };

  //================================================================================
  /*!
   * \brief Return a member of a std::pair
   */
  //================================================================================

  template< typename T >
  T& get( std::pair< T, T >& thePair, bool is2nd )
  {
    return is2nd ? thePair.second : thePair.first;
  }

  //================================================================================
  /*!
   * \brief Select two EDGEs from a map, either mapped to least values or to max values
   */
  //================================================================================

  // template< class TVal2EdgesMap >
  // void getTwo( bool                 least,
  //              TVal2EdgesMap&       map,
  //              vector<TopoDS_Edge>& twoEdges,
  //              vector<TopoDS_Edge>& otherEdges)
  // {
  //   twoEdges.clear();
  //   otherEdges.clear();
  //   if ( least )
  //   {
  //     TVal2EdgesMap::iterator i = map.begin();
  //     twoEdges.push_back( i->second );
  //     twoEdges.push_back( ++i->second );
  //     for ( ; i != map.end(); ++i )
  //       otherEdges.push_back( i->second );
  //   }
  //   else
  //   {
  //     TVal2EdgesMap::reverse_iterator i = map.rbegin();
  //     twoEdges.push_back( i->second );
  //     twoEdges.push_back( ++i->second );
  //     for ( ; i != map.rend(); ++i )
  //       otherEdges.push_back( i->second );
  //   }
  //   TopoDS_Vertex v;
  //   if ( TopExp::CommonVertex( twoEdges[0], twoEdges[1], v ))
  //   {
  //     twoEdges.clear(); // two EDGEs must not be connected
  //     otherEdges.clear();
  //   }
  // }

  //================================================================================
  /*!
   * \brief Finds out a minimal segment length given EDGEs will be divided into.
   *        This length is further used to discretize the Medial Axis
   */
  //================================================================================

  double getMinSegLen(SMESH_MesherHelper&        theHelper,
                      const vector<TopoDS_Edge>& theEdges)
  {
    TmpMesh tmpMesh;
    SMESH_Mesh* mesh = theHelper.GetMesh();

    vector< SMESH_Algo* > algos( theEdges.size() );
    for ( size_t i = 0; i < theEdges.size(); ++i )
    {
      SMESH_subMesh* sm = mesh->GetSubMesh( theEdges[i] );
      algos[i] = sm->GetAlgo();
    }

    const int nbSegDflt = mesh->GetGen()->GetDefaultNbSegments();
    double minSegLen    = Precision::Infinite();

    for ( size_t i = 0; i < theEdges.size(); ++i )
    {
      SMESH_subMesh* sm = mesh->GetSubMesh( theEdges[i] );
      if ( SMESH_Algo::IsStraight( theEdges[i], /*degenResult=*/true ))
        continue;
      // get algo
      size_t iOpp = ( theEdges.size() == 4 ? (i+2)%4 : i );
      SMESH_Algo*  algo = sm->GetAlgo();
      if ( !algo ) algo = algos[ iOpp ];
      // get hypo
      SMESH_Hypothesis::Hypothesis_Status status = SMESH_Hypothesis::HYP_MISSING;
      if ( algo )
      {
        if ( !algo->CheckHypothesis( *mesh, theEdges[i], status ))
          algo->CheckHypothesis( *mesh, theEdges[iOpp], status );
      }
      // compute
      if ( status != SMESH_Hypothesis::HYP_OK )
      {
        minSegLen = Min( minSegLen, SMESH_Algo::EdgeLength( theEdges[i] ) / nbSegDflt );
      }
      else
      {
        tmpMesh.Clear();
        tmpMesh.ShapeToMesh( TopoDS_Shape());
        tmpMesh.ShapeToMesh( theEdges[i] );
        try {
          mesh->GetGen()->Compute( tmpMesh, theEdges[i], true, true ); // make nodes on VERTEXes
          if ( !algo->Compute( tmpMesh, theEdges[i] ))
            continue;
        }
        catch (...) {
          continue;
        }
        SMDS_EdgeIteratorPtr segIt = tmpMesh.GetMeshDS()->edgesIterator();
        while ( segIt->more() )
        {
          const SMDS_MeshElement* seg = segIt->next();
          double len = SMESH_TNodeXYZ( seg->GetNode(0) ).Distance( seg->GetNode(1) );
          minSegLen = Min( minSegLen, len );
        }
      }
    }
    if ( Precision::IsInfinite( minSegLen ))
      minSegLen = mesh->GetShapeDiagonalSize() / nbSegDflt;

    return minSegLen;
  }

  //================================================================================
  /*!
   * \brief Returns EDGEs located between two VERTEXes at which given MA branches end
   *  \param [in] br1 - one MA branch
   *  \param [in] br2 - one more MA branch
   *  \param [in] allEdges - all EDGEs of a FACE
   *  \param [out] shortEdges - the found EDGEs
   *  \return bool - is OK or not
   */
  //================================================================================

  bool getConnectedEdges( const SMESH_MAT2d::Branch* br1,
                          const SMESH_MAT2d::Branch* br2,
                          const vector<TopoDS_Edge>& allEdges,
                          vector<TopoDS_Edge>&       shortEdges)
  {
    vector< size_t > edgeIDs[4];
    br1->getGeomEdges( edgeIDs[0], edgeIDs[1] );
    br2->getGeomEdges( edgeIDs[2], edgeIDs[3] );

    // EDGEs returned by a Branch form a connected chain with a VERTEX where
    // the Branch ends at the chain middle. One of end EDGEs of the chain is common
    // with either end EDGE of the chain of the other Branch, or the chains are connected
    // at a common VERTEX;

    // Get indices of end EDGEs of the branches
    bool vAtStart1 = ( br1->getEnd(0)->_type == SMESH_MAT2d::BE_ON_VERTEX );
    bool vAtStart2 = ( br2->getEnd(0)->_type == SMESH_MAT2d::BE_ON_VERTEX );
    size_t iEnd[4] = {
      vAtStart1 ? edgeIDs[0].back() : edgeIDs[0][0],
      vAtStart1 ? edgeIDs[1].back() : edgeIDs[1][0],
      vAtStart2 ? edgeIDs[2].back() : edgeIDs[2][0],
      vAtStart2 ? edgeIDs[3].back() : edgeIDs[3][0]
    };

    set< size_t > connectedIDs;
    TopoDS_Vertex vCommon;
    // look for the same EDGEs
    for ( int i = 0; i < 2; ++i )
      for ( int j = 2; j < 4; ++j )
        if ( iEnd[i] == iEnd[j] )
        {
          connectedIDs.insert( edgeIDs[i].begin(), edgeIDs[i].end() );
          connectedIDs.insert( edgeIDs[j].begin(), edgeIDs[j].end() );
          i = j = 4;
        }
    if ( connectedIDs.empty() )
      // look for connected EDGEs
      for ( int i = 0; i < 2; ++i )
        for ( int j = 2; j < 4; ++j )
          if ( TopExp::CommonVertex( allEdges[ iEnd[i]], allEdges[ iEnd[j]], vCommon ))
          {
            connectedIDs.insert( edgeIDs[i].begin(), edgeIDs[i].end() );
            connectedIDs.insert( edgeIDs[j].begin(), edgeIDs[j].end() );
            i = j = 4;
          }
    if ( connectedIDs.empty() ||                     // nothing
         allEdges.size() - connectedIDs.size() < 2 ) // too many
      return false;

    // set shortEdges in the order as in allEdges
    if ( connectedIDs.count( 0 ) &&
         connectedIDs.count( allEdges.size()-1 ))
    {
      size_t iE = allEdges.size()-1;
      while ( connectedIDs.count( iE-1 ))
        --iE;
      for ( size_t i = 0; i < connectedIDs.size(); ++i )
      {
        shortEdges.push_back( allEdges[ iE ]);
        iE = ( iE + 1 ) % allEdges.size();
      }
    }
    else
    {
      set< size_t >::iterator i = connectedIDs.begin();
      for ( ; i != connectedIDs.end(); ++i )
        shortEdges.push_back( allEdges[ *i ]);
    }
    return true;
  }

  //================================================================================
  /*!
   * \brief Find EDGEs to discretize using projection from MA
   *  \param [in,out] theSinuFace - the FACE to be meshed
   *  \return bool - OK or not
   *
   * It separates all EDGEs into four sides of a quadrangle connected in the order:
   * theSinuEdges[0], theShortEdges[0], theSinuEdges[1], theShortEdges[1]
   */
  //================================================================================

  bool getSinuousEdges( SMESH_MesherHelper& theHelper,
                        SinuousFace&        theSinuFace)
  {
    vector<TopoDS_Edge> * theSinuEdges  = & theSinuFace._sinuSide [0];
    vector<TopoDS_Edge> * theShortEdges = & theSinuFace._shortSide[0];
    theSinuEdges[0].clear();
    theSinuEdges[1].clear();
    theShortEdges[0].clear();
    theShortEdges[1].clear();
   
    vector<TopoDS_Edge> & allEdges = theSinuFace._edges;
    const size_t nbEdges = allEdges.size();
    if ( nbEdges < 4 && theSinuFace._nbWires == 1 )
      return false;

    if ( theSinuFace._nbWires == 2 ) // ring
    {
      size_t nbOutEdges = theSinuFace._nbEdgesInWire.front();
      theSinuEdges[0].assign ( allEdges.begin(), allEdges.begin() + nbOutEdges );
      theSinuEdges[1].assign ( allEdges.begin() + nbOutEdges, allEdges.end() );
      return true;
    }
    if ( theSinuFace._nbWires > 2 )
      return false;

    // create MedialAxis to find short edges by analyzing MA branches
    double minSegLen = getMinSegLen( theHelper, allEdges );
    SMESH_MAT2d::MedialAxis ma( theSinuFace.Face(), allEdges, minSegLen * 3 );

    // in an initial request case, theFace represents a part of a river with almost parallel banks
    // so there should be two branch points
    using SMESH_MAT2d::BranchEnd;
    using SMESH_MAT2d::Branch;
    const vector< const BranchEnd* >& braPoints = ma.getBranchPoints();
    if ( braPoints.size() < 2 )
      return false;
    TopTools_MapOfShape shortMap;
    size_t nbBranchPoints = 0;
    for ( size_t i = 0; i < braPoints.size(); ++i )
    {
      vector< const Branch* > vertBranches; // branches with an end on VERTEX
      for ( size_t ib = 0; ib < braPoints[i]->_branches.size(); ++ib )
      {
        const Branch* branch = braPoints[i]->_branches[ ib ];
        if ( branch->hasEndOfType( SMESH_MAT2d::BE_ON_VERTEX ))
          vertBranches.push_back( branch );
      }
      if ( vertBranches.size() != 2 || braPoints[i]->_branches.size() != 3)
        continue;

      // get common EDGEs of two branches
      if ( !getConnectedEdges( vertBranches[0], vertBranches[1],
                               allEdges, theShortEdges[ nbBranchPoints > 0 ] ))
        return false;

      for ( size_t iS = 0; iS < theShortEdges[ nbBranchPoints ].size(); ++iS )
        shortMap.Add( theShortEdges[ nbBranchPoints ][ iS ]);

      ++nbBranchPoints;
    }

    if ( nbBranchPoints != 2 )
      return false;

    // add to theSinuEdges all edges that are not theShortEdges
    vector< vector<TopoDS_Edge> > sinuEdges(1);
    TopoDS_Vertex vCommon;
    for ( size_t i = 0; i < allEdges.size(); ++i )
    {
      if ( !shortMap.Contains( allEdges[i] ))
      {
        if ( !sinuEdges.back().empty() )
          if ( !TopExp::CommonVertex( sinuEdges.back().back(), allEdges[ i ], vCommon ))
            sinuEdges.resize( sinuEdges.size() + 1 );

        sinuEdges.back().push_back( allEdges[i] );
      }
    }
    if ( sinuEdges.size() == 3 )
    {
      if ( !TopExp::CommonVertex( sinuEdges.back().back(), sinuEdges[0][0], vCommon ))
        return false;
      vector<TopoDS_Edge>& last = sinuEdges.back();
      last.insert( last.end(), sinuEdges[0].begin(), sinuEdges[0].end() );
      sinuEdges[0].swap( last );
      sinuEdges.resize( 2 );
    }
    if ( sinuEdges.size() != 2 )
      return false;

    theSinuEdges[0].swap( sinuEdges[0] );
    theSinuEdges[1].swap( sinuEdges[1] );

    if ( !TopExp::CommonVertex( theSinuEdges[0].back(), theShortEdges[0][0], vCommon ) ||
         !vCommon.IsSame( theHelper.IthVertex( 1, theSinuEdges[0].back() )))
      theShortEdges[0].swap( theShortEdges[1] );

    theSinuFace._sinuEdges = theSinuEdges[0];
    theSinuFace._sinuEdges.insert( theSinuFace._sinuEdges.end(),
                                   theSinuEdges[1].begin(), theSinuEdges[1].end() );

    return ( theShortEdges[0].size() > 0 && theShortEdges[1].size() > 0 &&
             theSinuEdges [0].size() > 0 && theSinuEdges [1].size() > 0 );

    // the sinuous EDGEs can be composite and C0 continuous,
    // therefor we use a complex criterion to find TWO short non-sinuous EDGEs
    // and the rest EDGEs will be treated as sinuous.
    // A short edge should have the following features:
    // a) straight
    // b) short
    // c) with convex corners at ends
    // d) far from the other short EDGE

    // vector< double > isStraightEdge( nbEdges, 0 ); // criterion value

    // // a0) evaluate continuity
    // const double contiWgt = 0.5; // weight of continuity in the criterion
    // multimap< int, TopoDS_Edge > continuity;
    // for ( size_t i = 0; i < nbEdges; ++I )
    // {
    //   BRepAdaptor_Curve curve( allEdges[i] );
    //   GeomAbs_Shape C = GeomAbs_CN;
    //   try:
    //     C = curve.Continuity(); // C0, G1, C1, G2, C2, C3, CN
    //   catch ( Standard_Failure ) {}
    //   continuity.insert( make_pair( C, allEdges[i] ));
    //   isStraight[i] += double( C ) / double( CN ) * contiWgt;
    // }

    // // try to choose by continuity
    // int mostStraight = (int) continuity.rbegin()->first;
    // int lessStraight = (int) continuity.begin()->first;
    // if ( mostStraight != lessStraight )
    // {
    //   int nbStraight = continuity.count( mostStraight );
    //   if ( nbStraight == 2 )
    //   {
    //     getTwo( /*least=*/false, continuity, theShortEdges, theSinuEdges );
    //   }
    //   else if ( nbStraight == 3 && nbEdges == 4 )
    //   {
    //     theSinuEdges.push_back( continuity.begin()->second );
    //     vector<TopoDS_Edge>::iterator it =
    //       std::find( allEdges.begin(), allEdges.end(), theSinuEdges[0] );
    //     int i = std::distance( allEdges.begin(), it );
    //     theSinuEdges .push_back( allEdges[( i+2 )%4 ]);
    //     theShortEdges.push_back( allEdges[( i+1 )%4 ]);
    //     theShortEdges.push_back( allEdges[( i+3 )%4 ]);
    //   }
    //   if ( theShortEdges.size() == 2 )
    //     return true;
    // }

    // // a) curvature; evaluate aspect ratio
    // {
    //   const double curvWgt = 0.5;
    //   for ( size_t i = 0; i < nbEdges; ++I )
    //   {
    //     BRepAdaptor_Curve curve( allEdges[i] );
    //     double curvature = 1;
    //     if ( !curve.IsClosed() )
    //     {
    //       const double f = curve.FirstParameter(), l = curve.LastParameter();
    //       gp_Pnt pf = curve.Value( f ), pl = curve.Value( l );
    //       gp_Lin line( pf, pl.XYZ() - pf.XYZ() );
    //       double distMax = 0;
    //       for ( double u = f; u < l; u += (l-f)/30. )
    //         distMax = Max( distMax, line.SquareDistance( curve.Value( u )));
    //       curvature = Sqrt( distMax ) / ( pf.Distance( pl ));
    //     }
    //     isStraight[i] += curvWgt / (              curvature + 1e-20 );
    //   }
    // }
    // // b) length
    // {
    //   const double lenWgt = 0.5;
    //   for ( size_t i = 0; i < nbEdges; ++I )
    //   {
    //     double length = SMESH_Algo::Length( allEdges[i] );
    //     if ( length > 0 )
    //       isStraight[i] += lenWgt / length;
    //   }
    // }
    // // c) with convex corners at ends
    // {
    //   const double cornerWgt = 0.25;
    //   for ( size_t i = 0; i < nbEdges; ++I )
    //   {
    //     double convex = 0;
    //     int iPrev = SMESH_MesherHelper::WrapIndex( int(i)-1, nbEdges );
    //     int iNext = SMESH_MesherHelper::WrapIndex( int(i)+1, nbEdges );
    //     TopoDS_Vertex v = helper.IthVertex( 0, allEdges[i] );
    //     double angle = SMESH_MesherHelper::GetAngle( allEdges[iPrev], allEdges[i], theFace, v );
    //     if ( angle < M_PI ) // [-PI; PI]
    //       convex += ( angle + M_PI ) / M_PI / M_PI;
    //     v = helper.IthVertex( 1, allEdges[i] );
    //     angle = SMESH_MesherHelper::GetAngle( allEdges[iNext], allEdges[i], theFace, v );
    //     if ( angle < M_PI ) // [-PI; PI]
    //       convex += ( angle + M_PI ) / M_PI / M_PI;
    //     isStraight[i] += cornerWgt * convex;
    //   }
    // }
  }

  //================================================================================
  /*!
   * \brief Creates an EDGE from a sole branch of MA
   */
  //================================================================================

  TopoDS_Edge makeEdgeFromMA( SMESH_MesherHelper&            theHelper,
                              const SMESH_MAT2d::MedialAxis& theMA )
  {
    if ( theMA.getBranches().size() != 1 )
      return TopoDS_Edge();

    vector< gp_XY > uv;
    theMA.getPoints( theMA.getBranches()[0], uv );
    if ( uv.size() < 2 )
      return TopoDS_Edge();

    TopoDS_Face face = TopoDS::Face( theHelper.GetSubShape() );
    Handle(Geom_Surface) surface = BRep_Tool::Surface( face );

    // cout << "from salome.geom import geomBuilder" << endl;
    // cout << "geompy = geomBuilder.New(salome.myStudy)" << endl;
    Handle(TColgp_HArray1OfPnt) points = new TColgp_HArray1OfPnt(1, uv.size());
    for ( size_t i = 0; i < uv.size(); ++i )
    {
      gp_Pnt p = surface->Value( uv[i].X(), uv[i].Y() );
      points->SetValue( i+1, p );
      //cout << "geompy.MakeVertex( "<< p.X()<<", " << p.Y()<<", " << p.Z()<<" )" << endl;
    }

    GeomAPI_Interpolate interpol( points, /*isClosed=*/false, gp::Resolution());
    interpol.Perform();
    if ( !interpol.IsDone())
      return TopoDS_Edge();

    TopoDS_Edge branchEdge = BRepBuilderAPI_MakeEdge(interpol.Curve());
    return branchEdge;
  }

  //================================================================================
  /*!
   * \brief Returns a type of shape, to which a hypothesis used to mesh a given edge is assigned
   */
  //================================================================================

  TopAbs_ShapeEnum getHypShape( SMESH_Mesh* mesh, const TopoDS_Shape& edge )
  {
    TopAbs_ShapeEnum shapeType = TopAbs_SHAPE;

    SMESH_subMesh* sm = mesh->GetSubMesh( edge );
    SMESH_Algo*  algo = sm->GetAlgo();
    if ( !algo ) return shapeType;

    const list <const SMESHDS_Hypothesis *> & hyps =
      algo->GetUsedHypothesis( *mesh, edge, /*ignoreAuxiliary=*/true );
    if ( hyps.empty() ) return shapeType;

    TopoDS_Shape shapeOfHyp =
      SMESH_MesherHelper::GetShapeOfHypothesis( hyps.front(), edge, mesh);

    return SMESH_MesherHelper::GetGroupType( shapeOfHyp, /*woCompound=*/true);
  }

  //================================================================================
  /*!
   * \brief Discretize a sole branch of MA an returns parameters of divisions on MA
   */
  //================================================================================

  bool divideMA( SMESH_MesherHelper&            theHelper,
                 const SMESH_MAT2d::MedialAxis& theMA,
                 const SinuousFace&             theSinuFace,
                 SMESH_Algo*                    the1dAlgo,
                 vector<double>&                theMAParams )
  {
    // check if all EDGEs of one size are meshed, then MA discretization is not needed
    SMESH_Mesh* mesh = theHelper.GetMesh();
    size_t nbComputedEdges[2] = { 0, 0 };
    for ( size_t iS = 0; iS < 2; ++iS )
      for ( size_t i = 0; i < theSinuFace._sinuSide[iS].size(); ++i )
      {
        bool isComputed = ( ! mesh->GetSubMesh( theSinuFace._sinuSide[iS][i] )->IsEmpty() );
        nbComputedEdges[ iS ] += isComputed;
      }
    if ( nbComputedEdges[0] == theSinuFace._sinuSide[0].size() ||
         nbComputedEdges[1] == theSinuFace._sinuSide[1].size() )
      return true; // discretization is not needed


    TopoDS_Edge branchEdge = makeEdgeFromMA( theHelper, theMA );
    if ( branchEdge.IsNull() )
      return false;

    // const char* file = "/misc/dn25/salome/eap/salome/misc/tmp/MAedge.brep";
    // BRepTools::Write( branchEdge, file);
    // cout << "Write " << file << endl;

    // look for a most local hyps assigned to theSinuEdges
    TopoDS_Edge edge = theSinuFace._sinuEdges[0];
    int mostSimpleShape = (int) getHypShape( mesh, edge );
    for ( size_t i = 1; i < theSinuFace._sinuEdges.size(); ++i )
    {
      int shapeType = (int) getHypShape( mesh, theSinuFace._sinuEdges[i] );
      if ( shapeType > mostSimpleShape )
        edge = theSinuFace._sinuEdges[i];
    }

    SMESH_Algo* algo = the1dAlgo;
    if ( mostSimpleShape != TopAbs_SHAPE )
    {
      algo = mesh->GetSubMesh( edge )->GetAlgo();
      SMESH_Hypothesis::Hypothesis_Status status;
      if ( !algo->CheckHypothesis( *mesh, edge, status ))
        algo = the1dAlgo;
    }

    TmpMesh tmpMesh;
    tmpMesh.ShapeToMesh( branchEdge );
    try {
      mesh->GetGen()->Compute( tmpMesh, branchEdge, true, true ); // make nodes on VERTEXes
      if ( !algo->Compute( tmpMesh, branchEdge ))
        return false;
    }
    catch (...) {
      return false;
    }
    return SMESH_Algo::GetNodeParamOnEdge( tmpMesh.GetMeshDS(), branchEdge, theMAParams );
  }

  //================================================================================
  /*!
   * \brief Select division parameters on MA and make them coincide at ends with
   *        projections of VERTEXes to MA for a given pair of opposite EDGEs
   *  \param [in] theEdgePairInd - index of the EDGE pair
   *  \param [in] theDivPoints - the BranchPoint's dividing MA into parts each
   *         corresponding to a unique pair of opposite EDGEs
   *  \param [in] theMAParams - the MA division parameters
   *  \param [out] theSelectedMAParams - the selected MA parameters
   *  \return bool - is OK
   */
  //================================================================================

  bool getParamsForEdgePair( const size_t                              theEdgePairInd,
                             const vector< SMESH_MAT2d::BranchPoint >& theDivPoints,
                             const vector<double>&                     theMAParams,
                             vector<double>&                           theSelectedMAParams)
  {
    if ( theDivPoints.empty() )
    {
      theSelectedMAParams = theMAParams;
      return true;
    }
    if ( theEdgePairInd > theDivPoints.size() || theMAParams.empty() )
      return false;

    // find a range of params to copy

    double par1 = 0;
    size_t iPar1 = 0;
    if ( theEdgePairInd > 0 )
    {
      const SMESH_MAT2d::BranchPoint& bp = theDivPoints[ theEdgePairInd-1 ];
      bp._branch->getParameter( bp, par1 );
      while ( theMAParams[ iPar1 ] < par1 ) ++iPar1;
      if ( par1 - theMAParams[ iPar1-1 ] < theMAParams[ iPar1 ] - par1 )
        --iPar1;
    }

    double par2 = 1;
    size_t iPar2 = theMAParams.size() - 1;
    if ( theEdgePairInd < theDivPoints.size() )
    {
      const SMESH_MAT2d::BranchPoint& bp = theDivPoints[ theEdgePairInd ];
      bp._branch->getParameter( bp, par2 );
      iPar2 = iPar1;
      while ( theMAParams[ iPar2 ] < par2 ) ++iPar2;
      if ( par2 - theMAParams[ iPar2-1 ] < theMAParams[ iPar2 ] - par2 )
        --iPar2;
    }

    theSelectedMAParams.assign( theMAParams.begin() + iPar1,
                                theMAParams.begin() + iPar2 + 1 );

    // adjust theSelectedMAParams to fit between par1 and par2

    double d = par1 - theSelectedMAParams[0];
    double f = ( par2 - par1 ) / ( theSelectedMAParams.back() - theSelectedMAParams[0] );

    for ( size_t i = 0; i < theSelectedMAParams.size(); ++i )
    {
      theSelectedMAParams[i] += d;
      theSelectedMAParams[i] = par1 + ( theSelectedMAParams[i] - par1 ) * f;
    }

    return true;
  }

  //--------------------------------------------------------------------------------
  // node or node parameter on EDGE
  struct NodePoint
  {
    const SMDS_MeshNode* _node;
    double               _u;
    int                  _edgeInd; // index in theSinuEdges vector

    NodePoint(): _node(0), _u(0), _edgeInd(-1) {}
    NodePoint(const SMDS_MeshNode* n, double u, size_t iEdge ): _node(n), _u(u), _edgeInd(iEdge) {}
    NodePoint(double u, size_t iEdge) : _node(0), _u(u), _edgeInd(iEdge) {}
    NodePoint(const SMESH_MAT2d::BoundaryPoint& p) : _node(0), _u(p._param), _edgeInd(p._edgeIndex) {}
    gp_Pnt Point(const vector< Handle(Geom_Curve) >& curves) const
    {
      return curves[ _edgeInd ]->Value( _u );
    }
  };

  //================================================================================
  /*!
   * \brief Finds a VERTEX corresponding to a point on EDGE, which is also filled
   *        with a node on the VERTEX, present or created
   *  \param [in,out] theNodePnt - the node position on the EDGE
   *  \param [in] theSinuEdges - the sinuous EDGEs
   *  \param [in] theMeshDS - the mesh
   *  \return bool - true if the \a theBndPnt is on VERTEX
   */
  //================================================================================

  bool findVertex( NodePoint&                  theNodePnt,
                   const vector<TopoDS_Edge>&  theSinuEdges,
                   SMESHDS_Mesh*               theMeshDS)
  {
    if ( theNodePnt._edgeInd >= theSinuEdges.size() )
      return false;

    double f,l;
    BRep_Tool::Range( theSinuEdges[ theNodePnt._edgeInd ], f,l );
    const double tol = 1e-3 * ( l - f );

    TopoDS_Vertex V;
    if      ( Abs( f - theNodePnt._u ) < tol )
      V = SMESH_MesherHelper::IthVertex( 0, theSinuEdges[ theNodePnt._edgeInd ], /*CumOri=*/false);
    else if ( Abs( l - theNodePnt._u ) < tol )
      V = SMESH_MesherHelper::IthVertex( 1, theSinuEdges[ theNodePnt._edgeInd ], /*CumOri=*/false);

    if ( !V.IsNull() )
    {
      theNodePnt._node = SMESH_Algo::VertexNode( V, theMeshDS );
      if ( !theNodePnt._node )
      {
        gp_Pnt p = BRep_Tool::Pnt( V );
        theNodePnt._node = theMeshDS->AddNode( p.X(), p.Y(), p.Z() );
        theMeshDS->SetNodeOnVertex( theNodePnt._node, V );
      }
      return true;
    }
    return false;
  }

  //================================================================================
  /*!
   * \brief Add to the map of NodePoint's those on VERTEXes
   *  \param [in,out] theHelper - the helper
   *  \param [in] theMA - Medial Axis
   *  \param [in] theMinSegLen - minimal segment length
   *  \param [in] theDivPoints - projections of VERTEXes to MA
   *  \param [in] theSinuEdges - the sinuous EDGEs
   *  \param [in] theSideEdgeIDs - indices of sinuous EDGEs per side
   *  \param [in] theIsEdgeComputed - is sinuous EGDE is meshed
   *  \param [in,out] thePointsOnE - the map to fill
   *  \param [out] theNodes2Merge - the map of nodes to merge
   */
  //================================================================================

  bool projectVertices( SMESH_MesherHelper&                           theHelper,
                        //const double                                  theMinSegLen,
                        const SMESH_MAT2d::MedialAxis&                theMA,
                        const vector< SMESH_MAT2d::BranchPoint >&     theDivPoints,
                        const vector<TopoDS_Edge>&                    theSinuEdges,
                        const vector< Handle(Geom_Curve) >&           theCurves,
                        const vector< bool >&                         theIsEdgeComputed,
                        map< double, pair< NodePoint, NodePoint > > & thePointsOnE,
                        TMergeMap&                                    theNodes2Merge)
  {
    if ( theDivPoints.empty() )
      return true;

    SMESHDS_Mesh* meshDS = theHelper.GetMeshDS();

    double uMA;
    SMESH_MAT2d::BoundaryPoint bp[2];
    const SMESH_MAT2d::Branch& branch = theMA.getBranches()[0];

    for ( size_t i = 0; i < theDivPoints.size(); ++i )
    {
      if ( !branch.getParameter( theDivPoints[i], uMA ))
        return false;
      if ( !branch.getBoundaryPoints( theDivPoints[i], bp[0], bp[1] ))
        return false;

      NodePoint  np[2] = { NodePoint( bp[0] ),
                           NodePoint( bp[1] )};
      bool isVertex[2] = { findVertex( np[0], theSinuEdges, meshDS ),
                           findVertex( np[1], theSinuEdges, meshDS )};

      map< double, pair< NodePoint, NodePoint > >::iterator u2NP =
        thePointsOnE.insert( make_pair( uMA, make_pair( np[0], np[1]))).first;

      if ( !isVertex[0] && !isVertex[1] ) return false; // error
      if ( isVertex[0] && isVertex[1] )
        continue;
      const size_t iVertex = isVertex[0] ? 0 : 1;
      const size_t iNode   = 1 - iVertex;

      bool isOppComputed = theIsEdgeComputed[ np[ iNode ]._edgeInd ];
      if ( !isOppComputed )
        continue;

      // a VERTEX is projected on a meshed EDGE; there are two options:
      // 1) a projected point is joined with a closet node if a strip between this and neighbor
      // projection is WIDE enough; joining is done by creating a node coincident with the
      //  existing node which will be merged together after all;
      // 2) a neighbor projection is merged with this one if it is TOO CLOSE; a node of deleted
      // projection is set to the BoundaryPoint of this projection

      // evaluate distance to neighbor projections
      const double rShort = 0.2;
      bool isShortPrev[2], isShortNext[2];
      map< double, pair< NodePoint, NodePoint > >::iterator u2NPPrev = u2NP, u2NPNext = u2NP;
      --u2NPPrev; ++u2NPNext;
      for ( int iS = 0; iS < 2; ++iS ) // side with Vertex and side with Nodes
      {
        NodePoint np     = get( u2NP->second,     iS );
        NodePoint npPrev = get( u2NPPrev->second, iS );
        NodePoint npNext = get( u2NPNext->second, iS );
        gp_Pnt     p     = np    .Point( theCurves );
        gp_Pnt     pPrev = npPrev.Point( theCurves );
        gp_Pnt     pNext = npNext.Point( theCurves );
        double  distPrev = p.Distance( pPrev );
        double  distNext = p.Distance( pNext );
        double         r = distPrev / ( distPrev + distNext );
        isShortPrev[iS] = ( r < rShort );
        isShortNext[iS] = (( 1 - r ) > ( 1 - rShort ));
      }

      map< double, pair< NodePoint, NodePoint > >::iterator u2NPClose;

      if (( isShortPrev[0] && isShortPrev[1] ) || // option 2) -> remove a too close projection
          ( isShortNext[0] && isShortNext[1] ))
      {
        u2NPClose = isShortPrev[0] ? u2NPPrev : u2NPNext;
        NodePoint& npProj  = get( u2NP->second, iNode );       // NP of VERTEX projection
        NodePoint npCloseN = get( u2NPClose->second, iNode);   // NP close to npProj
        NodePoint npCloseV = get( u2NPClose->second, iVertex); // NP close to VERTEX
        if ( !npCloseV._node )
        {
          npProj = npCloseN;
          thePointsOnE.erase( isShortPrev[0] ? u2NPPrev : u2NPNext );
          continue;
        }
        else
        {
          // can't remove the neighbor projection as it is also from VERTEX, -> option 1)
        }
      }
      // else option 1) - wide enough -> "duplicate" existing node
      {
        u2NPClose = isShortPrev[ iNode ] ? u2NPPrev : u2NPNext;
        NodePoint& npProj   = get( u2NP->second, iNode );       // NP of VERTEX projection
        NodePoint& npCloseN = get( u2NPClose->second, iNode );  // NP close to npProj
        // npProj._edgeInd = npCloseN._edgeInd;
        // npProj._u       = npCloseN._u + 1e-3 * Abs( get( u2NPPrev->second, iNode )._u -
        //                                             get( u2NPNext->second, iNode )._u );
        gp_Pnt        p = npProj.Point( theCurves );
        npProj._node    = meshDS->AddNode( p.X(), p.Y(), p.Z() );
        meshDS->SetNodeOnEdge( npProj._node, theSinuEdges[ npProj._edgeInd ], npProj._u  );

        theNodes2Merge[ npCloseN._node ].push_back( npProj._node );
      }
    }
    return true;
  }

  //================================================================================
  /*!
   * \brief Divide the sinuous EDGEs by projecting the division point of Medial
   *        Axis to the EGDEs
   *  \param [in] theHelper - the helper
   *  \param [in] theMinSegLen - minimal segment length
   *  \param [in] theMA - the Medial Axis
   *  \param [in] theMAParams - parameters of division points of \a theMA
   *  \param [in] theSinuEdges - the EDGEs to make nodes on
   *  \param [in] theSinuSide0Size - the number of EDGEs in the 1st sinuous side
   *  \return bool - is OK or not
   */
  //================================================================================

  bool computeSinuEdges( SMESH_MesherHelper&        theHelper,
                         double                     /*theMinSegLen*/,
                         SMESH_MAT2d::MedialAxis&   theMA,
                         vector<double>&            theMAParams,
                         SinuousFace&               theSinuFace)
  {
    if ( theMA.getBranches().size() != 1 )
      return false;

    // normalize theMAParams
    for ( size_t i = 0; i < theMAParams.size(); ++i )
      theMAParams[i] /= theMAParams.back();


    SMESH_Mesh*     mesh = theHelper.GetMesh();
    SMESHDS_Mesh* meshDS = theHelper.GetMeshDS();
    double f,l;

    const vector< TopoDS_Edge >& theSinuEdges = theSinuFace._sinuEdges;
    vector< Handle(Geom_Curve) > curves ( theSinuEdges.size() );
    vector< int >                edgeIDs( theSinuEdges.size() );
    vector< bool >            isComputed( theSinuEdges.size() );
    //bool hasComputed = false;
    for ( size_t i = 0; i < theSinuEdges.size(); ++i )
    {
      curves[i] = BRep_Tool::Curve( theSinuEdges[i], f,l );
      if ( !curves[i] )
        return false;
      SMESH_subMesh* sm = mesh->GetSubMesh( theSinuEdges[i] );
      edgeIDs   [i] = sm->GetId();
      isComputed[i] = ( !sm->IsEmpty() );
      if ( isComputed[i] )
      {
        TopAbs_ShapeEnum shape = getHypShape( mesh, theSinuEdges[i] );
        if ( shape == TopAbs_SHAPE || shape <= TopAbs_FACE )
        {
          // EDGE computed using global hypothesis -> clear it
          bool hasComputedFace = false;
          PShapeIteratorPtr faceIt = theHelper.GetAncestors( theSinuEdges[i], *mesh, TopAbs_FACE );
          while ( const TopoDS_Shape* face = faceIt->next() )
            if (( !face->IsSame( theSinuFace.Face())) &&
                ( hasComputedFace = !mesh->GetSubMesh( *face )->IsEmpty() ))
              break;
          if ( !hasComputedFace )
            sm->ComputeStateEngine( SMESH_subMesh::CLEAN );
          isComputed[i] = false;
        }
      }
    }

    const SMESH_MAT2d::Branch& branch = theMA.getBranches()[0];
    SMESH_MAT2d::BoundaryPoint bp[2];

    vector< std::size_t > edgeIDs1, edgeIDs2;
    vector< SMESH_MAT2d::BranchPoint > divPoints;
    branch.getOppositeGeomEdges( edgeIDs1, edgeIDs2, divPoints );
    for ( size_t i = 0; i < edgeIDs1.size(); ++i )
      if ( isComputed[ edgeIDs1[i]] &&
           isComputed[ edgeIDs2[i]])
        return false;

    // map param on MA to parameters of nodes on a pair of theSinuEdges
    typedef map< double, pair< NodePoint, NodePoint > > TMAPar2NPoints;
    TMAPar2NPoints pointsOnE;
    vector<double> maParams;

    // compute params of nodes on EDGEs by projecting division points from MA
    //const double tol = 1e-5 * theMAParams.back();
    size_t iEdgePair = 0;
    while ( iEdgePair < edgeIDs1.size() )
    {
      if ( isComputed[ edgeIDs1[ iEdgePair ]] ||
           isComputed[ edgeIDs2[ iEdgePair ]])
      {
        // "projection" from one side to the other

        size_t iEdgeComputed = edgeIDs1[iEdgePair], iSideComputed = 0;
        if ( !isComputed[ iEdgeComputed ])
          ++iSideComputed, iEdgeComputed = edgeIDs2[iEdgePair];

        map< double, const SMDS_MeshNode* > nodeParams; // params of existing nodes
        if ( !SMESH_Algo::GetSortedNodesOnEdge( meshDS, theSinuEdges[ iEdgeComputed ], /*skipMedium=*/true, nodeParams ))
          return false;

        SMESH_MAT2d::BoundaryPoint& bndPnt = bp[ 1-iSideComputed ];
        SMESH_MAT2d::BranchPoint brp;
        NodePoint npN, npB;
        NodePoint& np0 = iSideComputed ? npB : npN;
        NodePoint& np1 = iSideComputed ? npN : npB;

        double maParam1st, maParamLast, maParam;
        if ( !theMA.getBoundary().getBranchPoint( iEdgeComputed, nodeParams.begin()->first, brp ))
            return false;
        branch.getParameter( brp, maParam1st );
        if ( !theMA.getBoundary().getBranchPoint( iEdgeComputed, nodeParams.rbegin()->first, brp ))
            return false;
        branch.getParameter( brp, maParamLast );

        map< double, const SMDS_MeshNode* >::iterator u2n = nodeParams.begin(), u2nEnd = --nodeParams.end();
        TMAPar2NPoints::iterator end = pointsOnE.end(), pos = end;
        TMAPar2NPoints::iterator & hint = (maParamLast > maParam1st) ? end : pos;
        for ( ++u2n; u2n != u2nEnd; ++u2n )
        {
          if ( !theMA.getBoundary().getBranchPoint( iEdgeComputed, u2n->first, brp ))
            return false;
          if ( !branch.getBoundaryPoints( brp, bp[0], bp[1] ))
            return false;
          if ( !branch.getParameter( brp, maParam ))
            return false;

          npN = NodePoint( u2n->second, u2n->first, iEdgeComputed );
          npB = NodePoint( bndPnt );
          pos = pointsOnE.insert( hint, make_pair( maParam, make_pair( np0, np1 )));
        }

        // move iEdgePair forward
        while ( iEdgePair < edgeIDs1.size() )
          if ( edgeIDs1[ iEdgePair ] == bp[0]._edgeIndex &&
               edgeIDs2[ iEdgePair ] == bp[1]._edgeIndex )
            break;
          else
            ++iEdgePair;
      }
      else
      {
        // projection from MA
        maParams.clear();
        if ( !getParamsForEdgePair( iEdgePair, divPoints, theMAParams, maParams ))
          return false;

        for ( size_t i = 1; i < maParams.size()-1; ++i )
        {
          if ( !branch.getBoundaryPoints( maParams[i], bp[0], bp[1] ))
            return false;

          pointsOnE.insert( pointsOnE.end(), make_pair( maParams[i], make_pair( NodePoint(bp[0]),
                                                                                NodePoint(bp[1]))));
        }
      }
      ++iEdgePair;
    }

    if ( !projectVertices( theHelper, theMA, divPoints, theSinuEdges, curves,
                           isComputed, pointsOnE, theSinuFace._nodesToMerge ))
      return false;

    // create nodes
    TMAPar2NPoints::iterator u2np = pointsOnE.begin();
    for ( ; u2np != pointsOnE.end(); ++u2np )
    {
      NodePoint* np[2] = { & u2np->second.first, & u2np->second.second };
      for ( int iSide = 0; iSide < 2; ++iSide )
      {
        if ( np[ iSide ]->_node ) continue;
        size_t       iEdge = np[ iSide ]->_edgeInd;
        double           u = np[ iSide ]->_u;
        gp_Pnt           p = curves[ iEdge ]->Value( u );
        np[ iSide ]->_node = meshDS->AddNode( p.X(), p.Y(), p.Z() );
        meshDS->SetNodeOnEdge( np[ iSide ]->_node, edgeIDs[ iEdge ], u );
      }
    }

    // create mesh segments on EDGEs
    theHelper.SetElementsOnShape( false );
    TopoDS_Face face = TopoDS::Face( theHelper.GetSubShape() );
    for ( size_t i = 0; i < theSinuEdges.size(); ++i )
    {
      SMESH_subMesh* sm = mesh->GetSubMesh( theSinuEdges[i] );
      if ( sm->GetSubMeshDS() && sm->GetSubMeshDS()->NbElements() > 0 )
        continue;

      StdMeshers_FaceSide side( face, theSinuEdges[i], mesh,
                                /*isFwd=*/true, /*skipMediumNodes=*/true );
      vector<const SMDS_MeshNode*> nodes = side.GetOrderedNodes();
      for ( size_t in = 1; in < nodes.size(); ++in )
      {
        const SMDS_MeshElement* seg = theHelper.AddEdge( nodes[in-1], nodes[in], 0, false );
        meshDS->SetMeshElementOnShape( seg, edgeIDs[ i ] );
      }
    }

    // update sub-meshes on VERTEXes
    for ( size_t i = 0; i < theSinuEdges.size(); ++i )
    {
      mesh->GetSubMesh( theHelper.IthVertex( 0, theSinuEdges[i] ))
        ->ComputeStateEngine( SMESH_subMesh::CHECK_COMPUTE_STATE );
      mesh->GetSubMesh( theHelper.IthVertex( 1, theSinuEdges[i] ))
        ->ComputeStateEngine( SMESH_subMesh::CHECK_COMPUTE_STATE );
    }

    return true;
  }

  //================================================================================
  /*!
   * \brief Mesh short EDGEs
   */
  //================================================================================

  bool computeShortEdges( SMESH_MesherHelper&        theHelper,
                          const vector<TopoDS_Edge>& theShortEdges,
                          SMESH_Algo*                the1dAlgo )
  {
    for ( size_t i = 0; i < theShortEdges.size(); ++i )
    {
      theHelper.GetGen()->Compute( *theHelper.GetMesh(), theShortEdges[i], true, true );

      SMESH_subMesh* sm = theHelper.GetMesh()->GetSubMesh(theShortEdges[i] );
      if ( sm->IsEmpty() )
      {
        try {
          if ( !the1dAlgo->Compute( *theHelper.GetMesh(), theShortEdges[i] ))
            return false;
        }
        catch (...) {
          return false;
        }
        sm->ComputeStateEngine( SMESH_subMesh::CHECK_COMPUTE_STATE );
        if ( sm->IsEmpty() )
          return false;
      }
    }
    return true;
  }

  inline double area( const UVPtStruct& p1, const UVPtStruct& p2, const UVPtStruct& p3 )
  {
    gp_XY v1 = p2.UV() - p1.UV();
    gp_XY v2 = p3.UV() - p1.UV();
    return v2 ^ v1;
  }

  bool ellipticSmooth( FaceQuadStruct::Ptr quad, int nbLoops )
  {
    //nbLoops = 10;
    if ( quad->uv_grid.empty() )
      return true;

    int nbhoriz  = quad->iSize;
    int nbvertic = quad->jSize;

    const double dksi = 0.5, deta = 0.5;
    const double  dksi2 = dksi*dksi, deta2 = deta*deta;
    double err = 0., g11, g22, g12;
    int nbErr = 0;

    FaceQuadStruct& q = *quad;
    UVPtStruct pNew;

    double refArea = area( q.UVPt(0,0), q.UVPt(1,0), q.UVPt(1,1) );

    for ( int iLoop = 0; iLoop < nbLoops; ++iLoop )
    {
      err = 0;
      for ( int i = 1; i < nbhoriz - 1; i++ )
        for ( int j = 1; j < nbvertic - 1; j++ )
        {
          g11 = ( (q.U(i,j+1) - q.U(i,j-1))*(q.U(i,j+1) - q.U(i,j-1))/dksi2 +
                  (q.V(i,j+1) - q.V(i,j-1))*(q.V(i,j+1) - q.V(i,j-1))/deta2 )/4;

          g22 = ( (q.U(i+1,j) - q.U(i-1,j))*(q.U(i+1,j) - q.U(i-1,j))/dksi2 +
                  (q.V(i+1,j) - q.V(i-1,j))*(q.V(i+1,j) - q.V(i-1,j))/deta2 )/4;

          g12 = ( (q.U(i+1,j) - q.U(i-1,j))*(q.U(i,j+1) - q.U(i,j-1))/dksi2 +
                  (q.V(i+1,j) - q.V(i-1,j))*(q.V(i,j+1) - q.V(i,j-1))/deta2 )/(4*dksi*deta);

          pNew.u = dksi2/(2*(g11+g22)) * (g11*(q.U(i+1,j) + q.U(i-1,j))/dksi2 +
                                          g22*(q.U(i,j+1) + q.U(i,j-1))/dksi2
                                          - 0.5*g12*q.U(i+1,j+1) + 0.5*g12*q.U(i-1,j+1) +
                                          - 0.5*g12*q.U(i-1,j-1) + 0.5*g12*q.U(i+1,j-1));

          pNew.v = deta2/(2*(g11+g22)) * (g11*(q.V(i+1,j) + q.V(i-1,j))/deta2 +
                                          g22*(q.V(i,j+1) + q.V(i,j-1))/deta2
                                          - 0.5*g12*q.V(i+1,j+1) + 0.5*g12*q.V(i-1,j+1) +
                                          - 0.5*g12*q.V(i-1,j-1) + 0.5*g12*q.V(i+1,j-1));

          // if (( refArea * area( q.UVPt(i-1,j-1), q.UVPt(i,j-1), pNew ) > 0 ) &&
          //     ( refArea * area( q.UVPt(i+1,j-1), q.UVPt(i+1,j), pNew ) > 0 ) &&
          //     ( refArea * area( q.UVPt(i+1,j+1), q.UVPt(i,j+1), pNew ) > 0 ) &&
          //     ( refArea * area( q.UVPt(i-1,j), q.UVPt(i-1,j-1), pNew ) > 0 ))
          {
            err += sqrt(( q.U(i,j) - pNew.u ) * ( q.U(i,j) - pNew.u ) +
                        ( q.V(i,j) - pNew.v ) * ( q.V(i,j) - pNew.v ));
            q.U(i,j) = pNew.u;
            q.V(i,j) = pNew.v;
          }
          // else if ( ++nbErr < 10 )
          // {
          //   cout << i << ", " << j << endl;
          //   cout << "x = ["
          //        << "[ " << q.U(i-1,j-1) << ", " <<q.U(i,j-1) << ", " << q.U(i+1,j-1) << " ],"
          //        << "[ " << q.U(i-1,j-0) << ", " <<q.U(i,j-0) << ", " << q.U(i+1,j-0) << " ],"
          //        << "[ " << q.U(i-1,j+1) << ", " <<q.U(i,j+1) << ", " << q.U(i+1,j+1) << " ]]" << endl;
          //   cout << "y = ["
          //        << "[ " << q.V(i-1,j-1) << ", " <<q.V(i,j-1) << ", " << q.V(i+1,j-1) << " ],"
          //        << "[ " << q.V(i-1,j-0) << ", " <<q.V(i,j-0) << ", " << q.V(i+1,j-0) << " ],"
          //        << "[ " << q.V(i-1,j+1) << ", " <<q.V(i,j+1) << ", " << q.V(i+1,j+1) << " ]]" << endl<<endl;
          // }
        }

      if ( err / ( nbhoriz - 2 ) / ( nbvertic - 2 ) < 1e-6 )
        break;
    }
    //cout << " ERR " << err / ( nbhoriz - 2 ) / ( nbvertic - 2 ) << endl;

    return true;
  }

  //================================================================================
  /*!
   * \brief Remove temporary node
   */
  //================================================================================

  void mergeNodes( SMESH_MesherHelper& theHelper,
                   SinuousFace&        theSinuFace )
  {
    SMESH_MeshEditor editor( theHelper.GetMesh() );
    SMESH_MeshEditor::TListOfListOfNodes nodesGroups;

    TMergeMap::iterator n2nn = theSinuFace._nodesToMerge.begin();
    for ( ; n2nn != theSinuFace._nodesToMerge.end(); ++n2nn )
    {
      nodesGroups.push_back( list< const SMDS_MeshNode* >() );
      list< const SMDS_MeshNode* > & group = nodesGroups.back();

      group.push_back( n2nn->first );
      group.splice( group.end(), n2nn->second );
    }
    editor.MergeNodes( nodesGroups );
  }

} // namespace

//================================================================================
/*!
 * \brief Create quadrangle elements
 *  \param [in] theHelper - the helper
 *  \param [in] theFace - the face to mesh
 *  \param [in] theSinuEdges - the sinuous EDGEs
 *  \param [in] theShortEdges - the short EDGEs
 *  \return bool - is OK or not
 */
//================================================================================

bool StdMeshers_QuadFromMedialAxis_1D2D::computeQuads( SMESH_MesherHelper&       theHelper,
                                                       const TopoDS_Face&        theFace,
                                                       const vector<TopoDS_Edge> theSinuEdges[2],
                                                       const vector<TopoDS_Edge> theShortEdges[2])
{
  SMESH_Mesh* mesh = theHelper.GetMesh();
  SMESH_ProxyMesh::Ptr proxyMesh = StdMeshers_ViscousLayers2D::Compute( *mesh, theFace );
  if ( !proxyMesh )
    return false;

  StdMeshers_Quadrangle_2D::myProxyMesh  = proxyMesh;
  StdMeshers_Quadrangle_2D::myHelper     = &theHelper;
  StdMeshers_Quadrangle_2D::myNeedSmooth = false;
  StdMeshers_Quadrangle_2D::myCheckOri   = false;
  StdMeshers_Quadrangle_2D::myQuadList.clear();

  // fill FaceQuadStruct

  list< TopoDS_Edge > side[4];
  side[0].insert( side[0].end(), theShortEdges[0].begin(), theShortEdges[0].end() );
  side[1].insert( side[1].end(), theSinuEdges[1].begin(),  theSinuEdges[1].end() );
  side[2].insert( side[2].end(), theShortEdges[1].begin(), theShortEdges[1].end() );
  side[3].insert( side[3].end(), theSinuEdges[0].begin(),  theSinuEdges[0].end() );

  FaceQuadStruct::Ptr quad( new FaceQuadStruct );
  quad->side.resize( 4 );
  quad->face = theFace;
  for ( int i = 0; i < 4; ++i )
  {
    quad->side[i] = StdMeshers_FaceSide::New( theFace, side[i], mesh, i < QUAD_TOP_SIDE,
                                              /*skipMediumNodes=*/true, proxyMesh );
  }
  int nbNodesShort0 = quad->side[0].NbPoints();
  int nbNodesShort1 = quad->side[2].NbPoints();

  // compute UV of internal points
  myQuadList.push_back( quad );
  if ( !StdMeshers_Quadrangle_2D::setNormalizedGrid( quad ))
    return false;

  // elliptic smooth of internal points to get boundary cell normal to the boundary
  ellipticSmooth( quad, 1 );

  // create quadrangles
  bool ok;
  if ( nbNodesShort0 == nbNodesShort1 )
    ok = StdMeshers_Quadrangle_2D::computeQuadDominant( *mesh, theFace, quad );
  else
    ok = StdMeshers_Quadrangle_2D::computeTriangles( *mesh, theFace, quad );

  StdMeshers_Quadrangle_2D::myProxyMesh.reset();
  StdMeshers_Quadrangle_2D::myHelper = 0;

  return ok;
}

//================================================================================
/*!
 * \brief Generate quadrangle mesh
 */
//================================================================================

bool StdMeshers_QuadFromMedialAxis_1D2D::Compute(SMESH_Mesh&         theMesh,
                                                 const TopoDS_Shape& theShape)
{
  SMESH_MesherHelper helper( theMesh );
  helper.SetSubShape( theShape );

  TopoDS_Face F = TopoDS::Face( theShape );
  if ( F.Orientation() >= TopAbs_INTERNAL ) F.Orientation( TopAbs_FORWARD );

  SinuousFace sinuFace( F );

  _progress = 0.01;

  if ( getSinuousEdges( helper, sinuFace ))
  {
    _progress = 0.2;

    // if ( sinuFace._sinuEdges.size() > 2 )
    //   return error(COMPERR_BAD_SHAPE, "Not yet supported case" );

    double minSegLen = getMinSegLen( helper, sinuFace._sinuEdges );
    SMESH_MAT2d::MedialAxis ma( F, sinuFace._sinuEdges, minSegLen, /*ignoreCorners=*/true );

    if ( !_regular1D )
      _regular1D = new Algo1D( _studyId, _gen );
    _regular1D->SetSegmentLength( minSegLen );

    vector<double> maParams;
    if ( ! divideMA( helper, ma, sinuFace, _regular1D, maParams ))
      return error(COMPERR_BAD_SHAPE);

    _progress = 0.4;

    if ( !computeShortEdges( helper, sinuFace._shortSide[0], _regular1D ) ||
         !computeShortEdges( helper, sinuFace._shortSide[1], _regular1D ))
      return error("Failed to mesh short edges");

    _progress = 0.6;

    if ( !computeSinuEdges( helper, minSegLen, ma, maParams, sinuFace ))
      return error("Failed to mesh sinuous edges");

    _progress = 0.8;

    bool ok = computeQuads( helper, F, sinuFace._sinuSide, sinuFace._shortSide );

    if ( ok )
      mergeNodes( helper, sinuFace );

    _progress = 1.;

    return ok;
  }

  return error(COMPERR_BAD_SHAPE, "Not implemented so far");
}

//================================================================================
/*!
 * \brief Predict nb of elements
 */
//================================================================================

bool StdMeshers_QuadFromMedialAxis_1D2D::Evaluate(SMESH_Mesh &         theMesh,
                                                  const TopoDS_Shape & theShape,
                                                  MapShapeNbElems&     theResMap)
{
  return StdMeshers_Quadrangle_2D::Evaluate(theMesh,theShape,theResMap);
}