smesh/src/StdMeshers/StdMeshers_Cartesian_3D.cxx

// Copyright (C) 2007-2011  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.
//
// 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_Cartesian_3D.cxx
//  Module : SMESH
//
#include "StdMeshers_Cartesian_3D.hxx"

#include "SMDS_MeshNode.hxx"
#include "SMESH_Block.hxx"
#include "SMESH_Comment.hxx"
#include "SMESH_Mesh.hxx"
#include "SMESH_MesherHelper.hxx"
#include "SMESH_subMesh.hxx"
#include "SMESH_subMeshEventListener.hxx"
#include "StdMeshers_CartesianParameters3D.hxx"

#include "utilities.h"
#include "Utils_ExceptHandlers.hxx"

#include <BRepAdaptor_Surface.hxx>
#include <BRepBndLib.hxx>
#include <BRepTools.hxx>
#include <BRep_Tool.hxx>
#include <Bnd_Box.hxx>
#include <ElSLib.hxx>
#include <IntAna_IntConicQuad.hxx>
#include <IntAna_IntLinTorus.hxx>
#include <IntAna_Quadric.hxx>
#include <IntCurveSurface_TransitionOnCurve.hxx>
#include <IntCurvesFace_Intersector.hxx>
#include <Poly_Triangulation.hxx>
#include <Precision.hxx>
#include <TopExp.hxx>
#include <TopExp_Explorer.hxx>
#include <TopTools_MapIteratorOfMapOfShape.hxx>
#include <TopTools_MapOfShape.hxx>
#include <TopoDS.hxx>
#include <TopoDS_Face.hxx>
#include <gp_Cone.hxx>
#include <gp_Cylinder.hxx>
#include <gp_Lin.hxx>
#include <gp_Pln.hxx>
#include <gp_Pnt2d.hxx>
#include <gp_Sphere.hxx>
#include <gp_Torus.hxx>

using namespace std;

#define _MY_DEBUG_

//=============================================================================
/*!
 * Constructor
 */
//=============================================================================

StdMeshers_Cartesian_3D::StdMeshers_Cartesian_3D(int hypId, int studyId, SMESH_Gen * gen)
  :SMESH_3D_Algo(hypId, studyId, gen)
{
  _name = "Cartesian_3D";
  _shapeType = (1 << TopAbs_SOLID);       // 1 bit /shape type
  _compatibleHypothesis.push_back("CartesianParameters3D");

  _onlyUnaryInput = false;         // to mesh all SOLIDs at once
  _requireDescretBoundary = false; // 2D mesh not needed
  _supportSubmeshes = false;       // do not use any existing mesh
}

//=============================================================================
/*!
 * Check presence of a hypothesis
 */
//=============================================================================

bool StdMeshers_Cartesian_3D::CheckHypothesis (SMESH_Mesh&          aMesh,
                                               const TopoDS_Shape&  aShape,
                                               Hypothesis_Status&   aStatus)
{
  aStatus = SMESH_Hypothesis::HYP_MISSING;

  const list<const SMESHDS_Hypothesis*>& hyps = GetUsedHypothesis(aMesh, aShape);
  list <const SMESHDS_Hypothesis* >::const_iterator h = hyps.begin();
  if ( h == hyps.end())
  {
    return false;
  }

  for ( ; h != hyps.end(); ++h )
  {
    if (( _hyp = dynamic_cast<const StdMeshers_CartesianParameters3D*>( *h )))
    {
      aStatus = _hyp->IsDefined() ? HYP_OK : HYP_BAD_PARAMETER;
      break;
    }
  }

  return aStatus == HYP_OK;
}

namespace
{
  //=============================================================================
  // Definitions of internal utils
  // --------------------------------------------------------------------------
  enum Transition {
    Trans_TANGENT = IntCurveSurface_Tangent,
    Trans_IN      = IntCurveSurface_In,
    Trans_OUT     = IntCurveSurface_Out,
    Trans_APEX
  };
  /*!
   * \brief Data of intersection between a GridLine and a TopoDS_Face
   */
  struct IntersectionPoint
  {
    double                       _paramOnLine;
    mutable Transition           _transition;
    mutable const SMDS_MeshNode* _node;

    IntersectionPoint(): _node(0) {}
    bool operator< ( const IntersectionPoint& o ) const { return _paramOnLine < o._paramOnLine; }
  };
  // --------------------------------------------------------------------------
  /*!
   * \brief A line of the grid and its intersections with 2D geometry
   */
  struct GridLine
  {
    gp_Lin _line;
    double _length; // line length
    multiset< IntersectionPoint > _intPoints;

    void RemoveExcessIntPoints( const double tol );
    bool GetIsOutBefore( multiset< IntersectionPoint >::iterator ip, bool prevIsOut );
  };
  // --------------------------------------------------------------------------
  /*!
   * \brief Iterator on the grid lines in one direction
   */
  struct LineIndexer
  {
    size_t _size  [3];
    size_t _curInd[3];
    size_t _iVar1, _iVar2, _iConst;
    string _name1, _name2, _nameConst;
    LineIndexer() {}
    LineIndexer( size_t sz1, size_t sz2, size_t sz3,
                 size_t iv1, size_t iv2, size_t iConst,
                 const string& nv1, const string& nv2, const string& nConst )
    {
      _size[0] = sz1; _size[1] = sz2; _size[2] = sz3;
      _curInd[0] = _curInd[1] = _curInd[2] = 0;
      _iVar1 = iv1; _iVar2 = iv2; _iConst = iConst; 
      _name1 = nv1; _name2 = nv2; _nameConst = nConst;
    }

    size_t I() { return _curInd[0]; }
    size_t J() { return _curInd[1]; }
    size_t K() { return _curInd[2]; }
    void SetIJK( size_t i, size_t j, size_t k )
    {
      _curInd[0] = i; _curInd[1] = j; _curInd[2] = k;
    }
    void operator++()
    {
      if ( ++_curInd[_iVar1] == _size[_iVar1] )
        _curInd[_iVar1] = 0, ++_curInd[_iVar2];
    }
    bool More() const { return _curInd[_iVar2] < _size[_iVar2]; }
    size_t LineIndex () const { return _curInd[_iVar1] + _curInd[_iVar2]* _size[_iVar1]; }
    size_t LineIndex10 () const { return (_curInd[_iVar1] + 1 ) + _curInd[_iVar2]* _size[_iVar1]; }
    size_t LineIndex01 () const { return _curInd[_iVar1] + (_curInd[_iVar2] + 1 )* _size[_iVar1]; }
    size_t LineIndex11 () const { return (_curInd[_iVar1] + 1 ) + (_curInd[_iVar2] + 1 )* _size[_iVar1]; }
    void SetIndexOnLine (size_t i)  { _curInd[ _iConst ] = i; }
    size_t NbLines() const { return _size[_iVar1] * _size[_iVar2]; }
  };
  // --------------------------------------------------------------------------
  /*!
   * \brief Container of GridLine's
   */
  struct Grid
  {
    vector< double >   _coords[3]; // coordinates of grid nodes
    vector< GridLine > _lines [3]; // in 3 directions
    double             _tol, _minCellSize;

    vector< const SMDS_MeshNode* > _nodes; // mesh nodes at grid nodes

    size_t NodeIndex( size_t i, size_t j, size_t k ) const
    {
      return i + j*_coords[0].size() + k*_coords[0].size()*_coords[1].size();
    }
    size_t NodeIndexDX() const { return 1; }
    size_t NodeIndexDY() const { return _coords[0].size(); }
    size_t NodeIndexDZ() const { return _coords[0].size() * _coords[1].size(); }

    LineIndexer GetLineIndexer(size_t iDir) const;

    void SetCoordinates(const vector<double>& xCoords,
                        const vector<double>& yCoords,
                        const vector<double>& zCoords,
                        const TopoDS_Shape&   shape );
    void ComputeNodes(SMESH_MesherHelper& helper);
  };
  // --------------------------------------------------------------------------
  /*!
   * \brief Intersector of TopoDS_Face with all GridLine's
   */
  struct FaceGridIntersector
  {
    TopoDS_Face _face;
    Grid*       _grid;
    Bnd_Box     _bndBox;
    IntCurvesFace_Intersector* _surfaceInt;
    vector< std::pair< GridLine*, IntersectionPoint > > _intersections;

    FaceGridIntersector(): _grid(0), _surfaceInt(0) {}
    void Intersect();
    bool IsInGrid(const Bnd_Box& gridBox);

    void StoreIntersections()
    {
      for ( size_t i = 0; i < _intersections.size(); ++i )
        _intersections[i].first->_intPoints.insert( _intersections[i].second );
    }
    const Bnd_Box& GetFaceBndBox()
    {
      GetCurveFaceIntersector();
      return _bndBox;
    }
    IntCurvesFace_Intersector* GetCurveFaceIntersector()
    {
      if ( !_surfaceInt )
      {
        _surfaceInt = new IntCurvesFace_Intersector( _face, Precision::PConfusion() );
        _bndBox     = _surfaceInt->Bounding();
        if ( _bndBox.IsVoid() )
          BRepBndLib::Add (_face, _bndBox);
      }
      return _surfaceInt;
    }
  };
  // --------------------------------------------------------------------------
  /*!
   * \brief Intersector of a surface with a GridLine
   */
  struct FaceLineIntersector
  {
    double      _tol;
    double      _u, _v, _w; // params on the face and the line
    Transition  _transition; // transition of at intersection (see IntCurveSurface.cdl)
    Transition  _transIn, _transOut; // IN and OUT transitions depending of face orientation

    gp_Pln      _plane;
    gp_Cylinder _cylinder;
    gp_Cone     _cone;
    gp_Sphere   _sphere;
    gp_Torus    _torus;
    IntCurvesFace_Intersector* _surfaceInt;

    vector< IntersectionPoint > _intPoints;

    void IntersectWithPlane   (const GridLine& gridLine);
    void IntersectWithCylinder(const GridLine& gridLine);
    void IntersectWithCone    (const GridLine& gridLine);
    void IntersectWithSphere  (const GridLine& gridLine);
    void IntersectWithTorus   (const GridLine& gridLine);
    void IntersectWithSurface (const GridLine& gridLine);

    void addIntPoint(const bool toClassify=true);
    bool isParamOnLineOK( const double linLength )
    {
      return -_tol < _w && _w < linLength + _tol;
    }
    FaceLineIntersector():_surfaceInt(0) {}
    ~FaceLineIntersector() { if (_surfaceInt ) delete _surfaceInt; _surfaceInt = 0; }
  };
  // --------------------------------------------------------------------------
  /*!
   * \brief Class representing topology of the hexahedron and creating a mesh
   *        volume basing on analysis of hexahedron intersection with geometry
   */
  class Hexahedron
  {
    // --------------------------------------------------------------------------------
    struct _Face;
    struct _Link;
    // --------------------------------------------------------------------------------
    struct _Node //!< node either at a hexahedron corner or at GridLine intersection
    {
      const SMDS_MeshNode*     _node; // mesh node at hexahedron corner
      const IntersectionPoint* _intPoint;

      _Node(const SMDS_MeshNode* n=0, const IntersectionPoint* ip=0):_node(n), _intPoint(ip) {} 
      const SMDS_MeshNode* Node() const { return _intPoint ? _intPoint->_node : _node; }
      bool IsCorner() const { return _node; }
    };
    // --------------------------------------------------------------------------------
    struct _Link // link connection two _Node's
    {
      _Node* _nodes[2];
      vector< _Node>  _intNodes; // _Node's at GridLine intersections
      vector< _Link > _splits;
      vector< _Face*> _faces;
    };
    // --------------------------------------------------------------------------------
    struct _OrientedLink
    {
      _Link* _link;
      bool   _reverse;
      _OrientedLink( _Link* link=0, bool reverse=false ): _link(link), _reverse(reverse) {}
      void Reverse() { _reverse = !_reverse; }
      int NbResultLinks() const { return _link->_splits.size(); }
      _OrientedLink ResultLink(int i) const
      {
        return _OrientedLink(&_link->_splits[_reverse ? NbResultLinks()-i-1 : i],_reverse);
      }
      _Node* FirstNode() const { return _link->_nodes[ _reverse ]; }
      _Node* LastNode() const { return _link->_nodes[ !_reverse ]; }
      // int NbNodes() const { return 2 + _link->_intNodes.size(); }
      // _Node* GetNode(const int i)
      // {
      //   return ( 0 < i && i < NbNodes()-1 ) ? _link->_intNodes[i-1] : ( _link->_nodes[bool(i)]);
      // }
    };
    // --------------------------------------------------------------------------------
    struct _Face
    {
      vector< _OrientedLink > _links;
      vector< _Link >         _polyLinks; // links added to close a polygonal face
    };
    // --------------------------------------------------------------------------------
    int   _nodeShift[8];
    _Node _hexNodes[8];
    _Link _hexLinks[12];
    _Face _hexQuads[6];

    vector< _Face > _polygons;

    Grid* _grid;
    LineIndexer _lineInd[3];

    double _sizeThreshold, _sideLength[3];

    int _nbCornerNodes, _nbIntNodes;

  public:
    Hexahedron(const double sizeThreshold, Grid* grid);
    void Init( size_t i, size_t j, size_t k );
    int MakeElements(SMESH_MesherHelper& helper);
  private:
    bool checkPolyhedronSize() const;
    bool addHexa (SMESH_MesherHelper& helper);
    bool addTetra(SMESH_MesherHelper& helper);
    bool addPenta(SMESH_MesherHelper& helper);
    bool addPyra (SMESH_MesherHelper& helper);
  };
 
  // --------------------------------------------------------------------------
  /*!
   * \brief Structure intersecting certain nb of faces with GridLine's in one thread
   */
#ifdef WITH_TBB
  struct ParallelIntersector
  {
    vector< FaceGridIntersector >& _faceVec;
    ParallelIntersector( vector< FaceGridIntersector >& faceVec): _faceVec(faceVec){}
    void operator() ( const tbb::blocked_range<size_t>& r ) const
    {
      for ( size_t i = r.begin(); i != r.end(); ++i )
        _faceVec[i]->Intersect();
    }
  };
#endif
  //=============================================================================
  // Implementation of internal utils
  //=============================================================================
  /*
   * Remove coincident intersection points
   */
  void GridLine::RemoveExcessIntPoints( const double tol )
  {
    if ( _intPoints.size() < 2 ) return;

    set< Transition > tranSet;
    multiset< IntersectionPoint >::iterator ip2 = _intPoints.begin(), ip1 = ip2++;
    for ( ; ip2 != _intPoints.end(); ip1 = ip2++ )
    {
      tranSet.clear();
      while ( ip2->_paramOnLine - ip1->_paramOnLine <= tol  && ip2 != _intPoints.end())
      {
        tranSet.insert( ip1->_transition );
        tranSet.insert( ip2->_transition );
        _intPoints.erase( ip1 );
        ip1 = ip2++;
      }
      if ( tranSet.size() > 1 ) // points with different transition coincide
      {
        bool isIN  = tranSet.count( Trans_IN );
        bool isOUT = tranSet.count( Trans_OUT );
        if ( isIN && isOUT )
          (*ip1)._transition = Trans_TANGENT;
        else
          (*ip1)._transition = isIN ? Trans_IN : Trans_OUT;
      }
    }
  }
  //================================================================================
  /*
   * Return "is OUT" state for nodes before the given intersention point
   */
  bool GridLine::GetIsOutBefore( multiset< IntersectionPoint >::iterator ip, bool prevIsOut )
  {
    if ( ip->_transition == Trans_IN )
      return true;
    if ( ip->_transition == Trans_OUT )
      return false;
    if ( ip->_transition == Trans_APEX )
    {
      // singularity point (apex of a cone)
      if ( _intPoints.size() == 1 || ip == _intPoints.begin() )
        return true;
      multiset< IntersectionPoint >::iterator ipBef = ip, ipAft = ++ip;
      if ( ipAft == _intPoints.end() )
        return false;
      --ipBef;
      if ( ipBef->_transition != ipAft->_transition )
        return ( ipBef->_transition == Trans_OUT );
      return ( ipBef->_transition != Trans_OUT );
    }
    return prevIsOut; // _transition == Trans_TANGENT
  }
  //================================================================================
  /*
   * Return an iterator on GridLine's in a given direction
   */
  LineIndexer Grid::GetLineIndexer(size_t iDir) const
  {
    const size_t indices[] = { 1,2,0, 0,2,1, 0,1,2 };
    const string s[] = { "X", "Y", "Z" };
    LineIndexer li( _coords[0].size(),  _coords[1].size(),    _coords[2].size(),
                    indices[iDir*3],    indices[iDir*3+1],    indices[iDir*3+2],
                    s[indices[iDir*3]], s[indices[iDir*3+1]], s[indices[iDir*3+2]]);
    return li;
  }
  //=============================================================================
  /*
   * Creates GridLine's of the grid
   */
  void Grid::SetCoordinates(const vector<double>& xCoords,
                            const vector<double>& yCoords,
                            const vector<double>& zCoords,
                            const TopoDS_Shape&   shape)
  {
    _coords[0] = xCoords;
    _coords[1] = yCoords;
    _coords[2] = zCoords;

    // compute tolerance
    _minCellSize = Precision::Infinite();
    for ( int iDir = 0; iDir < 3; ++iDir ) // loop on 3 line directions
    {
      for ( size_t i = 1; i < _coords[ iDir ].size(); ++i )
      {
        double cellLen = _coords[ iDir ][ i ] - _coords[ iDir ][ i-1 ];
        if ( cellLen < _minCellSize )
          _minCellSize = cellLen;
      }
    }
    if ( _minCellSize < Precision::Confusion() )
      throw SMESH_ComputeError (COMPERR_ALGO_FAILED,
                                SMESH_Comment("Too small cell size: ") << _tol );
    _tol = _minCellSize / 1000.;

    // attune grid extremities to shape bounding box computed by vertices
    Bnd_Box shapeBox;
    for ( TopExp_Explorer vExp( shape, TopAbs_VERTEX ); vExp.More(); vExp.Next() )
      shapeBox.Add( BRep_Tool::Pnt( TopoDS::Vertex( vExp.Current() )));
    
    double sP[6]; // aXmin, aYmin, aZmin, aXmax, aYmax, aZmax
    shapeBox.Get(sP[0],sP[1],sP[2],sP[3],sP[4],sP[5]);
    double* cP[6] = { &_coords[0].front(), &_coords[1].front(), &_coords[2].front(),
                      &_coords[0].back(),  &_coords[1].back(),  &_coords[2].back() };
    for ( int i = 0; i < 6; ++i )
      if ( fabs( sP[i] - *cP[i] ) < _tol )
        *cP[i] = sP[i] + _tol/1000. * ( i < 3 ? +1 : -1 );

    // create lines
    for ( int iDir = 0; iDir < 3; ++iDir ) // loop on 3 line directions
    {
      LineIndexer li = GetLineIndexer( iDir );
      _lines[iDir].resize( li.NbLines() );
      double len = _coords[ iDir ].back() - _coords[iDir].front();
      gp_Vec dir( iDir==0, iDir==1, iDir==2 );
      for ( ; li.More(); ++li )
      {
        GridLine& gl = _lines[iDir][ li.LineIndex() ];
        gl._line.SetLocation(gp_Pnt(_coords[0][li.I()], _coords[1][li.J()], _coords[2][li.K()])); 
        gl._line.SetDirection( dir );
        gl._length = len;
      }
    }
  }
  //================================================================================
  /*
   * Creates all nodes
   */
  void Grid::ComputeNodes(SMESH_MesherHelper& helper)
  {
    // state of each node of the grid relative to the geomerty
    vector< bool > isNodeOut( _coords[0].size() * _coords[1].size() * _coords[2].size(), false );
    _nodes.resize( isNodeOut.size(), 0 );

    for ( int iDir = 0; iDir < 3; ++iDir ) // loop on 3 line directions
    {
      LineIndexer li = GetLineIndexer( iDir );

      // find out a shift of node index while walking along a GridLine in this direction
      li.SetIndexOnLine( 0 );
      size_t nIndex0 = NodeIndex( li.I(), li.J(), li.K() );
      li.SetIndexOnLine( 1 );
      const size_t nShift = NodeIndex( li.I(), li.J(), li.K() ) - nIndex0;
      
      const vector<double> & coords = _coords[ iDir ];
      for ( ; li.More(); ++li ) // loop on lines in iDir
      {
        li.SetIndexOnLine( 0 );
        nIndex0 = NodeIndex( li.I(), li.J(), li.K() );

        GridLine& line = _lines[ iDir ][ li.LineIndex() ];
        line.RemoveExcessIntPoints( _tol );
        multiset< IntersectionPoint >& intPnts = _lines[ iDir ][ li.LineIndex() ]._intPoints;
        multiset< IntersectionPoint >::iterator ip = intPnts.begin();

        bool isOut = true;
        const double* nodeCoord = & coords[0], *coord0 = nodeCoord, *coordEnd = coord0 + coords.size();
        double nodeParam = 0;
        for ( ; ip != intPnts.end(); ++ip )
        {
          // set OUT state or just skip IN nodes before ip
          if ( nodeParam < ip->_paramOnLine - _tol )
          {
            isOut = line.GetIsOutBefore( ip, isOut );

            while ( nodeParam < ip->_paramOnLine - _tol )
            {
              if ( isOut )
                isNodeOut[ nIndex0 + nShift * ( nodeCoord-coord0 ) ] = isOut;
              if ( ++nodeCoord <  coordEnd )
                nodeParam = *nodeCoord - *coord0;
              else
                break;
            }
            if ( nodeCoord == coordEnd ) break;
          }
          // create a mesh node on a GridLine at ip if it does not coincide with a grid node
          if ( nodeParam > ip->_paramOnLine + _tol )
          {
            li.SetIndexOnLine( 0 );
            double xyz[3] = { _coords[0][ li.I() ], _coords[1][ li.J() ], _coords[2][ li.K() ]};
            xyz[ li._iConst ] += ip->_paramOnLine;
            ip->_node = helper.AddNode( xyz[0], xyz[1], xyz[2] );
          }
          // create a mesh node at ip concident with a grid node
          else
          {
            int nodeIndex = nIndex0 + nShift * ( nodeCoord-coord0 );
            if ( ! _nodes[ nodeIndex ] )
            {
              li.SetIndexOnLine( nodeCoord-coord0 );
              double xyz[3] = { _coords[0][ li.I() ], _coords[1][ li.J() ], _coords[2][ li.K() ]};
              _nodes[ nodeIndex ] = helper.AddNode( xyz[0], xyz[1], xyz[2] );
            }
            if ( ++nodeCoord < coordEnd )
              nodeParam = *nodeCoord - *coord0;
          }
        }
        // set OUT state to nodes after the last ip
        for ( ; nodeCoord < coordEnd; ++nodeCoord )
          isNodeOut[ nIndex0 + nShift * ( nodeCoord-coord0 ) ] = true;
      }
    }

    // Create mesh nodes at !OUT nodes of the grid

    for ( size_t z = 0; z < _coords[2].size(); ++z )
      for ( size_t y = 0; y < _coords[1].size(); ++y )
        for ( size_t x = 0; x < _coords[0].size(); ++x )
        {
          size_t nodeIndex = NodeIndex( x, y, z );
          if ( !isNodeOut[ nodeIndex ] && !_nodes[ nodeIndex] )
            _nodes[ nodeIndex ] = helper.AddNode( _coords[0][x], _coords[1][y], _coords[2][z] );
        }

#ifdef _MY_DEBUG_
    // check validity of transitions
    const char* trName[] = { "TANGENT", "IN", "OUT", "APEX" };
    for ( int iDir = 0; iDir < 3; ++iDir ) // loop on 3 line directions
    {
      LineIndexer li = GetLineIndexer( iDir );
      for ( ; li.More(); ++li )
      {
        multiset< IntersectionPoint >& intPnts = _lines[ iDir ][ li.LineIndex() ]._intPoints;
        if ( intPnts.empty() ) continue;
        if ( intPnts.size() == 1 )
        {
          if ( intPnts.begin()->_transition != Trans_TANGENT &&
               intPnts.begin()->_transition != Trans_APEX )
          throw SMESH_ComputeError (COMPERR_ALGO_FAILED,
                                    SMESH_Comment("Wrong SOLE transition of GridLine (")
                                    << li._curInd[li._iVar1] << ", " << li._curInd[li._iVar2]
                                    << ") along " << li._nameConst
                                    << ": " << trName[ intPnts.begin()->_transition] );
        }
        else
        {
          if ( intPnts.begin()->_transition == Trans_OUT )
            throw SMESH_ComputeError (COMPERR_ALGO_FAILED,
                                      SMESH_Comment("Wrong START transition of GridLine (")
                                      << li._curInd[li._iVar1] << ", " << li._curInd[li._iVar2]
                                      << ") along " << li._nameConst
                                      << ": " << trName[ intPnts.begin()->_transition ]);
          if ( intPnts.rbegin()->_transition == Trans_IN )
            throw SMESH_ComputeError (COMPERR_ALGO_FAILED,
                                      SMESH_Comment("Wrong END transition of GridLine (")
                                      << li._curInd[li._iVar1] << ", " << li._curInd[li._iVar2]
                                      << ") along " << li._nameConst
                                    << ": " << trName[ intPnts.rbegin()->_transition ]);
        }
      }
    }
#endif
  }

  //=============================================================================
  /*
   * Checks if the face is encosed by the grid
   */
  bool FaceGridIntersector::IsInGrid(const Bnd_Box& gridBox)
  {
    double x0,y0,z0, x1,y1,z1;
    const Bnd_Box& faceBox = GetFaceBndBox();
    faceBox.Get(x0,y0,z0, x1,y1,z1);

    if ( !gridBox.IsOut( gp_Pnt( x0,y0,z0 )) &&
         !gridBox.IsOut( gp_Pnt( x1,y1,z1 )))
      return true;

    double X0,Y0,Z0, X1,Y1,Z1;
    gridBox.Get(X0,Y0,Z0, X1,Y1,Z1);
    double faceP[6] = { x0,y0,z0, x1,y1,z1 };
    double gridP[6] = { X0,Y0,Z0, X1,Y1,Z1 };
    gp_Dir axes[3]  = { gp::DX(), gp::DY(), gp::DZ() };
    for ( int iDir = 0; iDir < 6; ++iDir )
    {
      if ( iDir < 3  && gridP[ iDir ] <= faceP[ iDir ] ) continue;
      if ( iDir >= 3 && gridP[ iDir ] >= faceP[ iDir ] ) continue;

      // check if the face intersects a side of a gridBox

      gp_Pnt p = iDir < 3 ? gp_Pnt( X0,Y0,Z0 ) : gp_Pnt( X1,Y1,Z1 );
      gp_Ax1 norm( p, axes[ iDir % 3 ] );
      if ( iDir < 3 ) norm.Reverse();

      gp_XYZ O = norm.Location().XYZ(), N = norm.Direction().XYZ();

      TopLoc_Location loc = _face.Location();
      Handle(Poly_Triangulation) aPoly = BRep_Tool::Triangulation(_face,loc);
      if ( !aPoly.IsNull() )
      {
        if ( !loc.IsIdentity() )
        {
          norm.Transform( loc.Transformation().Inverted() );
          O = norm.Location().XYZ(), N = norm.Direction().XYZ();
        }
        const double deflection = aPoly->Deflection();

        const TColgp_Array1OfPnt& nodes = aPoly->Nodes();
        for ( int i = nodes.Lower(); i <= nodes.Upper(); ++i )
          if (( nodes( i ).XYZ() - O ) * N > _grid->_tol + deflection )
            return false;
      }
      else
      {
        BRepAdaptor_Surface surf( _face );
        double u0, u1, v0, v1, du, dv, u, v;
        BRepTools::UVBounds( _face, u0, u1, v0, v1);
        if ( surf.GetType() == GeomAbs_Plane ) {
          du = u1 - u0, dv = v1 - v0;
        }
        else {
          du = surf.UResolution( _grid->_minCellSize / 10. );
          dv = surf.VResolution( _grid->_minCellSize / 10. );
        }
        for ( u = u0, v = v0; u <= u1 && v <= v1; u += du, v += dv )
        {
          gp_Pnt p = surf.Value( u, v );
          if (( p.XYZ() - O ) * N > _grid->_tol )
          {
            TopAbs_State state = GetCurveFaceIntersector()->ClassifyUVPoint(gp_Pnt2d( u, v ));
            if ( state == TopAbs_IN || state == TopAbs_ON )
              return false;
          }
        }
      }
    }
    return true;
  }
  //=============================================================================
  /*
   * Intersects TopoDS_Face with all GridLine's
   */
  void FaceGridIntersector::Intersect()
  {
    FaceLineIntersector intersector;
    intersector._surfaceInt = GetCurveFaceIntersector();
    intersector._tol        = _grid->_tol;
    intersector._transOut   = _face.Orientation() == TopAbs_REVERSED ? Trans_IN : Trans_OUT;
    intersector._transIn    = _face.Orientation() == TopAbs_REVERSED ? Trans_OUT : Trans_IN;

    typedef void (FaceLineIntersector::* PIntFun )(const GridLine& gridLine);
    PIntFun interFunction;

    BRepAdaptor_Surface surf( _face );
    switch ( surf.GetType() ) {
    case GeomAbs_Plane:
      intersector._plane = surf.Plane();
      interFunction = &FaceLineIntersector::IntersectWithPlane;
      break;
    case GeomAbs_Cylinder:
      intersector._cylinder = surf.Cylinder();
      interFunction = &FaceLineIntersector::IntersectWithCylinder;
      break;
    case GeomAbs_Cone:
      intersector._cone = surf.Cone();
      interFunction = &FaceLineIntersector::IntersectWithCone;
      break;
    case GeomAbs_Sphere:
      intersector._sphere = surf.Sphere();
      interFunction = &FaceLineIntersector::IntersectWithSphere;
      break;
    case GeomAbs_Torus:
      intersector._torus = surf.Torus();
      interFunction = &FaceLineIntersector::IntersectWithTorus;
      break;
    default:
      interFunction = &FaceLineIntersector::IntersectWithSurface;
    }

    _intersections.clear();
    for ( int iDir = 0; iDir < 3; ++iDir ) // loop on 3 line directions
    {
      if ( surf.GetType() == GeomAbs_Plane )
      {
        // check if all lines in this direction are parallel to a plane
        if ( intersector._plane.Axis().IsNormal( _grid->_lines[iDir][0]._line.Position(),
                                                 Precision::Angular()))
          continue;
        // find out a transition, that is the same for all lines of a direction
        gp_Dir plnNorm = intersector._plane.Axis().Direction();
        gp_Dir lineDir = _grid->_lines[iDir][0]._line.Direction();
        intersector._transition =
          ( plnNorm * lineDir < 0 ) ? intersector._transIn : intersector._transOut;
      }
      if ( surf.GetType() == GeomAbs_Cylinder )
      {
        // check if all lines in this direction are parallel to a cylinder
        if ( intersector._cylinder.Axis().IsParallel( _grid->_lines[iDir][0]._line.Position(),
                                                      Precision::Angular()))
          continue;
      }

      // intersect the grid lines with the face
      for ( size_t iL = 0; iL < _grid->_lines[iDir].size(); ++iL )
      {
        GridLine& gridLine = _grid->_lines[iDir][iL];
        if ( _bndBox.IsOut( gridLine._line )) continue;

        intersector._intPoints.clear();
        (intersector.*interFunction)( gridLine );
        for ( size_t i = 0; i < intersector._intPoints.size(); ++i )
          _intersections.push_back( make_pair( &gridLine, intersector._intPoints[i] ));
      }
    }
  }
  //================================================================================
  /*
   * Store an intersection if it is In or ON the face
   */
  void FaceLineIntersector::addIntPoint(const bool toClassify)
  {
    TopAbs_State state = toClassify ? _surfaceInt->ClassifyUVPoint(gp_Pnt2d( _u, _v )) : TopAbs_IN;
    if ( state == TopAbs_IN || state == TopAbs_ON )
    {
      IntersectionPoint p;
      p._paramOnLine = _w;
      p._transition  = _transition;
      _intPoints.push_back( p );
    }
  }
  //================================================================================
  /*
   * Intersect a line with a plane
   */
  void FaceLineIntersector::IntersectWithPlane   (const GridLine& gridLine)
  {
    IntAna_IntConicQuad linPlane( gridLine._line, _plane, Precision::Angular());
    _w = linPlane.ParamOnConic(1);
    if ( isParamOnLineOK( gridLine._length ))
    {
      ElSLib::Parameters(_plane, linPlane.Point(1) ,_u,_v);
      addIntPoint();
    }
  }
  //================================================================================
  /*
   * Intersect a line with a cylinder
   */
  void FaceLineIntersector::IntersectWithCylinder(const GridLine& gridLine)
  {
    IntAna_IntConicQuad linCylinder( gridLine._line,_cylinder);
    if ( linCylinder.IsDone() && linCylinder.NbPoints() > 0 )
    {
      _w = linCylinder.ParamOnConic(1);
      if ( linCylinder.NbPoints() == 1 )
        _transition = Trans_TANGENT;
      else
        _transition = _w < linCylinder.ParamOnConic(2) ? _transIn : _transOut;
      if ( isParamOnLineOK( gridLine._length ))
      {
        ElSLib::Parameters(_cylinder, linCylinder.Point(1) ,_u,_v);
        addIntPoint();
      }
      if ( linCylinder.NbPoints() > 1 )
      {
        _w = linCylinder.ParamOnConic(2);
        if ( isParamOnLineOK( gridLine._length ))
        {
          ElSLib::Parameters(_cylinder, linCylinder.Point(2) ,_u,_v);
          _transition = ( _transition == Trans_OUT ) ? Trans_IN : Trans_OUT;
          addIntPoint();
        }
      }
    }
  }
  //================================================================================
  /*
   * Intersect a line with a cone
   */
  void FaceLineIntersector::IntersectWithCone (const GridLine& gridLine)
  {
    IntAna_IntConicQuad linCone(gridLine._line,_cone);
    if ( !linCone.IsDone() ) return;
    gp_Pnt P;
    gp_Vec du, dv, norm;
    for ( int i = 1; i <= linCone.NbPoints(); ++i )
    {
      _w = linCone.ParamOnConic( i );
      if ( !isParamOnLineOK( gridLine._length )) continue;
      ElSLib::Parameters(_cone, linCone.Point(i) ,_u,_v);
      TopAbs_State state = _surfaceInt->ClassifyUVPoint(gp_Pnt2d( _u, _v ));
      if ( state == TopAbs_IN || state == TopAbs_ON )
      {
        ElSLib::D1( _u, _v, _cone, P, du, dv );
        norm = du ^ dv;
        double normSize2 = norm.SquareMagnitude();
        if ( normSize2 > Precision::Angular() * Precision::Angular() )
        {
          double cos = norm.XYZ() * gridLine._line.Direction().XYZ();
          cos /= sqrt( normSize2 );
          if ( cos < -Precision::Angular() )
            _transition = _transIn;
          else if ( cos > Precision::Angular() )
            _transition = _transOut;
          else
            _transition = Trans_TANGENT;
        }
        else
        {
          _transition = Trans_APEX;
        }
        addIntPoint( /*toClassify=*/false);
      }
    }
  }
  //================================================================================
  /*
   * Intersect a line with a sphere
   */
  void FaceLineIntersector::IntersectWithSphere  (const GridLine& gridLine)
  {
    IntAna_IntConicQuad linSphere(gridLine._line,_sphere);
    if ( linSphere.IsDone() && linSphere.NbPoints() > 0 )
    {
      _w = linSphere.ParamOnConic(1);
      if ( linSphere.NbPoints() == 1 )
        _transition = Trans_TANGENT;
      else
        _transition = _w < linSphere.ParamOnConic(2) ? _transIn : _transOut;
      if ( isParamOnLineOK( gridLine._length ))
      {
        ElSLib::Parameters(_sphere, linSphere.Point(1) ,_u,_v);
        addIntPoint();
      }
      if ( linSphere.NbPoints() > 1 )
      {
        _w = linSphere.ParamOnConic(2);
        if ( isParamOnLineOK( gridLine._length ))
        {
          ElSLib::Parameters(_sphere, linSphere.Point(2) ,_u,_v);
          _transition = ( _transition == Trans_OUT ) ? Trans_IN : Trans_OUT;
          addIntPoint();
        }
      }
    }
  }
  //================================================================================
  /*
   * Intersect a line with a torus
   */
  void FaceLineIntersector::IntersectWithTorus   (const GridLine& gridLine)
  {
    IntAna_IntLinTorus linTorus(gridLine._line,_torus);
    if ( !linTorus.IsDone()) return;
    gp_Pnt P;
    gp_Vec du, dv, norm;
    for ( int i = 1; i <= linTorus.NbPoints(); ++i )
    {
      _w = linTorus.ParamOnLine( i );
      if ( !isParamOnLineOK( gridLine._length )) continue;
      linTorus.ParamOnTorus( i, _u,_v );
      TopAbs_State state = _surfaceInt->ClassifyUVPoint(gp_Pnt2d( _u, _v ));
      if ( state == TopAbs_IN || state == TopAbs_ON )
      {
        ElSLib::D1( _u, _v, _torus, P, du, dv );
        norm = du ^ dv;
        double normSize = norm.Magnitude();
        double cos = norm.XYZ() * gridLine._line.Direction().XYZ();
        cos /= normSize;
        if ( cos < -Precision::Angular() )
          _transition = _transIn;
        else if ( cos > Precision::Angular() )
          _transition = _transOut;
        else
          _transition = Trans_TANGENT;
        addIntPoint( /*toClassify=*/false);
      }
    }
  }
  //================================================================================
  /*
   * Intersect a line with a non-analytical surface
   */
  void FaceLineIntersector::IntersectWithSurface (const GridLine& gridLine)
  {
    _surfaceInt->Perform( gridLine._line, 0.0, gridLine._length );
    if ( !_surfaceInt->IsDone() ) return;
    for ( int i = 1; i <= _surfaceInt->NbPnt(); ++i )
    {
      _transition = Transition( _surfaceInt->Transition( i ) );
      _w = _surfaceInt->WParameter( i );
      addIntPoint(/*toClassify=*/false);
    }
  }

  //================================================================================
  /*!
   * \brief Creates topology of the hexahedron
   */
  Hexahedron::Hexahedron(const double sizeThreshold, Grid* grid)
    : _grid( grid ), _sizeThreshold(sizeThreshold)
  {
    _lineInd[0] = grid->GetLineIndexer( 0 );
    _lineInd[1] = grid->GetLineIndexer( 1 );
    _lineInd[2] = grid->GetLineIndexer( 2 );

    _polygons.reserve(100); // to avoid reallocation;

    //set nodes shift within grid->_nodes from the node 000 
    size_t dx = _grid->NodeIndexDX();
    size_t dy = _grid->NodeIndexDY();
    size_t dz = _grid->NodeIndexDZ();
    size_t i000 = 0;
    size_t i100 = i000 + dx;
    size_t i010 = i000 + dy;
    size_t i110 = i010 + dx;
    size_t i001 = i000 + dz;
    size_t i101 = i100 + dz;
    size_t i011 = i010 + dz;
    size_t i111 = i110 + dz;
    _nodeShift[ SMESH_Block::ShapeIndex( SMESH_Block::ID_V000 )] = i000;
    _nodeShift[ SMESH_Block::ShapeIndex( SMESH_Block::ID_V100 )] = i100;
    _nodeShift[ SMESH_Block::ShapeIndex( SMESH_Block::ID_V010 )] = i010;
    _nodeShift[ SMESH_Block::ShapeIndex( SMESH_Block::ID_V110 )] = i110;
    _nodeShift[ SMESH_Block::ShapeIndex( SMESH_Block::ID_V001 )] = i001;
    _nodeShift[ SMESH_Block::ShapeIndex( SMESH_Block::ID_V101 )] = i101;
    _nodeShift[ SMESH_Block::ShapeIndex( SMESH_Block::ID_V011 )] = i011;
    _nodeShift[ SMESH_Block::ShapeIndex( SMESH_Block::ID_V111 )] = i111;

    vector< int > idVec;
    // set nodes to links
    for ( int linkID = SMESH_Block::ID_Ex00; linkID <= SMESH_Block::ID_E11z; ++linkID )
    {
      SMESH_Block::GetEdgeVertexIDs( linkID, idVec );
      _Link& link = _hexLinks[ SMESH_Block::ShapeIndex( linkID )];
      link._nodes[0] = &_hexNodes[ SMESH_Block::ShapeIndex( idVec[0] )];
      link._nodes[1] = &_hexNodes[ SMESH_Block::ShapeIndex( idVec[1] )];
      link._intNodes.reserve( 10 ); // to avoid reallocation
      link._splits.reserve( 10 );
    }

    // set links to faces
    int interlace[4] = { 0, 3, 1, 2 }; // to walk by links around a face: { u0, 1v, u1, 0v }
    for ( int faceID = SMESH_Block::ID_Fxy0; faceID <= SMESH_Block::ID_F1yz; ++faceID )
    {
      SMESH_Block::GetFaceEdgesIDs( faceID, idVec );
      _Face& quad = _hexQuads[ SMESH_Block::ShapeIndex( faceID )];
      bool revFace = ( faceID == SMESH_Block::ID_Fxy0 ||
                       faceID == SMESH_Block::ID_Fx1z ||
                       faceID == SMESH_Block::ID_F0yz );
      quad._links.resize(4);
      vector<_OrientedLink>::iterator         frwLinkIt = quad._links.begin();
      vector<_OrientedLink>::reverse_iterator revLinkIt = quad._links.rbegin();
      for ( int i = 0; i < 4; ++i )
      {
        bool revLink = revFace;
        if ( i > 1 ) // to reverse u1 and v0
          revLink = !revLink;
        _OrientedLink& link = revFace ? *revLinkIt++ : *frwLinkIt++;
        link = _OrientedLink( & _hexLinks[ SMESH_Block::ShapeIndex( idVec[interlace[i]] )],
                              revLink );
      }
    }
  }
  //================================================================================
  /*!
   * \brief Initializes its data by given grid cell
   */
  void Hexahedron::Init( size_t i, size_t j, size_t k )
  {
    // set nodes of grid to nodes of the hexahedron and
    // count nodes at hexahedron corners located IN geometry
    _nbCornerNodes = _nbIntNodes = 0;
    size_t i000 = _grid->NodeIndex( i,j,k );
    for ( int iN = 0; iN < 8; ++iN )
      _nbCornerNodes += bool(( _hexNodes[iN]._node = _grid->_nodes[ i000 + _nodeShift[iN] ]));

    // set intersection nodes from GridLine's to hexahedron links
    int linkID = 0;
    _Link split;
    IntersectionPoint curIntPnt;
    size_t ijk[3] = { i, j, k };
    for ( int iDir = 0; iDir < 3; ++iDir )
    {
      _lineInd[ iDir ].SetIJK( i,j,k );
      size_t lineIndex[4] = {
        _lineInd[ iDir ].LineIndex(),
        _lineInd[ iDir ].LineIndex10(),
        _lineInd[ iDir ].LineIndex01(),
        _lineInd[ iDir ].LineIndex11()
      };
      const vector<double>& coords = _grid->_coords[ iDir ];
      double nodeParam1 = coords[ ijk[ iDir ]    ] - coords[0] + _grid->_tol;
      double nodeParam2 = coords[ ijk[ iDir ] + 1] - coords[0] - _grid->_tol;
      _sideLength[ iDir ] = nodeParam2 - nodeParam1 + 2 * _grid->_tol;      
      for ( int iL = 0; iL < 4; ++iL  )
      {
        GridLine& line = _grid->_lines[ iDir ][ lineIndex[ iL ]];
        _Link&    link = _hexLinks[ linkID++ ];
        link._intNodes.clear();
        link._splits.clear();
        split._nodes[ 0 ] = link._nodes[0];
        curIntPnt._paramOnLine = nodeParam1;
        multiset< IntersectionPoint >::const_iterator ip = line._intPoints.lower_bound( curIntPnt );
        while ( ip != line._intPoints.end() &&
                ip->_paramOnLine <= nodeParam2 &&
                ip->_node )
        {
          link._intNodes.push_back( _Node( 0, &(*ip) ));
          ++_nbIntNodes;
          ++ip;
          // create sub-links (_splits) by splitting a link with _intNodes
          if ( split._nodes[ 0 ]->Node() )
          {
            split._nodes[ 1 ] = &link._intNodes.back();
            link._splits.push_back( split );
          }
          split._nodes[ 0 ] = &link._intNodes.back();
        }
        if ( link._nodes[ 1 ]->Node() && split._nodes[ 0 ]->Node() )
        {
          split._nodes[ 1 ] = link._nodes[1];
          link._splits.push_back( split );
        }
      }
    }
  }

  //================================================================================
  /*!
   * \brief Creates mesh volumes
   */
  int Hexahedron::MakeElements(SMESH_MesherHelper& helper)
  {
    int nbAddedVols = 0;
    if ( _nbCornerNodes == 8 && _nbIntNodes == 0 )
    {
      // order of _hexNodes is defined by enum SMESH_Block::TShapeID
      helper.AddVolume( _hexNodes[0].Node(), _hexNodes[2].Node(),
                        _hexNodes[3].Node(), _hexNodes[1].Node(),
                        _hexNodes[4].Node(), _hexNodes[6].Node(),
                        _hexNodes[7].Node(), _hexNodes[5].Node() );
      return 1;
    }
    if ( _nbCornerNodes + _nbIntNodes < 4 )
      return nbAddedVols;

    _polygons.clear();

    vector<const SMDS_MeshNode* > polyhedraNodes;
    vector<int>                   quantities;

    // create polygons from quadrangles and get their nodes

    vector<_Node*> nodes;
    nodes.reserve( _nbCornerNodes + _nbIntNodes );

    _Link polyLink;
    polyLink._faces.reserve( 1 );

    for ( int iF = 0; iF < 6; ++iF )
    {
      const _Face& quad = _hexQuads[ iF ] ;

      _polygons.resize( _polygons.size() + 1 );
      _Face& polygon = _polygons.back();
      polygon._links.clear();
      polygon._polyLinks.clear(); polygon._polyLinks.reserve( 10 );

      // add splits of a link to a polygon and collect info on nodes
      //int nbIn = 0, nbOut = 0, nbCorners = 0;
      nodes.clear();
      for ( int iE = 0; iE < 4; ++iE )
      {
        int nbSpits = quad._links[ iE ].NbResultLinks();
        for ( int iS = 0; iS < nbSpits; ++iS )
        {
          _OrientedLink split = quad._links[ iE ].ResultLink( iS );
          _Node* n = split.FirstNode();
          if ( !polygon._links.empty() )
          {
            _Node* nPrev = polygon._links.back().LastNode();
            if ( nPrev != n )
            {
              polyLink._nodes[0] = nPrev;
              polyLink._nodes[1] = n;
              polygon._polyLinks.push_back( polyLink );
              polygon._links.push_back( _OrientedLink( &polygon._polyLinks.back() ));
              nodes.push_back( nPrev );
            }
          }
          polygon._links.push_back( split );
          nodes.push_back( n );

          // if ( n->IsCorner() )
          //   ++nbCorners;
          // if ( n->_intPoint )
          // {
          //   if ( n->_intPoint->_transition == Trans_IN )
          //     ++nbIn;
          //   else if ( n->_intPoint->_transition == Trans_OUT )
          //     ++nbOut;
          //   else
          //     ++nbIn, ++nbOut;
          // }
        }
      }
      if ( polygon._links.size() > 1 )
      {
        _Node* n1 = polygon._links.back().LastNode();
        _Node* n2 = polygon._links.front().FirstNode();
        if ( n1 != n2 )
        {
          polyLink._nodes[0] = n1;
          polyLink._nodes[1] = n2;
          polygon._polyLinks.push_back( polyLink );
          polygon._links.push_back( _OrientedLink( &polygon._polyLinks.back() ));
          nodes.push_back( n1 );
        }
        // add polygon to its links
        for ( size_t iL = 0; iL < polygon._links.size(); ++iL )
          polygon._links[ iL ]._link->_faces.push_back( &polygon );
        // store polygon nodes
        quantities.push_back( nodes.size() );
        for ( size_t i = 0; i < nodes.size(); ++i )
          polyhedraNodes.push_back( nodes[i]->Node() );
      }
      else
      {
        _polygons.resize( _polygons.size() - 1 );
      }
    }

    // create polygons closing holes in a polyhedron

    // find free links
    vector< _OrientedLink* > freeLinks;
    for ( size_t iP = 0; iP < _polygons.size(); ++iP )
    {
      _Face& polygon = _polygons[ iP ];
      for ( size_t iL = 0; iL < polygon._links.size(); ++iL )
        if ( polygon._links[ iL ]._link->_faces.size() < 2 )
          freeLinks.push_back( & polygon._links[ iL ]);
    }
    // make closed chains of free links
    int nbFreeLinks = freeLinks.size();
    if ( 0 < nbFreeLinks && nbFreeLinks < 3 ) return nbAddedVols;
    while ( nbFreeLinks > 0 )
    {
      nodes.clear();
      _polygons.resize( _polygons.size() + 1 );
      _Face& polygon = _polygons.back();
      polygon._links.clear();

      // get a remaining link to start from
      _OrientedLink* curLink = 0;
      for ( size_t iL = 0; iL < freeLinks.size() && !curLink; ++iL )
        if (( curLink = freeLinks[ iL ] ))
          freeLinks[ iL ] = 0;
      nodes.push_back( curLink->LastNode() );
      polygon._links.push_back( *curLink );

      // find all links connected to curLink
      _Node* curNode = 0;
      do
      {
        curNode = curLink->FirstNode();
        curLink = 0;
        for ( size_t iL = 0; iL < freeLinks.size() && !curLink; ++iL )
          if ( freeLinks[ iL ] && freeLinks[ iL ]->LastNode() == curNode )
          {
            curLink = freeLinks[ iL ];
            freeLinks[ iL ] = 0;
            nodes.push_back( curNode );
            polygon._links.push_back( *curLink );
          }
      } while ( curLink );

      nbFreeLinks -= polygon._links.size();

      if ( curNode != nodes.front() || polygon._links.size() < 3 )
        return nbAddedVols; // closed polygon not found -> invalid polyhedron

      quantities.push_back( nodes.size() );
      for ( size_t i = 0; i < nodes.size(); ++i )
        polyhedraNodes.push_back( nodes[i]->Node() );

      // add polygon to its links and reverse links
      for ( size_t i = 0; i < polygon._links.size(); ++i )
      {
        polygon._links[i].Reverse();
        polygon._links[i]._link->_faces.push_back( &polygon );
      }

      //const size_t firstPoly = _polygons.size();
    }

    if ( ! checkPolyhedronSize() )
      return nbAddedVols;

    // create a classic cell if possible
    const int nbNodes = _nbCornerNodes + _nbIntNodes;
    if (      nbNodes == 8 && _polygons.size() == 6 && addHexa ( helper ))
      ++nbAddedVols;
    else if ( nbNodes == 4 && _polygons.size() == 4 && addTetra( helper ))
      ++nbAddedVols;
    else if ( nbNodes == 6 && _polygons.size() == 5 && addPenta( helper ))
      ++nbAddedVols;
    else if ( nbNodes == 5 && _polygons.size() == 5 && addPyra ( helper ))
      ++nbAddedVols;
    else
    {
      ++nbAddedVols;
      helper.AddPolyhedralVolume( polyhedraNodes, quantities );
    }
    return nbAddedVols;
  }

  //================================================================================
  /*!
   * \brief Return true if a polyhedron passes _sizeThreshold criterion
   */
  bool Hexahedron::checkPolyhedronSize() const
  {
    double volume = 0;
    for ( size_t iP = 0; iP < _polygons.size(); ++iP )
    {
      const _Face& polygon = _polygons[iP];
      gp_XYZ area (0,0,0);
      SMESH_TNodeXYZ p1 ( polygon._links[ 0 ].FirstNode()->Node() );
      for ( size_t iL = 0; iL < polygon._links.size(); ++iL )
      {
        SMESH_TNodeXYZ p2 ( polygon._links[ iL ].LastNode()->Node() );
        area += p1 ^ p2;
        p1 = p2;
      }
      volume += p1 * area;
    }
    volume /= 6;

    double initVolume = _sideLength[0] * _sideLength[1] * _sideLength[2];

    return volume > initVolume / _sizeThreshold;
  }
  //================================================================================
  /*!
   * \brief Tries to create a hexahedron
   */
  bool Hexahedron::addHexa(SMESH_MesherHelper& helper)
  {
    if ( _polygons[0]._links.size() != 4 ||
         _polygons[1]._links.size() != 4 ||
         _polygons[2]._links.size() != 4 ||
         _polygons[3]._links.size() != 4 ||
         _polygons[4]._links.size() != 4 ||
         _polygons[5]._links.size() != 4   )
      return false;
    const SMDS_MeshNode* nodes[8];
    int nbN = 0;
    for ( int iL = 0; iL < 4; ++iL )
    {
      // a base node
      nodes[iL] = _polygons[0]._links[iL].FirstNode()->Node();
      ++nbN;

      // find a top node above the base node
      _Link* link = _polygons[0]._links[iL]._link;
      ASSERT( link->_faces.size() > 1 );
      // a quadrangle sharing <link> with _polygons[0]
      _Face* quad = link->_faces[ bool( link->_faces[0] == & _polygons[0] )];
      for ( int i = 0; i < 4; ++i )
        if ( quad->_links[i]._link == link )
        {
          // 1st node of a link opposite to <link> in <quad>
          nodes[iL+4] = quad->_links[(i+2)%4].FirstNode()->Node();
          ++nbN;
          break;
        }
    }
    if ( nbN == 8 )
      helper.AddVolume( nodes[0],nodes[1],nodes[2],nodes[3],
                        nodes[4],nodes[5],nodes[6],nodes[7] );
    return ( nbN == 8 );
  }
  //================================================================================
  /*!
   * \brief Tries to create a tetrahedron
   */
  bool Hexahedron::addTetra(SMESH_MesherHelper& helper)
  {
    const SMDS_MeshNode* nodes[4];
    nodes[0] = _polygons[0]._links[0].FirstNode()->Node();
    nodes[1] = _polygons[0]._links[1].FirstNode()->Node();
    nodes[2] = _polygons[0]._links[2].FirstNode()->Node();

    _Link* link = _polygons[0]._links[0]._link;
    ASSERT( link->_faces.size() > 1 );

    // a triangle sharing <link> with _polygons[0]
    _Face* tria = link->_faces[ bool( link->_faces[0] == & _polygons[0] )];
    for ( int i = 0; i < 3; ++i )
      if ( tria->_links[i]._link == link )
      {
        nodes[3] = tria->_links[(i+1)%3].LastNode()->Node();
        helper.AddVolume( nodes[0],nodes[1],nodes[2],nodes[3] );
        return true;
      }

    return false;
  }
  //================================================================================
  /*!
   * \brief Tries to create a pentahedron
   */
  bool Hexahedron::addPenta(SMESH_MesherHelper& helper)
  {
    // find a base triangular face
    int iTri = -1;
    for ( int iF = 0; iF < 5 && iTri < 0; ++iF )
      if ( _polygons[ iF ]._links.size() == 3 )
        iTri = iF;
    if ( iTri < 0 ) return false;

    // find nodes
    const SMDS_MeshNode* nodes[6];
    int nbN = 0;
    for ( int iL = 0; iL < 3; ++iL )
    {
      // a base node
      nodes[iL] = _polygons[ iTri ]._links[iL].FirstNode()->Node();
      ++nbN;

      // find a top node above the base node
      _Link* link = _polygons[ iTri ]._links[iL]._link;
      ASSERT( link->_faces.size() > 1 );
      // a quadrangle sharing <link> with a base triangle
      _Face* quad = link->_faces[ bool( link->_faces[0] == & _polygons[ iTri ] )];
      if ( quad->_links.size() != 4 ) return false;
      for ( int i = 0; i < 4; ++i )
        if ( quad->_links[i]._link == link )
        {
          // 1st node of a link opposite to <link> in <quad>
          nodes[iL+3] = quad->_links[(i+2)%4].FirstNode()->Node();
          ++nbN;
          break;
        }
    }
    if ( nbN == 6 )
      helper.AddVolume( nodes[0],nodes[1],nodes[2],nodes[3], nodes[4],nodes[5] );

    return ( nbN == 6 );
  }
  //================================================================================
  /*!
   * \brief Tries to create a pyramid
   */
  bool Hexahedron::addPyra(SMESH_MesherHelper& helper)
  {
    // find a base quadrangle
    int iQuad = -1;
    for ( int iF = 0; iF < 5 && iQuad < 0; ++iF )
      if ( _polygons[ iF ]._links.size() == 4 )
        iQuad = iF;
    if ( iQuad < 0 ) return false;

    // find nodes
    const SMDS_MeshNode* nodes[5];
    nodes[0] = _polygons[iQuad]._links[0].FirstNode()->Node();
    nodes[1] = _polygons[iQuad]._links[1].FirstNode()->Node();
    nodes[2] = _polygons[iQuad]._links[2].FirstNode()->Node();
    nodes[3] = _polygons[iQuad]._links[3].FirstNode()->Node();

    _Link* link = _polygons[iQuad]._links[0]._link;
    ASSERT( link->_faces.size() > 1 );

    // a triangle sharing <link> with a base quadrangle
    _Face* tria = link->_faces[ bool( link->_faces[0] == & _polygons[ iQuad ] )];
    if ( tria->_links.size() != 3 ) return false;
    for ( int i = 0; i < 3; ++i )
      if ( tria->_links[i]._link == link )
      {
        nodes[4] = tria->_links[(i+1)%3].LastNode()->Node();
        helper.AddVolume( nodes[0],nodes[1],nodes[2],nodes[3],nodes[4] );
        return true;
      }

    return false;
  }

} // namespace

//=============================================================================
/*!
 * \brief Generates 3D structured Cartesian mesh in the internal part of
 * solid shapes and polyhedral volumes near the shape boundary.
 *  \param theMesh - mesh to fill in
 *  \param theShape - a compound of all SOLIDs to mesh
 *  \retval bool - true in case of success
 */
//=============================================================================

bool StdMeshers_Cartesian_3D::Compute(SMESH_Mesh &         theMesh,
                                      const TopoDS_Shape & theShape)
{
  // The algorithm generates the mesh in following steps:

  // 1) Intersection of grid lines with the geometry boundary.
  // This step allows to find out if a given node of the initial grid is
  // inside or outside the geometry.

  // 2) For each cell of the grid, check how many of it's nodes are outside
  // of the geometry boundary. Depending on a result of this check
  // - skip a cell, if all it's nodes are outside
  // - skip a cell, if it is too small according to the size threshold
  // - add a hexahedron in the mesh, if all nodes are inside
  // - add a polyhedron in the mesh, if some nodes are inside and some outside

  try {
    Grid grid;

    TopTools_MapOfShape faceMap;
    for ( TopExp_Explorer fExp( theShape, TopAbs_FACE ); fExp.More(); fExp.Next() )
      if ( !faceMap.Add( fExp.Current() ))
        faceMap.Remove( fExp.Current() ); // remove a face shared by two solids

    Bnd_Box shapeBox;
    vector<FaceGridIntersector> facesItersectors( faceMap.Extent() );
    TopTools_MapIteratorOfMapOfShape faceMppIt( faceMap );
    for ( int i = 0; faceMppIt.More(); faceMppIt.Next(), ++i )
    {
      facesItersectors[i]._face = TopoDS::Face( faceMppIt.Key() );
      facesItersectors[i]._grid = &grid;
      shapeBox.Add( facesItersectors[i].GetFaceBndBox() );
    }

    vector<double> xCoords, yCoords, zCoords;
    _hyp->GetCoordinates( xCoords, yCoords, zCoords, shapeBox );

    grid.SetCoordinates( xCoords, yCoords, zCoords, theShape );

    // check if the grid encloses the shape
    if ( !_hyp->IsGridBySpacing(0) ||
         !_hyp->IsGridBySpacing(1) ||
         !_hyp->IsGridBySpacing(2) )
    {
      Bnd_Box gridBox;
      gridBox.Add( gp_Pnt( xCoords[0], yCoords[0], zCoords[0] ));
      gridBox.Add( gp_Pnt( xCoords.back(), yCoords.back(), zCoords.back() ));
      double x0,y0,z0, x1,y1,z1;
      shapeBox.Get(x0,y0,z0, x1,y1,z1);
      if ( gridBox.IsOut( gp_Pnt( x0,y0,z0 )) ||
           gridBox.IsOut( gp_Pnt( x1,y1,z1 )))
        for ( size_t i = 0; i < facesItersectors.size(); ++i )
          if ( !facesItersectors[i].IsInGrid( gridBox ))
            return error("The grid doesn't enclose the geometry");
    }

    // Intersection of grid lines with the geometry boundary.
#ifdef WITH_TBB
    tbb::parallel_for ( tbb::blocked_range<size_t>( 0, facesItersectors.size() ),
                        ParallelIntersector( facesItersectors ),
                        tbb::simple_partitioner());
#else
    for ( size_t i = 0; i < facesItersectors.size(); ++i )
      facesItersectors[i].Intersect();
#endif

    // put interesection points onto the GridLine's; this is done after intersection
    // to avoid contention of facesItersectors for writing into the same GridLine
    // in case of parallel work of facesItersectors
    for ( size_t i = 0; i < facesItersectors.size(); ++i )
      facesItersectors[i].StoreIntersections();

    SMESH_MesherHelper helper( theMesh );
    TopExp_Explorer solidExp (theShape, TopAbs_SOLID);
    helper.SetSubShape( solidExp.Current() );
    helper.SetElementsOnShape( true );

    // create nodes on the geometry
    grid.ComputeNodes(helper);

    Hexahedron hex( _hyp->GetSizeThreshold(), &grid );
    int nbAdded = 0;
    for ( size_t k = 1; k < zCoords.size(); ++k )
      for ( size_t j = 1; j < yCoords.size(); ++j )
        for ( size_t i = 1; i < xCoords.size(); ++i )
        {
          hex.Init( i-1, j-1, k-1 );
          nbAdded += hex.MakeElements( helper );
        }

    SMESHDS_Mesh* meshDS = theMesh.GetMeshDS();
    if ( nbAdded > 0 )
    {
      // make all SOLIDS computed
      if ( SMESHDS_SubMesh* sm1 = meshDS->MeshElements( solidExp.Current()) )
      {
        SMDS_ElemIteratorPtr volIt = sm1->GetElements();
        for ( ; solidExp.More() && volIt->more(); solidExp.Next() )
        {
          const SMDS_MeshElement* vol = volIt->next();
          sm1->RemoveElement( vol, /*isElemDeleted=*/false );
          meshDS->SetMeshElementOnShape( vol, solidExp.Current() );
        }
      }
      // make other sub-shapes computed
      setSubmeshesComputed( theMesh, theShape );
      return true;
    }

    // remove free nodes
    if ( SMESHDS_SubMesh * smDS = meshDS->MeshElements( helper.GetSubShapeID() ))
    {
      // grid nodes
      for ( size_t i = 0; i < grid._nodes.size(); ++i )
        if ( grid._nodes[i] && grid._nodes[i]->NbInverseElements() == 0 )
          meshDS->RemoveFreeNode( grid._nodes[i], smDS, /*fromGroups=*/false );

      // intersection nodes
      for ( int iDir = 0; iDir < 3; ++iDir )
      {
        vector< GridLine >& lines = grid._lines[ iDir ];
        for ( size_t i = 0; i < lines.size(); ++i )
        {
          multiset< IntersectionPoint >::iterator ip = lines[i]._intPoints.begin();
          for ( ; ip != lines[i]._intPoints.end(); ++ip )
            if ( ip->_node && ip->_node->NbInverseElements() == 0 )
              meshDS->RemoveFreeNode( grid._nodes[i], smDS, /*fromGroups=*/false );
        }
      }
    }

    // TODO: evalute time

  }
  // SMESH_ComputeError is not caught at SMESH_submesh level for an unknown reason
  catch ( SMESH_ComputeError& e)
  {
    return error( SMESH_ComputeErrorPtr( new SMESH_ComputeError( e )));
  }
  return false;
}

//=============================================================================
/*!
 *  Evaluate
 */
//=============================================================================

bool StdMeshers_Cartesian_3D::Evaluate(SMESH_Mesh &         theMesh,
                                       const TopoDS_Shape & theShape,
                                       MapShapeNbElems&     theResMap)
{
  // TODO
//   std::vector<int> aResVec(SMDSEntity_Last);
//   for(int i=SMDSEntity_Node; i<SMDSEntity_Last; i++) aResVec[i] = 0;
//   if(IsQuadratic) {
//     aResVec[SMDSEntity_Quad_Cartesian] = nb2d_face0 * ( nb2d/nb1d );
//     int nb1d_face0_int = ( nb2d_face0*4 - nb1d ) / 2;
//     aResVec[SMDSEntity_Node] = nb0d_face0 * ( 2*nb2d/nb1d - 1 ) - nb1d_face0_int * nb2d/nb1d;
//   }
//   else {
//     aResVec[SMDSEntity_Node] = nb0d_face0 * ( nb2d/nb1d - 1 );
//     aResVec[SMDSEntity_Cartesian] = nb2d_face0 * ( nb2d/nb1d );
//   }
//   SMESH_subMesh * sm = aMesh.GetSubMesh(aShape);
//   aResMap.insert(std::make_pair(sm,aResVec));

  return true;
}

//=============================================================================
namespace
{
  /*!
   * \brief Event listener setting/unsetting _alwaysComputed flag to
   *        submeshes of inferior levels to avoid their computing
   */
  struct _EventListener : public SMESH_subMeshEventListener
  {
    string _algoName;

    _EventListener(const string& algoName):
      SMESH_subMeshEventListener(/*isDeletable=*/true), _algoName(algoName) {}

    // --------------------------------------------------------------------------------
    // setting/unsetting _alwaysComputed flag to submeshes of inferior levels
    //
    static void setAlwaysComputed( const bool     isComputed,
                                   SMESH_subMesh* subMeshOfSolid)
    {
      SMESH_subMeshIteratorPtr smIt =
        subMeshOfSolid->getDependsOnIterator(/*includeSelf=*/false, /*complexShapeFirst=*/false);
      while ( smIt->more() )
      {
        SMESH_subMesh* sm = smIt->next();
        sm->SetIsAlwaysComputed( isComputed );
      }
    }

    // --------------------------------------------------------------------------------
    // unsetting _alwaysComputed flag if "Cartesian_3D" was removed
    //
    virtual void ProcessEvent(const int          event,
                              const int          eventType,
                              SMESH_subMesh*     subMeshOfSolid,
                              SMESH_subMeshEventListenerData* data,
                              const SMESH_Hypothesis*         hyp = 0)
    {
      if ( eventType == SMESH_subMesh::COMPUTE_EVENT )
      {
        setAlwaysComputed( subMeshOfSolid->GetComputeState() == SMESH_subMesh::COMPUTE_OK,
                           subMeshOfSolid );
      }
      else
      {
        SMESH_Algo* algo3D = subMeshOfSolid->GetAlgo();
        if ( !algo3D || _algoName != algo3D->GetName() )
          setAlwaysComputed( false, subMeshOfSolid );
      }
    }

    // --------------------------------------------------------------------------------
    // set the event listener
    //
    static void SetOn( SMESH_subMesh* subMeshOfSolid, const string& algoName )
    {
      subMeshOfSolid->SetEventListener( new _EventListener( algoName ),
                                        /*data=*/0,
                                        subMeshOfSolid );
    }

  }; // struct _EventListener

} // namespace

//================================================================================
/*!
 * \brief Sets event listener to submeshes if necessary
 *  \param subMesh - submesh where algo is set
 * This method is called when a submesh gets HYP_OK algo_state.
 * After being set, event listener is notified on each event of a submesh.
 */
//================================================================================

void StdMeshers_Cartesian_3D::SetEventListener(SMESH_subMesh* subMesh)
{
  _EventListener::SetOn( subMesh, GetName() );
}

//================================================================================
/*!
 * \brief Set _alwaysComputed flag to submeshes of inferior levels to avoid their computing
 */
//================================================================================

void StdMeshers_Cartesian_3D::setSubmeshesComputed(SMESH_Mesh&         theMesh,
                                                   const TopoDS_Shape& theShape)
{
  for ( TopExp_Explorer soExp( theShape, TopAbs_SOLID ); soExp.More(); soExp.Next() )
    _EventListener::setAlwaysComputed( true, theMesh.GetSubMesh( soExp.Current() ));
}