//  SMESH SMESH : idl implementation based on 'SMESH' unit's classes
//
//  Copyright (C) 2003  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      : SMESH_MeshEditor.cxx
// Created   : Mon Apr 12 16:10:22 2004
// Author    : Edward AGAPOV (eap)


#include "SMESH_MeshEditor.hxx"

#include "SMDS_FaceOfNodes.hxx"
#include "SMDS_VolumeTool.hxx"
#include "SMDS_EdgePosition.hxx"
#include "SMDS_PolyhedralVolumeOfNodes.hxx"
#include "SMDS_FacePosition.hxx"
#include "SMDS_SpacePosition.hxx"
#include "SMDS_QuadraticFaceOfNodes.hxx"
#include "SMDS_MeshGroup.hxx"

#include "SMESHDS_Group.hxx"
#include "SMESHDS_Mesh.hxx"

#include "SMESH_subMesh.hxx"
#include "SMESH_ControlsDef.hxx"
#include "SMESH_MesherHelper.hxx"
#include "SMESH_OctreeNode.hxx"
#include "SMESH_Group.hxx"

#include "utilities.h"

#include <BRep_Tool.hxx>
#include <ElCLib.hxx>
#include <Extrema_GenExtPS.hxx>
#include <Extrema_POnSurf.hxx>
#include <Geom2d_Curve.hxx>
#include <GeomAdaptor_Surface.hxx>
#include <Geom_Curve.hxx>
#include <Geom_Surface.hxx>
#include <TColStd_ListOfInteger.hxx>
#include <TopExp.hxx>
#include <TopExp_Explorer.hxx>
#include <TopTools_ListIteratorOfListOfShape.hxx>
#include <TopTools_ListOfShape.hxx>
#include <TopoDS.hxx>
#include <TopoDS_Face.hxx>
#include <gp.hxx>
#include <gp_Ax1.hxx>
#include <gp_Dir.hxx>
#include <gp_Lin.hxx>
#include <gp_Pln.hxx>
#include <gp_Trsf.hxx>
#include <gp_Vec.hxx>
#include <gp_XY.hxx>
#include <gp_XYZ.hxx>
#include <math.h>

#include <map>
#include <set>

#define cast2Node(elem) static_cast<const SMDS_MeshNode*>( elem )

using namespace std;
using namespace SMESH::Controls;

typedef map<const SMDS_MeshElement*, list<const SMDS_MeshNode*> >    TElemOfNodeListMap;
typedef map<const SMDS_MeshElement*, list<const SMDS_MeshElement*> > TElemOfElemListMap;
//typedef map<const SMDS_MeshNode*, vector<const SMDS_MeshNode*> >     TNodeOfNodeVecMap;
//typedef TNodeOfNodeVecMap::iterator                                  TNodeOfNodeVecMapItr;
//typedef map<const SMDS_MeshElement*, vector<TNodeOfNodeVecMapItr> >  TElemOfVecOfMapNodesMap;

struct TNodeXYZ : public gp_XYZ {
  TNodeXYZ( const SMDS_MeshNode* n ):gp_XYZ( n->X(), n->Y(), n->Z() ) {}
};

typedef pair< const SMDS_MeshNode*, const SMDS_MeshNode* > NLink;

//=======================================================================
/*!
 * \brief A sorted pair of nodes
 */
//=======================================================================

struct TLink: public NLink
{
  TLink(const SMDS_MeshNode* n1, const SMDS_MeshNode* n2 ):NLink( n1, n2 )
  { if ( n1->GetID() < n2->GetID() ) std::swap( first, second ); }
  TLink(const NLink& link ):NLink( link )
  { if ( first->GetID() < second->GetID() ) std::swap( first, second ); }
};

//=======================================================================
//function : SMESH_MeshEditor
//purpose  :
//=======================================================================

SMESH_MeshEditor::SMESH_MeshEditor( SMESH_Mesh* theMesh )
  :myMesh( theMesh ) // theMesh may be NULL
{
}

//=======================================================================
/*!
 * \brief Add element
 */
//=======================================================================

SMDS_MeshElement*
SMESH_MeshEditor::AddElement(const vector<const SMDS_MeshNode*> & node,
                             const SMDSAbs_ElementType            type,
                             const bool                           isPoly,
                             const int                            ID)
{
  SMDS_MeshElement* e = 0;
  int nbnode = node.size();
  SMESHDS_Mesh* mesh = GetMeshDS();
  switch ( type ) {
  case SMDSAbs_Edge:
    if ( nbnode == 2 )
      if ( ID ) e = mesh->AddEdgeWithID(node[0], node[1], ID);
      else      e = mesh->AddEdge      (node[0], node[1] );
    else if ( nbnode == 3 )
      if ( ID ) e = mesh->AddEdgeWithID(node[0], node[1], node[2], ID);
      else      e = mesh->AddEdge      (node[0], node[1], node[2] );
    break;
  case SMDSAbs_Face:
    if ( !isPoly ) {
      if      (nbnode == 3)
        if ( ID ) e = mesh->AddFaceWithID(node[0], node[1], node[2], ID);
        else      e = mesh->AddFace      (node[0], node[1], node[2] );
      else if (nbnode == 4) 
        if ( ID ) e = mesh->AddFaceWithID(node[0], node[1], node[2], node[3], ID);
        else      e = mesh->AddFace      (node[0], node[1], node[2], node[3] );
      else if (nbnode == 6)
        if ( ID ) e = mesh->AddFaceWithID(node[0], node[1], node[2], node[3],
                                          node[4], node[5], ID);
        else      e = mesh->AddFace      (node[0], node[1], node[2], node[3],
                                          node[4], node[5] );
      else if (nbnode == 8)
        if ( ID ) e = mesh->AddFaceWithID(node[0], node[1], node[2], node[3],
                                          node[4], node[5], node[6], node[7], ID);
        else      e = mesh->AddFace      (node[0], node[1], node[2], node[3],
                                          node[4], node[5], node[6], node[7] );
    } else {
      if ( ID ) e = mesh->AddPolygonalFaceWithID(node, ID);
      else      e = mesh->AddPolygonalFace      (node    );
    }
    break;
  case SMDSAbs_Volume:
    if ( !isPoly ) {
      if      (nbnode == 4)
        if ( ID ) e = mesh->AddVolumeWithID(node[0], node[1], node[2], node[3], ID);
        else      e = mesh->AddVolume      (node[0], node[1], node[2], node[3] );
      else if (nbnode == 5)
        if ( ID ) e = mesh->AddVolumeWithID(node[0], node[1], node[2], node[3],
                                            node[4], ID);
        else      e = mesh->AddVolume      (node[0], node[1], node[2], node[3],
                                            node[4] );
      else if (nbnode == 6)
        if ( ID ) e = mesh->AddVolumeWithID(node[0], node[1], node[2], node[3],
                                            node[4], node[5], ID);
        else      e = mesh->AddVolume      (node[0], node[1], node[2], node[3],
                                            node[4], node[5] );
      else if (nbnode == 8)
        if ( ID ) e = mesh->AddVolumeWithID(node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7], ID);
        else      e = mesh->AddVolume      (node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7] );
      else if (nbnode == 10)
        if ( ID ) e = mesh->AddVolumeWithID(node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7],
                                            node[8], node[9], ID);
        else      e = mesh->AddVolume      (node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7],
                                            node[8], node[9] );
      else if (nbnode == 13)
        if ( ID ) e = mesh->AddVolumeWithID(node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7],
                                            node[8], node[9], node[10],node[11],
                                            node[12],ID);
        else      e = mesh->AddVolume      (node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7],
                                            node[8], node[9], node[10],node[11],
                                            node[12] );
      else if (nbnode == 15)
        if ( ID ) e = mesh->AddVolumeWithID(node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7],
                                            node[8], node[9], node[10],node[11],
                                            node[12],node[13],node[14],ID);
        else      e = mesh->AddVolume      (node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7],
                                            node[8], node[9], node[10],node[11],
                                            node[12],node[13],node[14] );
      else if (nbnode == 20)
        if ( ID ) e = mesh->AddVolumeWithID(node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7],
                                            node[8], node[9], node[10],node[11],
                                            node[12],node[13],node[14],node[15],
                                            node[16],node[17],node[18],node[19],ID);
        else      e = mesh->AddVolume      (node[0], node[1], node[2], node[3],
                                            node[4], node[5], node[6], node[7],
                                            node[8], node[9], node[10],node[11],
                                            node[12],node[13],node[14],node[15],
                                            node[16],node[17],node[18],node[19] );
    }
  }
  return e;
}

//=======================================================================
/*!
 * \brief Add element
 */
//=======================================================================

SMDS_MeshElement* SMESH_MeshEditor::AddElement(const vector<int> &       nodeIDs,
                                               const SMDSAbs_ElementType type,
                                               const bool                isPoly,
                                               const int                 ID)
{
  vector<const SMDS_MeshNode*> nodes;
  nodes.reserve( nodeIDs.size() );
  vector<int>::const_iterator id = nodeIDs.begin();
  while ( id != nodeIDs.end() ) {
    if ( const SMDS_MeshNode* node = GetMeshDS()->FindNode( *id++ ))
      nodes.push_back( node );
    else
      return 0;
  }
  return AddElement( nodes, type, isPoly, ID );
}

//=======================================================================
//function : Remove
//purpose  : Remove a node or an element.
//           Modify a compute state of sub-meshes which become empty
//=======================================================================

bool SMESH_MeshEditor::Remove (const list< int >& theIDs,
                               const bool         isNodes )
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  SMESHDS_Mesh* aMesh = GetMeshDS();
  set< SMESH_subMesh *> smmap;

  list<int>::const_iterator it = theIDs.begin();
  for ( ; it != theIDs.end(); it++ ) {
    const SMDS_MeshElement * elem;
    if ( isNodes )
      elem = aMesh->FindNode( *it );
    else
      elem = aMesh->FindElement( *it );
    if ( !elem )
      continue;

    // Notify VERTEX sub-meshes about modification
    if ( isNodes ) {
      const SMDS_MeshNode* node = cast2Node( elem );
      if ( node->GetPosition()->GetTypeOfPosition() == SMDS_TOP_VERTEX )
        if ( int aShapeID = node->GetPosition()->GetShapeId() )
          if ( SMESH_subMesh * sm = GetMesh()->GetSubMeshContaining( aShapeID ) )
            smmap.insert( sm );
    }
    // Find sub-meshes to notify about modification
//     SMDS_ElemIteratorPtr nodeIt = elem->nodesIterator();
//     while ( nodeIt->more() ) {
//       const SMDS_MeshNode* node = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
//       const SMDS_PositionPtr& aPosition = node->GetPosition();
//       if ( aPosition.get() ) {
//         if ( int aShapeID = aPosition->GetShapeId() ) {
//           if ( SMESH_subMesh * sm = GetMesh()->GetSubMeshContaining( aShapeID ) )
//             smmap.insert( sm );
//         }
//       }
//     }

    // Do remove
    if ( isNodes )
      aMesh->RemoveNode( static_cast< const SMDS_MeshNode* >( elem ));
    else
      aMesh->RemoveElement( elem );
  }

  // Notify sub-meshes about modification
  if ( !smmap.empty() ) {
    set< SMESH_subMesh *>::iterator smIt;
    for ( smIt = smmap.begin(); smIt != smmap.end(); smIt++ )
      (*smIt)->ComputeStateEngine( SMESH_subMesh::MESH_ENTITY_REMOVED );
  }

//   // Check if the whole mesh becomes empty
//   if ( SMESH_subMesh * sm = GetMesh()->GetSubMeshContaining( 1 ) )
//     sm->ComputeStateEngine( SMESH_subMesh::CHECK_COMPUTE_STATE );

  return true;
}

//=======================================================================
//function : FindShape
//purpose  : Return an index of the shape theElem is on
//           or zero if a shape not found
//=======================================================================

int SMESH_MeshEditor::FindShape (const SMDS_MeshElement * theElem)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  SMESHDS_Mesh * aMesh = GetMeshDS();
  if ( aMesh->ShapeToMesh().IsNull() )
    return 0;

  if ( theElem->GetType() == SMDSAbs_Node ) {
    const SMDS_PositionPtr& aPosition =
      static_cast<const SMDS_MeshNode*>( theElem )->GetPosition();
    if ( aPosition.get() )
      return aPosition->GetShapeId();
    else
      return 0;
  }

  TopoDS_Shape aShape; // the shape a node is on
  SMDS_ElemIteratorPtr nodeIt = theElem->nodesIterator();
  while ( nodeIt->more() ) {
    const SMDS_MeshNode* node = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
    const SMDS_PositionPtr& aPosition = node->GetPosition();
    if ( aPosition.get() ) {
      int aShapeID = aPosition->GetShapeId();
      SMESHDS_SubMesh * sm = aMesh->MeshElements( aShapeID );
      if ( sm ) {
        if ( sm->Contains( theElem ))
          return aShapeID;
        if ( aShape.IsNull() )
          aShape = aMesh->IndexToShape( aShapeID );
      }
      else {
        //MESSAGE ( "::FindShape() No SubShape for aShapeID " << aShapeID );
      }
    }
  }

  // None of nodes is on a proper shape,
  // find the shape among ancestors of aShape on which a node is
  if ( aShape.IsNull() ) {
    //MESSAGE ("::FindShape() - NONE node is on shape")
    return 0;
  }
  TopTools_ListIteratorOfListOfShape ancIt( GetMesh()->GetAncestors( aShape ));
  for ( ; ancIt.More(); ancIt.Next() ) {
    SMESHDS_SubMesh * sm = aMesh->MeshElements( ancIt.Value() );
    if ( sm && sm->Contains( theElem ))
      return aMesh->ShapeToIndex( ancIt.Value() );
  }

  //MESSAGE ("::FindShape() - SHAPE NOT FOUND")
  return 0;
}

//=======================================================================
//function : IsMedium
//purpose  :
//=======================================================================

bool SMESH_MeshEditor::IsMedium(const SMDS_MeshNode*      node,
                                const SMDSAbs_ElementType typeToCheck)
{
  bool isMedium = false;
  SMDS_ElemIteratorPtr it = node->GetInverseElementIterator(typeToCheck);
  while (it->more() && !isMedium ) {
    const SMDS_MeshElement* elem = it->next();
    isMedium = elem->IsMediumNode(node);
  }
  return isMedium;
}

//=======================================================================
//function : ShiftNodesQuadTria
//purpose  : auxilary
//           Shift nodes in the array corresponded to quadratic triangle
//           example: (0,1,2,3,4,5) -> (1,2,0,4,5,3)
//=======================================================================
static void ShiftNodesQuadTria(const SMDS_MeshNode* aNodes[])
{
  const SMDS_MeshNode* nd1 = aNodes[0];
  aNodes[0] = aNodes[1];
  aNodes[1] = aNodes[2];
  aNodes[2] = nd1;
  const SMDS_MeshNode* nd2 = aNodes[3];
  aNodes[3] = aNodes[4];
  aNodes[4] = aNodes[5];
  aNodes[5] = nd2;
}

//=======================================================================
//function : GetNodesFromTwoTria
//purpose  : auxilary
//           Shift nodes in the array corresponded to quadratic triangle
//           example: (0,1,2,3,4,5) -> (1,2,0,4,5,3)
//=======================================================================
static bool GetNodesFromTwoTria(const SMDS_MeshElement * theTria1,
                                const SMDS_MeshElement * theTria2,
                                const SMDS_MeshNode* N1[],
                                const SMDS_MeshNode* N2[])
{
  SMDS_ElemIteratorPtr it = theTria1->nodesIterator();
  int i=0;
  while(i<6) {
    N1[i] = static_cast<const SMDS_MeshNode*>( it->next() );
    i++;
  }
  if(it->more()) return false;
  it = theTria2->nodesIterator();
  i=0;
  while(i<6) {
    N2[i] = static_cast<const SMDS_MeshNode*>( it->next() );
    i++;
  }
  if(it->more()) return false;

  int sames[3] = {-1,-1,-1};
  int nbsames = 0;
  int j;
  for(i=0; i<3; i++) {
    for(j=0; j<3; j++) {
      if(N1[i]==N2[j]) {
        sames[i] = j;
        nbsames++;
        break;
      }
    }
  }
  if(nbsames!=2) return false;
  if(sames[0]>-1) {
    ShiftNodesQuadTria(N1);
    if(sames[1]>-1) {
      ShiftNodesQuadTria(N1);
    }
  }
  i = sames[0] + sames[1] + sames[2];
  for(; i<2; i++) {
    ShiftNodesQuadTria(N2);
  }
  // now we receive following N1 and N2 (using numeration as above image)
  // tria1 : (1 2 4 5 9 7)  and  tria2 : (3 4 2 8 9 6)
  // i.e. first nodes from both arrays determ new diagonal
  return true;
}

//=======================================================================
//function : InverseDiag
//purpose  : Replace two neighbour triangles with ones built on the same 4 nodes
//           but having other common link.
//           Return False if args are improper
//=======================================================================

bool SMESH_MeshEditor::InverseDiag (const SMDS_MeshElement * theTria1,
                                    const SMDS_MeshElement * theTria2 )
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  if (!theTria1 || !theTria2)
    return false;

  const SMDS_FaceOfNodes* F1 = dynamic_cast<const SMDS_FaceOfNodes*>( theTria1 );
  const SMDS_FaceOfNodes* F2 = dynamic_cast<const SMDS_FaceOfNodes*>( theTria2 );
  if (F1 && F2) {

    //  1 +--+ A  theTria1: ( 1 A B ) A->2 ( 1 2 B ) 1 +--+ A
    //    | /|    theTria2: ( B A 2 ) B->1 ( 1 A 2 )   |\ |
    //    |/ |                                         | \|
    //  B +--+ 2                                     B +--+ 2

    // put nodes in array and find out indices of the same ones
    const SMDS_MeshNode* aNodes [6];
    int sameInd [] = { 0, 0, 0, 0, 0, 0 };
    int i = 0;
    SMDS_ElemIteratorPtr it = theTria1->nodesIterator();
    while ( it->more() ) {
      aNodes[ i ] = static_cast<const SMDS_MeshNode*>( it->next() );

      if ( i > 2 ) // theTria2
        // find same node of theTria1
        for ( int j = 0; j < 3; j++ )
          if ( aNodes[ i ] == aNodes[ j ]) {
            sameInd[ j ] = i;
            sameInd[ i ] = j;
            break;
          }
      // next
      i++;
      if ( i == 3 ) {
        if ( it->more() )
          return false; // theTria1 is not a triangle
        it = theTria2->nodesIterator();
      }
      if ( i == 6 && it->more() )
        return false; // theTria2 is not a triangle
    }

    // find indices of 1,2 and of A,B in theTria1
    int iA = 0, iB = 0, i1 = 0, i2 = 0;
    for ( i = 0; i < 6; i++ ) {
      if ( sameInd [ i ] == 0 )
        if ( i < 3 ) i1 = i;
        else         i2 = i;
      else if (i < 3)
        if ( iA ) iB = i;
        else      iA = i;
    }
    // nodes 1 and 2 should not be the same
    if ( aNodes[ i1 ] == aNodes[ i2 ] )
      return false;

    // theTria1: A->2
    aNodes[ iA ] = aNodes[ i2 ];
    // theTria2: B->1
    aNodes[ sameInd[ iB ]] = aNodes[ i1 ];

    //MESSAGE( theTria1 << theTria2 );

    GetMeshDS()->ChangeElementNodes( theTria1, aNodes, 3 );
    GetMeshDS()->ChangeElementNodes( theTria2, &aNodes[ 3 ], 3 );

    //MESSAGE( theTria1 << theTria2 );

    return true;

  } // end if(F1 && F2)

  // check case of quadratic faces
  const SMDS_QuadraticFaceOfNodes* QF1 =
    dynamic_cast<const SMDS_QuadraticFaceOfNodes*> (theTria1);
  if(!QF1) return false;
  const SMDS_QuadraticFaceOfNodes* QF2 =
    dynamic_cast<const SMDS_QuadraticFaceOfNodes*> (theTria2);
  if(!QF2) return false;

  //       5
  //  1 +--+--+ 2  theTria1: (1 2 4 5 9 7) or (2 4 1 9 7 5) or (4 1 2 7 5 9)
  //    |    /|    theTria2: (2 3 4 6 8 9) or (3 4 2 8 9 6) or (4 2 3 9 6 8)
  //    |   / |
  //  7 +  +  + 6
  //    | /9  |
  //    |/    |
  //  4 +--+--+ 3
  //       8

  const SMDS_MeshNode* N1 [6];
  const SMDS_MeshNode* N2 [6];
  if(!GetNodesFromTwoTria(theTria1,theTria2,N1,N2))
    return false;
  // now we receive following N1 and N2 (using numeration as above image)
  // tria1 : (1 2 4 5 9 7)  and  tria2 : (3 4 2 8 9 6)
  // i.e. first nodes from both arrays determ new diagonal

  const SMDS_MeshNode* N1new [6];
  const SMDS_MeshNode* N2new [6];
  N1new[0] = N1[0];
  N1new[1] = N2[0];
  N1new[2] = N2[1];
  N1new[3] = N1[4];
  N1new[4] = N2[3];
  N1new[5] = N1[5];
  N2new[0] = N1[0];
  N2new[1] = N1[1];
  N2new[2] = N2[0];
  N2new[3] = N1[3];
  N2new[4] = N2[5];
  N2new[5] = N1[4];
  // replaces nodes in faces
  GetMeshDS()->ChangeElementNodes( theTria1, N1new, 6 );
  GetMeshDS()->ChangeElementNodes( theTria2, N2new, 6 );

  return true;
}

//=======================================================================
//function : findTriangles
//purpose  : find triangles sharing theNode1-theNode2 link
//=======================================================================

static bool findTriangles(const SMDS_MeshNode *    theNode1,
                          const SMDS_MeshNode *    theNode2,
                          const SMDS_MeshElement*& theTria1,
                          const SMDS_MeshElement*& theTria2)
{
  if ( !theNode1 || !theNode2 ) return false;

  theTria1 = theTria2 = 0;

  set< const SMDS_MeshElement* > emap;
  SMDS_ElemIteratorPtr it = theNode1->GetInverseElementIterator(SMDSAbs_Face);
  while (it->more()) {
    const SMDS_MeshElement* elem = it->next();
    if ( elem->NbNodes() == 3 )
      emap.insert( elem );
  }
  it = theNode2->GetInverseElementIterator(SMDSAbs_Face);
  while (it->more()) {
    const SMDS_MeshElement* elem = it->next();
    if ( emap.find( elem ) != emap.end() )
      if ( theTria1 ) {
        // theTria1 must be element with minimum ID
        if( theTria1->GetID() < elem->GetID() ) {
          theTria2 = elem;
        }
        else {
          theTria2 = theTria1;
          theTria1 = elem;
        }
        break;
      }
      else {
        theTria1 = elem;
      }
  }
  return ( theTria1 && theTria2 );
}

//=======================================================================
//function : InverseDiag
//purpose  : Replace two neighbour triangles sharing theNode1-theNode2 link
//           with ones built on the same 4 nodes but having other common link.
//           Return false if proper faces not found
//=======================================================================

bool SMESH_MeshEditor::InverseDiag (const SMDS_MeshNode * theNode1,
                                    const SMDS_MeshNode * theNode2)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  MESSAGE( "::InverseDiag()" );

  const SMDS_MeshElement *tr1, *tr2;
  if ( !findTriangles( theNode1, theNode2, tr1, tr2 ))
    return false;

  const SMDS_FaceOfNodes* F1 = dynamic_cast<const SMDS_FaceOfNodes*>( tr1 );
  //if (!F1) return false;
  const SMDS_FaceOfNodes* F2 = dynamic_cast<const SMDS_FaceOfNodes*>( tr2 );
  //if (!F2) return false;
  if (F1 && F2) {

    //  1 +--+ A  tr1: ( 1 A B ) A->2 ( 1 2 B ) 1 +--+ A
    //    | /|    tr2: ( B A 2 ) B->1 ( 1 A 2 )   |\ |
    //    |/ |                                    | \|
    //  B +--+ 2                                B +--+ 2

    // put nodes in array
    // and find indices of 1,2 and of A in tr1 and of B in tr2
    int i, iA1 = 0, i1 = 0;
    const SMDS_MeshNode* aNodes1 [3];
    SMDS_ElemIteratorPtr it;
    for (i = 0, it = tr1->nodesIterator(); it->more(); i++ ) {
      aNodes1[ i ] = static_cast<const SMDS_MeshNode*>( it->next() );
      if ( aNodes1[ i ] == theNode1 )
        iA1 = i; // node A in tr1
      else if ( aNodes1[ i ] != theNode2 )
        i1 = i;  // node 1
    }
    int iB2 = 0, i2 = 0;
    const SMDS_MeshNode* aNodes2 [3];
    for (i = 0, it = tr2->nodesIterator(); it->more(); i++ ) {
      aNodes2[ i ] = static_cast<const SMDS_MeshNode*>( it->next() );
      if ( aNodes2[ i ] == theNode2 )
        iB2 = i; // node B in tr2
      else if ( aNodes2[ i ] != theNode1 )
        i2 = i;  // node 2
    }

    // nodes 1 and 2 should not be the same
    if ( aNodes1[ i1 ] == aNodes2[ i2 ] )
      return false;

    // tr1: A->2
    aNodes1[ iA1 ] = aNodes2[ i2 ];
    // tr2: B->1
    aNodes2[ iB2 ] = aNodes1[ i1 ];

    //MESSAGE( tr1 << tr2 );

    GetMeshDS()->ChangeElementNodes( tr1, aNodes1, 3 );
    GetMeshDS()->ChangeElementNodes( tr2, aNodes2, 3 );

    //MESSAGE( tr1 << tr2 );

    return true;
  }

  // check case of quadratic faces
  const SMDS_QuadraticFaceOfNodes* QF1 =
    dynamic_cast<const SMDS_QuadraticFaceOfNodes*> (tr1);
  if(!QF1) return false;
  const SMDS_QuadraticFaceOfNodes* QF2 =
    dynamic_cast<const SMDS_QuadraticFaceOfNodes*> (tr2);
  if(!QF2) return false;
  return InverseDiag(tr1,tr2);
}

//=======================================================================
//function : getQuadrangleNodes
//purpose  : fill theQuadNodes - nodes of a quadrangle resulting from
//           fusion of triangles tr1 and tr2 having shared link on
//           theNode1 and theNode2
//=======================================================================

bool getQuadrangleNodes(const SMDS_MeshNode *    theQuadNodes [],
                        const SMDS_MeshNode *    theNode1,
                        const SMDS_MeshNode *    theNode2,
                        const SMDS_MeshElement * tr1,
                        const SMDS_MeshElement * tr2 )
{
  if( tr1->NbNodes() != tr2->NbNodes() )
    return false;
  // find the 4-th node to insert into tr1
  const SMDS_MeshNode* n4 = 0;
  SMDS_ElemIteratorPtr it = tr2->nodesIterator();
  int i=0;
  while ( !n4 && i<3 ) {
    const SMDS_MeshNode * n = cast2Node( it->next() );
    i++;
    bool isDiag = ( n == theNode1 || n == theNode2 );
    if ( !isDiag )
      n4 = n;
  }
  // Make an array of nodes to be in a quadrangle
  int iNode = 0, iFirstDiag = -1;
  it = tr1->nodesIterator();
  i=0;
  while ( i<3 ) {
    const SMDS_MeshNode * n = cast2Node( it->next() );
    i++;
    bool isDiag = ( n == theNode1 || n == theNode2 );
    if ( isDiag ) {
      if ( iFirstDiag < 0 )
        iFirstDiag = iNode;
      else if ( iNode - iFirstDiag == 1 )
        theQuadNodes[ iNode++ ] = n4; // insert the 4-th node between diagonal nodes
    }
    else if ( n == n4 ) {
      return false; // tr1 and tr2 should not have all the same nodes
    }
    theQuadNodes[ iNode++ ] = n;
  }
  if ( iNode == 3 ) // diagonal nodes have 0 and 2 indices
    theQuadNodes[ iNode ] = n4;

  return true;
}

//=======================================================================
//function : DeleteDiag
//purpose  : Replace two neighbour triangles sharing theNode1-theNode2 link
//           with a quadrangle built on the same 4 nodes.
//           Return false if proper faces not found
//=======================================================================

bool SMESH_MeshEditor::DeleteDiag (const SMDS_MeshNode * theNode1,
                                   const SMDS_MeshNode * theNode2)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  MESSAGE( "::DeleteDiag()" );

  const SMDS_MeshElement *tr1, *tr2;
  if ( !findTriangles( theNode1, theNode2, tr1, tr2 ))
    return false;

  const SMDS_FaceOfNodes* F1 = dynamic_cast<const SMDS_FaceOfNodes*>( tr1 );
  //if (!F1) return false;
  const SMDS_FaceOfNodes* F2 = dynamic_cast<const SMDS_FaceOfNodes*>( tr2 );
  //if (!F2) return false;
  if (F1 && F2) {

    const SMDS_MeshNode* aNodes [ 4 ];
    if ( ! getQuadrangleNodes( aNodes, theNode1, theNode2, tr1, tr2 ))
      return false;

    //MESSAGE( endl << tr1 << tr2 );

    GetMeshDS()->ChangeElementNodes( tr1, aNodes, 4 );
    myLastCreatedElems.Append(tr1);
    GetMeshDS()->RemoveElement( tr2 );

    //MESSAGE( endl << tr1 );

    return true;
  }

  // check case of quadratic faces
  const SMDS_QuadraticFaceOfNodes* QF1 =
    dynamic_cast<const SMDS_QuadraticFaceOfNodes*> (tr1);
  if(!QF1) return false;
  const SMDS_QuadraticFaceOfNodes* QF2 =
    dynamic_cast<const SMDS_QuadraticFaceOfNodes*> (tr2);
  if(!QF2) return false;

  //       5
  //  1 +--+--+ 2  tr1: (1 2 4 5 9 7) or (2 4 1 9 7 5) or (4 1 2 7 5 9)
  //    |    /|    tr2: (2 3 4 6 8 9) or (3 4 2 8 9 6) or (4 2 3 9 6 8)
  //    |   / |
  //  7 +  +  + 6
  //    | /9  |
  //    |/    |
  //  4 +--+--+ 3
  //       8

  const SMDS_MeshNode* N1 [6];
  const SMDS_MeshNode* N2 [6];
  if(!GetNodesFromTwoTria(tr1,tr2,N1,N2))
    return false;
  // now we receive following N1 and N2 (using numeration as above image)
  // tria1 : (1 2 4 5 9 7)  and  tria2 : (3 4 2 8 9 6)
  // i.e. first nodes from both arrays determ new diagonal

  const SMDS_MeshNode* aNodes[8];
  aNodes[0] = N1[0];
  aNodes[1] = N1[1];
  aNodes[2] = N2[0];
  aNodes[3] = N2[1];
  aNodes[4] = N1[3];
  aNodes[5] = N2[5];
  aNodes[6] = N2[3];
  aNodes[7] = N1[5];

  GetMeshDS()->ChangeElementNodes( tr1, aNodes, 8 );
  myLastCreatedElems.Append(tr1);
  GetMeshDS()->RemoveElement( tr2 );

  // remove middle node (9)
  GetMeshDS()->RemoveNode( N1[4] );

  return true;
}

//=======================================================================
//function : Reorient
//purpose  : Reverse theElement orientation
//=======================================================================

bool SMESH_MeshEditor::Reorient (const SMDS_MeshElement * theElem)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  if (!theElem)
    return false;
  SMDS_ElemIteratorPtr it = theElem->nodesIterator();
  if ( !it || !it->more() )
    return false;

  switch ( theElem->GetType() ) {

  case SMDSAbs_Edge:
  case SMDSAbs_Face: {
    if(!theElem->IsQuadratic()) {
      int i = theElem->NbNodes();
      vector<const SMDS_MeshNode*> aNodes( i );
      while ( it->more() )
        aNodes[ --i ]= static_cast<const SMDS_MeshNode*>( it->next() );
      return GetMeshDS()->ChangeElementNodes( theElem, &aNodes[0], theElem->NbNodes() );
    }
    else {
      // quadratic elements
      if(theElem->GetType()==SMDSAbs_Edge) {
        vector<const SMDS_MeshNode*> aNodes(3);
        aNodes[1]= static_cast<const SMDS_MeshNode*>( it->next() );
        aNodes[0]= static_cast<const SMDS_MeshNode*>( it->next() );
        aNodes[2]= static_cast<const SMDS_MeshNode*>( it->next() );
        return GetMeshDS()->ChangeElementNodes( theElem, &aNodes[0], 3 );
      }
      else {
        int nbn = theElem->NbNodes();
        vector<const SMDS_MeshNode*> aNodes(nbn);
        aNodes[0]= static_cast<const SMDS_MeshNode*>( it->next() );
        int i=1;
        for(; i<nbn/2; i++) {
          aNodes[nbn/2-i]= static_cast<const SMDS_MeshNode*>( it->next() );
        }
        for(i=0; i<nbn/2; i++) {
          aNodes[nbn-i-1]= static_cast<const SMDS_MeshNode*>( it->next() );
        }
        return GetMeshDS()->ChangeElementNodes( theElem, &aNodes[0], nbn );
      }
    }
  }
  case SMDSAbs_Volume: {
    if (theElem->IsPoly()) {
      const SMDS_PolyhedralVolumeOfNodes* aPolyedre =
        static_cast<const SMDS_PolyhedralVolumeOfNodes*>( theElem );
      if (!aPolyedre) {
        MESSAGE("Warning: bad volumic element");
        return false;
      }

      int nbFaces = aPolyedre->NbFaces();
      vector<const SMDS_MeshNode *> poly_nodes;
      vector<int> quantities (nbFaces);

      // reverse each face of the polyedre
      for (int iface = 1; iface <= nbFaces; iface++) {
        int inode, nbFaceNodes = aPolyedre->NbFaceNodes(iface);
        quantities[iface - 1] = nbFaceNodes;

        for (inode = nbFaceNodes; inode >= 1; inode--) {
          const SMDS_MeshNode* curNode = aPolyedre->GetFaceNode(iface, inode);
          poly_nodes.push_back(curNode);
        }
      }

      return GetMeshDS()->ChangePolyhedronNodes( theElem, poly_nodes, quantities );

    }
    else {
      SMDS_VolumeTool vTool;
      if ( !vTool.Set( theElem ))
        return false;
      vTool.Inverse();
      return GetMeshDS()->ChangeElementNodes( theElem, vTool.GetNodes(), vTool.NbNodes() );
    }
  }
  default:;
  }

  return false;
}

//=======================================================================
//function : getBadRate
//purpose  :
//=======================================================================

static double getBadRate (const SMDS_MeshElement*               theElem,
                          SMESH::Controls::NumericalFunctorPtr& theCrit)
{
  SMESH::Controls::TSequenceOfXYZ P;
  if ( !theElem || !theCrit->GetPoints( theElem, P ))
    return 1e100;
  return theCrit->GetBadRate( theCrit->GetValue( P ), theElem->NbNodes() );
  //return theCrit->GetBadRate( theCrit->GetValue( theElem->GetID() ), theElem->NbNodes() );
}

//=======================================================================
//function : QuadToTri
//purpose  : Cut quadrangles into triangles.
//           theCrit is used to select a diagonal to cut
//=======================================================================

bool SMESH_MeshEditor::QuadToTri (TIDSortedElemSet &                   theElems,
                                  SMESH::Controls::NumericalFunctorPtr theCrit)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  MESSAGE( "::QuadToTri()" );

  if ( !theCrit.get() )
    return false;

  SMESHDS_Mesh * aMesh = GetMeshDS();

  Handle(Geom_Surface) surface;
  SMESH_MesherHelper   helper( *GetMesh() );

  TIDSortedElemSet::iterator itElem;
  for ( itElem = theElems.begin(); itElem != theElems.end(); itElem++ ) {
    const SMDS_MeshElement* elem = *itElem;
    if ( !elem || elem->GetType() != SMDSAbs_Face )
      continue;
    if ( elem->NbNodes() != ( elem->IsQuadratic() ? 8 : 4 ))
      continue;

    // retrieve element nodes
    const SMDS_MeshNode* aNodes [8];
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    int i = 0;
    while ( itN->more() )
      aNodes[ i++ ] = static_cast<const SMDS_MeshNode*>( itN->next() );

    // compare two sets of possible triangles
    double aBadRate1, aBadRate2; // to what extent a set is bad
    SMDS_FaceOfNodes tr1 ( aNodes[0], aNodes[1], aNodes[2] );
    SMDS_FaceOfNodes tr2 ( aNodes[2], aNodes[3], aNodes[0] );
    aBadRate1 = getBadRate( &tr1, theCrit ) + getBadRate( &tr2, theCrit );

    SMDS_FaceOfNodes tr3 ( aNodes[1], aNodes[2], aNodes[3] );
    SMDS_FaceOfNodes tr4 ( aNodes[3], aNodes[0], aNodes[1] );
    aBadRate2 = getBadRate( &tr3, theCrit ) + getBadRate( &tr4, theCrit );

    int aShapeId = FindShape( elem );
    const SMDS_MeshElement* newElem = 0;

    if( !elem->IsQuadratic() ) {

      // split liner quadrangle

      if ( aBadRate1 <= aBadRate2 ) {
        // tr1 + tr2 is better
        aMesh->ChangeElementNodes( elem, aNodes, 3 );
        newElem = aMesh->AddFace( aNodes[2], aNodes[3], aNodes[0] );
      }
      else {
        // tr3 + tr4 is better
        aMesh->ChangeElementNodes( elem, &aNodes[1], 3 );
        newElem = aMesh->AddFace( aNodes[3], aNodes[0], aNodes[1] );
      }
    }
    else {

      // split quadratic quadrangle

      // get surface elem is on
      if ( aShapeId != helper.GetSubShapeID() ) {
        surface.Nullify();
        TopoDS_Shape shape;
        if ( aShapeId > 0 )
          shape = aMesh->IndexToShape( aShapeId );
        if ( !shape.IsNull() && shape.ShapeType() == TopAbs_FACE ) {
          TopoDS_Face face = TopoDS::Face( shape );
          surface = BRep_Tool::Surface( face );
          if ( !surface.IsNull() )
            helper.SetSubShape( shape );
        }
      }
      // get elem nodes
      const SMDS_MeshNode* aNodes [8];
      const SMDS_MeshNode* inFaceNode = 0;
      SMDS_ElemIteratorPtr itN = elem->nodesIterator();
      int i = 0;
      while ( itN->more() ) {
        aNodes[ i++ ] = static_cast<const SMDS_MeshNode*>( itN->next() );
        if ( !inFaceNode && helper.GetNodeUVneedInFaceNode() &&
             aNodes[ i-1 ]->GetPosition()->GetTypeOfPosition() == SMDS_TOP_FACE )
        {
          inFaceNode = aNodes[ i-1 ];
        }
      }
      // find middle point for (0,1,2,3)
      // and create a node in this point;
      gp_XYZ p( 0,0,0 );
      if ( surface.IsNull() ) {
        for(i=0; i<4; i++)
          p += gp_XYZ(aNodes[i]->X(), aNodes[i]->Y(), aNodes[i]->Z() );
        p /= 4;
      }
      else {
        TopoDS_Face face = TopoDS::Face( helper.GetSubShape() );
        gp_XY uv( 0,0 );
        for(i=0; i<4; i++)
          uv += helper.GetNodeUV( face, aNodes[i], inFaceNode );
        uv /= 4.;
        p = surface->Value( uv.X(), uv.Y() ).XYZ();
      }
      const SMDS_MeshNode* newN = aMesh->AddNode( p.X(), p.Y(), p.Z() );
      myLastCreatedNodes.Append(newN);

      // create a new element
      const SMDS_MeshNode* N[6];
      if ( aBadRate1 <= aBadRate2 ) {
        N[0] = aNodes[0];
        N[1] = aNodes[1];
        N[2] = aNodes[2];
        N[3] = aNodes[4];
        N[4] = aNodes[5];
        N[5] = newN;
        newElem = aMesh->AddFace(aNodes[2], aNodes[3], aNodes[0],
                                 aNodes[6], aNodes[7], newN );
      }
      else {
        N[0] = aNodes[1];
        N[1] = aNodes[2];
        N[2] = aNodes[3];
        N[3] = aNodes[5];
        N[4] = aNodes[6];
        N[5] = newN;
        newElem = aMesh->AddFace(aNodes[3], aNodes[0], aNodes[1],
                                 aNodes[7], aNodes[4], newN );
      }
      aMesh->ChangeElementNodes( elem, N, 6 );

    } // quadratic case

    // care of a new element

    myLastCreatedElems.Append(newElem);
    AddToSameGroups( newElem, elem, aMesh );

    // put a new triangle on the same shape
    if ( aShapeId )
      aMesh->SetMeshElementOnShape( newElem, aShapeId );
  }
  return true;
}

//=======================================================================
//function : BestSplit
//purpose  : Find better diagonal for cutting.
//=======================================================================
int SMESH_MeshEditor::BestSplit (const SMDS_MeshElement*              theQuad,
                                 SMESH::Controls::NumericalFunctorPtr theCrit)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  if (!theCrit.get())
    return -1;

  if (!theQuad || theQuad->GetType() != SMDSAbs_Face )
    return -1;

  if( theQuad->NbNodes()==4 ||
      (theQuad->NbNodes()==8 && theQuad->IsQuadratic()) ) {

    // retrieve element nodes
    const SMDS_MeshNode* aNodes [4];
    SMDS_ElemIteratorPtr itN = theQuad->nodesIterator();
    int i = 0;
    //while (itN->more())
    while (i<4) {
      aNodes[ i++ ] = static_cast<const SMDS_MeshNode*>( itN->next() );
    }
    // compare two sets of possible triangles
    double aBadRate1, aBadRate2; // to what extent a set is bad
    SMDS_FaceOfNodes tr1 ( aNodes[0], aNodes[1], aNodes[2] );
    SMDS_FaceOfNodes tr2 ( aNodes[2], aNodes[3], aNodes[0] );
    aBadRate1 = getBadRate( &tr1, theCrit ) + getBadRate( &tr2, theCrit );

    SMDS_FaceOfNodes tr3 ( aNodes[1], aNodes[2], aNodes[3] );
    SMDS_FaceOfNodes tr4 ( aNodes[3], aNodes[0], aNodes[1] );
    aBadRate2 = getBadRate( &tr3, theCrit ) + getBadRate( &tr4, theCrit );

    if (aBadRate1 <= aBadRate2) // tr1 + tr2 is better
      return 1; // diagonal 1-3

    return 2; // diagonal 2-4
  }
  return -1;
}

//=======================================================================
//function : AddToSameGroups
//purpose  : add elemToAdd to the groups the elemInGroups belongs to
//=======================================================================

void SMESH_MeshEditor::AddToSameGroups (const SMDS_MeshElement* elemToAdd,
                                        const SMDS_MeshElement* elemInGroups,
                                        SMESHDS_Mesh *          aMesh)
{
  const set<SMESHDS_GroupBase*>& groups = aMesh->GetGroups();
  set<SMESHDS_GroupBase*>::const_iterator grIt = groups.begin();
  for ( ; grIt != groups.end(); grIt++ ) {
    SMESHDS_Group* group = dynamic_cast<SMESHDS_Group*>( *grIt );
    if ( group && group->Contains( elemInGroups ))
      group->SMDSGroup().Add( elemToAdd );
  }
}


//=======================================================================
//function : RemoveElemFromGroups
//purpose  : Remove removeelem to the groups the elemInGroups belongs to
//=======================================================================
void SMESH_MeshEditor::RemoveElemFromGroups (const SMDS_MeshElement* removeelem,
                                             SMESHDS_Mesh *          aMesh)
{
  const set<SMESHDS_GroupBase*>& groups = aMesh->GetGroups();
  if (!groups.empty())
  {
    set<SMESHDS_GroupBase*>::const_iterator GrIt = groups.begin();
    for (; GrIt != groups.end(); GrIt++)
    {
      SMESHDS_Group* grp = dynamic_cast<SMESHDS_Group*>(*GrIt);
      if (!grp || grp->IsEmpty()) continue;
      grp->SMDSGroup().Remove(removeelem);
    }
  }
}


//=======================================================================
//function : QuadToTri
//purpose  : Cut quadrangles into triangles.
//           theCrit is used to select a diagonal to cut
//=======================================================================

bool SMESH_MeshEditor::QuadToTri (TIDSortedElemSet & theElems,
                                  const bool         the13Diag)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  MESSAGE( "::QuadToTri()" );

  SMESHDS_Mesh * aMesh = GetMeshDS();

  Handle(Geom_Surface) surface;
  SMESH_MesherHelper   helper( *GetMesh() );

  TIDSortedElemSet::iterator itElem;
  for ( itElem = theElems.begin(); itElem != theElems.end(); itElem++ ) {
    const SMDS_MeshElement* elem = *itElem;
    if ( !elem || elem->GetType() != SMDSAbs_Face )
      continue;
    bool isquad = elem->NbNodes()==4 || elem->NbNodes()==8;
    if(!isquad) continue;

    if(elem->NbNodes()==4) {
      // retrieve element nodes
      const SMDS_MeshNode* aNodes [4];
      SMDS_ElemIteratorPtr itN = elem->nodesIterator();
      int i = 0;
      while ( itN->more() )
        aNodes[ i++ ] = static_cast<const SMDS_MeshNode*>( itN->next() );

      int aShapeId = FindShape( elem );
      const SMDS_MeshElement* newElem = 0;
      if ( the13Diag ) {
        aMesh->ChangeElementNodes( elem, aNodes, 3 );
        newElem = aMesh->AddFace( aNodes[2], aNodes[3], aNodes[0] );
      }
      else {
        aMesh->ChangeElementNodes( elem, &aNodes[1], 3 );
        newElem = aMesh->AddFace( aNodes[3], aNodes[0], aNodes[1] );
      }
      myLastCreatedElems.Append(newElem);
      // put a new triangle on the same shape and add to the same groups
      if ( aShapeId )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );
      AddToSameGroups( newElem, elem, aMesh );
    }

    // Quadratic quadrangle

    if( elem->NbNodes()==8 && elem->IsQuadratic() ) {

      // get surface elem is on
      int aShapeId = FindShape( elem );
      if ( aShapeId != helper.GetSubShapeID() ) {
        surface.Nullify();
        TopoDS_Shape shape;
        if ( aShapeId > 0 )
          shape = aMesh->IndexToShape( aShapeId );
        if ( !shape.IsNull() && shape.ShapeType() == TopAbs_FACE ) {
          TopoDS_Face face = TopoDS::Face( shape );
          surface = BRep_Tool::Surface( face );
          if ( !surface.IsNull() )
            helper.SetSubShape( shape );
        }
      }

      const SMDS_MeshNode* aNodes [8];
      const SMDS_MeshNode* inFaceNode = 0;
      SMDS_ElemIteratorPtr itN = elem->nodesIterator();
      int i = 0;
      while ( itN->more() ) {
        aNodes[ i++ ] = static_cast<const SMDS_MeshNode*>( itN->next() );
        if ( !inFaceNode && helper.GetNodeUVneedInFaceNode() &&
             aNodes[ i-1 ]->GetPosition()->GetTypeOfPosition() == SMDS_TOP_FACE )
        {
          inFaceNode = aNodes[ i-1 ];
        }
      }

      // find middle point for (0,1,2,3)
      // and create a node in this point;
      gp_XYZ p( 0,0,0 );
      if ( surface.IsNull() ) {
        for(i=0; i<4; i++)
          p += gp_XYZ(aNodes[i]->X(), aNodes[i]->Y(), aNodes[i]->Z() );
        p /= 4;
      }
      else {
        TopoDS_Face geomFace = TopoDS::Face( helper.GetSubShape() );
        gp_XY uv( 0,0 );
        for(i=0; i<4; i++)
          uv += helper.GetNodeUV( geomFace, aNodes[i], inFaceNode );
        uv /= 4.;
        p = surface->Value( uv.X(), uv.Y() ).XYZ();
      }
      const SMDS_MeshNode* newN = aMesh->AddNode( p.X(), p.Y(), p.Z() );
      myLastCreatedNodes.Append(newN);

      // create a new element
      const SMDS_MeshElement* newElem = 0;
      const SMDS_MeshNode* N[6];
      if ( the13Diag ) {
        N[0] = aNodes[0];
        N[1] = aNodes[1];
        N[2] = aNodes[2];
        N[3] = aNodes[4];
        N[4] = aNodes[5];
        N[5] = newN;
        newElem = aMesh->AddFace(aNodes[2], aNodes[3], aNodes[0],
                                 aNodes[6], aNodes[7], newN );
      }
      else {
        N[0] = aNodes[1];
        N[1] = aNodes[2];
        N[2] = aNodes[3];
        N[3] = aNodes[5];
        N[4] = aNodes[6];
        N[5] = newN;
        newElem = aMesh->AddFace(aNodes[3], aNodes[0], aNodes[1],
                                 aNodes[7], aNodes[4], newN );
      }
      myLastCreatedElems.Append(newElem);
      aMesh->ChangeElementNodes( elem, N, 6 );
      // put a new triangle on the same shape and add to the same groups
      if ( aShapeId )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );
      AddToSameGroups( newElem, elem, aMesh );
    }
  }

  return true;
}

//=======================================================================
//function : getAngle
//purpose  :
//=======================================================================

double getAngle(const SMDS_MeshElement * tr1,
                const SMDS_MeshElement * tr2,
                const SMDS_MeshNode *    n1,
                const SMDS_MeshNode *    n2)
{
  double angle = 2*PI; // bad angle

  // get normals
  SMESH::Controls::TSequenceOfXYZ P1, P2;
  if ( !SMESH::Controls::NumericalFunctor::GetPoints( tr1, P1 ) ||
       !SMESH::Controls::NumericalFunctor::GetPoints( tr2, P2 ))
    return angle;
  gp_Vec N1,N2;
  if(!tr1->IsQuadratic())
    N1 = gp_Vec( P1(2) - P1(1) ) ^ gp_Vec( P1(3) - P1(1) );
  else
    N1 = gp_Vec( P1(3) - P1(1) ) ^ gp_Vec( P1(5) - P1(1) );
  if ( N1.SquareMagnitude() <= gp::Resolution() )
    return angle;
  if(!tr2->IsQuadratic())
    N2 = gp_Vec( P2(2) - P2(1) ) ^ gp_Vec( P2(3) - P2(1) );
  else
    N2 = gp_Vec( P2(3) - P2(1) ) ^ gp_Vec( P2(5) - P2(1) );
  if ( N2.SquareMagnitude() <= gp::Resolution() )
    return angle;

  // find the first diagonal node n1 in the triangles:
  // take in account a diagonal link orientation
  const SMDS_MeshElement *nFirst[2], *tr[] = { tr1, tr2 };
  for ( int t = 0; t < 2; t++ ) {
    SMDS_ElemIteratorPtr it = tr[ t ]->nodesIterator();
    int i = 0, iDiag = -1;
    while ( it->more()) {
      const SMDS_MeshElement *n = it->next();
      if ( n == n1 || n == n2 )
        if ( iDiag < 0)
          iDiag = i;
        else {
          if ( i - iDiag == 1 )
            nFirst[ t ] = ( n == n1 ? n2 : n1 );
          else
            nFirst[ t ] = n;
          break;
        }
      i++;
    }
  }
  if ( nFirst[ 0 ] == nFirst[ 1 ] )
    N2.Reverse();

  angle = N1.Angle( N2 );
  //SCRUTE( angle );
  return angle;
}

// =================================================
// class generating a unique ID for a pair of nodes
// and able to return nodes by that ID
// =================================================
class LinkID_Gen {
 public:

  LinkID_Gen( const SMESHDS_Mesh* theMesh )
    :myMesh( theMesh ), myMaxID( theMesh->MaxNodeID() + 1)
  {}

  long GetLinkID (const SMDS_MeshNode * n1,
                  const SMDS_MeshNode * n2) const
  {
    return ( Min(n1->GetID(),n2->GetID()) * myMaxID + Max(n1->GetID(),n2->GetID()));
  }

  bool GetNodes (const long             theLinkID,
                 const SMDS_MeshNode* & theNode1,
                 const SMDS_MeshNode* & theNode2) const
  {
    theNode1 = myMesh->FindNode( theLinkID / myMaxID );
    if ( !theNode1 ) return false;
    theNode2 = myMesh->FindNode( theLinkID % myMaxID );
    if ( !theNode2 ) return false;
    return true;
  }

 private:
  LinkID_Gen();
  const SMESHDS_Mesh* myMesh;
  long                myMaxID;
};


//=======================================================================
//function : TriToQuad
//purpose  : Fuse neighbour triangles into quadrangles.
//           theCrit is used to select a neighbour to fuse with.
//           theMaxAngle is a max angle between element normals at which
//           fusion is still performed.
//=======================================================================

bool SMESH_MeshEditor::TriToQuad (TIDSortedElemSet &                   theElems,
                                  SMESH::Controls::NumericalFunctorPtr theCrit,
                                  const double                         theMaxAngle)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  MESSAGE( "::TriToQuad()" );

  if ( !theCrit.get() )
    return false;

  SMESHDS_Mesh * aMesh = GetMeshDS();

  // Prepare data for algo: build
  // 1. map of elements with their linkIDs
  // 2. map of linkIDs with their elements

  map< TLink, list< const SMDS_MeshElement* > > mapLi_listEl;
  map< TLink, list< const SMDS_MeshElement* > >::iterator itLE;
  map< const SMDS_MeshElement*, set< TLink > >  mapEl_setLi;
  map< const SMDS_MeshElement*, set< TLink > >::iterator itEL;

  TIDSortedElemSet::iterator itElem;
  for ( itElem = theElems.begin(); itElem != theElems.end(); itElem++ ) {
    const SMDS_MeshElement* elem = *itElem;
    if(!elem || elem->GetType() != SMDSAbs_Face ) continue;
    bool IsTria = elem->NbNodes()==3 || (elem->NbNodes()==6 && elem->IsQuadratic());
    if(!IsTria) continue;

    // retrieve element nodes
    const SMDS_MeshNode* aNodes [4];
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    int i = 0;
    while ( i<3 )
      aNodes[ i++ ] = cast2Node( itN->next() );
    aNodes[ 3 ] = aNodes[ 0 ];

    // fill maps
    for ( i = 0; i < 3; i++ ) {
      TLink link( aNodes[i], aNodes[i+1] );
      // check if elements sharing a link can be fused
      itLE = mapLi_listEl.find( link );
      if ( itLE != mapLi_listEl.end() ) {
        if ((*itLE).second.size() > 1 ) // consider only 2 elems adjacent by a link
          continue;
        const SMDS_MeshElement* elem2 = (*itLE).second.front();
        //if ( FindShape( elem ) != FindShape( elem2 ))
        //  continue; // do not fuse triangles laying on different shapes
        if ( getAngle( elem, elem2, aNodes[i], aNodes[i+1] ) > theMaxAngle )
          continue; // avoid making badly shaped quads
        (*itLE).second.push_back( elem );
      }
      else {
        mapLi_listEl[ link ].push_back( elem );
      }
      mapEl_setLi [ elem ].insert( link );
    }
  }
  // Clean the maps from the links shared by a sole element, ie
  // links to which only one element is bound in mapLi_listEl

  for ( itLE = mapLi_listEl.begin(); itLE != mapLi_listEl.end(); itLE++ ) {
    int nbElems = (*itLE).second.size();
    if ( nbElems < 2  ) {
      const SMDS_MeshElement* elem = (*itLE).second.front();
      TLink link = (*itLE).first;
      mapEl_setLi[ elem ].erase( link );
      if ( mapEl_setLi[ elem ].empty() )
        mapEl_setLi.erase( elem );
    }
  }

  // Algo: fuse triangles into quadrangles

  while ( ! mapEl_setLi.empty() ) {
    // Look for the start element:
    // the element having the least nb of shared links
    const SMDS_MeshElement* startElem = 0;
    int minNbLinks = 4;
    for ( itEL = mapEl_setLi.begin(); itEL != mapEl_setLi.end(); itEL++ ) {
      int nbLinks = (*itEL).second.size();
      if ( nbLinks < minNbLinks ) {
        startElem = (*itEL).first;
        minNbLinks = nbLinks;
        if ( minNbLinks == 1 )
          break;
      }
    }

    // search elements to fuse starting from startElem or links of elements
    // fused earlyer - startLinks
    list< TLink > startLinks;
    while ( startElem || !startLinks.empty() ) {
      while ( !startElem && !startLinks.empty() ) {
        // Get an element to start, by a link
        TLink linkId = startLinks.front();
        startLinks.pop_front();
        itLE = mapLi_listEl.find( linkId );
        if ( itLE != mapLi_listEl.end() ) {
          list< const SMDS_MeshElement* > & listElem = (*itLE).second;
          list< const SMDS_MeshElement* >::iterator itE = listElem.begin();
          for ( ; itE != listElem.end() ; itE++ )
            if ( mapEl_setLi.find( (*itE) ) != mapEl_setLi.end() )
              startElem = (*itE);
          mapLi_listEl.erase( itLE );
        }
      }

      if ( startElem ) {
        // Get candidates to be fused
        const SMDS_MeshElement *tr1 = startElem, *tr2 = 0, *tr3 = 0;
        const TLink *link12, *link13;
        startElem = 0;
        ASSERT( mapEl_setLi.find( tr1 ) != mapEl_setLi.end() );
        set< TLink >& setLi = mapEl_setLi[ tr1 ];
        ASSERT( !setLi.empty() );
        set< TLink >::iterator itLi;
        for ( itLi = setLi.begin(); itLi != setLi.end(); itLi++ )
        {
          const TLink & link = (*itLi);
          itLE = mapLi_listEl.find( link );
          if ( itLE == mapLi_listEl.end() )
            continue;

          const SMDS_MeshElement* elem = (*itLE).second.front();
          if ( elem == tr1 )
            elem = (*itLE).second.back();
          mapLi_listEl.erase( itLE );
          if ( mapEl_setLi.find( elem ) == mapEl_setLi.end())
            continue;
          if ( tr2 ) {
            tr3 = elem;
            link13 = &link;
          }
          else {
            tr2 = elem;
            link12 = &link;
          }

          // add other links of elem to list of links to re-start from
          set< TLink >& links = mapEl_setLi[ elem ];
          set< TLink >::iterator it;
          for ( it = links.begin(); it != links.end(); it++ ) {
            const TLink& link2 = (*it);
            if ( link2 != link )
              startLinks.push_back( link2 );
          }
        }

        // Get nodes of possible quadrangles
        const SMDS_MeshNode *n12 [4], *n13 [4];
        bool Ok12 = false, Ok13 = false;
        const SMDS_MeshNode *linkNode1, *linkNode2;
        if(tr2) {
          linkNode1 = link12->first;
          linkNode2 = link12->second;
          if ( tr2 && getQuadrangleNodes( n12, linkNode1, linkNode2, tr1, tr2 ))
            Ok12 = true;
        }
        if(tr3) {
          linkNode1 = link13->first;
          linkNode2 = link13->second;
          if ( tr3 && getQuadrangleNodes( n13, linkNode1, linkNode2, tr1, tr3 ))
            Ok13 = true;
        }

        // Choose a pair to fuse
        if ( Ok12 && Ok13 ) {
          SMDS_FaceOfNodes quad12 ( n12[ 0 ], n12[ 1 ], n12[ 2 ], n12[ 3 ] );
          SMDS_FaceOfNodes quad13 ( n13[ 0 ], n13[ 1 ], n13[ 2 ], n13[ 3 ] );
          double aBadRate12 = getBadRate( &quad12, theCrit );
          double aBadRate13 = getBadRate( &quad13, theCrit );
          if (  aBadRate13 < aBadRate12 )
            Ok12 = false;
          else
            Ok13 = false;
        }

        // Make quadrangles
        // and remove fused elems and removed links from the maps
        mapEl_setLi.erase( tr1 );
        if ( Ok12 ) {
          mapEl_setLi.erase( tr2 );
          mapLi_listEl.erase( *link12 );
          if(tr1->NbNodes()==3) {
            if( tr1->GetID() < tr2->GetID() ) {
              aMesh->ChangeElementNodes( tr1, n12, 4 );
              myLastCreatedElems.Append(tr1);
              aMesh->RemoveElement( tr2 );
            }
            else {
              aMesh->ChangeElementNodes( tr2, n12, 4 );
              myLastCreatedElems.Append(tr2);
              aMesh->RemoveElement( tr1);
            }
          }
          else {
            const SMDS_MeshNode* N1 [6];
            const SMDS_MeshNode* N2 [6];
            GetNodesFromTwoTria(tr1,tr2,N1,N2);
            // now we receive following N1 and N2 (using numeration as above image)
            // tria1 : (1 2 4 5 9 7)  and  tria2 : (3 4 2 8 9 6)
            // i.e. first nodes from both arrays determ new diagonal
            const SMDS_MeshNode* aNodes[8];
            aNodes[0] = N1[0];
            aNodes[1] = N1[1];
            aNodes[2] = N2[0];
            aNodes[3] = N2[1];
            aNodes[4] = N1[3];
            aNodes[5] = N2[5];
            aNodes[6] = N2[3];
            aNodes[7] = N1[5];
            if( tr1->GetID() < tr2->GetID() ) {
              GetMeshDS()->ChangeElementNodes( tr1, aNodes, 8 );
              myLastCreatedElems.Append(tr1);
              GetMeshDS()->RemoveElement( tr2 );
            }
            else {
              GetMeshDS()->ChangeElementNodes( tr2, aNodes, 8 );
              myLastCreatedElems.Append(tr2);
              GetMeshDS()->RemoveElement( tr1 );
            }
            // remove middle node (9)
            GetMeshDS()->RemoveNode( N1[4] );
          }
        }
        else if ( Ok13 ) {
          mapEl_setLi.erase( tr3 );
          mapLi_listEl.erase( *link13 );
          if(tr1->NbNodes()==3) {
            if( tr1->GetID() < tr2->GetID() ) {
              aMesh->ChangeElementNodes( tr1, n13, 4 );
              myLastCreatedElems.Append(tr1);
              aMesh->RemoveElement( tr3 );
            }
            else {
              aMesh->ChangeElementNodes( tr3, n13, 4 );
              myLastCreatedElems.Append(tr3);
              aMesh->RemoveElement( tr1 );
            }
          }
          else {
            const SMDS_MeshNode* N1 [6];
            const SMDS_MeshNode* N2 [6];
            GetNodesFromTwoTria(tr1,tr3,N1,N2);
            // now we receive following N1 and N2 (using numeration as above image)
            // tria1 : (1 2 4 5 9 7)  and  tria2 : (3 4 2 8 9 6)
            // i.e. first nodes from both arrays determ new diagonal
            const SMDS_MeshNode* aNodes[8];
            aNodes[0] = N1[0];
            aNodes[1] = N1[1];
            aNodes[2] = N2[0];
            aNodes[3] = N2[1];
            aNodes[4] = N1[3];
            aNodes[5] = N2[5];
            aNodes[6] = N2[3];
            aNodes[7] = N1[5];
            if( tr1->GetID() < tr2->GetID() ) {
              GetMeshDS()->ChangeElementNodes( tr1, aNodes, 8 );
              myLastCreatedElems.Append(tr1);
              GetMeshDS()->RemoveElement( tr3 );
            }
            else {
              GetMeshDS()->ChangeElementNodes( tr3, aNodes, 8 );
              myLastCreatedElems.Append(tr3);
              GetMeshDS()->RemoveElement( tr1 );
            }
            // remove middle node (9)
            GetMeshDS()->RemoveNode( N1[4] );
          }
        }

        // Next element to fuse: the rejected one
        if ( tr3 )
          startElem = Ok12 ? tr3 : tr2;

      } // if ( startElem )
    } // while ( startElem || !startLinks.empty() )
  } // while ( ! mapEl_setLi.empty() )

  return true;
}


/*#define DUMPSO(txt) \
//  cout << txt << endl;
//=============================================================================
//
//
//
//=============================================================================
static void swap( int i1, int i2, int idNodes[], gp_Pnt P[] )
{
  if ( i1 == i2 )
    return;
  int tmp = idNodes[ i1 ];
  idNodes[ i1 ] = idNodes[ i2 ];
  idNodes[ i2 ] = tmp;
  gp_Pnt Ptmp = P[ i1 ];
  P[ i1 ] = P[ i2 ];
  P[ i2 ] = Ptmp;
  DUMPSO( i1 << "(" << idNodes[ i2 ] << ") <-> " << i2 << "(" << idNodes[ i1 ] << ")");
}

//=======================================================================
//function : SortQuadNodes
//purpose  : Set 4 nodes of a quadrangle face in a good order.
//           Swap 1<->2 or 2<->3 nodes and correspondingly return
//           1 or 2 else 0.
//=======================================================================

int SMESH_MeshEditor::SortQuadNodes (const SMDS_Mesh * theMesh,
                                     int               idNodes[] )
{
  gp_Pnt P[4];
  int i;
  for ( i = 0; i < 4; i++ ) {
    const SMDS_MeshNode *n = theMesh->FindNode( idNodes[i] );
    if ( !n ) return 0;
    P[ i ].SetCoord( n->X(), n->Y(), n->Z() );
  }

  gp_Vec V1(P[0], P[1]);
  gp_Vec V2(P[0], P[2]);
  gp_Vec V3(P[0], P[3]);

  gp_Vec Cross1 = V1 ^ V2;
  gp_Vec Cross2 = V2 ^ V3;

  i = 0;
  if (Cross1.Dot(Cross2) < 0)
  {
    Cross1 = V2 ^ V1;
    Cross2 = V1 ^ V3;

    if (Cross1.Dot(Cross2) < 0)
      i = 2;
    else
      i = 1;
    swap ( i, i + 1, idNodes, P );

//     for ( int ii = 0; ii < 4; ii++ ) {
//       const SMDS_MeshNode *n = theMesh->FindNode( idNodes[ii] );
//       DUMPSO( ii << "(" << idNodes[ii] <<") : "<<n->X()<<" "<<n->Y()<<" "<<n->Z());
//     }
  }
  return i;
}

//=======================================================================
//function : SortHexaNodes
//purpose  : Set 8 nodes of a hexahedron in a good order.
//           Return success status
//=======================================================================

bool SMESH_MeshEditor::SortHexaNodes (const SMDS_Mesh * theMesh,
                                      int               idNodes[] )
{
  gp_Pnt P[8];
  int i;
  DUMPSO( "INPUT: ========================================");
  for ( i = 0; i < 8; i++ ) {
    const SMDS_MeshNode *n = theMesh->FindNode( idNodes[i] );
    if ( !n ) return false;
    P[ i ].SetCoord( n->X(), n->Y(), n->Z() );
    DUMPSO( i << "(" << idNodes[i] <<") : "<<n->X()<<" "<<n->Y()<<" "<<n->Z());
  }
  DUMPSO( "========================================");


  set<int> faceNodes;  // ids of bottom face nodes, to be found
  set<int> checkedId1; // ids of tried 2-nd nodes
  Standard_Real leastDist = DBL_MAX; // dist of the 4-th node from 123 plane
  const Standard_Real tol = 1.e-6;   // tolerance to find nodes in plane
  int iMin, iLoop1 = 0;

  // Loop to try the 2-nd nodes

  while ( leastDist > DBL_MIN && ++iLoop1 < 8 )
  {
    // Find not checked 2-nd node
    for ( i = 1; i < 8; i++ )
      if ( checkedId1.find( idNodes[i] ) == checkedId1.end() ) {
        int id1 = idNodes[i];
        swap ( 1, i, idNodes, P );
        checkedId1.insert ( id1 );
        break;
      }

    // Find the 3-d node so that 1-2-3 triangle to be on a hexa face,
    // ie that all but meybe one (id3 which is on the same face) nodes
    // lay on the same side from the triangle plane.

    bool manyInPlane = false; // more than 4 nodes lay in plane
    int iLoop2 = 0;
    while ( ++iLoop2 < 6 ) {

      // get 1-2-3 plane coeffs
      Standard_Real A, B, C, D;
      gp_Vec N = gp_Vec (P[0], P[1]).Crossed( gp_Vec (P[0], P[2]) );
      if ( N.SquareMagnitude() > gp::Resolution() )
      {
        gp_Pln pln ( P[0], N );
        pln.Coefficients( A, B, C, D );

        // find the node (iMin) closest to pln
        Standard_Real dist[ 8 ], minDist = DBL_MAX;
        set<int> idInPln;
        for ( i = 3; i < 8; i++ ) {
          dist[i] = A * P[i].X() + B * P[i].Y() + C * P[i].Z() + D;
          if ( fabs( dist[i] ) < minDist ) {
            minDist = fabs( dist[i] );
            iMin = i;
          }
          if ( fabs( dist[i] ) <= tol )
            idInPln.insert( idNodes[i] );
        }

        // there should not be more than 4 nodes in bottom plane
        if ( idInPln.size() > 1 )
        {
          DUMPSO( "### idInPln.size() = " << idInPln.size());
          // idInPlane does not contain the first 3 nodes
          if ( manyInPlane || idInPln.size() == 5)
            return false; // all nodes in one plane
          manyInPlane = true;

          // set the 1-st node to be not in plane
          for ( i = 3; i < 8; i++ ) {
            if ( idInPln.find( idNodes[ i ] ) == idInPln.end() ) {
              DUMPSO( "### Reset 0-th node");
              swap( 0, i, idNodes, P );
              break;
            }
          }

          // reset to re-check second nodes
          leastDist = DBL_MAX;
          faceNodes.clear();
          checkedId1.clear();
          iLoop1 = 0;
          break; // from iLoop2;
        }

        // check that the other 4 nodes are on the same side
        bool sameSide = true;
        bool isNeg = dist[ iMin == 3 ? 4 : 3 ] <= 0.;
        for ( i = 3; sameSide && i < 8; i++ ) {
          if ( i != iMin )
            sameSide = ( isNeg == dist[i] <= 0.);
        }

        // keep best solution
        if ( sameSide && minDist < leastDist ) {
          leastDist = minDist;
          faceNodes.clear();
          faceNodes.insert( idNodes[ 1 ] );
          faceNodes.insert( idNodes[ 2 ] );
          faceNodes.insert( idNodes[ iMin ] );
          DUMPSO( "loop " << iLoop2 << " id2 " << idNodes[ 1 ] << " id3 " << idNodes[ 2 ]
            << " leastDist = " << leastDist);
          if ( leastDist <= DBL_MIN )
            break;
        }
      }

      // set next 3-d node to check
      int iNext = 2 + iLoop2;
      if ( iNext < 8 ) {
        DUMPSO( "Try 2-nd");
        swap ( 2, iNext, idNodes, P );
      }
    } // while ( iLoop2 < 6 )
  } // iLoop1

  if ( faceNodes.empty() ) return false;

  // Put the faceNodes in proper places
  for ( i = 4; i < 8; i++ ) {
    if ( faceNodes.find( idNodes[ i ] ) != faceNodes.end() ) {
      // find a place to put
      int iTo = 1;
      while ( faceNodes.find( idNodes[ iTo ] ) != faceNodes.end() )
        iTo++;
      DUMPSO( "Set faceNodes");
      swap ( iTo, i, idNodes, P );
    }
  }


  // Set nodes of the found bottom face in good order
  DUMPSO( " Found bottom face: ");
  i = SortQuadNodes( theMesh, idNodes );
  if ( i ) {
    gp_Pnt Ptmp = P[ i ];
    P[ i ] = P[ i+1 ];
    P[ i+1 ] = Ptmp;
  }
//   else
//     for ( int ii = 0; ii < 4; ii++ ) {
//       const SMDS_MeshNode *n = theMesh->FindNode( idNodes[ii] );
//       DUMPSO( ii << "(" << idNodes[ii] <<") : "<<n->X()<<" "<<n->Y()<<" "<<n->Z());
//    }

  // Gravity center of the top and bottom faces
  gp_Pnt aGCb = ( P[0].XYZ() + P[1].XYZ() + P[2].XYZ() + P[3].XYZ() ) / 4.;
  gp_Pnt aGCt = ( P[4].XYZ() + P[5].XYZ() + P[6].XYZ() + P[7].XYZ() ) / 4.;

  // Get direction from the bottom to the top face
  gp_Vec upDir ( aGCb, aGCt );
  Standard_Real upDirSize = upDir.Magnitude();
  if ( upDirSize <= gp::Resolution() ) return false;
  upDir / upDirSize;

  // Assure that the bottom face normal points up
  gp_Vec Nb = gp_Vec (P[0], P[1]).Crossed( gp_Vec (P[0], P[2]) );
  Nb += gp_Vec (P[0], P[2]).Crossed( gp_Vec (P[0], P[3]) );
  if ( Nb.Dot( upDir ) < 0 ) {
    DUMPSO( "Reverse bottom face");
    swap( 1, 3, idNodes, P );
  }

  // Find 5-th node - the one closest to the 1-st among the last 4 nodes.
  Standard_Real minDist = DBL_MAX;
  for ( i = 4; i < 8; i++ ) {
    // projection of P[i] to the plane defined by P[0] and upDir
    gp_Pnt Pp = P[i].Translated( upDir * ( upDir.Dot( gp_Vec( P[i], P[0] ))));
    Standard_Real sqDist = P[0].SquareDistance( Pp );
    if ( sqDist < minDist ) {
      minDist = sqDist;
      iMin = i;
    }
  }
  DUMPSO( "Set 4-th");
  swap ( 4, iMin, idNodes, P );

  // Set nodes of the top face in good order
  DUMPSO( "Sort top face");
  i = SortQuadNodes( theMesh, &idNodes[4] );
  if ( i ) {
    i += 4;
    gp_Pnt Ptmp = P[ i ];
    P[ i ] = P[ i+1 ];
    P[ i+1 ] = Ptmp;
  }

  // Assure that direction of the top face normal is from the bottom face
  gp_Vec Nt = gp_Vec (P[4], P[5]).Crossed( gp_Vec (P[4], P[6]) );
  Nt += gp_Vec (P[4], P[6]).Crossed( gp_Vec (P[4], P[7]) );
  if ( Nt.Dot( upDir ) < 0 ) {
    DUMPSO( "Reverse top face");
    swap( 5, 7, idNodes, P );
  }

//   DUMPSO( "OUTPUT: ========================================");
//   for ( i = 0; i < 8; i++ ) {
//     float *p = ugrid->GetPoint(idNodes[i]);
//     DUMPSO( i << "(" << idNodes[i] << ") : " << p[0] << " " << p[1] << " " << p[2]);
//   }

  return true;
}*/

//================================================================================
/*!
 * \brief Return nodes linked to the given one
  * \param theNode - the node
  * \param linkedNodes - the found nodes
  * \param type - the type of elements to check
  *
  * Medium nodes are ignored
 */
//================================================================================

void SMESH_MeshEditor::GetLinkedNodes( const SMDS_MeshNode* theNode,
                                       TIDSortedElemSet &   linkedNodes,
                                       SMDSAbs_ElementType  type )
{
  SMDS_ElemIteratorPtr elemIt = theNode->GetInverseElementIterator(type);
  while ( elemIt->more() )
  {
    const SMDS_MeshElement* elem = elemIt->next();
    SMDS_ElemIteratorPtr nodeIt = elem->nodesIterator();
    if ( elem->GetType() == SMDSAbs_Volume )
    {
      SMDS_VolumeTool vol( elem );
      while ( nodeIt->more() ) {
        const SMDS_MeshNode* n = cast2Node( nodeIt->next() );
        if ( theNode != n && vol.IsLinked( theNode, n ))
          linkedNodes.insert( n );
      }
    }
    else
    {
      for ( int i = 0; nodeIt->more(); ++i ) {
        const SMDS_MeshNode* n = cast2Node( nodeIt->next() );
        if ( n == theNode ) {
          int iBefore = i - 1;
          int iAfter  = i + 1;
          if ( elem->IsQuadratic() ) {
            int nb = elem->NbNodes() / 2;
            iAfter  = SMESH_MesherHelper::WrapIndex( iAfter, nb );
            iBefore = SMESH_MesherHelper::WrapIndex( iBefore, nb );
          }
          linkedNodes.insert( elem->GetNode( iAfter ));
          linkedNodes.insert( elem->GetNode( iBefore ));
        }
      }
    }
  }
}

//=======================================================================
//function : laplacianSmooth
//purpose  : pulls theNode toward the center of surrounding nodes directly
//           connected to that node along an element edge
//=======================================================================

void laplacianSmooth(const SMDS_MeshNode*                 theNode,
                     const Handle(Geom_Surface)&          theSurface,
                     map< const SMDS_MeshNode*, gp_XY* >& theUVMap)
{
  // find surrounding nodes

  TIDSortedElemSet nodeSet;
  SMESH_MeshEditor::GetLinkedNodes( theNode, nodeSet, SMDSAbs_Face );

  // compute new coodrs

  double coord[] = { 0., 0., 0. };
  TIDSortedElemSet::iterator nodeSetIt = nodeSet.begin();
  for ( ; nodeSetIt != nodeSet.end(); nodeSetIt++ ) {
    const SMDS_MeshNode* node = cast2Node(*nodeSetIt);
    if ( theSurface.IsNull() ) { // smooth in 3D
      coord[0] += node->X();
      coord[1] += node->Y();
      coord[2] += node->Z();
    }
    else { // smooth in 2D
      ASSERT( theUVMap.find( node ) != theUVMap.end() );
      gp_XY* uv = theUVMap[ node ];
      coord[0] += uv->X();
      coord[1] += uv->Y();
    }
  }
  int nbNodes = nodeSet.size();
  if ( !nbNodes )
    return;
  coord[0] /= nbNodes;
  coord[1] /= nbNodes;

  if ( !theSurface.IsNull() ) {
    ASSERT( theUVMap.find( theNode ) != theUVMap.end() );
    theUVMap[ theNode ]->SetCoord( coord[0], coord[1] );
    gp_Pnt p3d = theSurface->Value( coord[0], coord[1] );
    coord[0] = p3d.X();
    coord[1] = p3d.Y();
    coord[2] = p3d.Z();
  }
  else
    coord[2] /= nbNodes;

  // move node

  const_cast< SMDS_MeshNode* >( theNode )->setXYZ(coord[0],coord[1],coord[2]);
}

//=======================================================================
//function : centroidalSmooth
//purpose  : pulls theNode toward the element-area-weighted centroid of the
//           surrounding elements
//=======================================================================

void centroidalSmooth(const SMDS_MeshNode*                 theNode,
                      const Handle(Geom_Surface)&          theSurface,
                      map< const SMDS_MeshNode*, gp_XY* >& theUVMap)
{
  gp_XYZ aNewXYZ(0.,0.,0.);
  SMESH::Controls::Area anAreaFunc;
  double totalArea = 0.;
  int nbElems = 0;

  // compute new XYZ

  SMDS_ElemIteratorPtr elemIt = theNode->GetInverseElementIterator(SMDSAbs_Face);
  while ( elemIt->more() )
  {
    const SMDS_MeshElement* elem = elemIt->next();
    nbElems++;

    gp_XYZ elemCenter(0.,0.,0.);
    SMESH::Controls::TSequenceOfXYZ aNodePoints;
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    int nn = elem->NbNodes();
    if(elem->IsQuadratic()) nn = nn/2;
    int i=0;
    //while ( itN->more() ) {
    while ( i<nn ) {
      const SMDS_MeshNode* aNode = static_cast<const SMDS_MeshNode*>( itN->next() );
      i++;
      gp_XYZ aP( aNode->X(), aNode->Y(), aNode->Z() );
      aNodePoints.push_back( aP );
      if ( !theSurface.IsNull() ) { // smooth in 2D
        ASSERT( theUVMap.find( aNode ) != theUVMap.end() );
        gp_XY* uv = theUVMap[ aNode ];
        aP.SetCoord( uv->X(), uv->Y(), 0. );
      }
      elemCenter += aP;
    }
    double elemArea = anAreaFunc.GetValue( aNodePoints );
    totalArea += elemArea;
    elemCenter /= nn;
    aNewXYZ += elemCenter * elemArea;
  }
  aNewXYZ /= totalArea;
  if ( !theSurface.IsNull() ) {
    theUVMap[ theNode ]->SetCoord( aNewXYZ.X(), aNewXYZ.Y() );
    aNewXYZ = theSurface->Value( aNewXYZ.X(), aNewXYZ.Y() ).XYZ();
  }

  // move node

  const_cast< SMDS_MeshNode* >( theNode )->setXYZ(aNewXYZ.X(),aNewXYZ.Y(),aNewXYZ.Z());
}

//=======================================================================
//function : getClosestUV
//purpose  : return UV of closest projection
//=======================================================================

static bool getClosestUV (Extrema_GenExtPS& projector,
                          const gp_Pnt&     point,
                          gp_XY &           result)
{
  projector.Perform( point );
  if ( projector.IsDone() ) {
    double u, v, minVal = DBL_MAX;
    for ( int i = projector.NbExt(); i > 0; i-- )
      if ( projector.Value( i ) < minVal ) {
        minVal = projector.Value( i );
        projector.Point( i ).Parameter( u, v );
      }
    result.SetCoord( u, v );
    return true;
  }
  return false;
}

//=======================================================================
//function : Smooth
//purpose  : Smooth theElements during theNbIterations or until a worst
//           element has aspect ratio <= theTgtAspectRatio.
//           Aspect Ratio varies in range [1.0, inf].
//           If theElements is empty, the whole mesh is smoothed.
//           theFixedNodes contains additionally fixed nodes. Nodes built
//           on edges and boundary nodes are always fixed.
//=======================================================================

void SMESH_MeshEditor::Smooth (TIDSortedElemSet &          theElems,
                               set<const SMDS_MeshNode*> & theFixedNodes,
                               const SmoothMethod          theSmoothMethod,
                               const int                   theNbIterations,
                               double                      theTgtAspectRatio,
                               const bool                  the2D)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  MESSAGE((theSmoothMethod==LAPLACIAN ? "LAPLACIAN" : "CENTROIDAL") << "--::Smooth()");

  if ( theTgtAspectRatio < 1.0 )
    theTgtAspectRatio = 1.0;

  const double disttol = 1.e-16;

  SMESH::Controls::AspectRatio aQualityFunc;

  SMESHDS_Mesh* aMesh = GetMeshDS();

  if ( theElems.empty() ) {
    // add all faces to theElems
    SMDS_FaceIteratorPtr fIt = aMesh->facesIterator();
    while ( fIt->more() ) {
      const SMDS_MeshElement* face = fIt->next();
      theElems.insert( face );
    }
  }
  // get all face ids theElems are on
  set< int > faceIdSet;
  TIDSortedElemSet::iterator itElem;
  if ( the2D )
    for ( itElem = theElems.begin(); itElem != theElems.end(); itElem++ ) {
      int fId = FindShape( *itElem );
      // check that corresponding submesh exists and a shape is face
      if (fId &&
          faceIdSet.find( fId ) == faceIdSet.end() &&
          aMesh->MeshElements( fId )) {
        TopoDS_Shape F = aMesh->IndexToShape( fId );
        if ( !F.IsNull() && F.ShapeType() == TopAbs_FACE )
          faceIdSet.insert( fId );
      }
    }
  faceIdSet.insert( 0 ); // to smooth elements that are not on any TopoDS_Face

  // ===============================================
  // smooth elements on each TopoDS_Face separately
  // ===============================================

  set< int >::reverse_iterator fId = faceIdSet.rbegin(); // treate 0 fId at the end
  for ( ; fId != faceIdSet.rend(); ++fId ) {
    // get face surface and submesh
    Handle(Geom_Surface) surface;
    SMESHDS_SubMesh* faceSubMesh = 0;
    TopoDS_Face face;
    double fToler2 = 0, vPeriod = 0., uPeriod = 0., f,l;
    double u1 = 0, u2 = 0, v1 = 0, v2 = 0;
    bool isUPeriodic = false, isVPeriodic = false;
    if ( *fId ) {
      face = TopoDS::Face( aMesh->IndexToShape( *fId ));
      surface = BRep_Tool::Surface( face );
      faceSubMesh = aMesh->MeshElements( *fId );
      fToler2 = BRep_Tool::Tolerance( face );
      fToler2 *= fToler2 * 10.;
      isUPeriodic = surface->IsUPeriodic();
      if ( isUPeriodic )
        vPeriod = surface->UPeriod();
      isVPeriodic = surface->IsVPeriodic();
      if ( isVPeriodic )
        uPeriod = surface->VPeriod();
      surface->Bounds( u1, u2, v1, v2 );
    }
    // ---------------------------------------------------------
    // for elements on a face, find movable and fixed nodes and
    // compute UV for them
    // ---------------------------------------------------------
    bool checkBoundaryNodes = false;
    bool isQuadratic = false;
    set<const SMDS_MeshNode*> setMovableNodes;
    map< const SMDS_MeshNode*, gp_XY* > uvMap, uvMap2;
    list< gp_XY > listUV; // uvs the 2 uvMaps refer to
    list< const SMDS_MeshElement* > elemsOnFace;

    Extrema_GenExtPS projector;
    GeomAdaptor_Surface surfAdaptor;
    if ( !surface.IsNull() ) {
      surfAdaptor.Load( surface );
      projector.Initialize( surfAdaptor, 20,20, 1e-5,1e-5 );
    }
    int nbElemOnFace = 0;
    itElem = theElems.begin();
     // loop on not yet smoothed elements: look for elems on a face
    while ( itElem != theElems.end() ) {
      if ( faceSubMesh && nbElemOnFace == faceSubMesh->NbElements() )
        break; // all elements found

      const SMDS_MeshElement* elem = *itElem;
      if ( !elem || elem->GetType() != SMDSAbs_Face || elem->NbNodes() < 3 ||
          ( faceSubMesh && !faceSubMesh->Contains( elem ))) {
        ++itElem;
        continue;
      }
      elemsOnFace.push_back( elem );
      theElems.erase( itElem++ );
      nbElemOnFace++;

      if ( !isQuadratic )
        isQuadratic = elem->IsQuadratic();

      // get movable nodes of elem
      const SMDS_MeshNode* node;
      SMDS_TypeOfPosition posType;
      SMDS_ElemIteratorPtr itN = elem->nodesIterator();
      int nn = 0, nbn =  elem->NbNodes();
      if(elem->IsQuadratic())
        nbn = nbn/2;
      while ( nn++ < nbn ) {
        node = static_cast<const SMDS_MeshNode*>( itN->next() );
        const SMDS_PositionPtr& pos = node->GetPosition();
        posType = pos.get() ? pos->GetTypeOfPosition() : SMDS_TOP_3DSPACE;
        if (posType != SMDS_TOP_EDGE &&
            posType != SMDS_TOP_VERTEX &&
            theFixedNodes.find( node ) == theFixedNodes.end())
        {
          // check if all faces around the node are on faceSubMesh
          // because a node on edge may be bound to face
          SMDS_ElemIteratorPtr eIt = node->GetInverseElementIterator(SMDSAbs_Face);
          bool all = true;
          if ( faceSubMesh ) {
            while ( eIt->more() && all ) {
              const SMDS_MeshElement* e = eIt->next();
              all = faceSubMesh->Contains( e );
            }
          }
          if ( all )
            setMovableNodes.insert( node );
          else
            checkBoundaryNodes = true;
        }
        if ( posType == SMDS_TOP_3DSPACE )
          checkBoundaryNodes = true;
      }

      if ( surface.IsNull() )
        continue;

      // get nodes to check UV
      list< const SMDS_MeshNode* > uvCheckNodes;
      itN = elem->nodesIterator();
      nn = 0; nbn =  elem->NbNodes();
      if(elem->IsQuadratic())
        nbn = nbn/2;
      while ( nn++ < nbn ) {
        node = static_cast<const SMDS_MeshNode*>( itN->next() );
        if ( uvMap.find( node ) == uvMap.end() )
          uvCheckNodes.push_back( node );
        // add nodes of elems sharing node
//         SMDS_ElemIteratorPtr eIt = node->GetInverseElementIterator(SMDSAbs_Face);
//         while ( eIt->more() ) {
//           const SMDS_MeshElement* e = eIt->next();
//           if ( e != elem ) {
//             SMDS_ElemIteratorPtr nIt = e->nodesIterator();
//             while ( nIt->more() ) {
//               const SMDS_MeshNode* n =
//                 static_cast<const SMDS_MeshNode*>( nIt->next() );
//               if ( uvMap.find( n ) == uvMap.end() )
//                 uvCheckNodes.push_back( n );
//             }
//           }
//         }
      }
      // check UV on face
      list< const SMDS_MeshNode* >::iterator n = uvCheckNodes.begin();
      for ( ; n != uvCheckNodes.end(); ++n ) {
        node = *n;
        gp_XY uv( 0, 0 );
        const SMDS_PositionPtr& pos = node->GetPosition();
        posType = pos.get() ? pos->GetTypeOfPosition() : SMDS_TOP_3DSPACE;
        // get existing UV
        switch ( posType ) {
        case SMDS_TOP_FACE: {
          SMDS_FacePosition* fPos = ( SMDS_FacePosition* ) pos.get();
          uv.SetCoord( fPos->GetUParameter(), fPos->GetVParameter() );
          break;
        }
        case SMDS_TOP_EDGE: {
          TopoDS_Shape S = aMesh->IndexToShape( pos->GetShapeId() );
          Handle(Geom2d_Curve) pcurve;
          if ( !S.IsNull() && S.ShapeType() == TopAbs_EDGE )
            pcurve = BRep_Tool::CurveOnSurface( TopoDS::Edge( S ), face, f,l );
          if ( !pcurve.IsNull() ) {
            double u = (( SMDS_EdgePosition* ) pos.get() )->GetUParameter();
            uv = pcurve->Value( u ).XY();
          }
          break;
        }
        case SMDS_TOP_VERTEX: {
          TopoDS_Shape S = aMesh->IndexToShape( pos->GetShapeId() );
          if ( !S.IsNull() && S.ShapeType() == TopAbs_VERTEX )
            uv = BRep_Tool::Parameters( TopoDS::Vertex( S ), face ).XY();
          break;
        }
        default:;
        }
        // check existing UV
        bool project = true;
        gp_Pnt pNode ( node->X(), node->Y(), node->Z() );
        double dist1 = DBL_MAX, dist2 = 0;
        if ( posType != SMDS_TOP_3DSPACE ) {
          dist1 = pNode.SquareDistance( surface->Value( uv.X(), uv.Y() ));
          project = dist1 > fToler2;
        }
        if ( project ) { // compute new UV
          gp_XY newUV;
          if ( !getClosestUV( projector, pNode, newUV )) {
            MESSAGE("Node Projection Failed " << node);
          }
          else {
            if ( isUPeriodic )
              newUV.SetX( ElCLib::InPeriod( newUV.X(), u1, u2 ));
            if ( isVPeriodic )
              newUV.SetY( ElCLib::InPeriod( newUV.Y(), v1, v2 ));
            // check new UV
            if ( posType != SMDS_TOP_3DSPACE )
              dist2 = pNode.SquareDistance( surface->Value( newUV.X(), newUV.Y() ));
            if ( dist2 < dist1 )
              uv = newUV;
          }
        }
        // store UV in the map
        listUV.push_back( uv );
        uvMap.insert( make_pair( node, &listUV.back() ));
      }
    } // loop on not yet smoothed elements

    if ( !faceSubMesh || nbElemOnFace != faceSubMesh->NbElements() )
      checkBoundaryNodes = true;

    // fix nodes on mesh boundary

    if ( checkBoundaryNodes ) {
      typedef pair<const SMDS_MeshNode*, const SMDS_MeshNode*> TLink;
      map< TLink, int > linkNbMap; // how many times a link encounters in elemsOnFace
      map< TLink, int >::iterator link_nb;
      // put all elements links to linkNbMap
      list< const SMDS_MeshElement* >::iterator elemIt = elemsOnFace.begin();
      for ( ; elemIt != elemsOnFace.end(); ++elemIt ) {
        const SMDS_MeshElement* elem = (*elemIt);
        int nbn =  elem->NbNodes();
        if(elem->IsQuadratic())
          nbn = nbn/2;
        // loop on elem links: insert them in linkNbMap
        const SMDS_MeshNode* curNode, *prevNode = elem->GetNode( nbn );
        for ( int iN = 0; iN < nbn; ++iN ) {
          curNode = elem->GetNode( iN );
          TLink link;
          if ( curNode < prevNode ) link = make_pair( curNode , prevNode );
          else                      link = make_pair( prevNode , curNode );
          prevNode = curNode;
          link_nb = linkNbMap.find( link );
          if ( link_nb == linkNbMap.end() )
            linkNbMap.insert( make_pair ( link, 1 ));
          else
            link_nb->second++;
        }
      }
      // remove nodes that are in links encountered only once from setMovableNodes
      for ( link_nb = linkNbMap.begin(); link_nb != linkNbMap.end(); ++link_nb ) {
        if ( link_nb->second == 1 ) {
          setMovableNodes.erase( link_nb->first.first );
          setMovableNodes.erase( link_nb->first.second );
        }
      }
    }

    // -----------------------------------------------------
    // for nodes on seam edge, compute one more UV ( uvMap2 );
    // find movable nodes linked to nodes on seam and which
    // are to be smoothed using the second UV ( uvMap2 )
    // -----------------------------------------------------

    set<const SMDS_MeshNode*> nodesNearSeam; // to smooth using uvMap2
    if ( !surface.IsNull() ) {
      TopExp_Explorer eExp( face, TopAbs_EDGE );
      for ( ; eExp.More(); eExp.Next() ) {
        TopoDS_Edge edge = TopoDS::Edge( eExp.Current() );
        if ( !BRep_Tool::IsClosed( edge, face ))
          continue;
        SMESHDS_SubMesh* sm = aMesh->MeshElements( edge );
        if ( !sm ) continue;
        // find out which parameter varies for a node on seam
        double f,l;
        gp_Pnt2d uv1, uv2;
        Handle(Geom2d_Curve) pcurve = BRep_Tool::CurveOnSurface( edge, face, f, l );
        if ( pcurve.IsNull() ) continue;
        uv1 = pcurve->Value( f );
        edge.Reverse();
        pcurve = BRep_Tool::CurveOnSurface( edge, face, f, l );
        if ( pcurve.IsNull() ) continue;
        uv2 = pcurve->Value( f );
        int iPar = Abs( uv1.X() - uv2.X() ) > Abs( uv1.Y() - uv2.Y() ) ? 1 : 2;
        // assure uv1 < uv2
        if ( uv1.Coord( iPar ) > uv2.Coord( iPar )) {
          gp_Pnt2d tmp = uv1; uv1 = uv2; uv2 = tmp;
        }
        // get nodes on seam and its vertices
        list< const SMDS_MeshNode* > seamNodes;
        SMDS_NodeIteratorPtr nSeamIt = sm->GetNodes();
        while ( nSeamIt->more() ) {
          const SMDS_MeshNode* node = nSeamIt->next();
          if ( !isQuadratic || !IsMedium( node ))
            seamNodes.push_back( node );
        }
        TopExp_Explorer vExp( edge, TopAbs_VERTEX );
        for ( ; vExp.More(); vExp.Next() ) {
          sm = aMesh->MeshElements( vExp.Current() );
          if ( sm ) {
            nSeamIt = sm->GetNodes();
            while ( nSeamIt->more() )
              seamNodes.push_back( nSeamIt->next() );
          }
        }
        // loop on nodes on seam
        list< const SMDS_MeshNode* >::iterator noSeIt = seamNodes.begin();
        for ( ; noSeIt != seamNodes.end(); ++noSeIt ) {
          const SMDS_MeshNode* nSeam = *noSeIt;
          map< const SMDS_MeshNode*, gp_XY* >::iterator n_uv = uvMap.find( nSeam );
          if ( n_uv == uvMap.end() )
            continue;
          // set the first UV
          n_uv->second->SetCoord( iPar, uv1.Coord( iPar ));
          // set the second UV
          listUV.push_back( *n_uv->second );
          listUV.back().SetCoord( iPar, uv2.Coord( iPar ));
          if ( uvMap2.empty() )
            uvMap2 = uvMap; // copy the uvMap contents
          uvMap2[ nSeam ] = &listUV.back();

          // collect movable nodes linked to ones on seam in nodesNearSeam
          SMDS_ElemIteratorPtr eIt = nSeam->GetInverseElementIterator(SMDSAbs_Face);
          while ( eIt->more() ) {
            const SMDS_MeshElement* e = eIt->next();
            int nbUseMap1 = 0, nbUseMap2 = 0;
            SMDS_ElemIteratorPtr nIt = e->nodesIterator();
            int nn = 0, nbn =  e->NbNodes();
            if(e->IsQuadratic()) nbn = nbn/2;
            while ( nn++ < nbn )
            {
              const SMDS_MeshNode* n =
                static_cast<const SMDS_MeshNode*>( nIt->next() );
              if (n == nSeam ||
                  setMovableNodes.find( n ) == setMovableNodes.end() )
                continue;
              // add only nodes being closer to uv2 than to uv1
              gp_Pnt pMid (0.5 * ( n->X() + nSeam->X() ),
                           0.5 * ( n->Y() + nSeam->Y() ),
                           0.5 * ( n->Z() + nSeam->Z() ));
              gp_XY uv;
              getClosestUV( projector, pMid, uv );
              if ( uv.Coord( iPar ) > uvMap[ n ]->Coord( iPar ) ) {
                nodesNearSeam.insert( n );
                nbUseMap2++;
              }
              else
                nbUseMap1++;
            }
            // for centroidalSmooth all element nodes must
            // be on one side of a seam
            if ( theSmoothMethod == CENTROIDAL && nbUseMap1 && nbUseMap2 ) {
              SMDS_ElemIteratorPtr nIt = e->nodesIterator();
              nn = 0;
              while ( nn++ < nbn ) {
                const SMDS_MeshNode* n =
                  static_cast<const SMDS_MeshNode*>( nIt->next() );
                setMovableNodes.erase( n );
              }
            }
          }
        } // loop on nodes on seam
      } // loop on edge of a face
    } // if ( !face.IsNull() )

    if ( setMovableNodes.empty() ) {
      MESSAGE( "Face id : " << *fId << " - NO SMOOTHING: no nodes to move!!!");
      continue; // goto next face
    }

    // -------------
    // SMOOTHING //
    // -------------

    int it = -1;
    double maxRatio = -1., maxDisplacement = -1.;
    set<const SMDS_MeshNode*>::iterator nodeToMove;
    for ( it = 0; it < theNbIterations; it++ ) {
      maxDisplacement = 0.;
      nodeToMove = setMovableNodes.begin();
      for ( ; nodeToMove != setMovableNodes.end(); nodeToMove++ ) {
        const SMDS_MeshNode* node = (*nodeToMove);
        gp_XYZ aPrevPos ( node->X(), node->Y(), node->Z() );

        // smooth
        bool map2 = ( nodesNearSeam.find( node ) != nodesNearSeam.end() );
        if ( theSmoothMethod == LAPLACIAN )
          laplacianSmooth( node, surface, map2 ? uvMap2 : uvMap );
        else
          centroidalSmooth( node, surface, map2 ? uvMap2 : uvMap );

        // node displacement
        gp_XYZ aNewPos ( node->X(), node->Y(), node->Z() );
        Standard_Real aDispl = (aPrevPos - aNewPos).SquareModulus();
        if ( aDispl > maxDisplacement )
          maxDisplacement = aDispl;
      }
      // no node movement => exit
      //if ( maxDisplacement < 1.e-16 ) {
      if ( maxDisplacement < disttol ) {
        MESSAGE("-- no node movement --");
        break;
      }

      // check elements quality
      maxRatio  = 0;
      list< const SMDS_MeshElement* >::iterator elemIt = elemsOnFace.begin();
      for ( ; elemIt != elemsOnFace.end(); ++elemIt ) {
        const SMDS_MeshElement* elem = (*elemIt);
        if ( !elem || elem->GetType() != SMDSAbs_Face )
          continue;
        SMESH::Controls::TSequenceOfXYZ aPoints;
        if ( aQualityFunc.GetPoints( elem, aPoints )) {
          double aValue = aQualityFunc.GetValue( aPoints );
          if ( aValue > maxRatio )
            maxRatio = aValue;
        }
      }
      if ( maxRatio <= theTgtAspectRatio ) {
        MESSAGE("-- quality achived --");
        break;
      }
      if (it+1 == theNbIterations) {
        MESSAGE("-- Iteration limit exceeded --");
      }
    } // smoothing iterations

    MESSAGE(" Face id: " << *fId <<
            " Nb iterstions: " << it <<
            " Displacement: " << maxDisplacement <<
            " Aspect Ratio " << maxRatio);

    // ---------------------------------------
    // new nodes positions are computed,
    // record movement in DS and set new UV
    // ---------------------------------------
    nodeToMove = setMovableNodes.begin();
    for ( ; nodeToMove != setMovableNodes.end(); nodeToMove++ ) {
      SMDS_MeshNode* node = const_cast< SMDS_MeshNode* > (*nodeToMove);
      aMesh->MoveNode( node, node->X(), node->Y(), node->Z() );
      map< const SMDS_MeshNode*, gp_XY* >::iterator node_uv = uvMap.find( node );
      if ( node_uv != uvMap.end() ) {
        gp_XY* uv = node_uv->second;
        node->SetPosition
          ( SMDS_PositionPtr( new SMDS_FacePosition( *fId, uv->X(), uv->Y() )));
      }
    }

    // move medium nodes of quadratic elements
    if ( isQuadratic )
    {
      SMESH_MesherHelper helper( *GetMesh() );
      if ( !face.IsNull() )
        helper.SetSubShape( face );
      list< const SMDS_MeshElement* >::iterator elemIt = elemsOnFace.begin();
      for ( ; elemIt != elemsOnFace.end(); ++elemIt ) {
        const SMDS_QuadraticFaceOfNodes* QF =
          dynamic_cast<const SMDS_QuadraticFaceOfNodes*> (*elemIt);
        if(QF) {
          vector<const SMDS_MeshNode*> Ns;
          Ns.reserve(QF->NbNodes()+1);
          SMDS_NodeIteratorPtr anIter = QF->interlacedNodesIterator();
          while ( anIter->more() )
            Ns.push_back( anIter->next() );
          Ns.push_back( Ns[0] );
          double x, y, z;
          for(int i=0; i<QF->NbNodes(); i=i+2) {
            if ( !surface.IsNull() ) {
              gp_XY uv1 = helper.GetNodeUV( face, Ns[i], Ns[i+2] );
              gp_XY uv2 = helper.GetNodeUV( face, Ns[i+2], Ns[i] );
              gp_XY uv = ( uv1 + uv2 ) / 2.;
              gp_Pnt xyz = surface->Value( uv.X(), uv.Y() );
              x = xyz.X(); y = xyz.Y(); z = xyz.Z();
            }
            else {
              x = (Ns[i]->X() + Ns[i+2]->X())/2;
              y = (Ns[i]->Y() + Ns[i+2]->Y())/2;
              z = (Ns[i]->Z() + Ns[i+2]->Z())/2;
            }
            if( fabs( Ns[i+1]->X() - x ) > disttol ||
                fabs( Ns[i+1]->Y() - y ) > disttol ||
                fabs( Ns[i+1]->Z() - z ) > disttol ) {
              // we have to move i+1 node
              aMesh->MoveNode( Ns[i+1], x, y, z );
            }
          }
        }
      }
    }

  } // loop on face ids

}

//=======================================================================
//function : isReverse
//purpose  : Return true if normal of prevNodes is not co-directied with
//           gp_Vec(prevNodes[iNotSame],nextNodes[iNotSame]).
//           iNotSame is where prevNodes and nextNodes are different
//=======================================================================

static bool isReverse(vector<const SMDS_MeshNode*> prevNodes,
                      vector<const SMDS_MeshNode*> nextNodes,
                      const int            nbNodes,
                      const int            iNotSame)
{
  int iBeforeNotSame = ( iNotSame == 0 ? nbNodes - 1 : iNotSame - 1 );
  int iAfterNotSame  = ( iNotSame + 1 == nbNodes ? 0 : iNotSame + 1 );

  const SMDS_MeshNode* nB = prevNodes[ iBeforeNotSame ];
  const SMDS_MeshNode* nA = prevNodes[ iAfterNotSame ];
  const SMDS_MeshNode* nP = prevNodes[ iNotSame ];
  const SMDS_MeshNode* nN = nextNodes[ iNotSame ];

  gp_Pnt pB ( nB->X(), nB->Y(), nB->Z() );
  gp_Pnt pA ( nA->X(), nA->Y(), nA->Z() );
  gp_Pnt pP ( nP->X(), nP->Y(), nP->Z() );
  gp_Pnt pN ( nN->X(), nN->Y(), nN->Z() );

  gp_Vec vB ( pP, pB ), vA ( pP, pA ), vN ( pP, pN );

  return (vA ^ vB) * vN < 0.0;
}

//=======================================================================
/*!
 * \brief Create elements by sweeping an element
 * \param elem - element to sweep
 * \param newNodesItVec - nodes generated from each node of the element
 * \param newElems - generated elements
 * \param nbSteps - number of sweeping steps
 * \param srcElements - to append elem for each generated element
 */
//=======================================================================

void SMESH_MeshEditor::sweepElement(const SMDS_MeshElement*               elem,
                                    const vector<TNodeOfNodeListMapItr> & newNodesItVec,
                                    list<const SMDS_MeshElement*>&        newElems,
                                    const int                             nbSteps,
                                    SMESH_SequenceOfElemPtr&              srcElements)
{
  SMESHDS_Mesh* aMesh = GetMeshDS();

  // Loop on elem nodes:
  // find new nodes and detect same nodes indices
  int nbNodes = elem->NbNodes();
  vector < list< const SMDS_MeshNode* >::const_iterator > itNN( nbNodes );
  vector<const SMDS_MeshNode*> prevNod( nbNodes );
  vector<const SMDS_MeshNode*> nextNod( nbNodes );
  vector<const SMDS_MeshNode*> midlNod( nbNodes );

  int iNode, nbSame = 0, iNotSameNode = 0, iSameNode = 0;
  vector<int> sames(nbNodes);

  //bool issimple[nbNodes];
  vector<bool> issimple(nbNodes);

  for ( iNode = 0; iNode < nbNodes; iNode++ ) {
    TNodeOfNodeListMapItr nnIt = newNodesItVec[ iNode ];
    const SMDS_MeshNode*                 node         = nnIt->first;
    const list< const SMDS_MeshNode* > & listNewNodes = nnIt->second;
    if ( listNewNodes.empty() )
      return;

    if(listNewNodes.size()==nbSteps) {
      issimple[iNode] = true;
    }
    else {
      issimple[iNode] = false;
    }

    itNN[ iNode ] = listNewNodes.begin();
    prevNod[ iNode ] = node;
    nextNod[ iNode ] = listNewNodes.front();
//cout<<"iNode="<<iNode<<endl;
//cout<<" prevNod[iNode]="<< prevNod[iNode]<<" nextNod[iNode]="<< nextNod[iNode]<<endl;
    if ( prevNod[ iNode ] != nextNod [ iNode ])
      iNotSameNode = iNode;
    else {
      iSameNode = iNode;
      //nbSame++;
      sames[nbSame++] = iNode;
    }
  }
//cout<<"1 nbSame="<<nbSame<<endl;
  if ( nbSame == nbNodes || nbSame > 2) {
    MESSAGE( " Too many same nodes of element " << elem->GetID() );
    return;
  }

//  if( elem->IsQuadratic() && nbSame>0 ) {
//    MESSAGE( "Can not rotate quadratic element " << elem->GetID() );
//    return;
//  }

  int iBeforeSame = 0, iAfterSame = 0, iOpposSame = 0;
  if ( nbSame > 0 ) {
    iBeforeSame = ( iSameNode == 0 ? nbNodes - 1 : iSameNode - 1 );
    iAfterSame  = ( iSameNode + 1 == nbNodes ? 0 : iSameNode + 1 );
    iOpposSame  = ( iSameNode - 2 < 0  ? iSameNode + 2 : iSameNode - 2 );
  }

//if(nbNodes==8)
//cout<<" prevNod[0]="<< prevNod[0]<<" prevNod[1]="<< prevNod[1]
//    <<" prevNod[2]="<< prevNod[2]<<" prevNod[3]="<< prevNod[4]
//    <<" prevNod[4]="<< prevNod[4]<<" prevNod[5]="<< prevNod[5]
//    <<" prevNod[6]="<< prevNod[6]<<" prevNod[7]="<< prevNod[7]<<endl;

  // check element orientation
  int i0 = 0, i2 = 2;
  if ( nbNodes > 2 && !isReverse( prevNod, nextNod, nbNodes, iNotSameNode )) {
    //MESSAGE("Reversed elem " << elem );
    i0 = 2;
    i2 = 0;
    if ( nbSame > 0 ) {
      int iAB = iAfterSame + iBeforeSame;
      iBeforeSame = iAB - iBeforeSame;
      iAfterSame  = iAB - iAfterSame;
    }
  }

  // make new elements
  for (int iStep = 0; iStep < nbSteps; iStep++ ) {
    // get next nodes
    for ( iNode = 0; iNode < nbNodes; iNode++ ) {
      if(issimple[iNode]) {
        nextNod[ iNode ] = *itNN[ iNode ];
        itNN[ iNode ]++;
      }
      else {
        if( elem->GetType()==SMDSAbs_Node ) {
          // we have to use two nodes
          midlNod[ iNode ] = *itNN[ iNode ];
          itNN[ iNode ]++;
          nextNod[ iNode ] = *itNN[ iNode ];
          itNN[ iNode ]++;
        }
        else if(!elem->IsQuadratic() ||
           elem->IsQuadratic() && elem->IsMediumNode(prevNod[iNode]) ) {
          // we have to use each second node
          itNN[ iNode ]++;
          nextNod[ iNode ] = *itNN[ iNode ];
          itNN[ iNode ]++;
        }
        else {
          // we have to use two nodes
          midlNod[ iNode ] = *itNN[ iNode ];
          itNN[ iNode ]++;
          nextNod[ iNode ] = *itNN[ iNode ];
          itNN[ iNode ]++;
        }
      }
    }
    SMDS_MeshElement* aNewElem = 0;
    if(!elem->IsPoly()) {
      switch ( nbNodes ) {
      case 0:
        return;
      case 1: { // NODE
        if ( nbSame == 0 ) {
          if(issimple[0])
            aNewElem = aMesh->AddEdge( prevNod[ 0 ], nextNod[ 0 ] );
          else
            aNewElem = aMesh->AddEdge( prevNod[ 0 ], nextNod[ 0 ], midlNod[ 0 ] );
        }
        break;
      }
      case 2: { // EDGE
        if ( nbSame == 0 )
          aNewElem = aMesh->AddFace(prevNod[ 0 ], prevNod[ 1 ],
                                    nextNod[ 1 ], nextNod[ 0 ] );
        else
          aNewElem = aMesh->AddFace(prevNod[ 0 ], prevNod[ 1 ],
                                    nextNod[ iNotSameNode ] );
        break;
      }

      case 3: { // TRIANGLE or quadratic edge
        if(elem->GetType() == SMDSAbs_Face) { // TRIANGLE

          if ( nbSame == 0 )       // --- pentahedron
            aNewElem = aMesh->AddVolume (prevNod[ i0 ], prevNod[ 1 ], prevNod[ i2 ],
                                         nextNod[ i0 ], nextNod[ 1 ], nextNod[ i2 ] );

          else if ( nbSame == 1 )  // --- pyramid
            aNewElem = aMesh->AddVolume (prevNod[ iBeforeSame ],  prevNod[ iAfterSame ],
                                         nextNod[ iAfterSame ], nextNod[ iBeforeSame ],
                                         nextNod[ iSameNode ]);

          else // 2 same nodes:      --- tetrahedron
            aNewElem = aMesh->AddVolume (prevNod[ i0 ], prevNod[ 1 ], prevNod[ i2 ],
                                         nextNod[ iNotSameNode ]);
        }
        else { // quadratic edge
          if(nbSame==0) {     // quadratic quadrangle
            aNewElem = aMesh->AddFace(prevNod[0], nextNod[0], nextNod[1], prevNod[1],
                                      midlNod[0], nextNod[2], midlNod[1], prevNod[2]);
          }
          else if(nbSame==1) { // quadratic triangle
            if(sames[0]==2)
              return; // medium node on axis
            else if(sames[0]==0) {
              aNewElem = aMesh->AddFace(prevNod[0], nextNod[1], prevNod[1],
                                        nextNod[2], midlNod[1], prevNod[2]);
            }
            else { // sames[0]==1
              aNewElem = aMesh->AddFace(prevNod[0], nextNod[0], prevNod[1],
                                        midlNod[0], nextNod[2], prevNod[2]);
            }
          }
          else
            return;
        }
        break;
      }
      case 4: { // QUADRANGLE

        if ( nbSame == 0 )       // --- hexahedron
          aNewElem = aMesh->AddVolume (prevNod[ i0 ], prevNod[ 1 ], prevNod[ i2 ], prevNod[ 3 ],
                                       nextNod[ i0 ], nextNod[ 1 ], nextNod[ i2 ], nextNod[ 3 ]);

        else if ( nbSame == 1 ) { // --- pyramid + pentahedron
          aNewElem = aMesh->AddVolume (prevNod[ iBeforeSame ],  prevNod[ iAfterSame ],
                                       nextNod[ iAfterSame ], nextNod[ iBeforeSame ],
                                       nextNod[ iSameNode ]);
          newElems.push_back( aNewElem );
          aNewElem = aMesh->AddVolume (prevNod[ iAfterSame ], prevNod[ iOpposSame ],
                                       prevNod[ iBeforeSame ],  nextNod[ iAfterSame ],
                                       nextNod[ iOpposSame ],  nextNod[ iBeforeSame ] );
        }
        else if ( nbSame == 2 ) { // pentahedron
          if ( prevNod[ iBeforeSame ] == nextNod[ iBeforeSame ] )
            // iBeforeSame is same too
            aNewElem = aMesh->AddVolume (prevNod[ iBeforeSame ], prevNod[ iOpposSame ],
                                         nextNod[ iOpposSame ], prevNod[ iSameNode ],
                                         prevNod[ iAfterSame ],  nextNod[ iAfterSame ]);
          else
            // iAfterSame is same too
            aNewElem = aMesh->AddVolume (prevNod[ iSameNode ], prevNod[ iBeforeSame ],
                                         nextNod[ iBeforeSame ], prevNod[ iAfterSame ],
                                         prevNod[ iOpposSame ],  nextNod[ iOpposSame ]);
        }
        break;
      }
      case 6: { // quadratic triangle
        // create pentahedron with 15 nodes
        if(i0>0) { // reversed case
          aNewElem = aMesh->AddVolume (prevNod[0], prevNod[2], prevNod[1],
                                       nextNod[0], nextNod[2], nextNod[1],
                                       prevNod[5], prevNod[4], prevNod[3],
                                       nextNod[5], nextNod[4], nextNod[3],
                                       midlNod[0], midlNod[2], midlNod[1]);
        }
        else { // not reversed case
          aNewElem = aMesh->AddVolume (prevNod[0], prevNod[1], prevNod[2],
                                       nextNod[0], nextNod[1], nextNod[2],
                                       prevNod[3], prevNod[4], prevNod[5],
                                       nextNod[3], nextNod[4], nextNod[5],
                                       midlNod[0], midlNod[1], midlNod[2]);
        }
        break;
      }
      case 8: { // quadratic quadrangle
        // create hexahedron with 20 nodes
        if(i0>0) { // reversed case
          aNewElem = aMesh->AddVolume (prevNod[0], prevNod[3], prevNod[2], prevNod[1],
                                       nextNod[0], nextNod[3], nextNod[2], nextNod[1],
                                       prevNod[7], prevNod[6], prevNod[5], prevNod[4],
                                       nextNod[7], nextNod[6], nextNod[5], nextNod[4],
                                       midlNod[0], midlNod[3], midlNod[2], midlNod[1]);
        }
        else { // not reversed case
          aNewElem = aMesh->AddVolume (prevNod[0], prevNod[1], prevNod[2], prevNod[3],
                                       nextNod[0], nextNod[1], nextNod[2], nextNod[3],
                                       prevNod[4], prevNod[5], prevNod[6], prevNod[7],
                                       nextNod[4], nextNod[5], nextNod[6], nextNod[7],
                                       midlNod[0], midlNod[1], midlNod[2], midlNod[3]);
        }
        break;
      }
      default: {
        // realized for extrusion only
        //vector<const SMDS_MeshNode*> polyedre_nodes (nbNodes*2 + 4*nbNodes);
        //vector<int> quantities (nbNodes + 2);

        //quantities[0] = nbNodes; // bottom of prism
        //for (int inode = 0; inode < nbNodes; inode++) {
        //  polyedre_nodes[inode] = prevNod[inode];
        //}

        //quantities[1] = nbNodes; // top of prism
        //for (int inode = 0; inode < nbNodes; inode++) {
        //  polyedre_nodes[nbNodes + inode] = nextNod[inode];
        //}

        //for (int iface = 0; iface < nbNodes; iface++) {
        //  quantities[iface + 2] = 4;
        //  int inextface = (iface == nbNodes - 1) ? 0 : iface + 1;
        //  polyedre_nodes[2*nbNodes + 4*iface + 0] = prevNod[iface];
        //  polyedre_nodes[2*nbNodes + 4*iface + 1] = prevNod[inextface];
        //  polyedre_nodes[2*nbNodes + 4*iface + 2] = nextNod[inextface];
        //  polyedre_nodes[2*nbNodes + 4*iface + 3] = nextNod[iface];
        //}
        //aNewElem = aMesh->AddPolyhedralVolume (polyedre_nodes, quantities);
        break;
      }
      }
    }

    if(!aNewElem) {
      // realized for extrusion only
      vector<const SMDS_MeshNode*> polyedre_nodes (nbNodes*2 + 4*nbNodes);
      vector<int> quantities (nbNodes + 2);

      quantities[0] = nbNodes; // bottom of prism
      for (int inode = 0; inode < nbNodes; inode++) {
        polyedre_nodes[inode] = prevNod[inode];
      }

      quantities[1] = nbNodes; // top of prism
      for (int inode = 0; inode < nbNodes; inode++) {
        polyedre_nodes[nbNodes + inode] = nextNod[inode];
      }

      for (int iface = 0; iface < nbNodes; iface++) {
        quantities[iface + 2] = 4;
        int inextface = (iface == nbNodes - 1) ? 0 : iface + 1;
        polyedre_nodes[2*nbNodes + 4*iface + 0] = prevNod[iface];
        polyedre_nodes[2*nbNodes + 4*iface + 1] = prevNod[inextface];
        polyedre_nodes[2*nbNodes + 4*iface + 2] = nextNod[inextface];
        polyedre_nodes[2*nbNodes + 4*iface + 3] = nextNod[iface];
      }
      aNewElem = aMesh->AddPolyhedralVolume (polyedre_nodes, quantities);
    }

    if ( aNewElem ) {
      newElems.push_back( aNewElem );
      myLastCreatedElems.Append(aNewElem);
      srcElements.Append( elem );
    }

    // set new prev nodes
    for ( iNode = 0; iNode < nbNodes; iNode++ )
      prevNod[ iNode ] = nextNod[ iNode ];

  } // for steps
}

//=======================================================================
/*!
 * \brief Create 1D and 2D elements around swept elements
 * \param mapNewNodes - source nodes and ones generated from them
 * \param newElemsMap - source elements and ones generated from them
 * \param elemNewNodesMap - nodes generated from each node of each element
 * \param elemSet - all swept elements
 * \param nbSteps - number of sweeping steps
 * \param srcElements - to append elem for each generated element
 */
//=======================================================================

void SMESH_MeshEditor::makeWalls (TNodeOfNodeListMap &     mapNewNodes,
                                  TElemOfElemListMap &     newElemsMap,
                                  TElemOfVecOfNnlmiMap &   elemNewNodesMap,
                                  TIDSortedElemSet&        elemSet,
                                  const int                nbSteps,
                                  SMESH_SequenceOfElemPtr& srcElements)
{
  ASSERT( newElemsMap.size() == elemNewNodesMap.size() );
  SMESHDS_Mesh* aMesh = GetMeshDS();

  // Find nodes belonging to only one initial element - sweep them to get edges.

  TNodeOfNodeListMapItr nList = mapNewNodes.begin();
  for ( ; nList != mapNewNodes.end(); nList++ ) {
    const SMDS_MeshNode* node =
      static_cast<const SMDS_MeshNode*>( nList->first );
    SMDS_ElemIteratorPtr eIt = node->GetInverseElementIterator();
    int nbInitElems = 0;
    const SMDS_MeshElement* el = 0;
    SMDSAbs_ElementType highType = SMDSAbs_Edge; // count most complex elements only
    while ( eIt->more() && nbInitElems < 2 ) {
      el = eIt->next();
      SMDSAbs_ElementType type = el->GetType();
      if ( type == SMDSAbs_Volume || type < highType ) continue;
      if ( type > highType ) {
        nbInitElems = 0;
        highType = type;
      }
      if ( elemSet.find(el) != elemSet.end() )
        nbInitElems++;
    }
    if ( nbInitElems < 2 ) {
      bool NotCreateEdge = el && el->IsQuadratic() && el->IsMediumNode(node);
      if(!NotCreateEdge) {
        vector<TNodeOfNodeListMapItr> newNodesItVec( 1, nList );
        list<const SMDS_MeshElement*> newEdges;
        sweepElement( node, newNodesItVec, newEdges, nbSteps, srcElements );
      }
    }
  }

  // Make a ceiling for each element ie an equal element of last new nodes.
  // Find free links of faces - make edges and sweep them into faces.

  TElemOfElemListMap::iterator   itElem      = newElemsMap.begin();
  TElemOfVecOfNnlmiMap::iterator itElemNodes = elemNewNodesMap.begin();
  for ( ; itElem != newElemsMap.end(); itElem++, itElemNodes++ ) {
    const SMDS_MeshElement* elem = itElem->first;
    vector<TNodeOfNodeListMapItr>& vecNewNodes = itElemNodes->second;

    if ( elem->GetType() == SMDSAbs_Edge ) {
      // create a ceiling edge
      if (!elem->IsQuadratic()) {
        if ( !aMesh->FindEdge( vecNewNodes[ 0 ]->second.back(),
                               vecNewNodes[ 1 ]->second.back())) {
          myLastCreatedElems.Append(aMesh->AddEdge(vecNewNodes[ 0 ]->second.back(),
                                                   vecNewNodes[ 1 ]->second.back()));
          srcElements.Append( myLastCreatedElems.Last() );
        }
      }
      else {
        if ( !aMesh->FindEdge( vecNewNodes[ 0 ]->second.back(),
                               vecNewNodes[ 1 ]->second.back(),
                               vecNewNodes[ 2 ]->second.back())) {
          myLastCreatedElems.Append(aMesh->AddEdge(vecNewNodes[ 0 ]->second.back(),
                                                   vecNewNodes[ 1 ]->second.back(),
                                                   vecNewNodes[ 2 ]->second.back()));
          srcElements.Append( myLastCreatedElems.Last() );
        }
      }
    }
    if ( elem->GetType() != SMDSAbs_Face )
      continue;

    if(itElem->second.size()==0) continue;

    bool hasFreeLinks = false;

    TIDSortedElemSet avoidSet;
    avoidSet.insert( elem );

    set<const SMDS_MeshNode*> aFaceLastNodes;
    int iNode, nbNodes = vecNewNodes.size();
    if(!elem->IsQuadratic()) {
      // loop on the face nodes
      for ( iNode = 0; iNode < nbNodes; iNode++ ) {
        aFaceLastNodes.insert( vecNewNodes[ iNode ]->second.back() );
        // look for free links of the face
        int iNext = ( iNode + 1 == nbNodes ) ? 0 : iNode + 1;
        const SMDS_MeshNode* n1 = vecNewNodes[ iNode ]->first;
        const SMDS_MeshNode* n2 = vecNewNodes[ iNext ]->first;
        // check if a link is free
        if ( ! SMESH_MeshEditor::FindFaceInSet ( n1, n2, elemSet, avoidSet )) {
          hasFreeLinks = true;
          // make an edge and a ceiling for a new edge
          if ( !aMesh->FindEdge( n1, n2 )) {
            myLastCreatedElems.Append(aMesh->AddEdge( n1, n2 )); // free link edge
            srcElements.Append( myLastCreatedElems.Last() );
          }
          n1 = vecNewNodes[ iNode ]->second.back();
          n2 = vecNewNodes[ iNext ]->second.back();
          if ( !aMesh->FindEdge( n1, n2 )) {
            myLastCreatedElems.Append(aMesh->AddEdge( n1, n2 )); // ceiling edge
            srcElements.Append( myLastCreatedElems.Last() );
          }
        }
      }
    }
    else { // elem is quadratic face
      int nbn = nbNodes/2;
      for ( iNode = 0; iNode < nbn; iNode++ ) {
        aFaceLastNodes.insert( vecNewNodes[ iNode ]->second.back() );
        int iNext = ( iNode + 1 == nbn ) ? 0 : iNode + 1;
        const SMDS_MeshNode* n1 = vecNewNodes[ iNode ]->first;
        const SMDS_MeshNode* n2 = vecNewNodes[ iNext ]->first;
        // check if a link is free
        if ( ! SMESH_MeshEditor::FindFaceInSet ( n1, n2, elemSet, avoidSet )) {
          hasFreeLinks = true;
          // make an edge and a ceiling for a new edge
          // find medium node
          const SMDS_MeshNode* n3 = vecNewNodes[ iNode+nbn ]->first;
          if ( !aMesh->FindEdge( n1, n2, n3 )) {
            myLastCreatedElems.Append(aMesh->AddEdge( n1, n2, n3 )); // free link edge
            srcElements.Append( myLastCreatedElems.Last() );
          }
          n1 = vecNewNodes[ iNode ]->second.back();
          n2 = vecNewNodes[ iNext ]->second.back();
          n3 = vecNewNodes[ iNode+nbn ]->second.back();
          if ( !aMesh->FindEdge( n1, n2, n3 )) {
            myLastCreatedElems.Append(aMesh->AddEdge( n1, n2, n3 )); // ceiling edge
            srcElements.Append( myLastCreatedElems.Last() );
          }
        }
      }
      for ( iNode = nbn; iNode < 2*nbn; iNode++ ) {
        aFaceLastNodes.insert( vecNewNodes[ iNode ]->second.back() );
      }
    }

    // sweep free links into faces

    if ( hasFreeLinks )  {
      list<const SMDS_MeshElement*> & newVolumes = itElem->second;
      int iVol, volNb, nbVolumesByStep = newVolumes.size() / nbSteps;

      set<const SMDS_MeshNode*> initNodeSet, topNodeSet, faceNodeSet;
      for ( iNode = 0; iNode < nbNodes; iNode++ ) {
        initNodeSet.insert( vecNewNodes[ iNode ]->first );
        topNodeSet .insert( vecNewNodes[ iNode ]->second.back() );
      }
      for ( volNb = 0; volNb < nbVolumesByStep; volNb++ ) {
        list<const SMDS_MeshElement*>::iterator v = newVolumes.begin();
        iVol = 0;
        while ( iVol++ < volNb ) v++;
        // find indices of free faces of a volume and their source edges
        list< int > freeInd;
        list< const SMDS_MeshElement* > srcEdges; // source edges of free faces
        SMDS_VolumeTool vTool( *v );
        int iF, nbF = vTool.NbFaces();
        for ( iF = 0; iF < nbF; iF ++ ) {
          if (vTool.IsFreeFace( iF ) &&
              vTool.GetFaceNodes( iF, faceNodeSet ) &&
              initNodeSet != faceNodeSet) // except an initial face
          {
            if ( nbSteps == 1 && faceNodeSet == topNodeSet )
              continue;
            freeInd.push_back( iF );
            // find source edge of a free face iF
            vector<const SMDS_MeshNode*> commonNodes; // shared by the initial and free faces
            commonNodes.resize( initNodeSet.size(), NULL ); // avoid spoiling memory
            std::set_intersection( faceNodeSet.begin(), faceNodeSet.end(),
                                   initNodeSet.begin(), initNodeSet.end(),
                                   commonNodes.begin());
            if ( (*v)->IsQuadratic() )
              srcEdges.push_back(aMesh->FindEdge (commonNodes[0],commonNodes[1],commonNodes[2]));
            else
              srcEdges.push_back(aMesh->FindEdge (commonNodes[0],commonNodes[1]));
#ifdef _DEBUG_
            if ( !srcEdges.back() )
            {
              cout << "SMESH_MeshEditor::makeWalls(), no source edge found for a free face #"
                   << iF << " of volume #" << vTool.ID() << endl;
            }
#endif
          }
        }
        if ( freeInd.empty() )
          continue;

        // create faces for all steps;
        // if such a face has been already created by sweep of edge,
        // assure that its orientation is OK
        for ( int iStep = 0; iStep < nbSteps; iStep++ )  {
          vTool.Set( *v );
          vTool.SetExternalNormal();
          list< int >::iterator ind = freeInd.begin();
          list< const SMDS_MeshElement* >::iterator srcEdge = srcEdges.begin();
          for ( ; ind != freeInd.end(); ++ind, ++srcEdge ) // loop on free faces
          {
            const SMDS_MeshNode** nodes = vTool.GetFaceNodes( *ind );
            int nbn = vTool.NbFaceNodes( *ind );
            switch ( nbn ) {
            case 3: { ///// triangle
              const SMDS_MeshFace * f = aMesh->FindFace( nodes[ 0 ], nodes[ 1 ], nodes[ 2 ]);
              if ( !f )
                myLastCreatedElems.Append(aMesh->AddFace( nodes[ 0 ], nodes[ 1 ], nodes[ 2 ] ));
              else if ( nodes[ 1 ] != f->GetNode( f->GetNodeIndex( nodes[ 0 ] ) + 1 ))
                aMesh->ChangeElementNodes( f, nodes, nbn );
              break;
            }
            case 4: { ///// quadrangle
              const SMDS_MeshFace * f = aMesh->FindFace( nodes[ 0 ], nodes[ 1 ], nodes[ 2 ], nodes[ 3 ]);
              if ( !f )
                myLastCreatedElems.Append(aMesh->AddFace( nodes[ 0 ], nodes[ 1 ], nodes[ 2 ], nodes[ 3 ] ));
              else if ( nodes[ 1 ] != f->GetNode( f->GetNodeIndex( nodes[ 0 ] ) + 1 ))
                aMesh->ChangeElementNodes( f, nodes, nbn );
              break;
            }
            default:
              if( (*v)->IsQuadratic() ) {
                if(nbn==6) { /////// quadratic triangle
                  const SMDS_MeshFace * f = aMesh->FindFace( nodes[0], nodes[2], nodes[4],
                                                             nodes[1], nodes[3], nodes[5] );
                  if ( !f )
                    myLastCreatedElems.Append(aMesh->AddFace(nodes[0], nodes[2], nodes[4],
                                                             nodes[1], nodes[3], nodes[5]));
                  else if ( nodes[ 2 ] != f->GetNode( f->GetNodeIndex( nodes[ 0 ] ) + 1 ))
                    aMesh->ChangeElementNodes( f, nodes, nbn );
                }
                else {       /////// quadratic quadrangle
                  const SMDS_MeshFace * f = aMesh->FindFace( nodes[0], nodes[2], nodes[4], nodes[6],
                                                             nodes[1], nodes[3], nodes[5], nodes[7] );
                  if ( !f )
                    myLastCreatedElems.Append(aMesh->AddFace(nodes[0], nodes[2], nodes[4], nodes[6],
                                                             nodes[1], nodes[3], nodes[5], nodes[7]));
                  else if ( nodes[ 2 ] != f->GetNode( f->GetNodeIndex( nodes[ 0 ] ) + 1 ))
                    aMesh->ChangeElementNodes( f, nodes, nbn );
                }
              }
              else { //////// polygon
                vector<const SMDS_MeshNode*> polygon_nodes ( nodes, &nodes[nbn] );
                const SMDS_MeshFace * f = aMesh->FindFace( polygon_nodes );
                if ( !f )
                  myLastCreatedElems.Append(aMesh->AddPolygonalFace(polygon_nodes));
                else if ( nodes[ 1 ] != f->GetNode( f->GetNodeIndex( nodes[ 0 ] ) + 1 ))
                  aMesh->ChangeElementNodes( f, nodes, nbn );
              }
            }
            while ( srcElements.Length() < myLastCreatedElems.Length() )
              srcElements.Append( *srcEdge );

          }  // loop on free faces

          // go to the next volume
          iVol = 0;
          while ( iVol++ < nbVolumesByStep ) v++;
        }
      }
    } // sweep free links into faces

    // Make a ceiling face with a normal external to a volume

    SMDS_VolumeTool lastVol( itElem->second.back() );

    int iF = lastVol.GetFaceIndex( aFaceLastNodes );
    if ( iF >= 0 ) {
      lastVol.SetExternalNormal();
      const SMDS_MeshNode** nodes = lastVol.GetFaceNodes( iF );
      int nbn = lastVol.NbFaceNodes( iF );
      switch ( nbn ) {
      case 3:
        if (!hasFreeLinks ||
            !aMesh->FindFace( nodes[ 0 ], nodes[ 1 ], nodes[ 2 ]))
          myLastCreatedElems.Append(aMesh->AddFace( nodes[ 0 ], nodes[ 1 ], nodes[ 2 ] ));
        break;
      case 4:
        if (!hasFreeLinks ||
            !aMesh->FindFace( nodes[ 0 ], nodes[ 1 ], nodes[ 2 ], nodes[ 3 ]))
          myLastCreatedElems.Append(aMesh->AddFace( nodes[ 0 ], nodes[ 1 ], nodes[ 2 ], nodes[ 3 ] ));
        break;
      default:
        if(itElem->second.back()->IsQuadratic()) {
          if(nbn==6) {
            if (!hasFreeLinks ||
                !aMesh->FindFace(nodes[0], nodes[2], nodes[4],
                                 nodes[1], nodes[3], nodes[5]) ) {
              myLastCreatedElems.Append(aMesh->AddFace(nodes[0], nodes[2], nodes[4],
                                                       nodes[1], nodes[3], nodes[5]));
            }
          }
          else { // nbn==8
            if (!hasFreeLinks ||
                !aMesh->FindFace(nodes[0], nodes[2], nodes[4], nodes[6],
                                 nodes[1], nodes[3], nodes[5], nodes[7]) )
              myLastCreatedElems.Append(aMesh->AddFace(nodes[0], nodes[2], nodes[4], nodes[6],
                                                       nodes[1], nodes[3], nodes[5], nodes[7]));
          }
        }
        else {
          vector<const SMDS_MeshNode*> polygon_nodes ( nodes, &nodes[nbn] );
          if (!hasFreeLinks || !aMesh->FindFace(polygon_nodes))
            myLastCreatedElems.Append(aMesh->AddPolygonalFace(polygon_nodes));
        }
      } // switch

      while ( srcElements.Length() < myLastCreatedElems.Length() )
        srcElements.Append( myLastCreatedElems.Last() );
    }
  } // loop on swept elements
}

//=======================================================================
//function : RotationSweep
//purpose  :
//=======================================================================

SMESH_MeshEditor::PGroupIDs
SMESH_MeshEditor::RotationSweep(TIDSortedElemSet & theElems,
                                const gp_Ax1&      theAxis,
                                const double       theAngle,
                                const int          theNbSteps,
                                const double       theTol,
                                const bool         theMakeGroups,
                                const bool         theMakeWalls)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  // source elements for each generated one
  SMESH_SequenceOfElemPtr srcElems, srcNodes;

  MESSAGE( "RotationSweep()");
  gp_Trsf aTrsf;
  aTrsf.SetRotation( theAxis, theAngle );
  gp_Trsf aTrsf2;
  aTrsf2.SetRotation( theAxis, theAngle/2. );

  gp_Lin aLine( theAxis );
  double aSqTol = theTol * theTol;

  SMESHDS_Mesh* aMesh = GetMeshDS();

  TNodeOfNodeListMap mapNewNodes;
  TElemOfVecOfNnlmiMap mapElemNewNodes;
  TElemOfElemListMap newElemsMap;

  // loop on theElems
  TIDSortedElemSet::iterator itElem;
  for ( itElem = theElems.begin(); itElem != theElems.end(); itElem++ ) {
    const SMDS_MeshElement* elem = *itElem;
    if ( !elem || elem->GetType() == SMDSAbs_Volume )
      continue;
    vector<TNodeOfNodeListMapItr> & newNodesItVec = mapElemNewNodes[ elem ];
    newNodesItVec.reserve( elem->NbNodes() );

    // loop on elem nodes
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    while ( itN->more() )
    {
      // check if a node has been already sweeped
      const SMDS_MeshNode* node = cast2Node( itN->next() );
      TNodeOfNodeListMapItr nIt = mapNewNodes.find( node );
      if ( nIt == mapNewNodes.end() ) {
        nIt = mapNewNodes.insert( make_pair( node, list<const SMDS_MeshNode*>() )).first;
        list<const SMDS_MeshNode*>& listNewNodes = nIt->second;

        // make new nodes
        gp_XYZ aXYZ( node->X(), node->Y(), node->Z() );
        double coord[3];
        aXYZ.Coord( coord[0], coord[1], coord[2] );
        bool isOnAxis = ( aLine.SquareDistance( aXYZ ) <= aSqTol );
        const SMDS_MeshNode * newNode = node;
        for ( int i = 0; i < theNbSteps; i++ ) {
          if ( !isOnAxis ) {
            if( elem->IsQuadratic() && !elem->IsMediumNode(node) ) {
              // create two nodes
              aTrsf2.Transforms( coord[0], coord[1], coord[2] );
              //aTrsf.Transforms( coord[0], coord[1], coord[2] );
              newNode = aMesh->AddNode( coord[0], coord[1], coord[2] );
              myLastCreatedNodes.Append(newNode);
              srcNodes.Append( node );
              listNewNodes.push_back( newNode );
              aTrsf2.Transforms( coord[0], coord[1], coord[2] );
              //aTrsf.Transforms( coord[0], coord[1], coord[2] );
            }
            else {
              aTrsf.Transforms( coord[0], coord[1], coord[2] );
            }
            newNode = aMesh->AddNode( coord[0], coord[1], coord[2] );
            myLastCreatedNodes.Append(newNode);
            srcNodes.Append( node );
          }
          listNewNodes.push_back( newNode );
        }
      }
      else {
        // if current elem is quadratic and current node is not medium
        // we have to check - may be it is needed to insert additional nodes
        if( elem->IsQuadratic() && !elem->IsMediumNode(node) ) {
          list< const SMDS_MeshNode* > & listNewNodes = nIt->second;
          if(listNewNodes.size()==theNbSteps) {
            listNewNodes.clear();
            // make new nodes
            gp_XYZ aXYZ( node->X(), node->Y(), node->Z() );
            double coord[3];
            aXYZ.Coord( coord[0], coord[1], coord[2] );
            const SMDS_MeshNode * newNode = node;
            for(int i = 0; i<theNbSteps; i++) {
              aTrsf2.Transforms( coord[0], coord[1], coord[2] );
              newNode = aMesh->AddNode( coord[0], coord[1], coord[2] );
              myLastCreatedNodes.Append(newNode);
              listNewNodes.push_back( newNode );
              srcNodes.Append( node );
              aTrsf2.Transforms( coord[0], coord[1], coord[2] );
              newNode = aMesh->AddNode( coord[0], coord[1], coord[2] );
              myLastCreatedNodes.Append(newNode);
              srcNodes.Append( node );
              listNewNodes.push_back( newNode );
            }
          }
        }
      }
      newNodesItVec.push_back( nIt );
    }
    // make new elements
    sweepElement( elem, newNodesItVec, newElemsMap[elem], theNbSteps, srcElems );
  }

  if ( theMakeWalls )
    makeWalls( mapNewNodes, newElemsMap, mapElemNewNodes, theElems, theNbSteps, srcElems );
  
  PGroupIDs newGroupIDs;
  if ( theMakeGroups )
    newGroupIDs = generateGroups( srcNodes, srcElems, "rotated");

  return newGroupIDs;
}


//=======================================================================
//function : CreateNode
//purpose  :
//=======================================================================
const SMDS_MeshNode* SMESH_MeshEditor::CreateNode(const double x,
                                                  const double y,
                                                  const double z,
                                                  const double tolnode,
                                                  SMESH_SequenceOfNode& aNodes)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  gp_Pnt P1(x,y,z);
  SMESHDS_Mesh * aMesh = myMesh->GetMeshDS();

  // try to search in sequence of existing nodes
  // if aNodes.Length()>0 we 'nave to use given sequence
  // else - use all nodes of mesh
  if(aNodes.Length()>0) {
    int i;
    for(i=1; i<=aNodes.Length(); i++) {
      gp_Pnt P2(aNodes.Value(i)->X(),aNodes.Value(i)->Y(),aNodes.Value(i)->Z());
      if(P1.Distance(P2)<tolnode)
        return aNodes.Value(i);
    }
  }
  else {
    SMDS_NodeIteratorPtr itn = aMesh->nodesIterator();
    while(itn->more()) {
      const SMDS_MeshNode* aN = static_cast<const SMDS_MeshNode*> (itn->next());
      gp_Pnt P2(aN->X(),aN->Y(),aN->Z());
      if(P1.Distance(P2)<tolnode)
        return aN;
    }
  }

  // create new node and return it
  const SMDS_MeshNode* NewNode = aMesh->AddNode(x,y,z);
  myLastCreatedNodes.Append(NewNode);
  return NewNode;
}


//=======================================================================
//function : ExtrusionSweep
//purpose  :
//=======================================================================

SMESH_MeshEditor::PGroupIDs
SMESH_MeshEditor::ExtrusionSweep (TIDSortedElemSet &  theElems,
                                  const gp_Vec&       theStep,
                                  const int           theNbSteps,
                                  TElemOfElemListMap& newElemsMap,
                                  const bool          theMakeGroups,
                                  const int           theFlags,
                                  const double        theTolerance)
{
  ExtrusParam aParams;
  aParams.myDir = gp_Dir(theStep);
  aParams.myNodes.Clear();
  aParams.mySteps = new TColStd_HSequenceOfReal;
  int i;
  for(i=1; i<=theNbSteps; i++)
    aParams.mySteps->Append(theStep.Magnitude());

  return
    ExtrusionSweep(theElems,aParams,newElemsMap,theMakeGroups,theFlags,theTolerance);
}


//=======================================================================
//function : ExtrusionSweep
//purpose  :
//=======================================================================

SMESH_MeshEditor::PGroupIDs
SMESH_MeshEditor::ExtrusionSweep (TIDSortedElemSet &  theElems,
                                  ExtrusParam&        theParams,
                                  TElemOfElemListMap& newElemsMap,
                                  const bool          theMakeGroups,
                                  const int           theFlags,
                                  const double        theTolerance)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  // source elements for each generated one
  SMESH_SequenceOfElemPtr srcElems, srcNodes;

  SMESHDS_Mesh* aMesh = GetMeshDS();

  int nbsteps = theParams.mySteps->Length();

  TNodeOfNodeListMap mapNewNodes;
  //TNodeOfNodeVecMap mapNewNodes;
  TElemOfVecOfNnlmiMap mapElemNewNodes;
  //TElemOfVecOfMapNodesMap mapElemNewNodes;

  // loop on theElems
  TIDSortedElemSet::iterator itElem;
  for ( itElem = theElems.begin(); itElem != theElems.end(); itElem++ ) {
    // check element type
    const SMDS_MeshElement* elem = *itElem;
    if ( !elem  || elem->GetType() == SMDSAbs_Volume )
      continue;

    vector<TNodeOfNodeListMapItr> & newNodesItVec = mapElemNewNodes[ elem ];
    //vector<TNodeOfNodeVecMapItr> & newNodesItVec = mapElemNewNodes[ elem ];
    newNodesItVec.reserve( elem->NbNodes() );

    // loop on elem nodes
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    while ( itN->more() )
    {
      // check if a node has been already sweeped
      const SMDS_MeshNode* node = cast2Node( itN->next() );
      TNodeOfNodeListMap::iterator nIt = mapNewNodes.find( node );
      //TNodeOfNodeVecMap::iterator nIt = mapNewNodes.find( node );
      if ( nIt == mapNewNodes.end() ) {
        nIt = mapNewNodes.insert( make_pair( node, list<const SMDS_MeshNode*>() )).first;
        //nIt = mapNewNodes.insert( make_pair( node, vector<const SMDS_MeshNode*>() )).first;
        list<const SMDS_MeshNode*>& listNewNodes = nIt->second;
        //vector<const SMDS_MeshNode*>& vecNewNodes = nIt->second;
        //vecNewNodes.reserve(nbsteps);

        // make new nodes
        double coord[] = { node->X(), node->Y(), node->Z() };
        //int nbsteps = theParams.mySteps->Length();
        for ( int i = 0; i < nbsteps; i++ ) {
          if( elem->IsQuadratic() && !elem->IsMediumNode(node) ) {
            // create additional node
            double x = coord[0] + theParams.myDir.X()*theParams.mySteps->Value(i+1)/2.;
            double y = coord[1] + theParams.myDir.Y()*theParams.mySteps->Value(i+1)/2.;
            double z = coord[2] + theParams.myDir.Z()*theParams.mySteps->Value(i+1)/2.;
            if( theFlags & EXTRUSION_FLAG_SEW ) {
              const SMDS_MeshNode * newNode = CreateNode(x, y, z,
                                                         theTolerance, theParams.myNodes);
              listNewNodes.push_back( newNode );
            }
            else {
              const SMDS_MeshNode * newNode = aMesh->AddNode(x, y, z);
              myLastCreatedNodes.Append(newNode);
              srcNodes.Append( node );
              listNewNodes.push_back( newNode );
            }
          }
          //aTrsf.Transforms( coord[0], coord[1], coord[2] );
          coord[0] = coord[0] + theParams.myDir.X()*theParams.mySteps->Value(i+1);
          coord[1] = coord[1] + theParams.myDir.Y()*theParams.mySteps->Value(i+1);
          coord[2] = coord[2] + theParams.myDir.Z()*theParams.mySteps->Value(i+1);
          if( theFlags & EXTRUSION_FLAG_SEW ) {
            const SMDS_MeshNode * newNode = CreateNode(coord[0], coord[1], coord[2],
                                                       theTolerance, theParams.myNodes);
            listNewNodes.push_back( newNode );
            //vecNewNodes[i]=newNode;
          }
          else {
            const SMDS_MeshNode * newNode = aMesh->AddNode( coord[0], coord[1], coord[2] );
            myLastCreatedNodes.Append(newNode);
            srcNodes.Append( node );
            listNewNodes.push_back( newNode );
            //vecNewNodes[i]=newNode;
          }
        }
      }
      else {
        // if current elem is quadratic and current node is not medium
        // we have to check - may be it is needed to insert additional nodes
        if( elem->IsQuadratic() && !elem->IsMediumNode(node) ) {
          list< const SMDS_MeshNode* > & listNewNodes = nIt->second;
          if(listNewNodes.size()==nbsteps) {
            listNewNodes.clear();
            double coord[] = { node->X(), node->Y(), node->Z() };
            for ( int i = 0; i < nbsteps; i++ ) {
              double x = coord[0] + theParams.myDir.X()*theParams.mySteps->Value(i+1);
              double y = coord[1] + theParams.myDir.Y()*theParams.mySteps->Value(i+1);
              double z = coord[2] + theParams.myDir.Z()*theParams.mySteps->Value(i+1);
              if( theFlags & EXTRUSION_FLAG_SEW ) {
                const SMDS_MeshNode * newNode = CreateNode(x, y, z,
                                                           theTolerance, theParams.myNodes);
                listNewNodes.push_back( newNode );
              }
              else {
                const SMDS_MeshNode * newNode = aMesh->AddNode(x, y, z);
                myLastCreatedNodes.Append(newNode);
                srcNodes.Append( node );
                listNewNodes.push_back( newNode );
              }
              coord[0] = coord[0] + theParams.myDir.X()*theParams.mySteps->Value(i+1);
              coord[1] = coord[1] + theParams.myDir.Y()*theParams.mySteps->Value(i+1);
              coord[2] = coord[2] + theParams.myDir.Z()*theParams.mySteps->Value(i+1);
              if( theFlags & EXTRUSION_FLAG_SEW ) {
                const SMDS_MeshNode * newNode = CreateNode(coord[0], coord[1], coord[2],
                                                           theTolerance, theParams.myNodes);
                listNewNodes.push_back( newNode );
              }
              else {
                const SMDS_MeshNode * newNode = aMesh->AddNode( coord[0], coord[1], coord[2] );
                myLastCreatedNodes.Append(newNode);
                srcNodes.Append( node );
                listNewNodes.push_back( newNode );
              }
            }
          }
        }
      }
      newNodesItVec.push_back( nIt );
    }
    // make new elements
    sweepElement( elem, newNodesItVec, newElemsMap[elem], nbsteps, srcElems );
  }

  if( theFlags & EXTRUSION_FLAG_BOUNDARY ) {
    makeWalls( mapNewNodes, newElemsMap, mapElemNewNodes, theElems, nbsteps, srcElems );
  }
  PGroupIDs newGroupIDs;
  if ( theMakeGroups )
    newGroupIDs = generateGroups( srcNodes, srcElems, "extruded");

  return newGroupIDs;
}


//=======================================================================
//class    : SMESH_MeshEditor_PathPoint
//purpose  : auxiliary class
//=======================================================================
class SMESH_MeshEditor_PathPoint {
public:
  SMESH_MeshEditor_PathPoint() {
    myPnt.SetCoord(99., 99., 99.);
    myTgt.SetCoord(1.,0.,0.);
    myAngle=0.;
    myPrm=0.;
  }
  void SetPnt(const gp_Pnt& aP3D){
    myPnt=aP3D;
  }
  void SetTangent(const gp_Dir& aTgt){
    myTgt=aTgt;
  }
  void SetAngle(const double& aBeta){
    myAngle=aBeta;
  }
  void SetParameter(const double& aPrm){
    myPrm=aPrm;
  }
  const gp_Pnt& Pnt()const{
    return myPnt;
  }
  const gp_Dir& Tangent()const{
    return myTgt;
  }
  double Angle()const{
    return myAngle;
  }
  double Parameter()const{
    return myPrm;
  }

protected:
  gp_Pnt myPnt;
  gp_Dir myTgt;
  double myAngle;
  double myPrm;
};

//=======================================================================
//function : ExtrusionAlongTrack
//purpose  :
//=======================================================================
SMESH_MeshEditor::Extrusion_Error
  SMESH_MeshEditor::ExtrusionAlongTrack (TIDSortedElemSet &   theElements,
					 SMESH_subMesh*       theTrack,
					 const SMDS_MeshNode* theN1,
					 const bool           theHasAngles,
					 list<double>&        theAngles,
					 const bool           theHasRefPoint,
					 const gp_Pnt&        theRefPoint,
                                         const bool           theMakeGroups)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  // source elements for each generated one
  SMESH_SequenceOfElemPtr srcElems, srcNodes;

  int j, aNbTP, aNbE, aNb;
  double aT1, aT2, aT, aAngle, aX, aY, aZ;
  std::list<double> aPrms;
  std::list<double>::iterator aItD;
  TIDSortedElemSet::iterator itElem;

  Standard_Real aTx1, aTx2, aL2, aTolVec, aTolVec2;
  gp_Pnt aP3D, aV0;
  gp_Vec aVec;
  gp_XYZ aGC;
  Handle(Geom_Curve) aC3D;
  TopoDS_Edge aTrackEdge;
  TopoDS_Vertex aV1, aV2;

  SMDS_ElemIteratorPtr aItE;
  SMDS_NodeIteratorPtr aItN;
  SMDSAbs_ElementType aTypeE;

  TNodeOfNodeListMap mapNewNodes;
  TElemOfVecOfNnlmiMap mapElemNewNodes;
  TElemOfElemListMap newElemsMap;

  aTolVec=1.e-7;
  aTolVec2=aTolVec*aTolVec;

  // 1. Check data
  aNbE = theElements.size();
  // nothing to do
  if ( !aNbE )
    return EXTR_NO_ELEMENTS;

  // 1.1 Track Pattern
  ASSERT( theTrack );

  SMESHDS_SubMesh* pSubMeshDS=theTrack->GetSubMeshDS();

  aItE = pSubMeshDS->GetElements();
  while ( aItE->more() ) {
    const SMDS_MeshElement* pE = aItE->next();
    aTypeE = pE->GetType();
    // Pattern must contain links only
    if ( aTypeE != SMDSAbs_Edge )
      return EXTR_PATH_NOT_EDGE;
  }

  const TopoDS_Shape& aS = theTrack->GetSubShape();
  // Sub shape for the Pattern must be an Edge
  if ( aS.ShapeType() != TopAbs_EDGE )
    return EXTR_BAD_PATH_SHAPE;

  aTrackEdge = TopoDS::Edge( aS );
  // the Edge must not be degenerated
  if ( BRep_Tool::Degenerated( aTrackEdge ) )
    return EXTR_BAD_PATH_SHAPE;

  TopExp::Vertices( aTrackEdge, aV1, aV2 );
  aT1=BRep_Tool::Parameter( aV1, aTrackEdge );
  aT2=BRep_Tool::Parameter( aV2, aTrackEdge );

  aItN = theTrack->GetFather()->GetSubMesh( aV1 )->GetSubMeshDS()->GetNodes();
  const SMDS_MeshNode* aN1 = aItN->next();

  aItN = theTrack->GetFather()->GetSubMesh( aV2 )->GetSubMeshDS()->GetNodes();
  const SMDS_MeshNode* aN2 = aItN->next();

  // starting node must be aN1 or aN2
  if ( !( aN1 == theN1 || aN2 == theN1 ) )
    return EXTR_BAD_STARTING_NODE;

  aNbTP = pSubMeshDS->NbNodes() + 2;

  // 1.2. Angles
  vector<double> aAngles( aNbTP );

  for ( j=0; j < aNbTP; ++j ) {
    aAngles[j] = 0.;
  }

  if ( theHasAngles ) {
    aItD = theAngles.begin();
    for ( j=1; (aItD != theAngles.end()) && (j<aNbTP); ++aItD, ++j ) {
      aAngle = *aItD;
      aAngles[j] = aAngle;
    }
  }

  // 2. Collect parameters on the track edge
  aPrms.push_back( aT1 );
  aPrms.push_back( aT2 );

  aItN = pSubMeshDS->GetNodes();
  while ( aItN->more() ) {
    const SMDS_MeshNode* pNode = aItN->next();
    const SMDS_EdgePosition* pEPos =
      static_cast<const SMDS_EdgePosition*>( pNode->GetPosition().get() );
    aT = pEPos->GetUParameter();
    aPrms.push_back( aT );
  }

  // sort parameters
  aPrms.sort();
  if ( aN1 == theN1 ) {
    if ( aT1 > aT2 ) {
      aPrms.reverse();
    }
  }
  else {
    if ( aT2 > aT1 ) {
      aPrms.reverse();
    }
  }

  // 3. Path Points
  SMESH_MeshEditor_PathPoint aPP;
  vector<SMESH_MeshEditor_PathPoint> aPPs( aNbTP );
  //
  aC3D = BRep_Tool::Curve( aTrackEdge, aTx1, aTx2 );
  //
  aItD = aPrms.begin();
  for ( j=0; aItD != aPrms.end(); ++aItD, ++j ) {
    aT = *aItD;
    aC3D->D1( aT, aP3D, aVec );
    aL2 = aVec.SquareMagnitude();
    if ( aL2 < aTolVec2 )
      return EXTR_CANT_GET_TANGENT;

    gp_Dir aTgt( aVec );
    aAngle = aAngles[j];

    aPP.SetPnt( aP3D );
    aPP.SetTangent( aTgt );
    aPP.SetAngle( aAngle );
    aPP.SetParameter( aT );
    aPPs[j]=aPP;
  }

  // 3. Center of rotation aV0
  aV0 = theRefPoint;
  if ( !theHasRefPoint ) {
    aNb = 0;
    aGC.SetCoord( 0.,0.,0. );

    itElem = theElements.begin();
    for ( ; itElem != theElements.end(); itElem++ ) {
      const SMDS_MeshElement* elem = *itElem;

      SMDS_ElemIteratorPtr itN = elem->nodesIterator();
      while ( itN->more() ) {
	const SMDS_MeshNode* node = static_cast<const SMDS_MeshNode*>( itN->next() );
	aX = node->X();
	aY = node->Y();
	aZ = node->Z();

	if ( mapNewNodes.find( node ) == mapNewNodes.end() ) {
	  list<const SMDS_MeshNode*> aLNx;
	  mapNewNodes[node] = aLNx;
	  //
	  gp_XYZ aXYZ( aX, aY, aZ );
	  aGC += aXYZ;
	  ++aNb;
	}
      }
    }
    aGC /= aNb;
    aV0.SetXYZ( aGC );
  } // if (!theHasRefPoint) {
  mapNewNodes.clear();

  // 4. Processing the elements
  SMESHDS_Mesh* aMesh = GetMeshDS();

  for ( itElem = theElements.begin(); itElem != theElements.end(); itElem++ ) {
    // check element type
    const SMDS_MeshElement* elem = *itElem;
    aTypeE = elem->GetType();
    if ( !elem || ( aTypeE != SMDSAbs_Face && aTypeE != SMDSAbs_Edge ) )
      continue;

    vector<TNodeOfNodeListMapItr> & newNodesItVec = mapElemNewNodes[ elem ];
    newNodesItVec.reserve( elem->NbNodes() );

    // loop on elem nodes
    int nodeIndex = -1;
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    while ( itN->more() )
    {
      ++nodeIndex;
      // check if a node has been already processed
      const SMDS_MeshNode* node =
	static_cast<const SMDS_MeshNode*>( itN->next() );
      TNodeOfNodeListMap::iterator nIt = mapNewNodes.find( node );
      if ( nIt == mapNewNodes.end() ) {
        nIt = mapNewNodes.insert( make_pair( node, list<const SMDS_MeshNode*>() )).first;
        list<const SMDS_MeshNode*>& listNewNodes = nIt->second;

	// make new nodes
	aX = node->X();  aY = node->Y(); aZ = node->Z();

	Standard_Real aAngle1x, aAngleT1T0, aTolAng;
	gp_Pnt aP0x, aP1x, aPN0, aPN1, aV0x, aV1x;
	gp_Ax1 anAx1, anAxT1T0;
	gp_Dir aDT1x, aDT0x, aDT1T0;

	aTolAng=1.e-4;

	aV0x = aV0;
	aPN0.SetCoord(aX, aY, aZ);

	const SMESH_MeshEditor_PathPoint& aPP0 = aPPs[0];
	aP0x = aPP0.Pnt();
	aDT0x= aPP0.Tangent();

	for ( j = 1; j < aNbTP; ++j ) {
	  const SMESH_MeshEditor_PathPoint& aPP1 = aPPs[j];
	  aP1x = aPP1.Pnt();
	  aDT1x = aPP1.Tangent();
	  aAngle1x = aPP1.Angle();

	  gp_Trsf aTrsf, aTrsfRot, aTrsfRotT1T0;
	  // Translation
	  gp_Vec aV01x( aP0x, aP1x );
	  aTrsf.SetTranslation( aV01x );

	  // traslated point
	  aV1x = aV0x.Transformed( aTrsf );
	  aPN1 = aPN0.Transformed( aTrsf );

	  // rotation 1 [ T1,T0 ]
	  aAngleT1T0=-aDT1x.Angle( aDT0x );
	  if (fabs(aAngleT1T0) > aTolAng) {
	    aDT1T0=aDT1x^aDT0x;
	    anAxT1T0.SetLocation( aV1x );
	    anAxT1T0.SetDirection( aDT1T0 );
	    aTrsfRotT1T0.SetRotation( anAxT1T0, aAngleT1T0 );

	    aPN1 = aPN1.Transformed( aTrsfRotT1T0 );
	  }

	  // rotation 2
	  if ( theHasAngles ) {
	    anAx1.SetLocation( aV1x );
	    anAx1.SetDirection( aDT1x );
	    aTrsfRot.SetRotation( anAx1, aAngle1x );

	    aPN1 = aPN1.Transformed( aTrsfRot );
	  }

	  // make new node
          if( elem->IsQuadratic() && !elem->IsMediumNode(node) ) {
            // create additional node
            double x = ( aPN1.X() + aPN0.X() )/2.;
            double y = ( aPN1.Y() + aPN0.Y() )/2.;
            double z = ( aPN1.Z() + aPN0.Z() )/2.;
            const SMDS_MeshNode* newNode = aMesh->AddNode(x,y,z);
            myLastCreatedNodes.Append(newNode);
            srcNodes.Append( node );
            listNewNodes.push_back( newNode );
          }
	  aX = aPN1.X();
	  aY = aPN1.Y();
	  aZ = aPN1.Z();
	  const SMDS_MeshNode* newNode = aMesh->AddNode( aX, aY, aZ );
          myLastCreatedNodes.Append(newNode);
          srcNodes.Append( node );
	  listNewNodes.push_back( newNode );

	  aPN0 = aPN1;
	  aP0x = aP1x;
	  aV0x = aV1x;
	  aDT0x = aDT1x;
	}
      }

      else {
        // if current elem is quadratic and current node is not medium
        // we have to check - may be it is needed to insert additional nodes
        if( elem->IsQuadratic() && !elem->IsMediumNode(node) ) {
          list< const SMDS_MeshNode* > & listNewNodes = nIt->second;
          if(listNewNodes.size()==aNbTP-1) {
            vector<const SMDS_MeshNode*> aNodes(2*(aNbTP-1));
            gp_XYZ P(node->X(), node->Y(), node->Z());
            list< const SMDS_MeshNode* >::iterator it = listNewNodes.begin();
            int i;
            for(i=0; i<aNbTP-1; i++) {
              const SMDS_MeshNode* N = *it;
              double x = ( N->X() + P.X() )/2.;
              double y = ( N->Y() + P.Y() )/2.;
              double z = ( N->Z() + P.Z() )/2.;
              const SMDS_MeshNode* newN = aMesh->AddNode(x,y,z);
              srcNodes.Append( node );
              myLastCreatedNodes.Append(newN);
              aNodes[2*i] = newN;
              aNodes[2*i+1] = N;
              P = gp_XYZ(N->X(),N->Y(),N->Z());
            }
            listNewNodes.clear();
            for(i=0; i<2*(aNbTP-1); i++) {
              listNewNodes.push_back(aNodes[i]);
            }
          }
        }
      }

      newNodesItVec.push_back( nIt );
    }
    // make new elements
    //sweepElement( aMesh, elem, newNodesItVec, newElemsMap[elem],
    //              newNodesItVec[0]->second.size(), myLastCreatedElems );
    sweepElement( elem, newNodesItVec, newElemsMap[elem], aNbTP-1, srcElems );
  }

  makeWalls( mapNewNodes, newElemsMap, mapElemNewNodes, theElements, aNbTP-1, srcElems );

  if ( theMakeGroups )
    generateGroups( srcNodes, srcElems, "extruded");

  return EXTR_OK;
}

//=======================================================================
//function : Transform
//purpose  :
//=======================================================================

SMESH_MeshEditor::PGroupIDs
SMESH_MeshEditor::Transform (TIDSortedElemSet & theElems,
                             const gp_Trsf&     theTrsf,
                             const bool         theCopy,
                             const bool         theMakeGroups,
                             SMESH_Mesh*        theTargetMesh)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  bool needReverse = false;
  string groupPostfix;
  switch ( theTrsf.Form() ) {
  case gp_PntMirror:
  case gp_Ax1Mirror:
  case gp_Ax2Mirror:
    needReverse = true;
    groupPostfix = "mirrored";
    break;
  case gp_Rotation:
    groupPostfix = "rotated";
    break;
  case gp_Translation:
    groupPostfix = "translated";
    break;
  case gp_Scale:
    groupPostfix = "scaled";
    break;
  default:
    needReverse = false;
    groupPostfix = "transformed";
  }

  SMESH_MeshEditor targetMeshEditor( theTargetMesh );
  SMESHDS_Mesh* aTgtMesh = theTargetMesh ? theTargetMesh->GetMeshDS() : 0;
  SMESHDS_Mesh* aMesh    = GetMeshDS();
  

  // map old node to new one
  TNodeNodeMap nodeMap;

  // elements sharing moved nodes; those of them which have all
  // nodes mirrored but are not in theElems are to be reversed
  TIDSortedElemSet inverseElemSet;

  // source elements for each generated one
  SMESH_SequenceOfElemPtr srcElems, srcNodes;

  // loop on theElems
  TIDSortedElemSet::iterator itElem;
  for ( itElem = theElems.begin(); itElem != theElems.end(); itElem++ ) {
    const SMDS_MeshElement* elem = *itElem;
    if ( !elem )
      continue;

    // loop on elem nodes
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    while ( itN->more() ) {

      // check if a node has been already transformed
      const SMDS_MeshNode* node = cast2Node( itN->next() );
      pair<TNodeNodeMap::iterator,bool> n2n_isnew =
        nodeMap.insert( make_pair ( node, node ));
      if ( !n2n_isnew.second )
        continue;

      double coord[3];
      coord[0] = node->X();
      coord[1] = node->Y();
      coord[2] = node->Z();
      theTrsf.Transforms( coord[0], coord[1], coord[2] );
      if ( theTargetMesh ) {
        const SMDS_MeshNode * newNode = aTgtMesh->AddNode( coord[0], coord[1], coord[2] );
        n2n_isnew.first->second = newNode;
        myLastCreatedNodes.Append(newNode);
        srcNodes.Append( node );
      }
      else if ( theCopy ) {
        const SMDS_MeshNode * newNode = aMesh->AddNode( coord[0], coord[1], coord[2] );
        n2n_isnew.first->second = newNode;
        myLastCreatedNodes.Append(newNode);
        srcNodes.Append( node );
      }
      else {
        aMesh->MoveNode( node, coord[0], coord[1], coord[2] );
        // node position on shape becomes invalid
        const_cast< SMDS_MeshNode* > ( node )->SetPosition
          ( SMDS_SpacePosition::originSpacePosition() );
      }

      // keep inverse elements
      if ( !theCopy && !theTargetMesh && needReverse ) {
        SMDS_ElemIteratorPtr invElemIt = node->GetInverseElementIterator();
        while ( invElemIt->more() ) {
          const SMDS_MeshElement* iel = invElemIt->next();
          inverseElemSet.insert( iel );
        }
      }
    }
  }

  // either create new elements or reverse mirrored ones
  if ( !theCopy && !needReverse && !theTargetMesh )
    return PGroupIDs();

  TIDSortedElemSet::iterator invElemIt = inverseElemSet.begin();
  for ( ; invElemIt != inverseElemSet.end(); invElemIt++ )
    theElems.insert( *invElemIt );

  // replicate or reverse elements

  enum {
    REV_TETRA   = 0,  //  = nbNodes - 4
    REV_PYRAMID = 1,  //  = nbNodes - 4
    REV_PENTA   = 2,  //  = nbNodes - 4
    REV_FACE    = 3,
    REV_HEXA    = 4,  //  = nbNodes - 4
    FORWARD     = 5
    };
  int index[][8] = {
    { 2, 1, 0, 3, 4, 0, 0, 0 },  // REV_TETRA
    { 2, 1, 0, 3, 4, 0, 0, 0 },  // REV_PYRAMID
    { 2, 1, 0, 5, 4, 3, 0, 0 },  // REV_PENTA
    { 2, 1, 0, 3, 0, 0, 0, 0 },  // REV_FACE
    { 2, 1, 0, 3, 6, 5, 4, 7 },  // REV_HEXA
    { 0, 1, 2, 3, 4, 5, 6, 7 }   // FORWARD
  };

  for ( itElem = theElems.begin(); itElem != theElems.end(); itElem++ )
  {
    const SMDS_MeshElement* elem = *itElem;
    if ( !elem || elem->GetType() == SMDSAbs_Node )
      continue;

    int nbNodes = elem->NbNodes();
    int elemType = elem->GetType();

    if (elem->IsPoly()) {
      // Polygon or Polyhedral Volume
      switch ( elemType ) {
      case SMDSAbs_Face:
        {
          vector<const SMDS_MeshNode*> poly_nodes (nbNodes);
          int iNode = 0;
          SMDS_ElemIteratorPtr itN = elem->nodesIterator();
          while (itN->more()) {
            const SMDS_MeshNode* node =
              static_cast<const SMDS_MeshNode*>(itN->next());
            TNodeNodeMap::iterator nodeMapIt = nodeMap.find(node);
            if (nodeMapIt == nodeMap.end())
              break; // not all nodes transformed
            if (needReverse) {
              // reverse mirrored faces and volumes
              poly_nodes[nbNodes - iNode - 1] = (*nodeMapIt).second;
            } else {
              poly_nodes[iNode] = (*nodeMapIt).second;
            }
            iNode++;
          }
          if ( iNode != nbNodes )
            continue; // not all nodes transformed

          if ( theTargetMesh ) {
            myLastCreatedElems.Append(aTgtMesh->AddPolygonalFace(poly_nodes));
            srcElems.Append( elem );
          }
          else if ( theCopy ) {
            myLastCreatedElems.Append(aMesh->AddPolygonalFace(poly_nodes));
            srcElems.Append( elem );
          }
          else {
            aMesh->ChangePolygonNodes(elem, poly_nodes);
          }
        }
        break;
      case SMDSAbs_Volume:
        {
          // ATTENTION: Reversing is not yet done!!!
          const SMDS_PolyhedralVolumeOfNodes* aPolyedre =
            dynamic_cast<const SMDS_PolyhedralVolumeOfNodes*>( elem );
          if (!aPolyedre) {
            MESSAGE("Warning: bad volumic element");
            continue;
          }

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

          bool allTransformed = true;
          int nbFaces = aPolyedre->NbFaces();
          for (int iface = 1; iface <= nbFaces && allTransformed; iface++) {
            int nbFaceNodes = aPolyedre->NbFaceNodes(iface);
            for (int inode = 1; inode <= nbFaceNodes && allTransformed; inode++) {
              const SMDS_MeshNode* node = aPolyedre->GetFaceNode(iface, inode);
              TNodeNodeMap::iterator nodeMapIt = nodeMap.find(node);
              if (nodeMapIt == nodeMap.end()) {
                allTransformed = false; // not all nodes transformed
              } else {
                poly_nodes.push_back((*nodeMapIt).second);
              }
            }
            quantities.push_back(nbFaceNodes);
          }
          if ( !allTransformed )
            continue; // not all nodes transformed

          if ( theTargetMesh ) {
            myLastCreatedElems.Append(aTgtMesh->AddPolyhedralVolume(poly_nodes, quantities));
            srcElems.Append( elem );
          }
          else if ( theCopy ) {
            myLastCreatedElems.Append(aMesh->AddPolyhedralVolume(poly_nodes, quantities));
            srcElems.Append( elem );
          }
          else {
            aMesh->ChangePolyhedronNodes(elem, poly_nodes, quantities);
          }
        }
        break;
    default:;
    }
    continue;
  }

  // Regular elements
  int* i = index[ FORWARD ];
  if ( needReverse && nbNodes > 2) // reverse mirrored faces and volumes
    if ( elemType == SMDSAbs_Face )
      i = index[ REV_FACE ];
    else
      i = index[ nbNodes - 4 ];

    if(elem->IsQuadratic()) {
      static int anIds[] = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19};
      i = anIds;
      if(needReverse) {
        if(nbNodes==3) { // quadratic edge
          static int anIds[] = {1,0,2};
          i = anIds;
        }
        else if(nbNodes==6) { // quadratic triangle
          static int anIds[] = {0,2,1,5,4,3};
          i = anIds;
        }
        else if(nbNodes==8) { // quadratic quadrangle
          static int anIds[] = {0,3,2,1,7,6,5,4};
          i = anIds;
        }
        else if(nbNodes==10) { // quadratic tetrahedron of 10 nodes
          static int anIds[] = {0,2,1,3,6,5,4,7,9,8};
          i = anIds;
        }
        else if(nbNodes==13) { // quadratic pyramid of 13 nodes
          static int anIds[] = {0,3,2,1,4,8,7,6,5,9,12,11,10};
          i = anIds;
        }
        else if(nbNodes==15) { // quadratic pentahedron with 15 nodes
          static int anIds[] = {0,2,1,3,5,4,8,7,6,11,10,9,12,14,13};
          i = anIds;
        }
        else { // nbNodes==20 - quadratic hexahedron with 20 nodes
          static int anIds[] = {0,3,2,1,4,7,6,5,11,10,9,8,15,14,13,12,16,19,18,17};
          i = anIds;
        }
      }
    }

    // find transformed nodes
    vector<const SMDS_MeshNode*> nodes(nbNodes);
    int iNode = 0;
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    while ( itN->more() ) {
      const SMDS_MeshNode* node =
        static_cast<const SMDS_MeshNode*>( itN->next() );
      TNodeNodeMap::iterator nodeMapIt = nodeMap.find( node );
      if ( nodeMapIt == nodeMap.end() )
        break; // not all nodes transformed
      nodes[ i [ iNode++ ]] = (*nodeMapIt).second;
    }
    if ( iNode != nbNodes )
      continue; // not all nodes transformed

    if ( theTargetMesh ) {
      if ( SMDS_MeshElement* copy =
           targetMeshEditor.AddElement( nodes, elem->GetType(), elem->IsPoly() )) {
        myLastCreatedElems.Append( copy );
        srcElems.Append( elem );
      }
    }
    else if ( theCopy ) {
      if ( SMDS_MeshElement* copy = AddElement( nodes, elem->GetType(), elem->IsPoly() )) {
        myLastCreatedElems.Append( copy );
        srcElems.Append( elem );
      }
    }
    else {
      // reverse element as it was reversed by transformation
      if ( nbNodes > 2 )
        aMesh->ChangeElementNodes( elem, &nodes[0], nbNodes );
    }
  }

  PGroupIDs newGroupIDs;

  if ( theMakeGroups && theCopy ||
       theMakeGroups && theTargetMesh )
    newGroupIDs = generateGroups( srcNodes, srcElems, groupPostfix, theTargetMesh );

  return newGroupIDs;
}

//=======================================================================
/*!
 * \brief Create groups of elements made during transformation
 * \param nodeGens - nodes making corresponding myLastCreatedNodes
 * \param elemGens - elements making corresponding myLastCreatedElems
 * \param postfix - to append to names of new groups
 */
//=======================================================================

SMESH_MeshEditor::PGroupIDs
SMESH_MeshEditor::generateGroups(const SMESH_SequenceOfElemPtr& nodeGens,
                                 const SMESH_SequenceOfElemPtr& elemGens,
                                 const std::string&             postfix,
                                 SMESH_Mesh*                    targetMesh)
{
  PGroupIDs newGroupIDs( new list<int> );
  SMESH_Mesh* mesh = targetMesh ? targetMesh : GetMesh();

  // Sort existing groups by types and collect their names

  // to store an old group and a generated new one
  typedef pair< SMESHDS_GroupBase*, SMDS_MeshGroup* > TOldNewGroup;
  vector< list< TOldNewGroup > > groupsByType( SMDSAbs_NbElementTypes );
  // group names
  set< string > groupNames;
  //
  SMDS_MeshGroup* nullNewGroup = (SMDS_MeshGroup*) 0;
  SMESH_Mesh::GroupIteratorPtr groupIt = GetMesh()->GetGroups();
  while ( groupIt->more() ) {
    SMESH_Group * group = groupIt->next();
    if ( !group ) continue;
    SMESHDS_GroupBase* groupDS = group->GetGroupDS();
    if ( !groupDS || groupDS->IsEmpty() ) continue;
    groupNames.insert( group->GetName() );
    groupDS->SetStoreName( group->GetName() );
    groupsByType[ groupDS->GetType() ].push_back( make_pair( groupDS, nullNewGroup ));
  }

  // Groups creation

  // loop on nodes and elements
  for ( int isNodes = 0; isNodes < 2; ++isNodes )
  {
    const SMESH_SequenceOfElemPtr& gens  = isNodes ? nodeGens : elemGens;
    const SMESH_SequenceOfElemPtr& elems = isNodes ? myLastCreatedNodes : myLastCreatedElems;
    if ( gens.Length() != elems.Length() )
      throw SALOME_Exception(LOCALIZED("invalid args"));

    // loop on created elements
    for (int iElem = 1; iElem <= elems.Length(); ++iElem )
    {
      const SMDS_MeshElement* sourceElem = gens( iElem );
      if ( !sourceElem ) {
        MESSAGE("generateGroups(): NULL source element");
        continue;
      }
      list< TOldNewGroup > & groupsOldNew = groupsByType[ sourceElem->GetType() ];
      if ( groupsOldNew.empty() ) {
        while ( iElem < gens.Length() && gens( iElem+1 ) == sourceElem )
          ++iElem; // skip all elements made by sourceElem
        continue;
      }
      // collect all elements made by sourceElem
      list< const SMDS_MeshElement* > resultElems;
      if ( const SMDS_MeshElement* resElem = elems( iElem ))
        if ( resElem != sourceElem )
          resultElems.push_back( resElem );
      while ( iElem < gens.Length() && gens( iElem+1 ) == sourceElem )
        if ( const SMDS_MeshElement* resElem = elems( ++iElem ))
          if ( resElem != sourceElem )
            resultElems.push_back( resElem );
      // do not generate element groups from node ones
      if ( sourceElem->GetType() == SMDSAbs_Node &&
           elems( iElem )->GetType() != SMDSAbs_Node )
        continue;

      // add resultElems to groups made by ones the sourceElem belongs to
      list< TOldNewGroup >::iterator gOldNew, gLast = groupsOldNew.end();
      for ( gOldNew = groupsOldNew.begin(); gOldNew != gLast; ++gOldNew )
      {
        SMESHDS_GroupBase* oldGroup = gOldNew->first;
        if ( oldGroup->Contains( sourceElem )) // sourceElem in oldGroup
        {
          SMDS_MeshGroup* & newGroup = gOldNew->second;
          if ( !newGroup )// create a new group
          {
            // make a name
            string name = oldGroup->GetStoreName();
            if ( !targetMesh ) {
              name += "_";
              name += postfix;
              int nb = 0;
              while ( !groupNames.insert( name ).second ) // name exists
              {
                if ( nb == 0 ) {
                  name += "_1";
                }
                else {
                  TCollection_AsciiString nbStr(nb+1);
                  name.resize( name.rfind('_')+1 );
                  name += nbStr.ToCString();
                }
                ++nb;
              }
            }
            // make a group
            int id;
            SMESH_Group* group = mesh->AddGroup( resultElems.back()->GetType(),
                                                 name.c_str(), id );
            SMESHDS_Group* groupDS = static_cast<SMESHDS_Group*>(group->GetGroupDS());
            newGroup = & groupDS->SMDSGroup();
            newGroupIDs->push_back( id );
          }

          // fill in a new group
          list< const SMDS_MeshElement* >::iterator resLast = resultElems.end(), resElemIt;
          for ( resElemIt = resultElems.begin(); resElemIt != resLast; ++resElemIt )
            newGroup->Add( *resElemIt );
        }
      }
    } // loop on created elements
  }// loop on nodes and elements

  return newGroupIDs;
}

//=======================================================================
//function : FindCoincidentNodes
//purpose  : Return list of group of nodes close to each other within theTolerance
//           Search among theNodes or in the whole mesh if theNodes is empty using
//           an Octree algorithm
//=======================================================================

void SMESH_MeshEditor::FindCoincidentNodes (set<const SMDS_MeshNode*> & theNodes,
                                            const double                theTolerance,
                                            TListOfListOfNodes &        theGroupsOfNodes)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  set<const SMDS_MeshNode*> nodes;
  if ( theNodes.empty() )
  { // get all nodes in the mesh
    SMDS_NodeIteratorPtr nIt = GetMeshDS()->nodesIterator();
    while ( nIt->more() )
      nodes.insert( nodes.end(),nIt->next());
  }
  else
    nodes=theNodes;
  SMESH_OctreeNode::FindCoincidentNodes ( nodes, &theGroupsOfNodes, theTolerance);

}

//=======================================================================
/*!
 * \brief Implementation of search for the node closest to point
 */
//=======================================================================

struct SMESH_NodeSearcherImpl: public SMESH_NodeSearcher
{
  /*!
   * \brief Constructor
   */
  SMESH_NodeSearcherImpl( const SMESHDS_Mesh* theMesh )
  {
    set<const SMDS_MeshNode*> nodes;
    if ( theMesh ) {
      SMDS_NodeIteratorPtr nIt = theMesh->nodesIterator();
      while ( nIt->more() )
        nodes.insert( nodes.end(), nIt->next() );
    }
    myOctreeNode = new SMESH_OctreeNode(nodes) ;
  }
  /*!
   * \brief Do it's job
   */
  const SMDS_MeshNode* FindClosestTo( const gp_Pnt& thePnt )
  {
    SMDS_MeshNode tgtNode( thePnt.X(), thePnt.Y(), thePnt.Z() );
    list<const SMDS_MeshNode*> nodes;
    const double precision = 1e-6;
    myOctreeNode->NodesAround( &tgtNode, &nodes, precision );

    double minSqDist = DBL_MAX;
    Bnd_B3d box;
    if ( nodes.empty() )  // get all nodes of OctreeNode's closest to thePnt
    {
      // sort leafs by their distance from thePnt
      typedef map< double, SMESH_OctreeNode* > TDistTreeMap;
      TDistTreeMap treeMap;
      list< SMESH_OctreeNode* > treeList;
      list< SMESH_OctreeNode* >::iterator trIt;
      treeList.push_back( myOctreeNode );
      for ( trIt = treeList.begin(); trIt != treeList.end(); ++trIt)
      {
        SMESH_OctreeNode* tree = *trIt;
        if ( !tree->isLeaf() ) { // put children to the queue
          SMESH_OctreeNodeIteratorPtr cIt = tree->GetChildrenIterator();
          while ( cIt->more() )
            treeList.push_back( cIt->next() );
        }
        else if ( tree->NbNodes() ) { // put tree to treeMap
          tree->getBox( box );
          double sqDist = thePnt.SquareDistance( 0.5 * ( box.CornerMin() + box.CornerMax() ));
          pair<TDistTreeMap::iterator,bool> it_in = treeMap.insert( make_pair( sqDist, tree ));
          if ( !it_in.second ) // not unique distance to box center
            treeMap.insert( it_in.first, make_pair( sqDist - 1e-13*treeMap.size(), tree ));
        }
      }
      // find distance after which there is no sense to check tree's
      double sqLimit = DBL_MAX;
      TDistTreeMap::iterator sqDist_tree = treeMap.begin();
      if ( treeMap.size() > 5 ) {
        SMESH_OctreeNode* closestTree = sqDist_tree->second;
        closestTree->getBox( box );
        double limit = sqrt( sqDist_tree->first ) + sqrt ( box.SquareExtent() );
        sqLimit = limit * limit;
      }
      // get all nodes from trees
      for ( ; sqDist_tree != treeMap.end(); ++sqDist_tree) {
        if ( sqDist_tree->first > sqLimit )
          break;
        SMESH_OctreeNode* tree = sqDist_tree->second;
        tree->NodesAround( tree->GetNodeIterator()->next(), &nodes );
      }
    }
    // find closest among nodes
    minSqDist = DBL_MAX;
    const SMDS_MeshNode* closestNode = 0;
    list<const SMDS_MeshNode*>::iterator nIt = nodes.begin();
    for ( ; nIt != nodes.end(); ++nIt ) {
      double sqDist = thePnt.SquareDistance( TNodeXYZ( *nIt ) );
      if ( minSqDist > sqDist ) {
        closestNode = *nIt;
        minSqDist = sqDist;
      }
    }
    return closestNode;
  }
  /*!
   * \brief Destructor
   */
  ~SMESH_NodeSearcherImpl() { delete myOctreeNode; }
private:
  SMESH_OctreeNode* myOctreeNode;
};

//=======================================================================
/*!
 * \brief Return SMESH_NodeSearcher
 */
//=======================================================================

SMESH_NodeSearcher* SMESH_MeshEditor::GetNodeSearcher() 
{
  return new SMESH_NodeSearcherImpl( GetMeshDS() );
}

//=======================================================================
//function : SimplifyFace
//purpose  :
//=======================================================================
int SMESH_MeshEditor::SimplifyFace (const vector<const SMDS_MeshNode *> faceNodes,
                                    vector<const SMDS_MeshNode *>&      poly_nodes,
                                    vector<int>&                        quantities) const
{
  int nbNodes = faceNodes.size();

  if (nbNodes < 3)
    return 0;

  set<const SMDS_MeshNode*> nodeSet;

  // get simple seq of nodes
  //const SMDS_MeshNode* simpleNodes[ nbNodes ];
  vector<const SMDS_MeshNode*> simpleNodes( nbNodes );
  int iSimple = 0, nbUnique = 0;

  simpleNodes[iSimple++] = faceNodes[0];
  nbUnique++;
  for (int iCur = 1; iCur < nbNodes; iCur++) {
    if (faceNodes[iCur] != simpleNodes[iSimple - 1]) {
      simpleNodes[iSimple++] = faceNodes[iCur];
      if (nodeSet.insert( faceNodes[iCur] ).second)
        nbUnique++;
    }
  }
  int nbSimple = iSimple;
  if (simpleNodes[nbSimple - 1] == simpleNodes[0]) {
    nbSimple--;
    iSimple--;
  }

  if (nbUnique < 3)
    return 0;

  // separate loops
  int nbNew = 0;
  bool foundLoop = (nbSimple > nbUnique);
  while (foundLoop) {
    foundLoop = false;
    set<const SMDS_MeshNode*> loopSet;
    for (iSimple = 0; iSimple < nbSimple && !foundLoop; iSimple++) {
      const SMDS_MeshNode* n = simpleNodes[iSimple];
      if (!loopSet.insert( n ).second) {
        foundLoop = true;

        // separate loop
        int iC = 0, curLast = iSimple;
        for (; iC < curLast; iC++) {
          if (simpleNodes[iC] == n) break;
        }
        int loopLen = curLast - iC;
        if (loopLen > 2) {
          // create sub-element
          nbNew++;
          quantities.push_back(loopLen);
          for (; iC < curLast; iC++) {
            poly_nodes.push_back(simpleNodes[iC]);
          }
        }
        // shift the rest nodes (place from the first loop position)
        for (iC = curLast + 1; iC < nbSimple; iC++) {
          simpleNodes[iC - loopLen] = simpleNodes[iC];
        }
        nbSimple -= loopLen;
        iSimple -= loopLen;
      }
    } // for (iSimple = 0; iSimple < nbSimple; iSimple++)
  } // while (foundLoop)

  if (iSimple > 2) {
    nbNew++;
    quantities.push_back(iSimple);
    for (int i = 0; i < iSimple; i++)
      poly_nodes.push_back(simpleNodes[i]);
  }

  return nbNew;
}

//=======================================================================
//function : MergeNodes
//purpose  : In each group, the cdr of nodes are substituted by the first one
//           in all elements.
//=======================================================================

void SMESH_MeshEditor::MergeNodes (TListOfListOfNodes & theGroupsOfNodes)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  SMESHDS_Mesh* aMesh = GetMeshDS();

  TNodeNodeMap nodeNodeMap; // node to replace - new node
  set<const SMDS_MeshElement*> elems; // all elements with changed nodes
  list< int > rmElemIds, rmNodeIds;

  // Fill nodeNodeMap and elems

  TListOfListOfNodes::iterator grIt = theGroupsOfNodes.begin();
  for ( ; grIt != theGroupsOfNodes.end(); grIt++ ) {
    list<const SMDS_MeshNode*>& nodes = *grIt;
    list<const SMDS_MeshNode*>::iterator nIt = nodes.begin();
    const SMDS_MeshNode* nToKeep = *nIt;
    for ( ++nIt; nIt != nodes.end(); nIt++ ) {
      const SMDS_MeshNode* nToRemove = *nIt;
      nodeNodeMap.insert( TNodeNodeMap::value_type( nToRemove, nToKeep ));
      if ( nToRemove != nToKeep ) {
        rmNodeIds.push_back( nToRemove->GetID() );
        AddToSameGroups( nToKeep, nToRemove, aMesh );
      }

      SMDS_ElemIteratorPtr invElemIt = nToRemove->GetInverseElementIterator();
      while ( invElemIt->more() ) {
        const SMDS_MeshElement* elem = invElemIt->next();
          elems.insert(elem);
      }
    }
  }
  // Change element nodes or remove an element

  set<const SMDS_MeshElement*>::iterator eIt = elems.begin();
  for ( ; eIt != elems.end(); eIt++ ) {
    const SMDS_MeshElement* elem = *eIt;
    int nbNodes = elem->NbNodes();
    int aShapeId = FindShape( elem );

    set<const SMDS_MeshNode*> nodeSet;
    vector< const SMDS_MeshNode*> curNodes( nbNodes ), uniqueNodes( nbNodes );
    int iUnique = 0, iCur = 0, nbRepl = 0;
    vector<int> iRepl( nbNodes );

    // get new seq of nodes
    SMDS_ElemIteratorPtr itN = elem->nodesIterator();
    while ( itN->more() ) {
      const SMDS_MeshNode* n =
        static_cast<const SMDS_MeshNode*>( itN->next() );

      TNodeNodeMap::iterator nnIt = nodeNodeMap.find( n );
      if ( nnIt != nodeNodeMap.end() ) { // n sticks
        n = (*nnIt).second;
        iRepl[ nbRepl++ ] = iCur;
      }
      curNodes[ iCur ] = n;
      bool isUnique = nodeSet.insert( n ).second;
      if ( isUnique )
        uniqueNodes[ iUnique++ ] = n;
      iCur++;
    }

    // Analyse element topology after replacement

    bool isOk = true;
    int nbUniqueNodes = nodeSet.size();
    if ( nbNodes != nbUniqueNodes ) { // some nodes stick
      // Polygons and Polyhedral volumes
      if (elem->IsPoly()) {

        if (elem->GetType() == SMDSAbs_Face) {
          // Polygon
          vector<const SMDS_MeshNode *> face_nodes (nbNodes);
          int inode = 0;
          for (; inode < nbNodes; inode++) {
            face_nodes[inode] = curNodes[inode];
          }

          vector<const SMDS_MeshNode *> polygons_nodes;
          vector<int> quantities;
          int nbNew = SimplifyFace(face_nodes, polygons_nodes, quantities);

          if (nbNew > 0) {
            inode = 0;
            for (int iface = 0; iface < nbNew - 1; iface++) {
              int nbNodes = quantities[iface];
              vector<const SMDS_MeshNode *> poly_nodes (nbNodes);
              for (int ii = 0; ii < nbNodes; ii++, inode++) {
                poly_nodes[ii] = polygons_nodes[inode];
              }
              SMDS_MeshElement* newElem = aMesh->AddPolygonalFace(poly_nodes);
              myLastCreatedElems.Append(newElem);
              if (aShapeId)
                aMesh->SetMeshElementOnShape(newElem, aShapeId);
            }
            aMesh->ChangeElementNodes(elem, &polygons_nodes[inode], quantities[nbNew - 1]);
          }
          else {
            rmElemIds.push_back(elem->GetID());
          }

        }
        else if (elem->GetType() == SMDSAbs_Volume) {
          // Polyhedral volume
          if (nbUniqueNodes < 4) {
            rmElemIds.push_back(elem->GetID());
          }
          else {
            // each face has to be analized in order to check volume validity
            const SMDS_PolyhedralVolumeOfNodes* aPolyedre =
              static_cast<const SMDS_PolyhedralVolumeOfNodes*>( elem );
            if (aPolyedre) {
              int nbFaces = aPolyedre->NbFaces();

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

              for (int iface = 1; iface <= nbFaces; iface++) {
                int nbFaceNodes = aPolyedre->NbFaceNodes(iface);
                vector<const SMDS_MeshNode *> faceNodes (nbFaceNodes);

                for (int inode = 1; inode <= nbFaceNodes; inode++) {
                  const SMDS_MeshNode * faceNode = aPolyedre->GetFaceNode(iface, inode);
                  TNodeNodeMap::iterator nnIt = nodeNodeMap.find(faceNode);
                  if (nnIt != nodeNodeMap.end()) { // faceNode sticks
                    faceNode = (*nnIt).second;
                  }
                  faceNodes[inode - 1] = faceNode;
                }

                SimplifyFace(faceNodes, poly_nodes, quantities);
              }

              if (quantities.size() > 3) {
                // to be done: remove coincident faces
              }

              if (quantities.size() > 3)
                aMesh->ChangePolyhedronNodes(elem, poly_nodes, quantities);
              else
                rmElemIds.push_back(elem->GetID());

            }
            else {
              rmElemIds.push_back(elem->GetID());
            }
          }
        }
        else {
        }

        continue;
      }

      // Regular elements
      switch ( nbNodes ) {
      case 2: ///////////////////////////////////// EDGE
        isOk = false; break;
      case 3: ///////////////////////////////////// TRIANGLE
        isOk = false; break;
      case 4:
        if ( elem->GetType() == SMDSAbs_Volume ) // TETRAHEDRON
          isOk = false;
        else { //////////////////////////////////// QUADRANGLE
          if ( nbUniqueNodes < 3 )
            isOk = false;
          else if ( nbRepl == 2 && iRepl[ 1 ] - iRepl[ 0 ] == 2 )
            isOk = false; // opposite nodes stick
        }
        break;
      case 6: ///////////////////////////////////// PENTAHEDRON
        if ( nbUniqueNodes == 4 ) {
          // ---------------------------------> tetrahedron
          if (nbRepl == 3 &&
              iRepl[ 0 ] > 2 && iRepl[ 1 ] > 2 && iRepl[ 2 ] > 2 ) {
            // all top nodes stick: reverse a bottom
            uniqueNodes[ 0 ] = curNodes [ 1 ];
            uniqueNodes[ 1 ] = curNodes [ 0 ];
          }
          else if (nbRepl == 3 &&
                   iRepl[ 0 ] < 3 && iRepl[ 1 ] < 3 && iRepl[ 2 ] < 3 ) {
            // all bottom nodes stick: set a top before
            uniqueNodes[ 3 ] = uniqueNodes [ 0 ];
            uniqueNodes[ 0 ] = curNodes [ 3 ];
            uniqueNodes[ 1 ] = curNodes [ 4 ];
            uniqueNodes[ 2 ] = curNodes [ 5 ];
          }
          else if (nbRepl == 4 &&
                   iRepl[ 2 ] - iRepl [ 0 ] == 3 && iRepl[ 3 ] - iRepl [ 1 ] == 3 ) {
            // a lateral face turns into a line: reverse a bottom
            uniqueNodes[ 0 ] = curNodes [ 1 ];
            uniqueNodes[ 1 ] = curNodes [ 0 ];
          }
          else
            isOk = false;
        }
        else if ( nbUniqueNodes == 5 ) {
          // PENTAHEDRON --------------------> 2 tetrahedrons
          if ( nbRepl == 2 && iRepl[ 1 ] - iRepl [ 0 ] == 3 ) {
            // a bottom node sticks with a linked top one
            // 1.
            SMDS_MeshElement* newElem =
              aMesh->AddVolume(curNodes[ 3 ],
                               curNodes[ 4 ],
                               curNodes[ 5 ],
                               curNodes[ iRepl[ 0 ] == 2 ? 1 : 2 ]);
            myLastCreatedElems.Append(newElem);
            if ( aShapeId )
              aMesh->SetMeshElementOnShape( newElem, aShapeId );
            // 2. : reverse a bottom
            uniqueNodes[ 0 ] = curNodes [ 1 ];
            uniqueNodes[ 1 ] = curNodes [ 0 ];
            nbUniqueNodes = 4;
          }
          else
            isOk = false;
        }
        else
          isOk = false;
        break;
      case 8: {
        if(elem->IsQuadratic()) { // Quadratic quadrangle
          //   1    5    2
          //    +---+---+
          //    |       |
          //    |       |
          //   4+       +6
          //    |       |
          //    |       |
          //    +---+---+
          //   0    7    3
          isOk = false;
          if(nbRepl==3) {
            nbUniqueNodes = 6;
            if( iRepl[0]==0 && iRepl[1]==1 && iRepl[2]==4 ) {
              uniqueNodes[0] = curNodes[0];
              uniqueNodes[1] = curNodes[2];
              uniqueNodes[2] = curNodes[3];
              uniqueNodes[3] = curNodes[5];
              uniqueNodes[4] = curNodes[6];
              uniqueNodes[5] = curNodes[7];
              isOk = true;
            }
            if( iRepl[0]==0 && iRepl[1]==3 && iRepl[2]==7 ) {
              uniqueNodes[0] = curNodes[0];
              uniqueNodes[1] = curNodes[1];
              uniqueNodes[2] = curNodes[2];
              uniqueNodes[3] = curNodes[4];
              uniqueNodes[4] = curNodes[5];
              uniqueNodes[5] = curNodes[6];
              isOk = true;
            }
            if( iRepl[0]==0 && iRepl[1]==4 && iRepl[2]==7 ) {
              uniqueNodes[0] = curNodes[1];
              uniqueNodes[1] = curNodes[2];
              uniqueNodes[2] = curNodes[3];
              uniqueNodes[3] = curNodes[5];
              uniqueNodes[4] = curNodes[6];
              uniqueNodes[5] = curNodes[0];
              isOk = true;
            }
            if( iRepl[0]==1 && iRepl[1]==2 && iRepl[2]==5 ) {
              uniqueNodes[0] = curNodes[0];
              uniqueNodes[1] = curNodes[1];
              uniqueNodes[2] = curNodes[3];
              uniqueNodes[3] = curNodes[4];
              uniqueNodes[4] = curNodes[6];
              uniqueNodes[5] = curNodes[7];
              isOk = true;
            }
            if( iRepl[0]==1 && iRepl[1]==4 && iRepl[2]==5 ) {
              uniqueNodes[0] = curNodes[0];
              uniqueNodes[1] = curNodes[2];
              uniqueNodes[2] = curNodes[3];
              uniqueNodes[3] = curNodes[1];
              uniqueNodes[4] = curNodes[6];
              uniqueNodes[5] = curNodes[7];
              isOk = true;
            }
            if( iRepl[0]==2 && iRepl[1]==3 && iRepl[2]==6 ) {
              uniqueNodes[0] = curNodes[0];
              uniqueNodes[1] = curNodes[1];
              uniqueNodes[2] = curNodes[2];
              uniqueNodes[3] = curNodes[4];
              uniqueNodes[4] = curNodes[5];
              uniqueNodes[5] = curNodes[7];
              isOk = true;
            }
            if( iRepl[0]==2 && iRepl[1]==5 && iRepl[2]==6 ) {
              uniqueNodes[0] = curNodes[0];
              uniqueNodes[1] = curNodes[1];
              uniqueNodes[2] = curNodes[3];
              uniqueNodes[3] = curNodes[4];
              uniqueNodes[4] = curNodes[2];
              uniqueNodes[5] = curNodes[7];
              isOk = true;
            }
            if( iRepl[0]==3 && iRepl[1]==6 && iRepl[2]==7 ) {
              uniqueNodes[0] = curNodes[0];
              uniqueNodes[1] = curNodes[1];
              uniqueNodes[2] = curNodes[2];
              uniqueNodes[3] = curNodes[4];
              uniqueNodes[4] = curNodes[5];
              uniqueNodes[5] = curNodes[3];
              isOk = true;
            }
          }
          break;
        }
        //////////////////////////////////// HEXAHEDRON
        isOk = false;
        SMDS_VolumeTool hexa (elem);
        hexa.SetExternalNormal();
        if ( nbUniqueNodes == 4 && nbRepl == 6 ) {
          //////////////////////// ---> tetrahedron
          for ( int iFace = 0; iFace < 6; iFace++ ) {
            const int *ind = hexa.GetFaceNodesIndices( iFace ); // indices of face nodes
            if (curNodes[ind[ 0 ]] == curNodes[ind[ 1 ]] &&
                curNodes[ind[ 0 ]] == curNodes[ind[ 2 ]] &&
                curNodes[ind[ 0 ]] == curNodes[ind[ 3 ]] ) {
              // one face turns into a point ...
              int iOppFace = hexa.GetOppFaceIndex( iFace );
              ind = hexa.GetFaceNodesIndices( iOppFace );
              int nbStick = 0;
              iUnique = 2; // reverse a tetrahedron bottom
              for ( iCur = 0; iCur < 4 && nbStick < 2; iCur++ ) {
                if ( curNodes[ind[ iCur ]] == curNodes[ind[ iCur + 1 ]] )
                  nbStick++;
                else if ( iUnique >= 0 )
                  uniqueNodes[ iUnique-- ] = curNodes[ind[ iCur ]];
              }
              if ( nbStick == 1 ) {
                // ... and the opposite one - into a triangle.
                // set a top node
                ind = hexa.GetFaceNodesIndices( iFace );
                uniqueNodes[ 3 ] = curNodes[ind[ 0 ]];
                isOk = true;
              }
              break;
            }
          }
        }
        else if (nbUniqueNodes == 5 && nbRepl == 4 ) {
          //////////////////// HEXAHEDRON ---> 2 tetrahedrons
          for ( int iFace = 0; iFace < 6; iFace++ ) {
            const int *ind = hexa.GetFaceNodesIndices( iFace ); // indices of face nodes
            if (curNodes[ind[ 0 ]] == curNodes[ind[ 1 ]] &&
                curNodes[ind[ 0 ]] == curNodes[ind[ 2 ]] &&
                curNodes[ind[ 0 ]] == curNodes[ind[ 3 ]] ) {
              // one face turns into a point ...
              int iOppFace = hexa.GetOppFaceIndex( iFace );
              ind = hexa.GetFaceNodesIndices( iOppFace );
              int nbStick = 0;
              iUnique = 2;  // reverse a tetrahedron 1 bottom
              for ( iCur = 0; iCur < 4 && nbStick == 0; iCur++ ) {
                if ( curNodes[ind[ iCur ]] == curNodes[ind[ iCur + 1 ]] )
                  nbStick++;
                else if ( iUnique >= 0 )
                  uniqueNodes[ iUnique-- ] = curNodes[ind[ iCur ]];
              }
              if ( nbStick == 0 ) {
                // ... and the opposite one is a quadrangle
                // set a top node
                const int* indTop = hexa.GetFaceNodesIndices( iFace );
                uniqueNodes[ 3 ] = curNodes[indTop[ 0 ]];
                nbUniqueNodes = 4;
                // tetrahedron 2
                SMDS_MeshElement* newElem =
                  aMesh->AddVolume(curNodes[ind[ 0 ]],
                                   curNodes[ind[ 3 ]],
                                   curNodes[ind[ 2 ]],
                                   curNodes[indTop[ 0 ]]);
                myLastCreatedElems.Append(newElem);
                if ( aShapeId )
                  aMesh->SetMeshElementOnShape( newElem, aShapeId );
                isOk = true;
              }
              break;
            }
          }
        }
        else if ( nbUniqueNodes == 6 && nbRepl == 4 ) {
          ////////////////// HEXAHEDRON ---> 2 tetrahedrons or 1 prism
          // find indices of quad and tri faces
          int iQuadFace[ 6 ], iTriFace[ 6 ], nbQuad = 0, nbTri = 0, iFace;
          for ( iFace = 0; iFace < 6; iFace++ ) {
            const int *ind = hexa.GetFaceNodesIndices( iFace ); // indices of face nodes
            nodeSet.clear();
            for ( iCur = 0; iCur < 4; iCur++ )
              nodeSet.insert( curNodes[ind[ iCur ]] );
            nbUniqueNodes = nodeSet.size();
            if ( nbUniqueNodes == 3 )
              iTriFace[ nbTri++ ] = iFace;
            else if ( nbUniqueNodes == 4 )
              iQuadFace[ nbQuad++ ] = iFace;
          }
          if (nbQuad == 2 && nbTri == 4 &&
              hexa.GetOppFaceIndex( iQuadFace[ 0 ] ) == iQuadFace[ 1 ]) {
            // 2 opposite quadrangles stuck with a diagonal;
            // sample groups of merged indices: (0-4)(2-6)
            // --------------------------------------------> 2 tetrahedrons
            const int *ind1 = hexa.GetFaceNodesIndices( iQuadFace[ 0 ]); // indices of quad1 nodes
            const int *ind2 = hexa.GetFaceNodesIndices( iQuadFace[ 1 ]);
            int i0, i1d, i2, i3d, i0t, i2t; // d-daigonal, t-top
            if (curNodes[ind1[ 0 ]] == curNodes[ind2[ 0 ]] &&
                curNodes[ind1[ 2 ]] == curNodes[ind2[ 2 ]]) {
              // stuck with 0-2 diagonal
              i0  = ind1[ 3 ];
              i1d = ind1[ 0 ];
              i2  = ind1[ 1 ];
              i3d = ind1[ 2 ];
              i0t = ind2[ 1 ];
              i2t = ind2[ 3 ];
            }
            else if (curNodes[ind1[ 1 ]] == curNodes[ind2[ 3 ]] &&
                     curNodes[ind1[ 3 ]] == curNodes[ind2[ 1 ]]) {
              // stuck with 1-3 diagonal
              i0  = ind1[ 0 ];
              i1d = ind1[ 1 ];
              i2  = ind1[ 2 ];
              i3d = ind1[ 3 ];
              i0t = ind2[ 0 ];
              i2t = ind2[ 1 ];
            }
            else {
              ASSERT(0);
            }
            // tetrahedron 1
            uniqueNodes[ 0 ] = curNodes [ i0 ];
            uniqueNodes[ 1 ] = curNodes [ i1d ];
            uniqueNodes[ 2 ] = curNodes [ i3d ];
            uniqueNodes[ 3 ] = curNodes [ i0t ];
            nbUniqueNodes = 4;
            // tetrahedron 2
            SMDS_MeshElement* newElem = aMesh->AddVolume(curNodes[ i1d ],
                                                         curNodes[ i2 ],
                                                         curNodes[ i3d ],
                                                         curNodes[ i2t ]);
            myLastCreatedElems.Append(newElem);
            if ( aShapeId )
              aMesh->SetMeshElementOnShape( newElem, aShapeId );
            isOk = true;
          }
          else if (( nbTri == 2 && nbQuad == 3 ) || // merged (0-4)(1-5)
                   ( nbTri == 4 && nbQuad == 2 )) { // merged (7-4)(1-5)
            // --------------------------------------------> prism
            // find 2 opposite triangles
            nbUniqueNodes = 6;
            for ( iFace = 0; iFace + 1 < nbTri; iFace++ ) {
              if ( hexa.GetOppFaceIndex( iTriFace[ iFace ] ) == iTriFace[ iFace + 1 ]) {
                // find indices of kept and replaced nodes
                // and fill unique nodes of 2 opposite triangles
                const int *ind1 = hexa.GetFaceNodesIndices( iTriFace[ iFace ]);
                const int *ind2 = hexa.GetFaceNodesIndices( iTriFace[ iFace + 1 ]);
                const SMDS_MeshNode** hexanodes = hexa.GetNodes();
                // fill unique nodes
                iUnique = 0;
                isOk = true;
                for ( iCur = 0; iCur < 4 && isOk; iCur++ ) {
                  const SMDS_MeshNode* n     = curNodes[ind1[ iCur ]];
                  const SMDS_MeshNode* nInit = hexanodes[ind1[ iCur ]];
                  if ( n == nInit ) {
                    // iCur of a linked node of the opposite face (make normals co-directed):
                    int iCurOpp = ( iCur == 1 || iCur == 3 ) ? 4 - iCur : iCur;
                    // check that correspondent corners of triangles are linked
                    if ( !hexa.IsLinked( ind1[ iCur ], ind2[ iCurOpp ] ))
                      isOk = false;
                    else {
                      uniqueNodes[ iUnique ] = n;
                      uniqueNodes[ iUnique + 3 ] = curNodes[ind2[ iCurOpp ]];
                      iUnique++;
                    }
                  }
                }
                break;
              }
            }
          }
        } // if ( nbUniqueNodes == 6 && nbRepl == 4 )
        break;
      } // HEXAHEDRON

      default:
        isOk = false;
      } // switch ( nbNodes )

    } // if ( nbNodes != nbUniqueNodes ) // some nodes stick

    if ( isOk ) {
      if (elem->IsPoly() && elem->GetType() == SMDSAbs_Volume) {
        // Change nodes of polyedre
        const SMDS_PolyhedralVolumeOfNodes* aPolyedre =
          static_cast<const SMDS_PolyhedralVolumeOfNodes*>( elem );
        if (aPolyedre) {
          int nbFaces = aPolyedre->NbFaces();

          vector<const SMDS_MeshNode *> poly_nodes;
          vector<int> quantities (nbFaces);

          for (int iface = 1; iface <= nbFaces; iface++) {
            int inode, nbFaceNodes = aPolyedre->NbFaceNodes(iface);
            quantities[iface - 1] = nbFaceNodes;

            for (inode = 1; inode <= nbFaceNodes; inode++) {
              const SMDS_MeshNode* curNode = aPolyedre->GetFaceNode(iface, inode);

              TNodeNodeMap::iterator nnIt = nodeNodeMap.find( curNode );
              if (nnIt != nodeNodeMap.end()) { // curNode sticks
                curNode = (*nnIt).second;
              }
              poly_nodes.push_back(curNode);
            }
          }
          aMesh->ChangePolyhedronNodes( elem, poly_nodes, quantities );
        }
      }
      else {
        // Change regular element or polygon
        aMesh->ChangeElementNodes( elem, & uniqueNodes[0], nbUniqueNodes );
      }
    }
    else {
      // Remove invalid regular element or invalid polygon
      rmElemIds.push_back( elem->GetID() );
    }

  } // loop on elements

  // Remove equal nodes and bad elements

  Remove( rmNodeIds, true );
  Remove( rmElemIds, false );

}


// ========================================================
// class   : SortableElement
// purpose : allow sorting elements basing on their nodes
// ========================================================
class SortableElement : public set <const SMDS_MeshElement*>
{
 public:

  SortableElement( const SMDS_MeshElement* theElem )
    {
      myElem = theElem;
      SMDS_ElemIteratorPtr nodeIt = theElem->nodesIterator();
      while ( nodeIt->more() )
        this->insert( nodeIt->next() );
    }

  const SMDS_MeshElement* Get() const
    { return myElem; }

  void Set(const SMDS_MeshElement* e) const
    { myElem = e; }


 private:
  mutable const SMDS_MeshElement* myElem;
};

//=======================================================================
//function : FindEqualElements
//purpose  : Return list of group of elements built on the same nodes.
//           Search among theElements or in the whole mesh if theElements is empty
//=======================================================================
void SMESH_MeshEditor::FindEqualElements(set<const SMDS_MeshElement*> & theElements,
					 TListOfListOfElementsID &      theGroupsOfElementsID)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  typedef set<const SMDS_MeshElement*> TElemsSet;
  typedef map< SortableElement, int > TMapOfNodeSet;
  typedef list<int> TGroupOfElems;

  TElemsSet elems;
  if ( theElements.empty() )
  { // get all elements in the mesh
    SMDS_ElemIteratorPtr eIt = GetMeshDS()->elementsIterator();
    while ( eIt->more() )
      elems.insert( elems.end(), eIt->next());
  }
  else
    elems = theElements;

  vector< TGroupOfElems > arrayOfGroups;
  TGroupOfElems groupOfElems;
  TMapOfNodeSet mapOfNodeSet;

  TElemsSet::iterator elemIt = elems.begin();
  for ( int i = 0, j=0; elemIt != elems.end(); ++elemIt, ++j ) {
    const SMDS_MeshElement* curElem = *elemIt;
    SortableElement SE(curElem);
    int ind = -1;
    // check uniqueness
    pair< TMapOfNodeSet::iterator, bool> pp = mapOfNodeSet.insert(make_pair(SE, i));
    if( !(pp.second) ) {
      TMapOfNodeSet::iterator& itSE = pp.first;
      ind = (*itSE).second;
      arrayOfGroups[ind].push_back(curElem->GetID());
    }
    else {
      groupOfElems.clear();
      groupOfElems.push_back(curElem->GetID());
      arrayOfGroups.push_back(groupOfElems);
      i++;
    }
  }

  vector< TGroupOfElems >::iterator groupIt = arrayOfGroups.begin();
  for ( ; groupIt != arrayOfGroups.end(); ++groupIt ) {
    groupOfElems = *groupIt;
    if ( groupOfElems.size() > 1 ) {
      groupOfElems.sort();
      theGroupsOfElementsID.push_back(groupOfElems);
    }
  }
}

//=======================================================================
//function : MergeElements
//purpose  : In each given group, substitute all elements by the first one.
//=======================================================================

void SMESH_MeshEditor::MergeElements(TListOfListOfElementsID & theGroupsOfElementsID)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  typedef list<int> TListOfIDs;
  TListOfIDs rmElemIds; // IDs of elems to remove

  SMESHDS_Mesh* aMesh = GetMeshDS();

  TListOfListOfElementsID::iterator groupsIt = theGroupsOfElementsID.begin();
  while ( groupsIt != theGroupsOfElementsID.end() ) {
    TListOfIDs& aGroupOfElemID = *groupsIt;
    aGroupOfElemID.sort();
    int elemIDToKeep = aGroupOfElemID.front();
    const SMDS_MeshElement* elemToKeep = aMesh->FindElement(elemIDToKeep);
    aGroupOfElemID.pop_front();
    TListOfIDs::iterator idIt = aGroupOfElemID.begin();
    while ( idIt != aGroupOfElemID.end() ) {
      int elemIDToRemove = *idIt;
      const SMDS_MeshElement* elemToRemove = aMesh->FindElement(elemIDToRemove);
      // add the kept element in groups of removed one (PAL15188)
      AddToSameGroups( elemToKeep, elemToRemove, aMesh );
      rmElemIds.push_back( elemIDToRemove );
      ++idIt;
    }
    ++groupsIt;
  }

  Remove( rmElemIds, false );
}

//=======================================================================
//function : MergeEqualElements
//purpose  : Remove all but one of elements built on the same nodes.
//=======================================================================

void SMESH_MeshEditor::MergeEqualElements()
{
  set<const SMDS_MeshElement*> aMeshElements; /* empty input -
						 to merge equal elements in the whole mesh */
  TListOfListOfElementsID aGroupsOfElementsID;
  FindEqualElements(aMeshElements, aGroupsOfElementsID);
  MergeElements(aGroupsOfElementsID);
}

//=======================================================================
//function : FindFaceInSet
//purpose  : Return a face having linked nodes n1 and n2 and which is
//           - not in avoidSet,
//           - in elemSet provided that !elemSet.empty()
//=======================================================================

const SMDS_MeshElement*
  SMESH_MeshEditor::FindFaceInSet(const SMDS_MeshNode*    n1,
                                  const SMDS_MeshNode*    n2,
                                  const TIDSortedElemSet& elemSet,
                                  const TIDSortedElemSet& avoidSet)

{
  SMDS_ElemIteratorPtr invElemIt = n1->GetInverseElementIterator(SMDSAbs_Face);
  while ( invElemIt->more() ) { // loop on inverse elements of n1
    const SMDS_MeshElement* elem = invElemIt->next();
    if (avoidSet.find( elem ) != avoidSet.end() )
      continue;
    if ( !elemSet.empty() && elemSet.find( elem ) == elemSet.end())
      continue;
    // get face nodes and find index of n1
    int i1, nbN = elem->NbNodes(), iNode = 0;
    //const SMDS_MeshNode* faceNodes[ nbN ], *n;
    vector<const SMDS_MeshNode*> faceNodes( nbN );
    const SMDS_MeshNode* n;
    SMDS_ElemIteratorPtr nIt = elem->nodesIterator();
    while ( nIt->more() ) {
      faceNodes[ iNode ] = static_cast<const SMDS_MeshNode*>( nIt->next() );
      if ( faceNodes[ iNode++ ] == n1 )
        i1 = iNode - 1;
    }
    // find a n2 linked to n1
    if(!elem->IsQuadratic()) {
      for ( iNode = 0; iNode < 2; iNode++ ) {
        if ( iNode ) // node before n1
          n = faceNodes[ i1 == 0 ? nbN - 1 : i1 - 1 ];
        else         // node after n1
          n = faceNodes[ i1 + 1 == nbN ? 0 : i1 + 1 ];
        if ( n == n2 )
          return elem;
      }
    }
    else { // analysis for quadratic elements
      bool IsFind = false;
      // check using only corner nodes
      for ( iNode = 0; iNode < 2; iNode++ ) {
        if ( iNode ) // node before n1
          n = faceNodes[ i1 == 0 ? nbN/2 - 1 : i1 - 1 ];
        else         // node after n1
          n = faceNodes[ i1 + 1 == nbN/2 ? 0 : i1 + 1 ];
        if ( n == n2 )
          IsFind = true;
      }
      if(IsFind) {
        return elem;
      }
      else {
        // check using all nodes
        const SMDS_QuadraticFaceOfNodes* F =
          static_cast<const SMDS_QuadraticFaceOfNodes*>(elem);
        // use special nodes iterator
        iNode = 0;
        SMDS_NodeIteratorPtr anIter = F->interlacedNodesIterator();
        while ( anIter->more() ) {
          faceNodes[iNode] = static_cast<const SMDS_MeshNode*>(anIter->next());
          if ( faceNodes[ iNode++ ] == n1 )
            i1 = iNode - 1;
        }
        for ( iNode = 0; iNode < 2; iNode++ ) {
          if ( iNode ) // node before n1
            n = faceNodes[ i1 == 0 ? nbN - 1 : i1 - 1 ];
          else         // node after n1
            n = faceNodes[ i1 + 1 == nbN ? 0 : i1 + 1 ];
          if ( n == n2 ) {
            return elem;
          }
        }
      }
    } // end analysis for quadratic elements
  }
  return 0;
}

//=======================================================================
//function : findAdjacentFace
//purpose  :
//=======================================================================

static const SMDS_MeshElement* findAdjacentFace(const SMDS_MeshNode* n1,
                                                const SMDS_MeshNode* n2,
                                                const SMDS_MeshElement* elem)
{
  TIDSortedElemSet elemSet, avoidSet;
  if ( elem )
    avoidSet.insert ( elem );
  return SMESH_MeshEditor::FindFaceInSet( n1, n2, elemSet, avoidSet );
}

//=======================================================================
//function : FindFreeBorder
//purpose  :
//=======================================================================

#define ControlFreeBorder SMESH::Controls::FreeEdges::IsFreeEdge

bool SMESH_MeshEditor::FindFreeBorder (const SMDS_MeshNode*             theFirstNode,
                                       const SMDS_MeshNode*             theSecondNode,
                                       const SMDS_MeshNode*             theLastNode,
                                       list< const SMDS_MeshNode* > &   theNodes,
                                       list< const SMDS_MeshElement* >& theFaces)
{
  if ( !theFirstNode || !theSecondNode )
    return false;
  // find border face between theFirstNode and theSecondNode
  const SMDS_MeshElement* curElem = findAdjacentFace( theFirstNode, theSecondNode, 0 );
  if ( !curElem )
    return false;

  theFaces.push_back( curElem );
  theNodes.push_back( theFirstNode );
  theNodes.push_back( theSecondNode );

  //vector<const SMDS_MeshNode*> nodes;
  const SMDS_MeshNode *nIgnore = theFirstNode, *nStart = theSecondNode;
  set < const SMDS_MeshElement* > foundElems;
  bool needTheLast = ( theLastNode != 0 );

  while ( nStart != theLastNode ) {
    if ( nStart == theFirstNode )
      return !needTheLast;

    // find all free border faces sharing form nStart

    list< const SMDS_MeshElement* > curElemList;
    list< const SMDS_MeshNode* > nStartList;
    SMDS_ElemIteratorPtr invElemIt = nStart->GetInverseElementIterator(SMDSAbs_Face);
    while ( invElemIt->more() ) {
      const SMDS_MeshElement* e = invElemIt->next();
      if ( e == curElem || foundElems.insert( e ).second ) {
        // get nodes
        int iNode = 0, nbNodes = e->NbNodes();
        //const SMDS_MeshNode* nodes[nbNodes+1];
        vector<const SMDS_MeshNode*> nodes(nbNodes+1);
        
        if(e->IsQuadratic()) {
          const SMDS_QuadraticFaceOfNodes* F =
            static_cast<const SMDS_QuadraticFaceOfNodes*>(e);
          // use special nodes iterator
          SMDS_NodeIteratorPtr anIter = F->interlacedNodesIterator();
          while( anIter->more() ) {
            nodes[ iNode++ ] = anIter->next();
          }
        }
        else {
          SMDS_ElemIteratorPtr nIt = e->nodesIterator();
          while ( nIt->more() )
            nodes[ iNode++ ] = static_cast<const SMDS_MeshNode*>( nIt->next() );
        }
        nodes[ iNode ] = nodes[ 0 ];
        // check 2 links
        for ( iNode = 0; iNode < nbNodes; iNode++ )
          if (((nodes[ iNode ] == nStart && nodes[ iNode + 1] != nIgnore ) ||
               (nodes[ iNode + 1] == nStart && nodes[ iNode ] != nIgnore )) &&
              ControlFreeBorder( &nodes[ iNode ], e->GetID() ))
          {
            nStartList.push_back( nodes[ iNode + ( nodes[ iNode ] == nStart ? 1 : 0 )]);
            curElemList.push_back( e );
          }
      }
    }
    // analyse the found

    int nbNewBorders = curElemList.size();
    if ( nbNewBorders == 0 ) {
      // no free border furthermore
      return !needTheLast;
    }
    else if ( nbNewBorders == 1 ) {
      // one more element found
      nIgnore = nStart;
      nStart = nStartList.front();
      curElem = curElemList.front();
      theFaces.push_back( curElem );
      theNodes.push_back( nStart );
    }
    else {
      // several continuations found
      list< const SMDS_MeshElement* >::iterator curElemIt;
      list< const SMDS_MeshNode* >::iterator nStartIt;
      // check if one of them reached the last node
      if ( needTheLast ) {
        for (curElemIt = curElemList.begin(), nStartIt = nStartList.begin();
             curElemIt!= curElemList.end();
             curElemIt++, nStartIt++ )
          if ( *nStartIt == theLastNode ) {
            theFaces.push_back( *curElemIt );
            theNodes.push_back( *nStartIt );
            return true;
          }
      }
      // find the best free border by the continuations
      list<const SMDS_MeshNode*>    contNodes[ 2 ], *cNL;
      list<const SMDS_MeshElement*> contFaces[ 2 ], *cFL;
      for (curElemIt = curElemList.begin(), nStartIt = nStartList.begin();
           curElemIt!= curElemList.end();
           curElemIt++, nStartIt++ )
      {
        cNL = & contNodes[ contNodes[0].empty() ? 0 : 1 ];
        cFL = & contFaces[ contFaces[0].empty() ? 0 : 1 ];
        // find one more free border
        if ( ! FindFreeBorder( nStart, *nStartIt, theLastNode, *cNL, *cFL )) {
          cNL->clear();
          cFL->clear();
        }
        else if ( !contNodes[0].empty() && !contNodes[1].empty() ) {
          // choice: clear a worse one
          int iLongest = ( contNodes[0].size() < contNodes[1].size() ? 1 : 0 );
          int iWorse = ( needTheLast ? 1 - iLongest : iLongest );
          contNodes[ iWorse ].clear();
          contFaces[ iWorse ].clear();
        }
      }
      if ( contNodes[0].empty() && contNodes[1].empty() )
        return false;

      // append the best free border
      cNL = & contNodes[ contNodes[0].empty() ? 1 : 0 ];
      cFL = & contFaces[ contFaces[0].empty() ? 1 : 0 ];
      theNodes.pop_back(); // remove nIgnore
      theNodes.pop_back(); // remove nStart
      theFaces.pop_back(); // remove curElem
      list< const SMDS_MeshNode* >::iterator nIt = cNL->begin();
      list< const SMDS_MeshElement* >::iterator fIt = cFL->begin();
      for ( ; nIt != cNL->end(); nIt++ ) theNodes.push_back( *nIt );
      for ( ; fIt != cFL->end(); fIt++ ) theFaces.push_back( *fIt );
      return true;

    } // several continuations found
  } // while ( nStart != theLastNode )

  return true;
}

//=======================================================================
//function : CheckFreeBorderNodes
//purpose  : Return true if the tree nodes are on a free border
//=======================================================================

bool SMESH_MeshEditor::CheckFreeBorderNodes(const SMDS_MeshNode* theNode1,
                                            const SMDS_MeshNode* theNode2,
                                            const SMDS_MeshNode* theNode3)
{
  list< const SMDS_MeshNode* > nodes;
  list< const SMDS_MeshElement* > faces;
  return FindFreeBorder( theNode1, theNode2, theNode3, nodes, faces);
}

//=======================================================================
//function : SewFreeBorder
//purpose  :
//=======================================================================

SMESH_MeshEditor::Sew_Error
  SMESH_MeshEditor::SewFreeBorder (const SMDS_MeshNode* theBordFirstNode,
                                   const SMDS_MeshNode* theBordSecondNode,
                                   const SMDS_MeshNode* theBordLastNode,
                                   const SMDS_MeshNode* theSideFirstNode,
                                   const SMDS_MeshNode* theSideSecondNode,
                                   const SMDS_MeshNode* theSideThirdNode,
                                   const bool           theSideIsFreeBorder,
                                   const bool           toCreatePolygons,
                                   const bool           toCreatePolyedrs)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  MESSAGE("::SewFreeBorder()");
  Sew_Error aResult = SEW_OK;

  // ====================================
  //    find side nodes and elements
  // ====================================

  list< const SMDS_MeshNode* > nSide[ 2 ];
  list< const SMDS_MeshElement* > eSide[ 2 ];
  list< const SMDS_MeshNode* >::iterator nIt[ 2 ];
  list< const SMDS_MeshElement* >::iterator eIt[ 2 ];

  // Free border 1
  // --------------
  if (!FindFreeBorder(theBordFirstNode,theBordSecondNode,theBordLastNode,
                      nSide[0], eSide[0])) {
    MESSAGE(" Free Border 1 not found " );
    aResult = SEW_BORDER1_NOT_FOUND;
  }
  if (theSideIsFreeBorder) {
    // Free border 2
    // --------------
    if (!FindFreeBorder(theSideFirstNode, theSideSecondNode, theSideThirdNode,
                        nSide[1], eSide[1])) {
      MESSAGE(" Free Border 2 not found " );
      aResult = ( aResult != SEW_OK ? SEW_BOTH_BORDERS_NOT_FOUND : SEW_BORDER2_NOT_FOUND );
    }
  }
  if ( aResult != SEW_OK )
    return aResult;

  if (!theSideIsFreeBorder) {
    // Side 2
    // --------------

    // -------------------------------------------------------------------------
    // Algo:
    // 1. If nodes to merge are not coincident, move nodes of the free border
    //    from the coord sys defined by the direction from the first to last
    //    nodes of the border to the correspondent sys of the side 2
    // 2. On the side 2, find the links most co-directed with the correspondent
    //    links of the free border
    // -------------------------------------------------------------------------

    // 1. Since sewing may brake if there are volumes to split on the side 2,
    //    we wont move nodes but just compute new coordinates for them
    typedef map<const SMDS_MeshNode*, gp_XYZ> TNodeXYZMap;
    TNodeXYZMap nBordXYZ;
    list< const SMDS_MeshNode* >& bordNodes = nSide[ 0 ];
    list< const SMDS_MeshNode* >::iterator nBordIt;

    gp_XYZ Pb1( theBordFirstNode->X(), theBordFirstNode->Y(), theBordFirstNode->Z() );
    gp_XYZ Pb2( theBordLastNode->X(), theBordLastNode->Y(), theBordLastNode->Z() );
    gp_XYZ Ps1( theSideFirstNode->X(), theSideFirstNode->Y(), theSideFirstNode->Z() );
    gp_XYZ Ps2( theSideSecondNode->X(), theSideSecondNode->Y(), theSideSecondNode->Z() );
    double tol2 = 1.e-8;
    gp_Vec Vbs1( Pb1 - Ps1 ),Vbs2( Pb2 - Ps2 );
    if ( Vbs1.SquareMagnitude() > tol2 || Vbs2.SquareMagnitude() > tol2 ) {
      // Need node movement.

      // find X and Z axes to create trsf
      gp_Vec Zb( Pb1 - Pb2 ), Zs( Ps1 - Ps2 );
      gp_Vec X = Zs ^ Zb;
      if ( X.SquareMagnitude() <= gp::Resolution() * gp::Resolution() )
        // Zb || Zs
        X = gp_Ax2( gp::Origin(), Zb ).XDirection();

      // coord systems
      gp_Ax3 toBordAx( Pb1, Zb, X );
      gp_Ax3 fromSideAx( Ps1, Zs, X );
      gp_Ax3 toGlobalAx( gp::Origin(), gp::DZ(), gp::DX() );
      // set trsf
      gp_Trsf toBordSys, fromSide2Sys;
      toBordSys.SetTransformation( toBordAx );
      fromSide2Sys.SetTransformation( fromSideAx, toGlobalAx );
      fromSide2Sys.SetScaleFactor( Zs.Magnitude() / Zb.Magnitude() );

      // move
      for ( nBordIt = bordNodes.begin(); nBordIt != bordNodes.end(); nBordIt++ ) {
        const SMDS_MeshNode* n = *nBordIt;
        gp_XYZ xyz( n->X(),n->Y(),n->Z() );
        toBordSys.Transforms( xyz );
        fromSide2Sys.Transforms( xyz );
        nBordXYZ.insert( TNodeXYZMap::value_type( n, xyz ));
      }
    }
    else {
      // just insert nodes XYZ in the nBordXYZ map
      for ( nBordIt = bordNodes.begin(); nBordIt != bordNodes.end(); nBordIt++ ) {
        const SMDS_MeshNode* n = *nBordIt;
        nBordXYZ.insert( TNodeXYZMap::value_type( n, gp_XYZ( n->X(),n->Y(),n->Z() )));
      }
    }

    // 2. On the side 2, find the links most co-directed with the correspondent
    //    links of the free border

    list< const SMDS_MeshElement* >& sideElems = eSide[ 1 ];
    list< const SMDS_MeshNode* >& sideNodes = nSide[ 1 ];
    sideNodes.push_back( theSideFirstNode );

    bool hasVolumes = false;
    LinkID_Gen aLinkID_Gen( GetMeshDS() );
    set<long> foundSideLinkIDs, checkedLinkIDs;
    SMDS_VolumeTool volume;
    //const SMDS_MeshNode* faceNodes[ 4 ];

    const SMDS_MeshNode*    sideNode;
    const SMDS_MeshElement* sideElem;
    const SMDS_MeshNode* prevSideNode = theSideFirstNode;
    const SMDS_MeshNode* prevBordNode = theBordFirstNode;
    nBordIt = bordNodes.begin();
    nBordIt++;
    // border node position and border link direction to compare with
    gp_XYZ bordPos = nBordXYZ[ *nBordIt ];
    gp_XYZ bordDir = bordPos - nBordXYZ[ prevBordNode ];
    // choose next side node by link direction or by closeness to
    // the current border node:
    bool searchByDir = ( *nBordIt != theBordLastNode );
    do {
      // find the next node on the Side 2
      sideNode = 0;
      double maxDot = -DBL_MAX, minDist = DBL_MAX;
      long linkID;
      checkedLinkIDs.clear();
      gp_XYZ prevXYZ( prevSideNode->X(), prevSideNode->Y(), prevSideNode->Z() );

      // loop on inverse elements of current node (prevSideNode) on the Side 2
      SMDS_ElemIteratorPtr invElemIt = prevSideNode->GetInverseElementIterator();
      while ( invElemIt->more() )
      {
        const SMDS_MeshElement* elem = invElemIt->next();
        // prepare data for a loop on links coming to prevSideNode, of a face or a volume
        int iPrevNode, iNode = 0, nbNodes = elem->NbNodes();
        vector< const SMDS_MeshNode* > faceNodes( nbNodes, (const SMDS_MeshNode*)0 );
        bool isVolume = volume.Set( elem );
        const SMDS_MeshNode** nodes = isVolume ? volume.GetNodes() : & faceNodes[0];
        if ( isVolume ) // --volume
          hasVolumes = true;
        else if ( elem->GetType()==SMDSAbs_Face ) { // --face
          // retrieve all face nodes and find iPrevNode - an index of the prevSideNode
          if(elem->IsQuadratic()) {
            const SMDS_QuadraticFaceOfNodes* F =
              static_cast<const SMDS_QuadraticFaceOfNodes*>(elem);
            // use special nodes iterator
            SMDS_NodeIteratorPtr anIter = F->interlacedNodesIterator();
            while( anIter->more() ) {
              nodes[ iNode ] = anIter->next();
              if ( nodes[ iNode++ ] == prevSideNode )
                iPrevNode = iNode - 1;
            }
          }
          else {
            SMDS_ElemIteratorPtr nIt = elem->nodesIterator();
            while ( nIt->more() ) {
              nodes[ iNode ] = cast2Node( nIt->next() );
              if ( nodes[ iNode++ ] == prevSideNode )
                iPrevNode = iNode - 1;
            }
          }
          // there are 2 links to check
          nbNodes = 2;
        }
        else // --edge
          continue;
        // loop on links, to be precise, on the second node of links
        for ( iNode = 0; iNode < nbNodes; iNode++ ) {
          const SMDS_MeshNode* n = nodes[ iNode ];
          if ( isVolume ) {
            if ( !volume.IsLinked( n, prevSideNode ))
              continue;
          }
          else {
            if ( iNode ) // a node before prevSideNode
              n = nodes[ iPrevNode == 0 ? elem->NbNodes() - 1 : iPrevNode - 1 ];
            else         // a node after prevSideNode
              n = nodes[ iPrevNode + 1 == elem->NbNodes() ? 0 : iPrevNode + 1 ];
          }
          // check if this link was already used
          long iLink = aLinkID_Gen.GetLinkID( prevSideNode, n );
          bool isJustChecked = !checkedLinkIDs.insert( iLink ).second;
          if (!isJustChecked &&
              foundSideLinkIDs.find( iLink ) == foundSideLinkIDs.end() )
          {
            // test a link geometrically
            gp_XYZ nextXYZ ( n->X(), n->Y(), n->Z() );
            bool linkIsBetter = false;
            double dot = 0.0, dist = 0.0;
            if ( searchByDir ) { // choose most co-directed link
              dot = bordDir * ( nextXYZ - prevXYZ ).Normalized();
              linkIsBetter = ( dot > maxDot );
            }
            else { // choose link with the node closest to bordPos
              dist = ( nextXYZ - bordPos ).SquareModulus();
              linkIsBetter = ( dist < minDist );
            }
            if ( linkIsBetter ) {
              maxDot = dot;
              minDist = dist;
              linkID = iLink;
              sideNode = n;
              sideElem = elem;
            }
          }
        }
      } // loop on inverse elements of prevSideNode

      if ( !sideNode ) {
        MESSAGE(" Cant find path by links of the Side 2 ");
        return SEW_BAD_SIDE_NODES;
      }
      sideNodes.push_back( sideNode );
      sideElems.push_back( sideElem );
      foundSideLinkIDs.insert ( linkID );
      prevSideNode = sideNode;

      if ( *nBordIt == theBordLastNode )
        searchByDir = false;
      else {
        // find the next border link to compare with
        gp_XYZ sidePos( sideNode->X(), sideNode->Y(), sideNode->Z() );
        searchByDir = ( bordDir * ( sidePos - bordPos ) <= 0 );
        // move to next border node if sideNode is before forward border node (bordPos)
        while ( *nBordIt != theBordLastNode && !searchByDir ) {
          prevBordNode = *nBordIt;
          nBordIt++;
          bordPos = nBordXYZ[ *nBordIt ];
          bordDir = bordPos - nBordXYZ[ prevBordNode ];
          searchByDir = ( bordDir * ( sidePos - bordPos ) <= 0 );
        }
      }
    }
    while ( sideNode != theSideSecondNode );

    if ( hasVolumes && sideNodes.size () != bordNodes.size() && !toCreatePolyedrs) {
      MESSAGE("VOLUME SPLITTING IS FORBIDDEN");
      return SEW_VOLUMES_TO_SPLIT; // volume splitting is forbidden
    }
  } // end nodes search on the side 2

  // ============================
  // sew the border to the side 2
  // ============================

  int nbNodes[]  = { nSide[0].size(), nSide[1].size() };
  int maxNbNodes = Max( nbNodes[0], nbNodes[1] );

  TListOfListOfNodes nodeGroupsToMerge;
  if ( nbNodes[0] == nbNodes[1] ||
      ( theSideIsFreeBorder && !theSideThirdNode)) {

    // all nodes are to be merged

    for (nIt[0] = nSide[0].begin(), nIt[1] = nSide[1].begin();
         nIt[0] != nSide[0].end() && nIt[1] != nSide[1].end();
         nIt[0]++, nIt[1]++ )
    {
      nodeGroupsToMerge.push_back( list<const SMDS_MeshNode*>() );
      nodeGroupsToMerge.back().push_back( *nIt[1] ); // to keep
      nodeGroupsToMerge.back().push_back( *nIt[0] ); // to remove
    }
  }
  else {

    // insert new nodes into the border and the side to get equal nb of segments

    // get normalized parameters of nodes on the borders
    //double param[ 2 ][ maxNbNodes ];
    double* param[ 2 ];
    param[0] = new double [ maxNbNodes ];
    param[1] = new double [ maxNbNodes ];
    int iNode, iBord;
    for ( iBord = 0; iBord < 2; iBord++ ) { // loop on 2 borders
      list< const SMDS_MeshNode* >& nodes = nSide[ iBord ];
      list< const SMDS_MeshNode* >::iterator nIt = nodes.begin();
      const SMDS_MeshNode* nPrev = *nIt;
      double bordLength = 0;
      for ( iNode = 0; nIt != nodes.end(); nIt++, iNode++ ) { // loop on border nodes
        const SMDS_MeshNode* nCur = *nIt;
        gp_XYZ segment (nCur->X() - nPrev->X(),
                        nCur->Y() - nPrev->Y(),
                        nCur->Z() - nPrev->Z());
        double segmentLen = segment.Modulus();
        bordLength += segmentLen;
        param[ iBord ][ iNode ] = bordLength;
        nPrev = nCur;
      }
      // normalize within [0,1]
      for ( iNode = 0; iNode < nbNodes[ iBord ]; iNode++ ) {
        param[ iBord ][ iNode ] /= bordLength;
      }
    }

    // loop on border segments
    const SMDS_MeshNode *nPrev[ 2 ] = { 0, 0 };
    int i[ 2 ] = { 0, 0 };
    nIt[0] = nSide[0].begin(); eIt[0] = eSide[0].begin();
    nIt[1] = nSide[1].begin(); eIt[1] = eSide[1].begin();

    TElemOfNodeListMap insertMap;
    TElemOfNodeListMap::iterator insertMapIt;
    // insertMap is
    // key:   elem to insert nodes into
    // value: 2 nodes to insert between + nodes to be inserted
    do {
      bool next[ 2 ] = { false, false };

      // find min adjacent segment length after sewing
      double nextParam = 10., prevParam = 0;
      for ( iBord = 0; iBord < 2; iBord++ ) { // loop on 2 borders
        if ( i[ iBord ] + 1 < nbNodes[ iBord ])
          nextParam = Min( nextParam, param[iBord][ i[iBord] + 1 ]);
        if ( i[ iBord ] > 0 )
          prevParam = Max( prevParam, param[iBord][ i[iBord] - 1 ]);
      }
      double minParam = Min( param[ 0 ][ i[0] ], param[ 1 ][ i[1] ]);
      double maxParam = Max( param[ 0 ][ i[0] ], param[ 1 ][ i[1] ]);
      double minSegLen = Min( nextParam - minParam, maxParam - prevParam );

      // choose to insert or to merge nodes
      double du = param[ 1 ][ i[1] ] - param[ 0 ][ i[0] ];
      if ( Abs( du ) <= minSegLen * 0.2 ) {
        // merge
        // ------
        nodeGroupsToMerge.push_back( list<const SMDS_MeshNode*>() );
        const SMDS_MeshNode* n0 = *nIt[0];
        const SMDS_MeshNode* n1 = *nIt[1];
        nodeGroupsToMerge.back().push_back( n1 );
        nodeGroupsToMerge.back().push_back( n0 );
        // position of node of the border changes due to merge
        param[ 0 ][ i[0] ] += du;
        // move n1 for the sake of elem shape evaluation during insertion.
        // n1 will be removed by MergeNodes() anyway
        const_cast<SMDS_MeshNode*>( n0 )->setXYZ( n1->X(), n1->Y(), n1->Z() );
        next[0] = next[1] = true;
      }
      else {
        // insert
        // ------
        int intoBord = ( du < 0 ) ? 0 : 1;
        const SMDS_MeshElement* elem = *eIt[ intoBord ];
        const SMDS_MeshNode*    n1   = nPrev[ intoBord ];
        const SMDS_MeshNode*    n2   = *nIt[ intoBord ];
        const SMDS_MeshNode*    nIns = *nIt[ 1 - intoBord ];
        if ( intoBord == 1 ) {
          // move node of the border to be on a link of elem of the side
          gp_XYZ p1 (n1->X(), n1->Y(), n1->Z());
          gp_XYZ p2 (n2->X(), n2->Y(), n2->Z());
          double ratio = du / ( param[ 1 ][ i[1] ] - param[ 1 ][ i[1]-1 ]);
          gp_XYZ p = p2 * ( 1 - ratio ) + p1 * ratio;
          GetMeshDS()->MoveNode( nIns, p.X(), p.Y(), p.Z() );
        }
        insertMapIt = insertMap.find( elem );
        bool notFound = ( insertMapIt == insertMap.end() );
        bool otherLink = ( !notFound && (*insertMapIt).second.front() != n1 );
        if ( otherLink ) {
          // insert into another link of the same element:
          // 1. perform insertion into the other link of the elem
          list<const SMDS_MeshNode*> & nodeList = (*insertMapIt).second;
          const SMDS_MeshNode* n12 = nodeList.front(); nodeList.pop_front();
          const SMDS_MeshNode* n22 = nodeList.front(); nodeList.pop_front();
          InsertNodesIntoLink( elem, n12, n22, nodeList, toCreatePolygons );
          // 2. perform insertion into the link of adjacent faces
          while (true) {
            const SMDS_MeshElement* adjElem = findAdjacentFace( n12, n22, elem );
            if ( adjElem )
              InsertNodesIntoLink( adjElem, n12, n22, nodeList, toCreatePolygons );
            else
              break;
          }
          if (toCreatePolyedrs) {
            // perform insertion into the links of adjacent volumes
            UpdateVolumes(n12, n22, nodeList);
          }
          // 3. find an element appeared on n1 and n2 after the insertion
          insertMap.erase( elem );
          elem = findAdjacentFace( n1, n2, 0 );
        }
        if ( notFound || otherLink ) {
          // add element and nodes of the side into the insertMap
          insertMapIt = insertMap.insert
            ( TElemOfNodeListMap::value_type( elem, list<const SMDS_MeshNode*>() )).first;
          (*insertMapIt).second.push_back( n1 );
          (*insertMapIt).second.push_back( n2 );
        }
        // add node to be inserted into elem
        (*insertMapIt).second.push_back( nIns );
        next[ 1 - intoBord ] = true;
      }

      // go to the next segment
      for ( iBord = 0; iBord < 2; iBord++ ) { // loop on 2 borders
        if ( next[ iBord ] ) {
          if ( i[ iBord ] != 0 && eIt[ iBord ] != eSide[ iBord ].end())
            eIt[ iBord ]++;
          nPrev[ iBord ] = *nIt[ iBord ];
          nIt[ iBord ]++; i[ iBord ]++;
        }
      }
    }
    while ( nIt[0] != nSide[0].end() && nIt[1] != nSide[1].end());

    // perform insertion of nodes into elements

    for (insertMapIt = insertMap.begin();
         insertMapIt != insertMap.end();
         insertMapIt++ )
    {
      const SMDS_MeshElement* elem = (*insertMapIt).first;
      list<const SMDS_MeshNode*> & nodeList = (*insertMapIt).second;
      const SMDS_MeshNode* n1 = nodeList.front(); nodeList.pop_front();
      const SMDS_MeshNode* n2 = nodeList.front(); nodeList.pop_front();

      InsertNodesIntoLink( elem, n1, n2, nodeList, toCreatePolygons );

      if ( !theSideIsFreeBorder ) {
        // look for and insert nodes into the faces adjacent to elem
        while (true) {
          const SMDS_MeshElement* adjElem = findAdjacentFace( n1, n2, elem );
          if ( adjElem )
            InsertNodesIntoLink( adjElem, n1, n2, nodeList, toCreatePolygons );
          else
            break;
        }
      }
      if (toCreatePolyedrs) {
        // perform insertion into the links of adjacent volumes
        UpdateVolumes(n1, n2, nodeList);
      }
    }

    delete param[0];
    delete param[1];
  } // end: insert new nodes

  MergeNodes ( nodeGroupsToMerge );

  return aResult;
}

//=======================================================================
//function : InsertNodesIntoLink
//purpose  : insert theNodesToInsert into theFace between theBetweenNode1
//           and theBetweenNode2 and split theElement
//=======================================================================

void SMESH_MeshEditor::InsertNodesIntoLink(const SMDS_MeshElement*     theFace,
                                           const SMDS_MeshNode*        theBetweenNode1,
                                           const SMDS_MeshNode*        theBetweenNode2,
                                           list<const SMDS_MeshNode*>& theNodesToInsert,
                                           const bool                  toCreatePoly)
{
  if ( theFace->GetType() != SMDSAbs_Face ) return;

  // find indices of 2 link nodes and of the rest nodes
  int iNode = 0, il1, il2, i3, i4;
  il1 = il2 = i3 = i4 = -1;
  //const SMDS_MeshNode* nodes[ theFace->NbNodes() ];
  vector<const SMDS_MeshNode*> nodes( theFace->NbNodes() );

  if(theFace->IsQuadratic()) {
    const SMDS_QuadraticFaceOfNodes* F =
      static_cast<const SMDS_QuadraticFaceOfNodes*>(theFace);
    // use special nodes iterator
    SMDS_NodeIteratorPtr anIter = F->interlacedNodesIterator();
    while( anIter->more() ) {
      const SMDS_MeshNode* n = anIter->next();
      if ( n == theBetweenNode1 )
        il1 = iNode;
      else if ( n == theBetweenNode2 )
        il2 = iNode;
      else if ( i3 < 0 )
        i3 = iNode;
      else
        i4 = iNode;
      nodes[ iNode++ ] = n;
    }
  }
  else {
    SMDS_ElemIteratorPtr nodeIt = theFace->nodesIterator();
    while ( nodeIt->more() ) {
      const SMDS_MeshNode* n = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
      if ( n == theBetweenNode1 )
        il1 = iNode;
      else if ( n == theBetweenNode2 )
        il2 = iNode;
      else if ( i3 < 0 )
        i3 = iNode;
      else
        i4 = iNode;
      nodes[ iNode++ ] = n;
    }
  }
  if ( il1 < 0 || il2 < 0 || i3 < 0 )
    return ;

  // arrange link nodes to go one after another regarding the face orientation
  bool reverse = ( Abs( il2 - il1 ) == 1 ? il2 < il1 : il1 < il2 );
  list<const SMDS_MeshNode *> aNodesToInsert = theNodesToInsert;
  if ( reverse ) {
    iNode = il1;
    il1 = il2;
    il2 = iNode;
    aNodesToInsert.reverse();
  }
  // check that not link nodes of a quadrangles are in good order
  int nbFaceNodes = theFace->NbNodes();
  if ( nbFaceNodes == 4 && i4 - i3 != 1 ) {
    iNode = i3;
    i3 = i4;
    i4 = iNode;
  }

  if (toCreatePoly || theFace->IsPoly()) {

    iNode = 0;
    vector<const SMDS_MeshNode *> poly_nodes (nbFaceNodes + aNodesToInsert.size());

    // add nodes of face up to first node of link
    bool isFLN = false;

    if(theFace->IsQuadratic()) {
      const SMDS_QuadraticFaceOfNodes* F =
        static_cast<const SMDS_QuadraticFaceOfNodes*>(theFace);
      // use special nodes iterator
      SMDS_NodeIteratorPtr anIter = F->interlacedNodesIterator();
      while( anIter->more()  && !isFLN ) {
        const SMDS_MeshNode* n = anIter->next();
        poly_nodes[iNode++] = n;
        if (n == nodes[il1]) {
          isFLN = true;
        }
      }
      // add nodes to insert
      list<const SMDS_MeshNode*>::iterator nIt = aNodesToInsert.begin();
      for (; nIt != aNodesToInsert.end(); nIt++) {
        poly_nodes[iNode++] = *nIt;
      }
      // add nodes of face starting from last node of link
      while ( anIter->more() ) {
        poly_nodes[iNode++] = anIter->next();
      }
    }
    else {
      SMDS_ElemIteratorPtr nodeIt = theFace->nodesIterator();
      while ( nodeIt->more() && !isFLN ) {
        const SMDS_MeshNode* n = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
        poly_nodes[iNode++] = n;
        if (n == nodes[il1]) {
          isFLN = true;
        }
      }
      // add nodes to insert
      list<const SMDS_MeshNode*>::iterator nIt = aNodesToInsert.begin();
      for (; nIt != aNodesToInsert.end(); nIt++) {
        poly_nodes[iNode++] = *nIt;
      }
      // add nodes of face starting from last node of link
      while ( nodeIt->more() ) {
        const SMDS_MeshNode* n = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
        poly_nodes[iNode++] = n;
      }
    }

    // edit or replace the face
    SMESHDS_Mesh *aMesh = GetMeshDS();

    if (theFace->IsPoly()) {
      aMesh->ChangePolygonNodes(theFace, poly_nodes);
    }
    else {
      int aShapeId = FindShape( theFace );

      SMDS_MeshElement* newElem = aMesh->AddPolygonalFace(poly_nodes);
      myLastCreatedElems.Append(newElem);
      if ( aShapeId && newElem )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );

      aMesh->RemoveElement(theFace);
    }
    return;
  }

  if( !theFace->IsQuadratic() ) {

    // put aNodesToInsert between theBetweenNode1 and theBetweenNode2
    int nbLinkNodes = 2 + aNodesToInsert.size();
    //const SMDS_MeshNode* linkNodes[ nbLinkNodes ];
    vector<const SMDS_MeshNode*> linkNodes( nbLinkNodes );
    linkNodes[ 0 ] = nodes[ il1 ];
    linkNodes[ nbLinkNodes - 1 ] = nodes[ il2 ];
    list<const SMDS_MeshNode*>::iterator nIt = aNodesToInsert.begin();
    for ( iNode = 1; nIt != aNodesToInsert.end(); nIt++ ) {
      linkNodes[ iNode++ ] = *nIt;
    }
    // decide how to split a quadrangle: compare possible variants
    // and choose which of splits to be a quadrangle
    int i1, i2, iSplit, nbSplits = nbLinkNodes - 1, iBestQuad;
    if ( nbFaceNodes == 3 ) {
      iBestQuad = nbSplits;
      i4 = i3;
    }
    else if ( nbFaceNodes == 4 ) {
      SMESH::Controls::NumericalFunctorPtr aCrit( new SMESH::Controls::AspectRatio);
      double aBestRate = DBL_MAX;
      for ( int iQuad = 0; iQuad < nbSplits; iQuad++ ) {
        i1 = 0; i2 = 1;
        double aBadRate = 0;
        // evaluate elements quality
        for ( iSplit = 0; iSplit < nbSplits; iSplit++ ) {
          if ( iSplit == iQuad ) {
            SMDS_FaceOfNodes quad (linkNodes[ i1++ ],
                                   linkNodes[ i2++ ],
                                   nodes[ i3 ],
                                   nodes[ i4 ]);
            aBadRate += getBadRate( &quad, aCrit );
          }
          else {
            SMDS_FaceOfNodes tria (linkNodes[ i1++ ],
                                   linkNodes[ i2++ ],
                                   nodes[ iSplit < iQuad ? i4 : i3 ]);
            aBadRate += getBadRate( &tria, aCrit );
          }
        }
        // choice
        if ( aBadRate < aBestRate ) {
          iBestQuad = iQuad;
          aBestRate = aBadRate;
        }
      }
    }

    // create new elements
    SMESHDS_Mesh *aMesh = GetMeshDS();
    int aShapeId = FindShape( theFace );

    i1 = 0; i2 = 1;
    for ( iSplit = 0; iSplit < nbSplits - 1; iSplit++ ) {
      SMDS_MeshElement* newElem = 0;
      if ( iSplit == iBestQuad )
        newElem = aMesh->AddFace (linkNodes[ i1++ ],
                                  linkNodes[ i2++ ],
                                  nodes[ i3 ],
                                  nodes[ i4 ]);
      else
        newElem = aMesh->AddFace (linkNodes[ i1++ ],
                                  linkNodes[ i2++ ],
                                  nodes[ iSplit < iBestQuad ? i4 : i3 ]);
      myLastCreatedElems.Append(newElem);
      if ( aShapeId && newElem )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );
    }

    // change nodes of theFace
    const SMDS_MeshNode* newNodes[ 4 ];
    newNodes[ 0 ] = linkNodes[ i1 ];
    newNodes[ 1 ] = linkNodes[ i2 ];
    newNodes[ 2 ] = nodes[ iSplit >= iBestQuad ? i3 : i4 ];
    newNodes[ 3 ] = nodes[ i4 ];
    aMesh->ChangeElementNodes( theFace, newNodes, iSplit == iBestQuad ? 4 : 3 );
  } // end if(!theFace->IsQuadratic())
  else { // theFace is quadratic
    // we have to split theFace on simple triangles and one simple quadrangle
    int tmp = il1/2;
    int nbshift = tmp*2;
    // shift nodes in nodes[] by nbshift
    int i,j;
    for(i=0; i<nbshift; i++) {
      const SMDS_MeshNode* n = nodes[0];
      for(j=0; j<nbFaceNodes-1; j++) {
        nodes[j] = nodes[j+1];
      }
      nodes[nbFaceNodes-1] = n;
    }
    il1 = il1 - nbshift;
    // now have to insert nodes between n0 and n1 or n1 and n2 (see below)
    //   n0      n1     n2    n0      n1     n2
    //     +-----+-----+        +-----+-----+
    //      \         /         |           |
    //       \       /          |           |
    //      n5+     +n3       n7+           +n3
    //         \   /            |           |
    //          \ /             |           |
    //           +              +-----+-----+
    //           n4           n6      n5     n4

    // create new elements
    SMESHDS_Mesh *aMesh = GetMeshDS();
    int aShapeId = FindShape( theFace );

    int n1,n2,n3;
    if(nbFaceNodes==6) { // quadratic triangle
      SMDS_MeshElement* newElem =
        aMesh->AddFace(nodes[3],nodes[4],nodes[5]);
      myLastCreatedElems.Append(newElem);
      if ( aShapeId && newElem )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );
      if(theFace->IsMediumNode(nodes[il1])) {
        // create quadrangle
        newElem = aMesh->AddFace(nodes[0],nodes[1],nodes[3],nodes[5]);
        myLastCreatedElems.Append(newElem);
        if ( aShapeId && newElem )
          aMesh->SetMeshElementOnShape( newElem, aShapeId );
        n1 = 1;
        n2 = 2;
        n3 = 3;
      }
      else {
        // create quadrangle
        newElem = aMesh->AddFace(nodes[1],nodes[2],nodes[3],nodes[5]);
        myLastCreatedElems.Append(newElem);
        if ( aShapeId && newElem )
          aMesh->SetMeshElementOnShape( newElem, aShapeId );
        n1 = 0;
        n2 = 1;
        n3 = 5;
      }
    }
    else { // nbFaceNodes==8 - quadratic quadrangle
      SMDS_MeshElement* newElem =
        aMesh->AddFace(nodes[3],nodes[4],nodes[5]);
      myLastCreatedElems.Append(newElem);
      if ( aShapeId && newElem )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );
      newElem = aMesh->AddFace(nodes[5],nodes[6],nodes[7]);
      myLastCreatedElems.Append(newElem);
      if ( aShapeId && newElem )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );
      newElem = aMesh->AddFace(nodes[5],nodes[7],nodes[3]);
      myLastCreatedElems.Append(newElem);
      if ( aShapeId && newElem )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );
      if(theFace->IsMediumNode(nodes[il1])) {
        // create quadrangle
        newElem = aMesh->AddFace(nodes[0],nodes[1],nodes[3],nodes[7]);
        myLastCreatedElems.Append(newElem);
        if ( aShapeId && newElem )
          aMesh->SetMeshElementOnShape( newElem, aShapeId );
        n1 = 1;
        n2 = 2;
        n3 = 3;
      }
      else {
        // create quadrangle
        newElem = aMesh->AddFace(nodes[1],nodes[2],nodes[3],nodes[7]);
        myLastCreatedElems.Append(newElem);
        if ( aShapeId && newElem )
          aMesh->SetMeshElementOnShape( newElem, aShapeId );
        n1 = 0;
        n2 = 1;
        n3 = 7;
      }
    }
    // create needed triangles using n1,n2,n3 and inserted nodes
    int nbn = 2 + aNodesToInsert.size();
    //const SMDS_MeshNode* aNodes[nbn];
    vector<const SMDS_MeshNode*> aNodes(nbn);
    aNodes[0] = nodes[n1];
    aNodes[nbn-1] = nodes[n2];
    list<const SMDS_MeshNode*>::iterator nIt = aNodesToInsert.begin();
    for ( iNode = 1; nIt != aNodesToInsert.end(); nIt++ ) {
      aNodes[iNode++] = *nIt;
    }
    for(i=1; i<nbn; i++) {
      SMDS_MeshElement* newElem =
        aMesh->AddFace(aNodes[i-1],aNodes[i],nodes[n3]);
      myLastCreatedElems.Append(newElem);
      if ( aShapeId && newElem )
        aMesh->SetMeshElementOnShape( newElem, aShapeId );
    }
    // remove old quadratic face
    aMesh->RemoveElement(theFace);
  }
}

//=======================================================================
//function : UpdateVolumes
//purpose  :
//=======================================================================
void SMESH_MeshEditor::UpdateVolumes (const SMDS_MeshNode*        theBetweenNode1,
                                      const SMDS_MeshNode*        theBetweenNode2,
                                      list<const SMDS_MeshNode*>& theNodesToInsert)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  SMDS_ElemIteratorPtr invElemIt = theBetweenNode1->GetInverseElementIterator(SMDSAbs_Volume);
  while (invElemIt->more()) { // loop on inverse elements of theBetweenNode1
    const SMDS_MeshElement* elem = invElemIt->next();

    // check, if current volume has link theBetweenNode1 - theBetweenNode2
    SMDS_VolumeTool aVolume (elem);
    if (!aVolume.IsLinked(theBetweenNode1, theBetweenNode2))
      continue;

    // insert new nodes in all faces of the volume, sharing link theBetweenNode1 - theBetweenNode2
    int iface, nbFaces = aVolume.NbFaces();
    vector<const SMDS_MeshNode *> poly_nodes;
    vector<int> quantities (nbFaces);

    for (iface = 0; iface < nbFaces; iface++) {
      int nbFaceNodes = aVolume.NbFaceNodes(iface), nbInserted = 0;
      // faceNodes will contain (nbFaceNodes + 1) nodes, last = first
      const SMDS_MeshNode** faceNodes = aVolume.GetFaceNodes(iface);

      for (int inode = 0; inode < nbFaceNodes; inode++) {
        poly_nodes.push_back(faceNodes[inode]);

        if (nbInserted == 0) {
          if (faceNodes[inode] == theBetweenNode1) {
            if (faceNodes[inode + 1] == theBetweenNode2) {
              nbInserted = theNodesToInsert.size();

              // add nodes to insert
              list<const SMDS_MeshNode*>::iterator nIt = theNodesToInsert.begin();
              for (; nIt != theNodesToInsert.end(); nIt++) {
                poly_nodes.push_back(*nIt);
              }
            }
          }
          else if (faceNodes[inode] == theBetweenNode2) {
            if (faceNodes[inode + 1] == theBetweenNode1) {
              nbInserted = theNodesToInsert.size();

              // add nodes to insert in reversed order
              list<const SMDS_MeshNode*>::iterator nIt = theNodesToInsert.end();
              nIt--;
              for (; nIt != theNodesToInsert.begin(); nIt--) {
                poly_nodes.push_back(*nIt);
              }
              poly_nodes.push_back(*nIt);
            }
          }
          else {
          }
        }
      }
      quantities[iface] = nbFaceNodes + nbInserted;
    }

    // Replace or update the volume
    SMESHDS_Mesh *aMesh = GetMeshDS();

    if (elem->IsPoly()) {
      aMesh->ChangePolyhedronNodes(elem, poly_nodes, quantities);

    }
    else {
      int aShapeId = FindShape( elem );

      SMDS_MeshElement* newElem =
        aMesh->AddPolyhedralVolume(poly_nodes, quantities);
      myLastCreatedElems.Append(newElem);
      if (aShapeId && newElem)
        aMesh->SetMeshElementOnShape(newElem, aShapeId);

      aMesh->RemoveElement(elem);
    }
  }
}

//=======================================================================
/*!
 * \brief Convert elements contained in a submesh to quadratic
 * \retval int - nb of checked elements
 */
//=======================================================================

int SMESH_MeshEditor::convertElemToQuadratic(SMESHDS_SubMesh *   theSm,
                                              SMESH_MesherHelper& theHelper,
					      const bool          theForce3d)
{
  int nbElem = 0;
  if( !theSm ) return nbElem;
  SMDS_ElemIteratorPtr ElemItr = theSm->GetElements();
  while(ElemItr->more())
  {
    nbElem++;
    const SMDS_MeshElement* elem = ElemItr->next();
    if( !elem || elem->IsQuadratic() ) continue;

    int id = elem->GetID();
    int nbNodes = elem->NbNodes();
    vector<const SMDS_MeshNode *> aNds (nbNodes);

    for(int i = 0; i < nbNodes; i++)
    {
      aNds[i] = elem->GetNode(i);
    }
    SMDSAbs_ElementType aType = elem->GetType();

    theSm->RemoveElement(elem);
    GetMeshDS()->SMDS_Mesh::RemoveFreeElement(elem);

    const SMDS_MeshElement* NewElem = 0;

    switch( aType )
    {
    case SMDSAbs_Edge :
    {
      NewElem = theHelper.AddEdge(aNds[0], aNds[1], id, theForce3d);
      break;
    }
    case SMDSAbs_Face :
    {
      switch(nbNodes)
      {
      case 3:
	NewElem = theHelper.AddFace(aNds[0], aNds[1], aNds[2], id, theForce3d);
	break;
      case 4:
	NewElem = theHelper.AddFace(aNds[0], aNds[1], aNds[2], aNds[3], id, theForce3d);
	break;
      default:
	continue;
      }
      break;
    }
    case SMDSAbs_Volume :
    {
      switch(nbNodes)
      {
      case 4:
	NewElem = theHelper.AddVolume(aNds[0], aNds[1], aNds[2], aNds[3], id, true);
	break;
      case 6:
	NewElem = theHelper.AddVolume(aNds[0], aNds[1], aNds[2], aNds[3], aNds[4], aNds[5], id, true);
	break;
      case 8:
	NewElem = theHelper.AddVolume(aNds[0], aNds[1], aNds[2], aNds[3],
                                      aNds[4], aNds[5], aNds[6], aNds[7], id, true);
	break;
      default:
	continue;
      }
      break;
    }
    default :
      continue;
    }
    if( NewElem )
    {
      AddToSameGroups( NewElem, elem, GetMeshDS());
      theSm->AddElement( NewElem );
    }
    if ( NewElem != elem )
      RemoveElemFromGroups (elem, GetMeshDS());
  }
  return nbElem;
}

//=======================================================================
//function : ConvertToQuadratic
//purpose  :
//=======================================================================
void SMESH_MeshEditor::ConvertToQuadratic(const bool theForce3d)
{
  SMESHDS_Mesh* meshDS = GetMeshDS();

  SMESH_MesherHelper aHelper(*myMesh);
  aHelper.SetIsQuadratic( true );

  int nbCheckedElems = 0;
  if ( myMesh->HasShapeToMesh() )
  {
    if ( SMESH_subMesh *aSubMesh = myMesh->GetSubMeshContaining(myMesh->GetShapeToMesh()))
    {
      SMESH_subMeshIteratorPtr smIt = aSubMesh->getDependsOnIterator(true,false);
      while ( smIt->more() ) {
        SMESH_subMesh* sm = smIt->next();
        if ( SMESHDS_SubMesh *smDS = sm->GetSubMeshDS() ) {
          aHelper.SetSubShape( sm->GetSubShape() );
          nbCheckedElems += convertElemToQuadratic(smDS, aHelper, theForce3d);
        }
      }
    }
  }
  int totalNbElems = meshDS->NbEdges() + meshDS->NbFaces() + meshDS->NbVolumes();
  if ( nbCheckedElems < totalNbElems ) // not all elements in submeshes
  {
    SMDS_EdgeIteratorPtr aEdgeItr = meshDS->edgesIterator();
    while(aEdgeItr->more())
    {
      const SMDS_MeshEdge* edge = aEdgeItr->next();
      if(edge && !edge->IsQuadratic())
      {
	int id = edge->GetID();
	const SMDS_MeshNode* n1 = edge->GetNode(0);
	const SMDS_MeshNode* n2 = edge->GetNode(1);

	meshDS->SMDS_Mesh::RemoveFreeElement(edge);

        const SMDS_MeshEdge* NewEdge = aHelper.AddEdge(n1, n2, id, theForce3d);
        if ( NewEdge )
          AddToSameGroups(NewEdge, edge, meshDS);
        if ( NewEdge != edge )
          RemoveElemFromGroups (edge, meshDS);
      }
    }
    SMDS_FaceIteratorPtr aFaceItr = meshDS->facesIterator();
    while(aFaceItr->more())
    {
      const SMDS_MeshFace* face = aFaceItr->next();
      if(!face || face->IsQuadratic() ) continue;

      int id = face->GetID();
      int nbNodes = face->NbNodes();
      vector<const SMDS_MeshNode *> aNds (nbNodes);

      for(int i = 0; i < nbNodes; i++)
      {
	aNds[i] = face->GetNode(i);
      }

      meshDS->SMDS_Mesh::RemoveFreeElement(face);

      SMDS_MeshFace * NewFace = 0;
      switch(nbNodes)
      {
      case 3:
	NewFace = aHelper.AddFace(aNds[0], aNds[1], aNds[2], id, theForce3d);
	break;
      case 4:
	NewFace = aHelper.AddFace(aNds[0], aNds[1], aNds[2], aNds[3], id, theForce3d);
	break;
      default:
	continue;
      }
      if ( NewFace )
        AddToSameGroups(NewFace, face, meshDS);
      if ( NewFace != face )
        RemoveElemFromGroups (face, meshDS);
    }
    SMDS_VolumeIteratorPtr aVolumeItr = meshDS->volumesIterator();
    while(aVolumeItr->more())
    {
      const SMDS_MeshVolume* volume = aVolumeItr->next();
      if(!volume || volume->IsQuadratic() ) continue;

      int id = volume->GetID();
      int nbNodes = volume->NbNodes();
      vector<const SMDS_MeshNode *> aNds (nbNodes);

      for(int i = 0; i < nbNodes; i++)
      {
	aNds[i] = volume->GetNode(i);
      }

      meshDS->SMDS_Mesh::RemoveFreeElement(volume);

      SMDS_MeshVolume * NewVolume = 0;
      switch(nbNodes)
      {
      case 4:
	NewVolume = aHelper.AddVolume(aNds[0], aNds[1], aNds[2],
                                      aNds[3], id, true );
	break;
      case 6:
	NewVolume = aHelper.AddVolume(aNds[0], aNds[1], aNds[2],
                                      aNds[3], aNds[4], aNds[5], id, true);
	break;
      case 8:
	NewVolume = aHelper.AddVolume(aNds[0], aNds[1], aNds[2], aNds[3],
                                      aNds[4], aNds[5], aNds[6], aNds[7], id, true);
	break;
      default:
	continue;
      }
      if ( NewVolume )
        AddToSameGroups(NewVolume, volume, meshDS);
      if ( NewVolume != volume )
        RemoveElemFromGroups (volume, meshDS);
    }
  }
}

//=======================================================================
/*!
 * \brief Convert quadratic elements to linear ones and remove quadratic nodes
 * \retval int - nb of checked elements
 */
//=======================================================================

int SMESH_MeshEditor::removeQuadElem(SMESHDS_SubMesh *    theSm,
                                     SMDS_ElemIteratorPtr theItr,
                                     const int            theShapeID)
{
  int nbElem = 0;
  SMESHDS_Mesh* meshDS = GetMeshDS();
  while( theItr->more() )
  {
    const SMDS_MeshElement* elem = theItr->next();
    nbElem++;
    if( elem && elem->IsQuadratic())
    {
      int id = elem->GetID();
      int nbNodes = elem->NbNodes();
      vector<const SMDS_MeshNode *> aNds, mediumNodes;
      aNds.reserve( nbNodes );
      mediumNodes.reserve( nbNodes );

      for(int i = 0; i < nbNodes; i++)
      {
	const SMDS_MeshNode* n = elem->GetNode(i);

	if( elem->IsMediumNode( n ) )
          mediumNodes.push_back( n );
	else
	  aNds.push_back( n );
      }
      if( aNds.empty() ) continue;
      SMDSAbs_ElementType aType = elem->GetType();

      //remove old quadratic element
      meshDS->SMDS_Mesh::RemoveFreeElement( elem );
      if ( theSm )
        theSm->RemoveElement( elem );

      SMDS_MeshElement * NewElem = AddElement( aNds, aType, false, id );
      if ( NewElem )
        AddToSameGroups(NewElem, elem, meshDS);
      if ( NewElem != elem )
        RemoveElemFromGroups (elem, meshDS);
      if( theSm && NewElem )
	theSm->AddElement( NewElem );

      // remove medium nodes
      vector<const SMDS_MeshNode*>::iterator nIt = mediumNodes.begin();
      for ( ; nIt != mediumNodes.end(); ++nIt ) {
        const SMDS_MeshNode* n = *nIt;
        if ( n->NbInverseElements() == 0 ) {
          if ( n->GetPosition()->GetShapeId() != theShapeID )
            meshDS->RemoveFreeNode( n, meshDS->MeshElements
                                    ( n->GetPosition()->GetShapeId() ));
          else
            meshDS->RemoveFreeNode( n, theSm );
	}
      }
    }
  }
  return nbElem;
}

//=======================================================================
//function : ConvertFromQuadratic
//purpose  :
//=======================================================================
bool  SMESH_MeshEditor::ConvertFromQuadratic()
{
  int nbCheckedElems = 0;
  if ( myMesh->HasShapeToMesh() )
  {
    if ( SMESH_subMesh *aSubMesh = myMesh->GetSubMeshContaining(myMesh->GetShapeToMesh()))
    {
      SMESH_subMeshIteratorPtr smIt = aSubMesh->getDependsOnIterator(true,false);
      while ( smIt->more() ) {
        SMESH_subMesh* sm = smIt->next();
        if ( SMESHDS_SubMesh *smDS = sm->GetSubMeshDS() )
          nbCheckedElems += removeQuadElem( smDS, smDS->GetElements(), sm->GetId() );
      }
    }
  }
  
  int totalNbElems =
    GetMeshDS()->NbEdges() + GetMeshDS()->NbFaces() + GetMeshDS()->NbVolumes();
  if ( nbCheckedElems < totalNbElems ) // not all elements in submeshes
  {
    SMESHDS_SubMesh *aSM = 0;
    removeQuadElem( aSM, GetMeshDS()->elementsIterator(), 0 );
  }

  return true;
}

//=======================================================================
//function : SewSideElements
//purpose  :
//=======================================================================

SMESH_MeshEditor::Sew_Error
  SMESH_MeshEditor::SewSideElements (TIDSortedElemSet&    theSide1,
                                     TIDSortedElemSet&    theSide2,
                                     const SMDS_MeshNode* theFirstNode1,
                                     const SMDS_MeshNode* theFirstNode2,
                                     const SMDS_MeshNode* theSecondNode1,
                                     const SMDS_MeshNode* theSecondNode2)
{
  myLastCreatedElems.Clear();
  myLastCreatedNodes.Clear();

  MESSAGE ("::::SewSideElements()");
  if ( theSide1.size() != theSide2.size() )
    return SEW_DIFF_NB_OF_ELEMENTS;

  Sew_Error aResult = SEW_OK;
  // Algo:
  // 1. Build set of faces representing each side
  // 2. Find which nodes of the side 1 to merge with ones on the side 2
  // 3. Replace nodes in elements of the side 1 and remove replaced nodes

  // =======================================================================
  // 1. Build set of faces representing each side:
  // =======================================================================
  // a. build set of nodes belonging to faces
  // b. complete set of faces: find missing fices whose nodes are in set of nodes
  // c. create temporary faces representing side of volumes if correspondent
  //    face does not exist

  SMESHDS_Mesh* aMesh = GetMeshDS();
  SMDS_Mesh aTmpFacesMesh;
  set<const SMDS_MeshElement*> faceSet1, faceSet2;
  set<const SMDS_MeshElement*> volSet1,  volSet2;
  set<const SMDS_MeshNode*>    nodeSet1, nodeSet2;
  set<const SMDS_MeshElement*> * faceSetPtr[] = { &faceSet1, &faceSet2 };
  set<const SMDS_MeshElement*>  * volSetPtr[] = { &volSet1,  &volSet2  };
  set<const SMDS_MeshNode*>    * nodeSetPtr[] = { &nodeSet1, &nodeSet2 };
  TIDSortedElemSet * elemSetPtr[] = { &theSide1, &theSide2 };
  int iSide, iFace, iNode;

  for ( iSide = 0; iSide < 2; iSide++ ) {
    set<const SMDS_MeshNode*>    * nodeSet = nodeSetPtr[ iSide ];
    TIDSortedElemSet * elemSet = elemSetPtr[ iSide ];
    set<const SMDS_MeshElement*> * faceSet = faceSetPtr[ iSide ];
    set<const SMDS_MeshElement*> * volSet  = volSetPtr [ iSide ];
    set<const SMDS_MeshElement*>::iterator vIt;
    TIDSortedElemSet::iterator eIt;
    set<const SMDS_MeshNode*>::iterator    nIt;

    // check that given nodes belong to given elements
    const SMDS_MeshNode* n1 = ( iSide == 0 ) ? theFirstNode1 : theFirstNode2;
    const SMDS_MeshNode* n2 = ( iSide == 0 ) ? theSecondNode1 : theSecondNode2;
    int firstIndex = -1, secondIndex = -1;
    for (eIt = elemSet->begin(); eIt != elemSet->end(); eIt++ ) {
      const SMDS_MeshElement* elem = *eIt;
      if ( firstIndex  < 0 ) firstIndex  = elem->GetNodeIndex( n1 );
      if ( secondIndex < 0 ) secondIndex = elem->GetNodeIndex( n2 );
      if ( firstIndex > -1 && secondIndex > -1 ) break;
    }
    if ( firstIndex < 0 || secondIndex < 0 ) {
      // we can simply return until temporary faces created
      return (iSide == 0 ) ? SEW_BAD_SIDE1_NODES : SEW_BAD_SIDE2_NODES;
    }

    // -----------------------------------------------------------
    // 1a. Collect nodes of existing faces
    //     and build set of face nodes in order to detect missing
    //     faces corresponing to sides of volumes
    // -----------------------------------------------------------

    set< set <const SMDS_MeshNode*> > setOfFaceNodeSet;

    // loop on the given element of a side
    for (eIt = elemSet->begin(); eIt != elemSet->end(); eIt++ ) {
      //const SMDS_MeshElement* elem = *eIt;
      const SMDS_MeshElement* elem = *eIt;
      if ( elem->GetType() == SMDSAbs_Face ) {
        faceSet->insert( elem );
        set <const SMDS_MeshNode*> faceNodeSet;
        SMDS_ElemIteratorPtr nodeIt = elem->nodesIterator();
        while ( nodeIt->more() ) {
          const SMDS_MeshNode* n = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
          nodeSet->insert( n );
          faceNodeSet.insert( n );
        }
        setOfFaceNodeSet.insert( faceNodeSet );
      }
      else if ( elem->GetType() == SMDSAbs_Volume )
        volSet->insert( elem );
    }
    // ------------------------------------------------------------------------------
    // 1b. Complete set of faces: find missing fices whose nodes are in set of nodes
    // ------------------------------------------------------------------------------

    for ( nIt = nodeSet->begin(); nIt != nodeSet->end(); nIt++ ) { // loop on nodes of iSide
      SMDS_ElemIteratorPtr fIt = (*nIt)->GetInverseElementIterator(SMDSAbs_Face);
      while ( fIt->more() ) { // loop on faces sharing a node
        const SMDS_MeshElement* f = fIt->next();
        if ( faceSet->find( f ) == faceSet->end() ) {
          // check if all nodes are in nodeSet and
          // complete setOfFaceNodeSet if they are
          set <const SMDS_MeshNode*> faceNodeSet;
          SMDS_ElemIteratorPtr nodeIt = f->nodesIterator();
          bool allInSet = true;
          while ( nodeIt->more() && allInSet ) { // loop on nodes of a face
            const SMDS_MeshNode* n = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
            if ( nodeSet->find( n ) == nodeSet->end() )
              allInSet = false;
            else
              faceNodeSet.insert( n );
          }
          if ( allInSet ) {
            faceSet->insert( f );
            setOfFaceNodeSet.insert( faceNodeSet );
          }
        }
      }
    }

    // -------------------------------------------------------------------------
    // 1c. Create temporary faces representing sides of volumes if correspondent
    //     face does not exist
    // -------------------------------------------------------------------------

    if ( !volSet->empty() ) {
      //int nodeSetSize = nodeSet->size();

      // loop on given volumes
      for ( vIt = volSet->begin(); vIt != volSet->end(); vIt++ ) {
        SMDS_VolumeTool vol (*vIt);
        // loop on volume faces: find free faces
        // --------------------------------------
        list<const SMDS_MeshElement* > freeFaceList;
        for ( iFace = 0; iFace < vol.NbFaces(); iFace++ ) {
          if ( !vol.IsFreeFace( iFace ))
            continue;
          // check if there is already a face with same nodes in a face set
          const SMDS_MeshElement* aFreeFace = 0;
          const SMDS_MeshNode** fNodes = vol.GetFaceNodes( iFace );
          int nbNodes = vol.NbFaceNodes( iFace );
          set <const SMDS_MeshNode*> faceNodeSet;
          vol.GetFaceNodes( iFace, faceNodeSet );
          bool isNewFace = setOfFaceNodeSet.insert( faceNodeSet ).second;
          if ( isNewFace ) {
            // no such a face is given but it still can exist, check it
            if ( nbNodes == 3 ) {
              aFreeFace = aMesh->FindFace( fNodes[0],fNodes[1],fNodes[2] );
            }
            else if ( nbNodes == 4 ) {
              aFreeFace = aMesh->FindFace( fNodes[0],fNodes[1],fNodes[2],fNodes[3] );
            }
            else {
              vector<const SMDS_MeshNode *> poly_nodes ( fNodes, & fNodes[nbNodes]);
              aFreeFace = aMesh->FindFace(poly_nodes);
            }
          }
          if ( !aFreeFace ) {
            // create a temporary face
            if ( nbNodes == 3 ) {
              aFreeFace = aTmpFacesMesh.AddFace( fNodes[0],fNodes[1],fNodes[2] );
            }
            else if ( nbNodes == 4 ) {
              aFreeFace = aTmpFacesMesh.AddFace( fNodes[0],fNodes[1],fNodes[2],fNodes[3] );
            }
            else {
              vector<const SMDS_MeshNode *> poly_nodes ( fNodes, & fNodes[nbNodes]);
              aFreeFace = aTmpFacesMesh.AddPolygonalFace(poly_nodes);
            }
          }
          if ( aFreeFace )
            freeFaceList.push_back( aFreeFace );

        } // loop on faces of a volume

        // choose one of several free faces
        // --------------------------------------
        if ( freeFaceList.size() > 1 ) {
          // choose a face having max nb of nodes shared by other elems of a side
          int maxNbNodes = -1/*, nbExcludedFaces = 0*/;
          list<const SMDS_MeshElement* >::iterator fIt = freeFaceList.begin();
          while ( fIt != freeFaceList.end() ) { // loop on free faces
            int nbSharedNodes = 0;
            SMDS_ElemIteratorPtr nodeIt = (*fIt)->nodesIterator();
            while ( nodeIt->more() ) { // loop on free face nodes
              const SMDS_MeshNode* n =
                static_cast<const SMDS_MeshNode*>( nodeIt->next() );
              SMDS_ElemIteratorPtr invElemIt = n->GetInverseElementIterator();
              while ( invElemIt->more() ) {
                const SMDS_MeshElement* e = invElemIt->next();
                if ( faceSet->find( e ) != faceSet->end() )
                  nbSharedNodes++;
                if ( elemSet->find( e ) != elemSet->end() )
                  nbSharedNodes++;
              }
            }
            if ( nbSharedNodes >= maxNbNodes ) {
              maxNbNodes = nbSharedNodes;
              fIt++;
            }
            else
              freeFaceList.erase( fIt++ ); // here fIt++ occures before erase
          }
          if ( freeFaceList.size() > 1 )
          {
            // could not choose one face, use another way
            // choose a face most close to the bary center of the opposite side
            gp_XYZ aBC( 0., 0., 0. );
            set <const SMDS_MeshNode*> addedNodes;
            TIDSortedElemSet * elemSet2 = elemSetPtr[ 1 - iSide ];
            eIt = elemSet2->begin();
            for ( eIt = elemSet2->begin(); eIt != elemSet2->end(); eIt++ ) {
              SMDS_ElemIteratorPtr nodeIt = (*eIt)->nodesIterator();
              while ( nodeIt->more() ) { // loop on free face nodes
                const SMDS_MeshNode* n =
                  static_cast<const SMDS_MeshNode*>( nodeIt->next() );
                if ( addedNodes.insert( n ).second )
                  aBC += gp_XYZ( n->X(),n->Y(),n->Z() );
              }
            }
            aBC /= addedNodes.size();
            double minDist = DBL_MAX;
            fIt = freeFaceList.begin();
            while ( fIt != freeFaceList.end() ) { // loop on free faces
              double dist = 0;
              SMDS_ElemIteratorPtr nodeIt = (*fIt)->nodesIterator();
              while ( nodeIt->more() ) { // loop on free face nodes
                const SMDS_MeshNode* n =
                  static_cast<const SMDS_MeshNode*>( nodeIt->next() );
                gp_XYZ p( n->X(),n->Y(),n->Z() );
                dist += ( aBC - p ).SquareModulus();
              }
              if ( dist < minDist ) {
                minDist = dist;
                freeFaceList.erase( freeFaceList.begin(), fIt++ );
              }
              else
                fIt = freeFaceList.erase( fIt++ );
            }
          }
        } // choose one of several free faces of a volume

        if ( freeFaceList.size() == 1 ) {
          const SMDS_MeshElement* aFreeFace = freeFaceList.front();
          faceSet->insert( aFreeFace );
          // complete a node set with nodes of a found free face
//           for ( iNode = 0; iNode < ; iNode++ )
//             nodeSet->insert( fNodes[ iNode ] );
        }

      } // loop on volumes of a side

//       // complete a set of faces if new nodes in a nodeSet appeared
//       // ----------------------------------------------------------
//       if ( nodeSetSize != nodeSet->size() ) {
//         for ( ; nIt != nodeSet->end(); nIt++ ) { // loop on nodes of iSide
//           SMDS_ElemIteratorPtr fIt = (*nIt)->GetInverseElementIterator(SMDSAbs_Face);
//           while ( fIt->more() ) { // loop on faces sharing a node
//             const SMDS_MeshElement* f = fIt->next();
//             if ( faceSet->find( f ) == faceSet->end() ) {
//               // check if all nodes are in nodeSet and
//               // complete setOfFaceNodeSet if they are
//               set <const SMDS_MeshNode*> faceNodeSet;
//               SMDS_ElemIteratorPtr nodeIt = f->nodesIterator();
//               bool allInSet = true;
//               while ( nodeIt->more() && allInSet ) { // loop on nodes of a face
//                 const SMDS_MeshNode* n = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
//                 if ( nodeSet->find( n ) == nodeSet->end() )
//                   allInSet = false;
//                 else
//                   faceNodeSet.insert( n );
//               }
//               if ( allInSet ) {
//                 faceSet->insert( f );
//                 setOfFaceNodeSet.insert( faceNodeSet );
//               }
//             }
//           }
//         }
//       }
    } // Create temporary faces, if there are volumes given
  } // loop on sides

  if ( faceSet1.size() != faceSet2.size() ) {
    // delete temporary faces: they are in reverseElements of actual nodes
    SMDS_FaceIteratorPtr tmpFaceIt = aTmpFacesMesh.facesIterator();
    while ( tmpFaceIt->more() )
      aTmpFacesMesh.RemoveElement( tmpFaceIt->next() );
    MESSAGE("Diff nb of faces");
    return SEW_TOPO_DIFF_SETS_OF_ELEMENTS;
  }

  // ============================================================
  // 2. Find nodes to merge:
  //              bind a node to remove to a node to put instead
  // ============================================================

  TNodeNodeMap nReplaceMap; // bind a node to remove to a node to put instead
  if ( theFirstNode1 != theFirstNode2 )
    nReplaceMap.insert( TNodeNodeMap::value_type( theFirstNode1, theFirstNode2 ));
  if ( theSecondNode1 != theSecondNode2 )
    nReplaceMap.insert( TNodeNodeMap::value_type( theSecondNode1, theSecondNode2 ));

  LinkID_Gen aLinkID_Gen( GetMeshDS() );
  set< long > linkIdSet; // links to process
  linkIdSet.insert( aLinkID_Gen.GetLinkID( theFirstNode1, theSecondNode1 ));

  typedef pair< const SMDS_MeshNode*, const SMDS_MeshNode* > NLink;
  list< NLink > linkList[2];
  linkList[0].push_back( NLink( theFirstNode1, theSecondNode1 ));
  linkList[1].push_back( NLink( theFirstNode2, theSecondNode2 ));
  // loop on links in linkList; find faces by links and append links
  // of the found faces to linkList
  list< NLink >::iterator linkIt[] = { linkList[0].begin(), linkList[1].begin() } ;
  for ( ; linkIt[0] != linkList[0].end(); linkIt[0]++, linkIt[1]++ ) {
    NLink link[] = { *linkIt[0], *linkIt[1] };
    long linkID = aLinkID_Gen.GetLinkID( link[0].first, link[0].second );
    if ( linkIdSet.find( linkID ) == linkIdSet.end() )
      continue;

    // by links, find faces in the face sets,
    // and find indices of link nodes in the found faces;
    // in a face set, there is only one or no face sharing a link
    // ---------------------------------------------------------------

    const SMDS_MeshElement* face[] = { 0, 0 };
    //const SMDS_MeshNode* faceNodes[ 2 ][ 5 ];
    vector<const SMDS_MeshNode*> fnodes1(9);
    vector<const SMDS_MeshNode*> fnodes2(9);
    //const SMDS_MeshNode* notLinkNodes[ 2 ][ 2 ] = {{ 0, 0 },{ 0, 0 }} ;
    vector<const SMDS_MeshNode*> notLinkNodes1(6);
    vector<const SMDS_MeshNode*> notLinkNodes2(6);
    int iLinkNode[2][2];
    for ( iSide = 0; iSide < 2; iSide++ ) { // loop on 2 sides
      const SMDS_MeshNode* n1 = link[iSide].first;
      const SMDS_MeshNode* n2 = link[iSide].second;
      set<const SMDS_MeshElement*> * faceSet = faceSetPtr[ iSide ];
      set< const SMDS_MeshElement* > fMap;
      for ( int i = 0; i < 2; i++ ) { // loop on 2 nodes of a link
        const SMDS_MeshNode* n = i ? n1 : n2; // a node of a link
        SMDS_ElemIteratorPtr fIt = n->GetInverseElementIterator(SMDSAbs_Face);
        while ( fIt->more() ) { // loop on faces sharing a node
          const SMDS_MeshElement* f = fIt->next();
          if (faceSet->find( f ) != faceSet->end() && // f is in face set
              ! fMap.insert( f ).second ) // f encounters twice
          {
            if ( face[ iSide ] ) {
              MESSAGE( "2 faces per link " );
              aResult = iSide ? SEW_BAD_SIDE2_NODES : SEW_BAD_SIDE1_NODES;
              break;
            }
            face[ iSide ] = f;
            faceSet->erase( f );
            // get face nodes and find ones of a link
            iNode = 0;
            int nbl = -1;
            if(f->IsPoly()) {
              if(iSide==0) {
                fnodes1.resize(f->NbNodes()+1);
                notLinkNodes1.resize(f->NbNodes()-2);
              }
              else {
                fnodes2.resize(f->NbNodes()+1);
                notLinkNodes2.resize(f->NbNodes()-2);
              }
            }
            if(!f->IsQuadratic()) {
              SMDS_ElemIteratorPtr nIt = f->nodesIterator();
              while ( nIt->more() ) {
                const SMDS_MeshNode* n =
                  static_cast<const SMDS_MeshNode*>( nIt->next() );
                if ( n == n1 ) {
                  iLinkNode[ iSide ][ 0 ] = iNode;
                }
                else if ( n == n2 ) {
                  iLinkNode[ iSide ][ 1 ] = iNode;
                }
                //else if ( notLinkNodes[ iSide ][ 0 ] )
                //  notLinkNodes[ iSide ][ 1 ] = n;
                //else
                //  notLinkNodes[ iSide ][ 0 ] = n;
                else {
                  nbl++;
                  if(iSide==0)
                    notLinkNodes1[nbl] = n;
                    //notLinkNodes1.push_back(n);
                  else
                    notLinkNodes2[nbl] = n;
                    //notLinkNodes2.push_back(n);
                }
                //faceNodes[ iSide ][ iNode++ ] = n;
                if(iSide==0) {
                  fnodes1[iNode++] = n;
                }
                else {
                  fnodes2[iNode++] = n;
                }
              }
            }
            else { // f->IsQuadratic()
              const SMDS_QuadraticFaceOfNodes* F =
                static_cast<const SMDS_QuadraticFaceOfNodes*>(f);
              // use special nodes iterator
              SMDS_NodeIteratorPtr anIter = F->interlacedNodesIterator();
              while ( anIter->more() ) {
                const SMDS_MeshNode* n =
                  static_cast<const SMDS_MeshNode*>( anIter->next() );
                if ( n == n1 ) {
                  iLinkNode[ iSide ][ 0 ] = iNode;
                }
                else if ( n == n2 ) {
                  iLinkNode[ iSide ][ 1 ] = iNode;
                }
                else {
                  nbl++;
                  if(iSide==0) {
                    notLinkNodes1[nbl] = n;
                  }
                  else {
                    notLinkNodes2[nbl] = n;
                  }
                }
                if(iSide==0) {
                  fnodes1[iNode++] = n;
                }
                else {
                  fnodes2[iNode++] = n;
                }
              }
            }
            //faceNodes[ iSide ][ iNode ] = faceNodes[ iSide ][ 0 ];
            if(iSide==0) {
              fnodes1[iNode] = fnodes1[0];
            }
            else {
              fnodes2[iNode] = fnodes1[0];
            }
          }
        }
      }
    }

    // check similarity of elements of the sides
    if (aResult == SEW_OK && ( face[0] && !face[1] ) || ( !face[0] && face[1] )) {
      MESSAGE("Correspondent face not found on side " << ( face[0] ? 1 : 0 ));
      if ( nReplaceMap.size() == 2 ) { // faces on input nodes not found
        aResult = ( face[0] ? SEW_BAD_SIDE2_NODES : SEW_BAD_SIDE1_NODES );
      }
      else {
        aResult = SEW_TOPO_DIFF_SETS_OF_ELEMENTS;
      }
      break; // do not return because it s necessary to remove tmp faces
    }

    // set nodes to merge
    // -------------------

    if ( face[0] && face[1] )  {
      int nbNodes = face[0]->NbNodes();
      if ( nbNodes != face[1]->NbNodes() ) {
        MESSAGE("Diff nb of face nodes");
        aResult = SEW_TOPO_DIFF_SETS_OF_ELEMENTS;
        break; // do not return because it s necessary to remove tmp faces
      }
      bool reverse[] = { false, false }; // order of notLinkNodes of quadrangle
      if ( nbNodes == 3 ) {
        //nReplaceMap.insert( TNodeNodeMap::value_type
        //                   ( notLinkNodes[0][0], notLinkNodes[1][0] ));
        nReplaceMap.insert( TNodeNodeMap::value_type
                           ( notLinkNodes1[0], notLinkNodes2[0] ));
      }
      else {
        for ( iSide = 0; iSide < 2; iSide++ ) { // loop on 2 sides
          // analyse link orientation in faces
          int i1 = iLinkNode[ iSide ][ 0 ];
          int i2 = iLinkNode[ iSide ][ 1 ];
          reverse[ iSide ] = Abs( i1 - i2 ) == 1 ? i1 > i2 : i2 > i1;
          // if notLinkNodes are the first and the last ones, then
          // their order does not correspond to the link orientation
          if (( i1 == 1 && i2 == 2 ) ||
              ( i1 == 2 && i2 == 1 ))
            reverse[ iSide ] = !reverse[ iSide ];
        }
        if ( reverse[0] == reverse[1] ) {
          //nReplaceMap.insert( TNodeNodeMap::value_type
          //                   ( notLinkNodes[0][0], notLinkNodes[1][0] ));
          //nReplaceMap.insert( TNodeNodeMap::value_type
          //                   ( notLinkNodes[0][1], notLinkNodes[1][1] ));
          for(int nn=0; nn<nbNodes-2; nn++) {
            nReplaceMap.insert( TNodeNodeMap::value_type
                             ( notLinkNodes1[nn], notLinkNodes2[nn] ));
          }
        }
        else {
          //nReplaceMap.insert( TNodeNodeMap::value_type
          //                   ( notLinkNodes[0][0], notLinkNodes[1][1] ));
          //nReplaceMap.insert( TNodeNodeMap::value_type
          //                   ( notLinkNodes[0][1], notLinkNodes[1][0] ));
          for(int nn=0; nn<nbNodes-2; nn++) {
            nReplaceMap.insert( TNodeNodeMap::value_type
                             ( notLinkNodes1[nn], notLinkNodes2[nbNodes-3-nn] ));
          }
        }
      }

      // add other links of the faces to linkList
      // -----------------------------------------

      //const SMDS_MeshNode** nodes = faceNodes[ 0 ];
      for ( iNode = 0; iNode < nbNodes; iNode++ )  {
        //linkID = aLinkID_Gen.GetLinkID( nodes[iNode], nodes[iNode+1] );
        linkID = aLinkID_Gen.GetLinkID( fnodes1[iNode], fnodes1[iNode+1] );
        pair< set<long>::iterator, bool > iter_isnew = linkIdSet.insert( linkID );
        if ( !iter_isnew.second ) { // already in a set: no need to process
          linkIdSet.erase( iter_isnew.first );
        }
        else // new in set == encountered for the first time: add
        {
          //const SMDS_MeshNode* n1 = nodes[ iNode ];
          //const SMDS_MeshNode* n2 = nodes[ iNode + 1];
          const SMDS_MeshNode* n1 = fnodes1[ iNode ];
          const SMDS_MeshNode* n2 = fnodes1[ iNode + 1];
          linkList[0].push_back ( NLink( n1, n2 ));
          linkList[1].push_back ( NLink( nReplaceMap[n1], nReplaceMap[n2] ));
        }
      }
    } // 2 faces found
  } // loop on link lists

  if ( aResult == SEW_OK &&
      ( linkIt[0] != linkList[0].end() ||
       !faceSetPtr[0]->empty() || !faceSetPtr[1]->empty() )) {
    MESSAGE( (linkIt[0] != linkList[0].end()) <<" "<< (faceSetPtr[0]->empty()) <<
            " " << (faceSetPtr[1]->empty()));
    aResult = SEW_TOPO_DIFF_SETS_OF_ELEMENTS;
  }

  // ====================================================================
  // 3. Replace nodes in elements of the side 1 and remove replaced nodes
  // ====================================================================

  // delete temporary faces: they are in reverseElements of actual nodes
  SMDS_FaceIteratorPtr tmpFaceIt = aTmpFacesMesh.facesIterator();
  while ( tmpFaceIt->more() )
    aTmpFacesMesh.RemoveElement( tmpFaceIt->next() );

  if ( aResult != SEW_OK)
    return aResult;

  list< int > nodeIDsToRemove/*, elemIDsToRemove*/;
  // loop on nodes replacement map
  TNodeNodeMap::iterator nReplaceMapIt = nReplaceMap.begin(), nnIt;
  for ( ; nReplaceMapIt != nReplaceMap.end(); nReplaceMapIt++ )
    if ( (*nReplaceMapIt).first != (*nReplaceMapIt).second ) {
      const SMDS_MeshNode* nToRemove = (*nReplaceMapIt).first;
      nodeIDsToRemove.push_back( nToRemove->GetID() );
      // loop on elements sharing nToRemove
      SMDS_ElemIteratorPtr invElemIt = nToRemove->GetInverseElementIterator();
      while ( invElemIt->more() ) {
        const SMDS_MeshElement* e = invElemIt->next();
        // get a new suite of nodes: make replacement
        int nbReplaced = 0, i = 0, nbNodes = e->NbNodes();
        vector< const SMDS_MeshNode*> nodes( nbNodes );
        SMDS_ElemIteratorPtr nIt = e->nodesIterator();
        while ( nIt->more() ) {
          const SMDS_MeshNode* n =
            static_cast<const SMDS_MeshNode*>( nIt->next() );
          nnIt = nReplaceMap.find( n );
          if ( nnIt != nReplaceMap.end() ) {
            nbReplaced++;
            n = (*nnIt).second;
          }
          nodes[ i++ ] = n;
        }
        //       if ( nbReplaced == nbNodes && e->GetType() == SMDSAbs_Face )
        //         elemIDsToRemove.push_back( e->GetID() );
        //       else
        if ( nbReplaced )
          aMesh->ChangeElementNodes( e, & nodes[0], nbNodes );
      }
    }

  Remove( nodeIDsToRemove, true );

  return aResult;
}

//================================================================================
  /*!
   * \brief Find corresponding nodes in two sets of faces
    * \param theSide1 - first face set
    * \param theSide2 - second first face
    * \param theFirstNode1 - a boundary node of set 1
    * \param theFirstNode2 - a node of set 2 corresponding to theFirstNode1
    * \param theSecondNode1 - a boundary node of set 1 linked with theFirstNode1
    * \param theSecondNode2 - a node of set 2 corresponding to theSecondNode1
    * \param nReplaceMap - output map of corresponding nodes
    * \retval bool  - is a success or not
   */
//================================================================================

#ifdef _DEBUG_
//#define DEBUG_MATCHING_NODES
#endif

SMESH_MeshEditor::Sew_Error
SMESH_MeshEditor::FindMatchingNodes(set<const SMDS_MeshElement*>& theSide1,
                                    set<const SMDS_MeshElement*>& theSide2,
                                    const SMDS_MeshNode*          theFirstNode1,
                                    const SMDS_MeshNode*          theFirstNode2,
                                    const SMDS_MeshNode*          theSecondNode1,
                                    const SMDS_MeshNode*          theSecondNode2,
                                    TNodeNodeMap &                nReplaceMap)
{
  set<const SMDS_MeshElement*> * faceSetPtr[] = { &theSide1, &theSide2 };

  nReplaceMap.clear();
  if ( theFirstNode1 != theFirstNode2 )
    nReplaceMap.insert( make_pair( theFirstNode1, theFirstNode2 ));
  if ( theSecondNode1 != theSecondNode2 )
    nReplaceMap.insert( make_pair( theSecondNode1, theSecondNode2 ));

  set< TLink > linkSet; // set of nodes where order of nodes is ignored
  linkSet.insert( TLink( theFirstNode1, theSecondNode1 ));

  list< NLink > linkList[2];
  linkList[0].push_back( NLink( theFirstNode1, theSecondNode1 ));
  linkList[1].push_back( NLink( theFirstNode2, theSecondNode2 ));

  // loop on links in linkList; find faces by links and append links
  // of the found faces to linkList
  list< NLink >::iterator linkIt[] = { linkList[0].begin(), linkList[1].begin() } ;
  for ( ; linkIt[0] != linkList[0].end(); linkIt[0]++, linkIt[1]++ ) {
    NLink link[] = { *linkIt[0], *linkIt[1] };
    if ( linkSet.find( link[0] ) == linkSet.end() )
      continue;

    // by links, find faces in the face sets,
    // and find indices of link nodes in the found faces;
    // in a face set, there is only one or no face sharing a link
    // ---------------------------------------------------------------

    const SMDS_MeshElement* face[] = { 0, 0 };
    list<const SMDS_MeshNode*> notLinkNodes[2];
    //bool reverse[] = { false, false }; // order of notLinkNodes
    int nbNodes[2];
    for ( int iSide = 0; iSide < 2; iSide++ ) // loop on 2 sides
    {
      const SMDS_MeshNode* n1 = link[iSide].first;
      const SMDS_MeshNode* n2 = link[iSide].second;
      set<const SMDS_MeshElement*> * faceSet = faceSetPtr[ iSide ];
      set< const SMDS_MeshElement* > facesOfNode1;
      for ( int iNode = 0; iNode < 2; iNode++ ) // loop on 2 nodes of a link
      {
        // during a loop of the first node, we find all faces around n1,
        // during a loop of the second node, we find one face sharing both n1 and n2
        const SMDS_MeshNode* n = iNode ? n1 : n2; // a node of a link
        SMDS_ElemIteratorPtr fIt = n->GetInverseElementIterator(SMDSAbs_Face);
        while ( fIt->more() ) { // loop on faces sharing a node
          const SMDS_MeshElement* f = fIt->next();
          if (faceSet->find( f ) != faceSet->end() && // f is in face set
              ! facesOfNode1.insert( f ).second ) // f encounters twice
          {
            if ( face[ iSide ] ) {
              MESSAGE( "2 faces per link " );
              return ( iSide ? SEW_BAD_SIDE2_NODES : SEW_BAD_SIDE1_NODES );
            }
            face[ iSide ] = f;
            faceSet->erase( f );

            // get not link nodes
            int nbN = f->NbNodes();
            if ( f->IsQuadratic() )
              nbN /= 2;
            nbNodes[ iSide ] = nbN;
            list< const SMDS_MeshNode* > & nodes = notLinkNodes[ iSide ];
            int i1 = f->GetNodeIndex( n1 );
            int i2 = f->GetNodeIndex( n2 );
            int iEnd = nbN, iBeg = -1, iDelta = 1;
            bool reverse = ( Abs( i1 - i2 ) == 1 ? i1 > i2 : i2 > i1 );
            if ( reverse ) {
              std::swap( iEnd, iBeg ); iDelta = -1;
            }
            int i = i2;
            while ( true ) {
              i += iDelta;
              if ( i == iEnd ) i = iBeg + iDelta;
              if ( i == i1 ) break;
              nodes.push_back ( f->GetNode( i ) );
            }
          }
        }
      }
    }
    // check similarity of elements of the sides
    if (( face[0] && !face[1] ) || ( !face[0] && face[1] )) {
      MESSAGE("Correspondent face not found on side " << ( face[0] ? 1 : 0 ));
      if ( nReplaceMap.size() == 2 ) { // faces on input nodes not found
        return ( face[0] ? SEW_BAD_SIDE2_NODES : SEW_BAD_SIDE1_NODES );
      }
      else {
        return SEW_TOPO_DIFF_SETS_OF_ELEMENTS;
      }
    }

    // set nodes to merge
    // -------------------

    if ( face[0] && face[1] )  {
      if ( nbNodes[0] != nbNodes[1] ) {
        MESSAGE("Diff nb of face nodes");
        return SEW_TOPO_DIFF_SETS_OF_ELEMENTS;
      }
#ifdef DEBUG_MATCHING_NODES
      MESSAGE ( " Link 1: " << link[0].first->GetID() <<" "<< link[0].second->GetID()
             << " F 1: " << face[0] << "| Link 2: " << link[1].first->GetID() <<" "
	     << link[1].second->GetID() << " F 2: " << face[1] << " | Bind: " ) ;
#endif
      int nbN = nbNodes[0];
      {
        list<const SMDS_MeshNode*>::iterator n1 = notLinkNodes[0].begin();
        list<const SMDS_MeshNode*>::iterator n2 = notLinkNodes[1].begin();
        for ( int i = 0 ; i < nbN - 2; ++i ) {
#ifdef DEBUG_MATCHING_NODES
          MESSAGE ( (*n1)->GetID() << " to " << (*n2)->GetID() );
#endif
          nReplaceMap.insert( make_pair( *(n1++), *(n2++) ));
        }
      }

      // add other links of the face 1 to linkList
      // -----------------------------------------

      const SMDS_MeshElement* f0 = face[0];
      const SMDS_MeshNode* n1 = f0->GetNode( nbN - 1 );
      for ( int i = 0; i < nbN; i++ )
      {
        const SMDS_MeshNode* n2 = f0->GetNode( i );
        pair< set< TLink >::iterator, bool > iter_isnew =
          linkSet.insert( TLink( n1, n2 ));
        if ( !iter_isnew.second ) { // already in a set: no need to process
          linkSet.erase( iter_isnew.first );
        }
        else // new in set == encountered for the first time: add
        {
#ifdef DEBUG_MATCHING_NODES
          MESSAGE ( "Add link 1: " << n1->GetID() << " " << n2->GetID() << " "
	  << " | link 2: " << nReplaceMap[n1]->GetID() << " " << nReplaceMap[n2]->GetID() << " " );
#endif
          linkList[0].push_back ( NLink( n1, n2 ));
          linkList[1].push_back ( NLink( nReplaceMap[n1], nReplaceMap[n2] ));
        }
        n1 = n2;
      }
    } // 2 faces found
  } // loop on link lists

  return SEW_OK;
}