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[modules/smesh.git] / src / StdMeshers / StdMeshers_Projection_2D.cxx
index 7b3d1e1e1f157ff9157f722b9978e02af6f1dcdd..b73b3a0fe54d44ddd80eb78a98058443f5cef85b 100644 (file)
@@ -1,4 +1,4 @@
-// Copyright (C) 2007-2014  CEA/DEN, EDF R&D, OPEN CASCADE
+// Copyright (C) 2007-2024  CEA, EDF, OPEN CASCADE
 //
 // Copyright (C) 2003-2007  OPEN CASCADE, EADS/CCR, LIP6, CEA/DEN,
 // CEDRAT, EDF R&D, LEG, PRINCIPIA R&D, BUREAU VERITAS
@@ -20,7 +20,7 @@
 // See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
 //
 
-//  SMESH SMESH : implementaion of SMESH idl descriptions
+//  SMESH SMESH : implementation of SMESH idl descriptions
 // File      : StdMeshers_Projection_2D.cxx
 // Module    : SMESH
 // Created   : Fri Oct 20 11:37:07 2006
 //
 #include "StdMeshers_Projection_2D.hxx"
 
+#include "StdMeshers_FaceSide.hxx"
+#include "StdMeshers_NumberOfSegments.hxx"
 #include "StdMeshers_ProjectionSource2D.hxx"
 #include "StdMeshers_ProjectionUtils.hxx"
-#include "StdMeshers_FaceSide.hxx"
-
-#include "SMDS_EdgePosition.hxx"
-#include "SMDS_FacePosition.hxx"
-#include "SMESHDS_Hypothesis.hxx"
-#include "SMESHDS_SubMesh.hxx"
-#include "SMESH_Block.hxx"
-#include "SMESH_Comment.hxx"
-#include "SMESH_Gen.hxx"
-#include "SMESH_Mesh.hxx"
-#include "SMESH_MesherHelper.hxx"
-#include "SMESH_Pattern.hxx"
-#include "SMESH_subMesh.hxx"
-#include "SMESH_subMeshEventListener.hxx"
-
-#include "utilities.h"
-
+#include "StdMeshers_Quadrangle_2D.hxx"
+#include "StdMeshers_Regular_1D.hxx"
+
+#include <ObjectPool.hxx>
+#include <SMDS_EdgePosition.hxx>
+#include <SMDS_FacePosition.hxx>
+#include <SMESHDS_Hypothesis.hxx>
+#include <SMESHDS_Mesh.hxx>
+#include <SMESHDS_SubMesh.hxx>
+#include <SMESH_Block.hxx>
+#include <SMESH_Comment.hxx>
+#include <SMESH_Gen.hxx>
+#include <SMESH_Mesh.hxx>
+#include <SMESH_SequentialMesh.hxx>
+#include <SMESH_MeshAlgos.hxx>
+#include <SMESH_MeshEditor.hxx>
+#include <SMESH_MesherHelper.hxx>
+#include <SMESH_Pattern.hxx>
+#include <SMESH_subMesh.hxx>
+#include <SMESH_subMeshEventListener.hxx>
+
+#include <utilities.h>
+
+#include <BRepAdaptor_Curve.hxx>
 #include <BRepAdaptor_Surface.hxx>
+#include <BRepMesh_Delaun.hxx>
 #include <BRep_Tool.hxx>
 #include <Bnd_B2d.hxx>
+#include <GeomAPI_ExtremaCurveCurve.hxx>
 #include <GeomAPI_ProjectPointOnSurf.hxx>
+#include <GeomAdaptor_Curve.hxx>
+#include <GeomAdaptor_Surface.hxx>
+
+#include <Basics_OCCTVersion.hxx>
+
+#if OCC_VERSION_LARGE < 0x07070000
+#include <GeomAdaptor_HCurve.hxx>
+#include <GeomAdaptor_HSurface.hxx>
+#endif
+
 #include <GeomLib_IsPlanarSurface.hxx>
+#include <Geom_Line.hxx>
+#include <IntCurveSurface_HInter.hxx>
+#include <Precision.hxx>
 #include <TopExp.hxx>
 #include <TopExp_Explorer.hxx>
 #include <TopTools_DataMapIteratorOfDataMapOfShapeShape.hxx>
 #include <TopTools_ListIteratorOfListOfShape.hxx>
+#include <TopTools_MapOfShape.hxx>
 #include <TopoDS.hxx>
+#include <TopoDS_Solid.hxx>
 #include <gp_Ax2.hxx>
 #include <gp_Ax3.hxx>
+#include <gp_GTrsf.hxx>
 
 
 using namespace std;
 
 #define RETURN_BAD_RESULT(msg) { MESSAGE(")-: Error: " << msg); return false; }
+#ifdef _DEBUG_
+// enable printing algo + projection shapes while meshing
+//#define PRINT_WHO_COMPUTE_WHAT
+#endif
 
 namespace TAssocTool = StdMeshers_ProjectionUtils;
 //typedef StdMeshers_ProjectionUtils TAssocTool;
 
+// allow range iteration on NCollection_IndexedMap
+template < class IMAP >
+typename IMAP::const_iterator begin( const IMAP &  m ) { return m.cbegin(); }
+template < class IMAP >
+typename IMAP::const_iterator end( const IMAP &  m ) { return m.cend(); }
+
 //=======================================================================
 //function : StdMeshers_Projection_2D
-//purpose  : 
+//purpose  :
 //=======================================================================
 
-StdMeshers_Projection_2D::StdMeshers_Projection_2D(int hypId, int studyId, SMESH_Gen* gen)
-  :SMESH_2D_Algo(hypId, studyId, gen)
+StdMeshers_Projection_2D::StdMeshers_Projection_2D(int hypId, SMESH_Gen* gen)
+  :SMESH_2D_Algo(hypId, gen)
 {
   _name = "Projection_2D";
   _compatibleHypothesis.push_back("ProjectionSource2D");
@@ -92,7 +129,7 @@ StdMeshers_Projection_2D::~StdMeshers_Projection_2D()
 
 //=======================================================================
 //function : CheckHypothesis
-//purpose  : 
+//purpose  :
 //=======================================================================
 
 bool StdMeshers_Projection_2D::CheckHypothesis(SMESH_Mesh&                          theMesh,
@@ -256,7 +293,7 @@ namespace {
   //================================================================================
   /*!
    * \brief find new nodes belonging to one free border of mesh on face
-    * \param sm - submesh on edge or vertex containg nodes to choose from
+    * \param sm - submesh on edge or vertex containing nodes to choose from
     * \param face - the face bound by the submesh
     * \param u2nodes - map to fill with nodes
     * \param seamNodes - set of found nodes
@@ -265,7 +302,7 @@ namespace {
   //================================================================================
 
   bool getBoundaryNodes ( SMESH_subMesh*                        sm,
-                          const TopoDS_Face&                    face,
+                          const TopoDS_Face&                    /*face*/,
                           map< double, const SMDS_MeshNode* > & u2nodes,
                           set< const SMDS_MeshNode* > &         seamNodes)
   {
@@ -288,7 +325,7 @@ namespace {
       break;
     }
     case TopAbs_EDGE: {
-      
+
       // Get submeshes of sub-vertices
       const map< int, SMESH_subMesh * >& subSM = sm->DependsOn();
       if ( subSM.size() != 2 )
@@ -359,8 +396,7 @@ namespace {
         if ( node->GetPosition()->GetTypeOfPosition() != SMDS_TOP_EDGE )
           RETURN_BAD_RESULT("Bad node position type: node " << node->GetID() <<
                             " pos type " << node->GetPosition()->GetTypeOfPosition());
-        const SMDS_EdgePosition* pos =
-          static_cast<const SMDS_EdgePosition*>(node->GetPosition());
+        SMDS_EdgePositionPtr pos = node->GetPosition();
         u2nodes.insert( make_pair( pos->GetUParameter(), node ));
         seamNodes.insert( node );
       }
@@ -391,15 +427,16 @@ namespace {
   {
     double f,l;
     Handle(Geom2d_Curve) c1 = BRep_Tool::CurveOnSurface( E1, F, f, l );
-    gp_Pnt2d uvLast1 = c1->Value( E1.Orientation() == TopAbs_REVERSED ? f : l );
+    gp_Pnt2d uvFirst1 = c1->Value( f );
+    gp_Pnt2d uvLast1  = c1->Value( l );
 
     Handle(Geom2d_Curve) c2 = BRep_Tool::CurveOnSurface( E2, F, f, l );
-    gp_Pnt2d uvFirst2 = c2->Value( f );
-    gp_Pnt2d uvLast2  = c2->Value( l );
-    double tol2 = 1e-5 * uvLast2.SquareDistance( uvFirst2 );
+    gp_Pnt2d uvFirst2 = c2->Value( E2.Orientation() == TopAbs_REVERSED ? l : f );
+    double tol2 = Max( Precision::PConfusion() * Precision::PConfusion(),
+                       1e-5 * uvLast1.SquareDistance( uvFirst1 ));
 
-    return (( uvLast1.SquareDistance( uvFirst2 ) < tol2 ) ||
-            ( uvLast1.SquareDistance( uvLast2 ) < tol2 ));
+    return (( uvFirst2.SquareDistance( uvFirst1 ) < tol2 ) ||
+            ( uvFirst2.SquareDistance( uvLast1  ) < tol2 ));
   }
 
   //================================================================================
@@ -413,29 +450,34 @@ namespace {
                   const TopoDS_Face&                 srcFace,
                   SMESH_Mesh *                       tgtMesh,
                   SMESH_Mesh *                       srcMesh,
+                  SMESH_MesherHelper*                tgtHelper,
                   const TAssocTool::TShapeShapeMap&  shape2ShapeMap,
                   TSideVector&                       srcWires,
                   TSideVector&                       tgtWires,
                   TAssocTool::TNodeNodeMap&          src2tgtNodes,
                   bool&                              is1DComputed)
   {
-    SMESHDS_Mesh* tgtMeshDS = tgtMesh->GetMeshDS();
-    SMESHDS_Mesh* srcMeshDS = srcMesh->GetMeshDS();
-
     src2tgtNodes.clear();
 
     // get ordered src EDGEs
     TError err;
-    srcWires = StdMeshers_FaceSide::GetFaceWires( srcFace, *srcMesh,/*skipMediumNodes=*/0, err);
-    if ( err && !err->IsOK() )
+    srcWires = StdMeshers_FaceSide::GetFaceWires( srcFace, *srcMesh,/*skipMediumNodes=*/0, err );
+    if (( err && !err->IsOK() ) ||
+        ( srcWires.empty() ))
       return err;
+#ifdef PRINT_WHO_COMPUTE_WHAT
+    cout << "Projection_2D" <<  " F "
+         << tgtMesh->GetMeshDS()->ShapeToIndex( tgtFace ) << " <- "
+         << srcMesh->GetMeshDS()->ShapeToIndex( srcFace ) << endl;
+#endif
 
     // make corresponding sequence of tgt EDGEs
     tgtWires.resize( srcWires.size() );
     for ( size_t iW = 0; iW < srcWires.size(); ++iW )
     {
-      list< TopoDS_Edge > tgtEdges;
       StdMeshers_FaceSidePtr srcWire = srcWires[iW];
+
+      list< TopoDS_Edge > tgtEdges;
       TopTools_IndexedMapOfShape edgeMap; // to detect seam edges
       for ( int iE = 0; iE < srcWire->NbEdges(); ++iE )
       {
@@ -453,7 +495,8 @@ namespace {
           {
             list< TopoDS_Edge >::iterator eIt = tgtEdges.begin();
             std::advance( eIt, index-1 );
-            eIt->Reverse();
+            if ( are2dConnected( tgtEdges.back(), *eIt, tgtFace ))
+              eIt->Reverse();
           }
           else
           {
@@ -469,56 +512,66 @@ namespace {
             tgtE = nE.second;
         }
         tgtEdges.push_back( tgtE );
+      }
 
+      tgtWires[ iW ].reset( new StdMeshers_FaceSide( tgtFace, tgtEdges, tgtMesh,
+                                                     /*theIsForward = */ true,
+                                                     /*theIgnoreMediumNodes = */false,
+                                                     tgtHelper ));
+      StdMeshers_FaceSidePtr tgtWire = tgtWires[ iW ];
 
-        // Fill map of src to tgt nodes with nodes on edges
+      // Fill map of src to tgt nodes with nodes on edges
 
-        if ( srcMesh->GetSubMesh( srcE )->IsEmpty() ||
-             tgtMesh->GetSubMesh( tgtE )->IsEmpty() )
+      for ( int iE = 0; iE < srcWire->NbEdges(); ++iE )
+      {
+#ifdef PRINT_WHO_COMPUTE_WHAT
+        if ( tgtMesh->GetSubMesh( tgtWire->Edge(iE) )->IsEmpty() )
+          cout << "Projection_2D" <<  " E "
+               << tgtWire->EdgeID(iE) << " <- " << srcWire->EdgeID(iE) << endl;
+#endif
+        if ( srcMesh->GetSubMesh( srcWire->Edge(iE) )->IsEmpty() ||
+             tgtMesh->GetSubMesh( tgtWire->Edge(iE) )->IsEmpty() )
         {
           // add nodes on VERTEXes for a case of not meshes EDGEs
-          const TopoDS_Shape&  srcV = SMESH_MesherHelper::IthVertex( 0, srcE );
-          const TopoDS_Shape&  tgtV = shape2ShapeMap( srcV, /*isSrc=*/true );
-          const SMDS_MeshNode* srcN = SMESH_Algo::VertexNode( TopoDS::Vertex( srcV ), srcMeshDS );
-          const SMDS_MeshNode* tgtN = SMESH_Algo::VertexNode( TopoDS::Vertex( tgtV ), tgtMeshDS );
+          const SMDS_MeshNode* srcN = srcWire->VertexNode( iE );
+          const SMDS_MeshNode* tgtN = tgtWire->VertexNode( iE );
           if ( srcN && tgtN )
             src2tgtNodes.insert( make_pair( srcN, tgtN ));
         }
         else
         {
-          const bool skipMediumNodes = true;
-          map< double, const SMDS_MeshNode* > srcNodes, tgtNodes;
-          if ( !SMESH_Algo::GetSortedNodesOnEdge( srcMeshDS, srcE, skipMediumNodes, srcNodes) ||
-               !SMESH_Algo::GetSortedNodesOnEdge( tgtMeshDS, tgtE, skipMediumNodes, tgtNodes ))
-            return SMESH_ComputeError::New( COMPERR_BAD_INPUT_MESH,
-                                            "Invalid node parameters on edges");
+          const bool skipMedium = true, isFwd = true;
+          StdMeshers_FaceSide srcEdge( srcFace, srcWire->Edge(iE),
+                                       srcMesh, isFwd, skipMedium, srcWires[0]->FaceHelper() );
+          StdMeshers_FaceSide tgtEdge( tgtFace, tgtWire->Edge(iE),
+                                       tgtMesh, isFwd, skipMedium, tgtHelper);
+
+          vector< const SMDS_MeshNode* > srcNodes = srcEdge.GetOrderedNodes();
+          vector< const SMDS_MeshNode* > tgtNodes = tgtEdge.GetOrderedNodes();
 
           if (( srcNodes.size() != tgtNodes.size() ) && tgtNodes.size() > 0 )
             return SMESH_ComputeError::New( COMPERR_BAD_INPUT_MESH,
                                             "Different number of nodes on edges");
           if ( !tgtNodes.empty() )
           {
-            map< double, const SMDS_MeshNode* >::iterator u_tn = tgtNodes.begin();
-            if ( srcE.Orientation() == tgtE.Orientation() )
+            vector< const SMDS_MeshNode* >::iterator tn = tgtNodes.begin();
+            //if ( srcWire->Edge(iE).Orientation() == tgtWire->Edge(iE).Orientation() )
             {
-              map< double, const SMDS_MeshNode* >::iterator u_sn = srcNodes.begin();
-              for ( ; u_tn != tgtNodes.end(); ++u_tn, ++u_sn)
-                src2tgtNodes.insert( make_pair( u_sn->second, u_tn->second ));
-            }
-            else
-            {
-              map< double, const SMDS_MeshNode* >::reverse_iterator u_sn = srcNodes.rbegin();
-              for ( ; u_tn != tgtNodes.end(); ++u_tn, ++u_sn)
-                src2tgtNodes.insert( make_pair( u_sn->second, u_tn->second ));
+              vector< const SMDS_MeshNode* >::iterator sn = srcNodes.begin();
+              for ( ; tn != tgtNodes.end(); ++tn, ++sn)
+                src2tgtNodes.insert( make_pair( *sn, *tn ));
             }
+            // else
+            // {
+            //   vector< const SMDS_MeshNode* >::reverse_iterator sn = srcNodes.rbegin();
+            //   for ( ; tn != tgtNodes.end(); ++tn, ++sn)
+            //     src2tgtNodes.insert( make_pair( *sn, *tn ));
+            // }
             is1DComputed = true;
           }
         }
       } // loop on EDGEs of a WIRE
 
-      tgtWires[ iW ].reset( new StdMeshers_FaceSide( tgtFace, tgtEdges, tgtMesh,
-                                                     /*theIsForward = */ true,
-                                                     /*theIgnoreMediumNodes = */false));
     } // loop on WIREs
 
     return TError();
@@ -526,7 +579,7 @@ namespace {
 
   //================================================================================
   /*!
-   * \brief Preform projection in case if tgtFace.IsPartner( srcFace ) and in case
+   * \brief Perform projection in case if tgtFace.IsPartner( srcFace ) and in case
    * if projection by 3D transformation is possible
    */
   //================================================================================
@@ -539,28 +592,34 @@ namespace {
                       TAssocTool::TNodeNodeMap&          src2tgtNodes,
                       const bool                         is1DComputed)
   {
-    SMESH_Mesh *    tgtMesh = tgtWires[0]->GetMesh();
-    SMESH_Mesh *    srcMesh = srcWires[0]->GetMesh();
-    SMESHDS_Mesh* tgtMeshDS = tgtMesh->GetMeshDS();
-    SMESHDS_Mesh* srcMeshDS = srcMesh->GetMeshDS();
-    SMESH_MesherHelper helper( *tgtMesh );
+    SMESH_Mesh *       tgtMesh = tgtWires[0]->GetMesh();
+    SMESH_Mesh *       srcMesh = srcWires[0]->GetMesh();
+    SMESHDS_Mesh*    tgtMeshDS = tgtMesh->GetMeshDS();
+    SMESHDS_Mesh*    srcMeshDS = srcMesh->GetMeshDS();
+    SMESH_MesherHelper* helper = tgtWires[0]->FaceHelper();
 
     const double tol = 1.e-7 * srcMeshDS->getMaxDim();
 
     // transformation to get location of target nodes from source ones
     StdMeshers_ProjectionUtils::TrsfFinder3D trsf;
+    bool trsfIsOK = false;
     if ( tgtFace.IsPartner( srcFace ))
     {
-      gp_Trsf srcTrsf = srcFace.Location();
-      gp_Trsf tgtTrsf = tgtFace.Location();
-      trsf.Set( srcTrsf.Inverted() * tgtTrsf );
+      gp_GTrsf srcTrsf = srcFace.Location().Transformation();
+      gp_GTrsf tgtTrsf = tgtFace.Location().Transformation();
+      gp_GTrsf t = srcTrsf.Inverted().Multiplied( tgtTrsf );
+      trsf.Set( t );
       // check
       gp_Pnt srcP = BRep_Tool::Pnt( srcWires[0]->FirstVertex() );
       gp_Pnt tgtP = BRep_Tool::Pnt( tgtWires[0]->FirstVertex() );
-      if ( tgtP.Distance( trsf.Transform( srcP )) > tol )
-        trsf.Set( tgtTrsf.Inverted() * srcTrsf );
+      trsfIsOK = ( tgtP.Distance( trsf.Transform( srcP )) < tol );
+      if ( !trsfIsOK )
+      {
+        trsf.Set( tgtTrsf.Inverted().Multiplied( srcTrsf ));
+        trsfIsOK = ( tgtP.Distance( trsf.Transform( srcP )) < tol );
+      }
     }
-    else
+    if ( !trsfIsOK )
     {
       // Try to find the 3D transformation
 
@@ -574,7 +633,7 @@ namespace {
         const double minSegLen = srcWires[iW]->Length() / totNbSeg;
         for ( int iE = 0; iE < srcWires[iW]->NbEdges(); ++iE )
         {
-          int nbSeg    = Max( 1, int( srcWires[iW]->EdgeLength( iE ) / minSegLen ));
+          size_t nbSeg = Max( 1, int( srcWires[iW]->EdgeLength( iE ) / minSegLen ));
           double srcU  = srcWires[iW]->FirstParameter( iE );
           double tgtU  = tgtWires[iW]->FirstParameter( iE );
           double srcDu = ( srcWires[iW]->LastParameter( iE )- srcU ) / nbSeg;
@@ -595,7 +654,6 @@ namespace {
 
       // check trsf
 
-      bool trsfIsOK = true;
       const int nbTestPnt = 20;
       const size_t  iStep = Max( 1, int( srcPnts.size() / nbTestPnt ));
       // check boundary
@@ -615,7 +673,7 @@ namespace {
                          0.123 * ( srcSurf.FirstVParameter() + srcSurf.LastVParameter() ));
         gp_Pnt tgtTrsfP = trsf.Transform( srcP );
         TopLoc_Location loc;
-        GeomAPI_ProjectPointOnSurf& proj = helper.GetProjector( tgtFace, loc, 0.1*tol );
+        GeomAPI_ProjectPointOnSurf& proj = helper->GetProjector( tgtFace, loc, 0.1*tol );
         if ( !loc.IsIdentity() )
           tgtTrsfP.Transform( loc.Transformation().Inverted() );
         proj.Perform( tgtTrsfP );
@@ -630,15 +688,15 @@ namespace {
     // Make new faces
 
     // prepare the helper to adding quadratic elements if necessary
-    helper.SetSubShape( tgtFace );
-    helper.IsQuadraticSubMesh( tgtFace );
+    helper->IsQuadraticSubMesh( tgtFace );
 
     SMESHDS_SubMesh* srcSubDS = srcMeshDS->MeshElements( srcFace );
     if ( !is1DComputed && srcSubDS->NbElements() )
-      helper.SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
+      helper->SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
 
-    SMESH_MesherHelper srcHelper( *srcMesh );
-    srcHelper.SetSubShape( srcFace );
+    SMESH_MesherHelper* srcHelper = srcWires[0]->FaceHelper();
+    SMESH_MesherHelper  edgeHelper( *tgtMesh );
+    edgeHelper.ToFixNodeParameters( true );
 
     const SMDS_MeshNode* nullNode = 0;
     TAssocTool::TNodeNodeMap::iterator srcN_tgtN;
@@ -654,9 +712,9 @@ namespace {
     while ( elemIt->more() ) // loop on all mesh faces on srcFace
     {
       const SMDS_MeshElement* elem = elemIt->next();
-      const int nbN = elem->NbCornerNodes(); 
+      const int nbN = elem->NbCornerNodes();
       tgtNodes.resize( nbN );
-      helper.SetElementsOnShape( false );
+      helper->SetElementsOnShape( false );
       for ( int i = 0; i < nbN; ++i ) // loop on nodes of the source element
       {
         const SMDS_MeshNode* srcNode = elem->GetNode(i);
@@ -665,22 +723,41 @@ namespace {
         {
           // create a new node
           gp_Pnt tgtP = trsf.Transform( SMESH_TNodeXYZ( srcNode ));
-          SMDS_MeshNode* n = helper.AddNode( tgtP.X(), tgtP.Y(), tgtP.Z() );
+          SMDS_MeshNode* n = helper->AddNode( tgtP.X(), tgtP.Y(), tgtP.Z() );
           srcN_tgtN->second = n;
           switch ( srcNode->GetPosition()->GetTypeOfPosition() )
           {
           case SMDS_TOP_FACE:
           {
-            gp_Pnt2d srcUV = srcHelper.GetNodeUV( srcFace, srcNode );
-            tgtMeshDS->SetNodeOnFace( n, helper.GetSubShapeID(), srcUV.X(), srcUV.Y() );
+            gp_Pnt2d srcUV = srcHelper->GetNodeUV( srcFace, srcNode );
+            tgtMeshDS->SetNodeOnFace( n, helper->GetSubShapeID(), srcUV.X(), srcUV.Y() );
             break;
           }
           case SMDS_TOP_EDGE:
           {
-            const TopoDS_Shape & srcE = srcMeshDS->IndexToShape( srcNode->getshapeId() );
-            const TopoDS_Shape & tgtE = shape2ShapeMap( srcE, /*isSrc=*/true );
-            double srcU = srcHelper.GetNodeU( TopoDS::Edge( srcE ), srcNode );
-            tgtMeshDS->SetNodeOnEdge( n, TopoDS::Edge( tgtE ), srcU );
+            const TopoDS_Edge& srcE = TopoDS::Edge( srcMeshDS->IndexToShape( srcNode->getshapeId()));
+            const TopoDS_Edge& tgtE = TopoDS::Edge( shape2ShapeMap( srcE, /*isSrc=*/true ));
+            double srcU = srcHelper->GetNodeU( srcE, srcNode );
+            tgtMeshDS->SetNodeOnEdge( n, tgtE, srcU );
+            if ( !tgtFace.IsPartner( srcFace ))
+            {
+              edgeHelper.SetSubShape( tgtE );
+              double tol = BRep_Tool::Tolerance( tgtE );
+              bool isOk = edgeHelper.CheckNodeU( tgtE, n, srcU, 2 * tol, /*force=*/true );
+              if ( !isOk ) // projection of n to tgtE failed (23395)
+              {
+                double sF, sL, tF, tL;
+                BRep_Tool::Range( srcE, sF, sL );
+                BRep_Tool::Range( tgtE, tF, tL );
+                double srcR = ( srcU - sF ) / ( sL - sF );
+                double tgtU  = tF + srcR * ( tL - tF );
+                tgtMeshDS->SetNodeOnEdge( n, tgtE, tgtU );
+                gp_Pnt newP = BRepAdaptor_Curve( tgtE ).Value( tgtU );
+                double dist = newP.Distance( tgtP );
+                if ( tol < dist && dist < 1000*tol )
+                  tgtMeshDS->MoveNode( n, newP.X(), newP.Y(), newP.Z() );
+              }
+            }
             break;
           }
           case SMDS_TOP_VERTEX:
@@ -696,27 +773,24 @@ namespace {
         tgtNodes[i] = srcN_tgtN->second;
       }
       // create a new face
-      helper.SetElementsOnShape( true );
+      helper->SetElementsOnShape( true );
       switch ( nbN )
       {
-      case 3: helper.AddFace(tgtNodes[0], tgtNodes[tri1], tgtNodes[tri2]); break;
-      case 4: helper.AddFace(tgtNodes[0], tgtNodes[quad1], tgtNodes[2], tgtNodes[quad3]); break;
+      case 3: helper->AddFace(tgtNodes[0], tgtNodes[tri1], tgtNodes[tri2]); break;
+      case 4: helper->AddFace(tgtNodes[0], tgtNodes[quad1], tgtNodes[2], tgtNodes[quad3]); break;
       default:
         if ( isReverse ) std::reverse( tgtNodes.begin(), tgtNodes.end() );
-        helper.AddPolygonalFace( tgtNodes );
+        helper->AddPolygonalFace( tgtNodes );
       }
     }
 
     // check node positions
 
-    if ( !tgtFace.IsPartner( srcFace ) )
+    // if ( !tgtFace.IsPartner( srcFace ) ) for NETGEN 6 which sets wrong UV
     {
-      SMESH_MesherHelper edgeHelper( *tgtMesh );
-      edgeHelper.ToFixNodeParameters( true );
-      helper.ToFixNodeParameters( true );
+      helper->ToFixNodeParameters( true );
 
       int nbOkPos = 0;
-      bool toCheck = true;
       const double tol2d = 1e-12;
       srcN_tgtN = src2tgtNodes.begin();
       for ( ; srcN_tgtN != src2tgtNodes.end(); ++srcN_tgtN )
@@ -727,8 +801,8 @@ namespace {
         case SMDS_TOP_FACE:
         {
           if ( nbOkPos > 10 ) break;
-          gp_XY uv = helper.GetNodeUV( tgtFace, n ), uvBis = uv;
-          if (( helper.CheckNodeUV( tgtFace, n, uv, tol )) &&
+          gp_XY uv = helper->GetNodeUV( tgtFace, n ), uvBis = uv;
+          if (( helper->CheckNodeUV( tgtFace, n, uv, tol )) &&
               (( uv - uvBis ).SquareModulus() < tol2d ))
             ++nbOkPos;
           else
@@ -737,9 +811,9 @@ namespace {
         }
         case SMDS_TOP_EDGE:
         {
-          const TopoDS_Edge & tgtE = TopoDS::Edge( tgtMeshDS->IndexToShape( n->getshapeId() ));
-          edgeHelper.SetSubShape( tgtE );
-          edgeHelper.GetNodeU( tgtE, n, 0, &toCheck );
+          // const TopoDS_Edge & tgtE = TopoDS::Edge( tgtMeshDS->IndexToShape( n->getshapeId() ));
+          // edgeHelper.SetSubShape( tgtE );
+          // edgeHelper.GetNodeU( tgtE, n, 0, &toCheck );
           break;
         }
         default:;
@@ -753,7 +827,7 @@ namespace {
 
   //================================================================================
   /*!
-   * \brief Preform projection in case if the faces are similar in 2D space
+   * \brief Perform projection in case if the faces are similar in 2D space
    */
   //================================================================================
 
@@ -807,14 +881,14 @@ namespace {
         // find trsf
         const int totNbSeg = 50;
         vector< gp_XY > srcPnts, tgtPnts;
-        srcPnts.resize( totNbSeg );
-        tgtPnts.resize( totNbSeg );
+        srcPnts.reserve( totNbSeg );
+        tgtPnts.reserve( totNbSeg );
         for ( size_t iW = 0; iW < srcWires.size(); ++iW )
         {
           const double minSegLen = srcWires[iW]->Length() / totNbSeg;
           for ( int iE = 0; iE < srcWires[iW]->NbEdges(); ++iE )
           {
-            int nbSeg    = Max( 1, int( srcWires[iW]->EdgeLength( iE ) / minSegLen ));
+            size_t nbSeg = Max( 1, int( srcWires[iW]->EdgeLength( iE ) / minSegLen ));
             double srcU  = srcWires[iW]->FirstParameter( iE );
             double tgtU  = tgtWires[iW]->FirstParameter( iE );
             double srcDu = ( srcWires[iW]->LastParameter( iE )- srcU ) / nbSeg;
@@ -848,18 +922,16 @@ namespace {
 
     SMESHDS_SubMesh* srcSubDS = srcMesh->GetMeshDS()->MeshElements( srcFace );
 
-    SMESH_MesherHelper helper( *tgtMesh );
-    helper.SetSubShape( tgtFace );
+    SMESH_MesherHelper* helper = tgtWires[0]->FaceHelper();
     if ( is1DComputed )
-      helper.IsQuadraticSubMesh( tgtFace );
+      helper->IsQuadraticSubMesh( tgtFace );
     else
-      helper.SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
-    helper.SetElementsOnShape( true );
+      helper->SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
+    helper->SetElementsOnShape( true );
     Handle(Geom_Surface) tgtSurface = BRep_Tool::Surface( tgtFace );
     SMESHDS_Mesh* tgtMeshDS = tgtMesh->GetMeshDS();
 
-    SMESH_MesherHelper srcHelper( *srcMesh );
-    srcHelper.SetSubShape( srcFace );
+    SMESH_MesherHelper* srcHelper = srcWires[0]->FaceHelper();
 
     const SMDS_MeshNode* nullNode = 0;
     TAssocTool::TNodeNodeMap::iterator srcN_tgtN;
@@ -870,7 +942,7 @@ namespace {
     while ( elemIt->more() ) // loop on all mesh faces on srcFace
     {
       const SMDS_MeshElement* elem = elemIt->next();
-      const int nbN = elem->NbCornerNodes(); 
+      const int nbN = elem->NbCornerNodes();
       tgtNodes.resize( nbN );
       for ( int i = 0; i < nbN; ++i ) // loop on nodes of the source element
       {
@@ -879,31 +951,32 @@ namespace {
         if ( srcN_tgtN->second == nullNode )
         {
           // create a new node
-          gp_Pnt2d srcUV = srcHelper.GetNodeUV( srcFace, srcNode,
-                                                elem->GetNode( helper.WrapIndex(i+1,nbN)), &uvOK);
+          gp_Pnt2d srcUV = srcHelper->GetNodeUV( srcFace, srcNode,
+                                                 elem->GetNode( helper->WrapIndex(i+1,nbN)), &uvOK);
           gp_Pnt2d   tgtUV = trsf.Transform( srcUV );
           gp_Pnt      tgtP = tgtSurface->Value( tgtUV.X(), tgtUV.Y() );
           SMDS_MeshNode* n = tgtMeshDS->AddNode( tgtP.X(), tgtP.Y(), tgtP.Z() );
           switch ( srcNode->GetPosition()->GetTypeOfPosition() )
           {
           case SMDS_TOP_FACE: {
-            tgtMeshDS->SetNodeOnFace( n, helper.GetSubShapeID(), tgtUV.X(), tgtUV.Y() );
+            tgtMeshDS->SetNodeOnFace( n, helper->GetSubShapeID(), tgtUV.X(), tgtUV.Y() );
             break;
           }
           case SMDS_TOP_EDGE: {
-            TopoDS_Shape srcEdge = srcHelper.GetSubShapeByNode( srcNode, srcHelper.GetMeshDS() );
+            TopoDS_Shape srcEdge = srcHelper->GetSubShapeByNode( srcNode, srcHelper->GetMeshDS() );
             TopoDS_Edge  tgtEdge = TopoDS::Edge( shape2ShapeMap( srcEdge, /*isSrc=*/true ));
             double U = Precision::Infinite();
-            helper.CheckNodeU( tgtEdge, n, U, Precision::PConfusion());
+            helper->CheckNodeU( tgtEdge, n, U, Precision::PConfusion());
             tgtMeshDS->SetNodeOnEdge( n, TopoDS::Edge( tgtEdge ), U );
             break;
           }
           case SMDS_TOP_VERTEX: {
-            TopoDS_Shape srcV = srcHelper.GetSubShapeByNode( srcNode, srcHelper.GetMeshDS() );
+            TopoDS_Shape srcV = srcHelper->GetSubShapeByNode( srcNode, srcHelper->GetMeshDS() );
             TopoDS_Shape tgtV = shape2ShapeMap( srcV, /*isSrc=*/true );
             tgtMeshDS->SetNodeOnVertex( n, TopoDS::Vertex( tgtV ));
             break;
           }
+          default:;
           }
           srcN_tgtN->second = n;
         }
@@ -912,13 +985,519 @@ namespace {
       // create a new face (with reversed orientation)
       switch ( nbN )
       {
-      case 3: helper.AddFace(tgtNodes[0], tgtNodes[2], tgtNodes[1]); break;
-      case 4: helper.AddFace(tgtNodes[0], tgtNodes[3], tgtNodes[2], tgtNodes[1]); break;
+      case 3: helper->AddFace(tgtNodes[0], tgtNodes[2], tgtNodes[1]); break;
+      case 4: helper->AddFace(tgtNodes[0], tgtNodes[3], tgtNodes[2], tgtNodes[1]); break;
+      }
+    }  // loop on all mesh faces on srcFace
+
+    return true;
+
+  } // projectBy2DSimilarity()
+
+  //================================================================================
+  /*!
+   * \brief Quadrangle algorithm computing structured triangle mesh
+   */
+  //================================================================================
+
+  struct QuadAlgo : public StdMeshers_Quadrangle_2D
+  {
+    QuadAlgo( int hypId, SMESH_Gen* gen ): StdMeshers_Quadrangle_2D( hypId, gen ) {}
+
+    bool Compute( SMESH_MesherHelper & theHelper, const StdMeshers_FaceSidePtr& theWire )
+    {
+      SMESH_Mesh& theMesh = *theHelper.GetMesh();
+
+      // set sides of a quad FACE
+      FaceQuadStruct::Ptr quad( new FaceQuadStruct );
+      quad->side.reserve( 4 );
+      quad->face = theWire->Face();
+      for ( int i = 0; i < 4; ++i )
+        quad->side.push_back
+          ( StdMeshers_FaceSide::New( quad->face, theWire->Edge(i), &theMesh, i < QUAD_TOP_SIDE,
+                                      /*skipMedium=*/true, theWire->FaceHelper() ));
+      if ( !setNormalizedGrid( quad ))
+        return false;
+
+      // make internal nodes
+      SMESHDS_Mesh *  meshDS = theMesh.GetMeshDS();
+      int         geomFaceID = meshDS->ShapeToIndex( quad->face );
+      Handle(Geom_Surface) S = BRep_Tool::Surface( quad->face );
+      for (   int i = 1; i < quad->iSize - 1; i++)
+        for ( int j = 1; j < quad->jSize - 1; j++)
+        {
+          UVPtStruct& uvPnt = quad->UVPt( i, j );
+          gp_Pnt P          = S->Value( uvPnt.u, uvPnt.v );
+          uvPnt.node        = meshDS->AddNode(P.X(), P.Y(), P.Z());
+          meshDS->SetNodeOnFace( uvPnt.node, geomFaceID, uvPnt.u, uvPnt.v );
+        }
+
+      // make triangles
+      for (   int i = 0; i < quad->iSize-1; i++) {
+        for ( int j = 0; j < quad->jSize-1; j++)
+        {
+          const SMDS_MeshNode* a = quad->uv_grid[ j      * quad->iSize + i    ].node;
+          const SMDS_MeshNode* b = quad->uv_grid[ j      * quad->iSize + i + 1].node;
+          const SMDS_MeshNode* c = quad->uv_grid[(j + 1) * quad->iSize + i + 1].node;
+          const SMDS_MeshNode* d = quad->uv_grid[(j + 1) * quad->iSize + i    ].node;
+          theHelper.AddFace(a, b, c);
+          theHelper.AddFace(a, c, d);
+        }
+      }
+      return true;
+    }
+  };
+
+  //================================================================================
+  /*!
+   * \brief Local coordinate system of a triangle. Return barycentric coordinates of a point
+   */
+  //================================================================================
+
+  struct TriaCoordSys
+  {
+    gp_Pnt myO;   //!< origin
+    gp_Vec myX;   //!< X axis
+    gp_Vec myY;   //!< Y axis
+    gp_XY  myUV1; //!< UV of 2nd node in this CS
+    gp_XY  myUV2; //!< UV of 3d  node in this CS
+
+    void Init( const gp_Pnt p1, const gp_Pnt p2, const gp_Pnt p3 )
+    {
+      myO = p1;
+
+      myX = gp_Vec( p1, p2 );
+      myUV1.SetCoord( myX.Magnitude(), 0 );
+      myX /= myUV1.X();
+
+      gp_Vec v13( p1, p3 );
+      myY = myX.CrossCrossed( myX, v13 );
+      myY.Normalize();
+      myUV2.SetCoord( v13 * myX, v13 * myY );
+
+      return;
+    }
+
+    void GetBaryCoords( const gp_Pnt p, double& bc1, double& bc2, double& bc3 ) const
+    {
+      gp_Vec op( myO, p );
+      gp_XY uv( op * myX, op * myY );
+
+      SMESH_MeshAlgos::GetBarycentricCoords( uv,
+                                             gp::Origin2d().XY(), myUV1, myUV2,
+                                             bc1, bc2 );
+      bc3 = 1 - bc1 - bc2;
+    }
+  };
+
+
+  //================================================================================
+  /*!
+   * \brief Structured 2D mesh of a quadrilateral FACE; is used in projectQuads()
+   */
+  //================================================================================
+
+  struct QuadMesh : public SMESH_SequentialMesh
+  {
+    ObjectPool< TriaCoordSys > _traiLCSPool;
+    SMESH_ElementSearcher*     _elemSearcher;
+    SMESH_Gen                  _sgen;
+    SMESH_MesherHelper         _helper;
+
+    QuadMesh(const TopoDS_Face& face):
+      _elemSearcher( nullptr ), _helper( *this )
+    {
+      _meshDS = new SMESHDS_Mesh( 0, true );
+      _gen = &_sgen;
+      ShapeToMesh( face );
+    }
+    ~QuadMesh() { delete _elemSearcher; }
+
+    // --------------------------------------------------------------------------------
+    /*!
+     * \brief Compute quadrangle mesh and prepare for face search
+     */
+    bool Compute( const TSideVector& wires, int nbSeg1, int nbSeg2, bool isSourceMesh )
+    {
+      if ( wires.size() > 1 || wires[0]->NbEdges() != 4 )
+        return false;
+
+      // compute quadrangle mesh
+
+      SMESH_Hypothesis* algo1D = new StdMeshers_Regular_1D( _sgen.GetANewId(), &_sgen );
+      AddHypothesis( GetShapeToMesh(), algo1D->GetID() );
+
+      StdMeshers_NumberOfSegments * nbHyp1, *nbHyp2;
+      nbHyp1 = new StdMeshers_NumberOfSegments( _sgen.GetANewId(), &_sgen );
+      nbHyp1->SetNumberOfSegments( nbSeg1 );
+      AddHypothesis( wires[0]->Edge(0), nbHyp1->GetID() );
+      AddHypothesis( wires[0]->Edge(2), nbHyp1->GetID() );
+
+      nbHyp2 = new StdMeshers_NumberOfSegments( _sgen.GetANewId(), &_sgen );
+      nbHyp2->SetNumberOfSegments( nbSeg2 );
+      AddHypothesis( wires[0]->Edge(1), nbHyp2->GetID() );
+      AddHypothesis( wires[0]->Edge(3), nbHyp2->GetID() );
+
+      if ( !_sgen.Compute( *this, GetShapeToMesh(), SMESH_Gen::SHAPE_ONLY_UPWARD ))
+        return false;
+
+      QuadAlgo algo2D( _sgen.GetANewId(), &_sgen );
+      if ( !algo2D.Compute( _helper, wires[0] ))
+        return false;
+
+      // remove edges
+      // for ( SMDS_ElemIteratorPtr eIt = _meshDS->elementsIterator( SMDSAbs_Edge ); eIt->more(); )
+      //   _meshDS->RemoveFreeElement( eIt->next(), /*sm=*/0, /*groups=*/false );
+
+      // _meshDS->Modified(); // setMyModified();
+      // _meshDS->CompactMesh();
+
+      // create TriaCoordSys for every triangle
+      if ( isSourceMesh )
+      {
+        for ( SMDS_ElemIteratorPtr fIt = _meshDS->elementsIterator( SMDSAbs_Face ); fIt->more(); )
+        {
+          const SMDS_MeshElement* tria = fIt->next();
+          TriaCoordSys* triaLCS = _traiLCSPool.getNew();
+          triaLCS->Init( SMESH_NodeXYZ( tria->GetNode( 0 )),
+                         SMESH_NodeXYZ( tria->GetNode( 1 )),
+                         SMESH_NodeXYZ( tria->GetNode( 2 )));
+          // int i= tria->GetID() - NbEdges() - 1;
+          // cout << "ID from TRIA " << i << " - poolSize " << _traiLCSPool.nbElements() <<
+          //   ( _traiLCSPool[i]!= triaLCS ? " KO" : "" )  << endl;
+        }
+        _elemSearcher = SMESH_MeshAlgos::GetElementSearcher( *_meshDS );
+      }
+      return true;
+    }
+    // --------------------------------------------------------------------------------
+    /*!
+     * \brief Find a source triangle including a point and return its barycentric coordinates
+     */
+    const SMDS_MeshElement* FindFaceByPoint( const gp_Pnt p,
+                                             double & bc1, double & bc2, double & bc3 )
+    {
+      const SMDS_MeshElement* tria = nullptr;
+      gp_XYZ projPnt = _elemSearcher->Project( p, SMDSAbs_Face, &tria );
+
+      int lcsID = tria->GetID() - NbEdges() - 1;
+      const TriaCoordSys* triaLCS = _traiLCSPool[ lcsID ];
+      triaLCS->GetBaryCoords( projPnt, bc1, bc2, bc3 );
+
+      return tria;
+    }
+    // --------------------------------------------------------------------------------
+    /*!
+     * \brief Return a point lying on a corresponding target triangle
+     */
+    gp_Pnt GetPoint( const SMDS_MeshElement* srcTria, double & bc1, double & bc2, double & bc3 )
+    {
+      const SMDS_MeshElement* tgtTria = _meshDS->FindElement( srcTria->GetID() );
+      gp_Pnt p = ( bc1 * SMESH_NodeXYZ( tgtTria->GetNode(0) ) +
+                   bc2 * SMESH_NodeXYZ( tgtTria->GetNode(1) ) +
+                   bc3 * SMESH_NodeXYZ( tgtTria->GetNode(2) ) );
+      return p;
+    }
+    // --------------------------------------------------------------------------------
+    /*!
+     * \brief Return an UV of point lying on a corresponding target triangle
+     */
+    gp_XY GetUV( const SMDS_MeshElement* srcTria,
+                 double & bc1, double & bc2, double & bc3 )
+    {
+      const SMDS_MeshElement* tgtTria = _meshDS->FindElement( srcTria->GetID() );
+      TopoDS_Shape tgtShape = GetShapeToMesh();
+      const TopoDS_Face& face = TopoDS::Face( tgtShape );
+
+      gp_XY p = ( bc1 * _helper.GetNodeUV( face, tgtTria->GetNode(0) ) +
+                  bc2 * _helper.GetNodeUV( face, tgtTria->GetNode(1) ) +
+                  bc3 * _helper.GetNodeUV( face, tgtTria->GetNode(2) ) );
+      return p;
+    }
+  };
+
+  //================================================================================
+  /*!
+   * \brief Calculate average size of faces
+   *         Actually calculate average of min and max face size
+   */
+  //================================================================================
+
+  double calcAverageFaceSize( SMESHDS_SubMesh* sm )
+  {
+    double minLen = Precision::Infinite(), maxLen = 0;
+    for ( SMDS_ElemIteratorPtr fIt = sm->GetElements(); fIt->more(); )
+    {
+      const SMDS_MeshElement* face = fIt->next();
+      int nbNodes = face->NbCornerNodes();
+      gp_XYZ pPrev = SMESH_NodeXYZ( face->GetNode( nbNodes - 1 ));
+      for ( int i = 0; i < nbNodes; ++i )
+      {
+        SMESH_NodeXYZ p( face->GetNode( i ));
+        double len = ( p - pPrev ).SquareModulus();
+        minLen = Min( len, minLen );
+        maxLen = Max( len, maxLen );
+        pPrev = p;
       }
     }
+    return 0.5 * ( Sqrt( minLen ) + Sqrt( maxLen ));
+  }
+
+  //================================================================================
+  /*!
+   * \brief Perform projection from a quadrilateral FACE to another quadrilateral one
+   */
+  //================================================================================
+
+  bool projectQuads(const TopoDS_Face&                 tgtFace,
+                    const TopoDS_Face&                 srcFace,
+                    const TSideVector&                 tgtWires,
+                    const TSideVector&                 srcWires,
+                    const TAssocTool::TShapeShapeMap&  shape2ShapeMap,
+                    TAssocTool::TNodeNodeMap&          src2tgtNodes,
+                    const bool                         is1DComputed)
+  {
+    SMESH_Mesh * tgtMesh = tgtWires[0]->GetMesh();
+    SMESH_Mesh * srcMesh = srcWires[0]->GetMesh();
+    SMESHDS_Mesh * tgtMeshDS = tgtMesh->GetMeshDS();
+    SMESHDS_Mesh * srcMeshDS = srcMesh->GetMeshDS();
+
+    if ( srcWires.size() != 1 || // requirements below can be weaken
+         SMESH_MesherHelper::Count( tgtFace, TopAbs_EDGE, /*ignoreSame=*/true) != 4 ||
+         SMESH_MesherHelper::Count( srcFace, TopAbs_EDGE, /*ignoreSame=*/true) != 4 )
+      return false;
+
+    // make auxiliary structured meshes that will be used to get corresponding
+    // points on the target FACE
+    QuadMesh srcQuadMesh( srcFace ), tgtQuadMesh( tgtFace );
+    double avgSize = calcAverageFaceSize( srcMeshDS->MeshElements( srcFace ));
+    int nbSeg1 = (int) Max( 2., Max( srcWires[0]->EdgeLength(0),
+                                     srcWires[0]->EdgeLength(2)) / avgSize );
+    int nbSeg2 = (int) Max( 2., Max( srcWires[0]->EdgeLength(1),
+                                     srcWires[0]->EdgeLength(3)) / avgSize );
+    if ( !srcQuadMesh.Compute( srcWires, nbSeg1, nbSeg2, /*isSrc=*/true ) ||
+         !tgtQuadMesh.Compute( tgtWires, nbSeg1, nbSeg2, /*isSrc=*/false ))
+      return false;
+
+    // Make new faces
+
+    // prepare the helper to adding quadratic elements if necessary
+    SMESH_MesherHelper* helper = tgtWires[0]->FaceHelper();
+    helper->IsQuadraticSubMesh( tgtFace );
+
+    SMESHDS_SubMesh* srcSubDS = srcMeshDS->MeshElements( srcFace );
+    if ( !is1DComputed && srcSubDS->NbElements() )
+      helper->SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
+
+    SMESH_MesherHelper* srcHelper = srcWires[0]->FaceHelper();
+    SMESH_MesherHelper  edgeHelper( *tgtMesh );
+    edgeHelper.ToFixNodeParameters( true );
+
+    const SMDS_MeshNode* nullNode = 0;
+    TAssocTool::TNodeNodeMap::iterator srcN_tgtN;
+
+    SMDS_ElemIteratorPtr elemIt = srcSubDS->GetElements();
+    vector< const SMDS_MeshNode* > tgtNodes;
+    while ( elemIt->more() ) // loop on all mesh faces on srcFace
+    {
+      const SMDS_MeshElement* elem = elemIt->next();
+      const int nbN = elem->NbCornerNodes();
+      tgtNodes.resize( nbN );
+      helper->SetElementsOnShape( false );
+      for ( int i = 0; i < nbN; ++i ) // loop on nodes of the source element
+      {
+        const SMDS_MeshNode* srcNode = elem->GetNode(i);
+        srcN_tgtN = src2tgtNodes.insert( make_pair( srcNode, nullNode )).first;
+        if ( srcN_tgtN->second == nullNode )
+        {
+          // create a new node
+          gp_Pnt srcP = SMESH_TNodeXYZ( srcNode );
+          double bc[3];
+          const SMDS_MeshElement* auxF = srcQuadMesh.FindFaceByPoint( srcP, bc[0], bc[1], bc[2] );
+          gp_Pnt                  tgtP = tgtQuadMesh.GetPoint( auxF, bc[0], bc[1], bc[2] );
+          SMDS_MeshNode* n = helper->AddNode( tgtP.X(), tgtP.Y(), tgtP.Z() );
+          srcN_tgtN->second = n;
+          switch ( srcNode->GetPosition()->GetTypeOfPosition() )
+          {
+          case SMDS_TOP_FACE:
+          {
+            gp_XY tgtUV = tgtQuadMesh.GetUV( auxF, bc[0], bc[1], bc[2] );
+            tgtMeshDS->SetNodeOnFace( n, helper->GetSubShapeID(), tgtUV.X(), tgtUV.Y() );
+            break;
+          }
+          case SMDS_TOP_EDGE:
+          {
+            const TopoDS_Edge& srcE = TopoDS::Edge( srcMeshDS->IndexToShape( srcNode->GetShapeID()));
+            const TopoDS_Edge& tgtE = TopoDS::Edge( shape2ShapeMap( srcE, /*isSrc=*/true ));
+            double srcU = srcHelper->GetNodeU( srcE, srcNode );
+            tgtMeshDS->SetNodeOnEdge( n, tgtE, srcU );
+            edgeHelper.SetSubShape( tgtE );
+            double tol = BRep_Tool::MaxTolerance( tgtE, TopAbs_VERTEX ), distXYZ[4];
+            /*isOk = */edgeHelper.CheckNodeU( tgtE, n, srcU, 2 * tol, /*force=*/true, distXYZ );
+            //if ( isOk )
+            tgtMeshDS->MoveNode( n, distXYZ[1], distXYZ[2], distXYZ[3] );
+            SMDS_EdgePositionPtr( n->GetPosition() )->SetUParameter( srcU );
+            break;
+          }
+          case SMDS_TOP_VERTEX:
+          {
+            const TopoDS_Shape & srcV = srcMeshDS->IndexToShape( srcNode->getshapeId() );
+            const TopoDS_Shape & tgtV = shape2ShapeMap( srcV, /*isSrc=*/true );
+            tgtP = BRep_Tool::Pnt( TopoDS::Vertex( tgtV ));
+            tgtMeshDS->MoveNode( n, tgtP.X(), tgtP.Y(), tgtP.Z() );
+            tgtMeshDS->SetNodeOnVertex( n, TopoDS::Vertex( tgtV ));
+            break;
+          }
+          default:;
+          }
+        }
+        tgtNodes[i] = srcN_tgtN->second;
+      }
+      // create a new face
+      helper->SetElementsOnShape( true );
+      switch ( nbN )
+      {
+      case 3: helper->AddFace(tgtNodes[0], tgtNodes[1], tgtNodes[2]); break;
+      case 4: helper->AddFace(tgtNodes[0], tgtNodes[1], tgtNodes[2], tgtNodes[3]); break;
+      default: helper->AddPolygonalFace( tgtNodes );
+      }
+    } //  // loop on all mesh faces on srcFace
+
     return true;
 
-  } // bool projectBy2DSimilarity(...)
+    // below is projection of a structured source mesh
+
+    // if ( !is1DComputed )
+    //   return false;
+    // for ( int iE = 0; iE < 4; ++iE )
+    // {
+    //   SMESHDS_SubMesh* sm = srcMeshDS->MeshElements( srcWires[0]->Edge( iE ));
+    //   if ( !sm ) return false;
+    //   if ( sm->NbNodes() + sm->NbElements() == 0 ) return false;
+    // }
+    // if ( BRepAdaptor_Surface( tgtFace ).GetType() != GeomAbs_Plane )
+    //   return false;
+    // // if ( BRepAdaptor_Surface( tgtFace ).GetType() == GeomAbs_Plane &&
+    // //      BRepAdaptor_Surface( srcFace ).GetType() == GeomAbs_Plane )
+    // //   return false; // too easy
+
+    // // load EDGEs to SMESH_Block
+
+    // SMESH_Block block;
+    // TopTools_IndexedMapOfOrientedShape blockSubShapes;
+    // {
+    //   const TopoDS_Solid& box = srcMesh->PseudoShape();
+    //   TopoDS_Shell shell = TopoDS::Shell( TopExp_Explorer( box, TopAbs_SHELL ).Current() );
+    //   TopoDS_Vertex v;
+    //   block.LoadBlockShapes( shell, v, v, blockSubShapes ); // fill all since operator[] is missing
+    // }
+    // const SMESH_Block::TShapeID srcFaceBID = SMESH_Block::ID_Fxy0;
+    // const SMESH_Block::TShapeID tgtFaceBID = SMESH_Block::ID_Fxy1;
+    // vector< int > edgeBID;
+    // block.GetFaceEdgesIDs( srcFaceBID, edgeBID ); // u0, u1, 0v, 1v
+    // blockSubShapes.Substitute( edgeBID[0], srcWires[0]->Edge(0) );
+    // blockSubShapes.Substitute( edgeBID[1], srcWires[0]->Edge(2) );
+    // blockSubShapes.Substitute( edgeBID[2], srcWires[0]->Edge(3) );
+    // blockSubShapes.Substitute( edgeBID[3], srcWires[0]->Edge(1) );
+    // block.GetFaceEdgesIDs( tgtFaceBID, edgeBID ); // u0, u1, 0v, 1v
+    // blockSubShapes.Substitute( edgeBID[0], tgtWires[0]->Edge(0) );
+    // blockSubShapes.Substitute( edgeBID[1], tgtWires[0]->Edge(2) );
+    // blockSubShapes.Substitute( edgeBID[2], tgtWires[0]->Edge(3) );
+    // blockSubShapes.Substitute( edgeBID[3], tgtWires[0]->Edge(1) );
+    // block.LoadFace( srcFace, srcFaceBID, blockSubShapes );
+    // block.LoadFace( tgtFace, tgtFaceBID, blockSubShapes );
+
+    // // remember connectivity of new faces in terms of ( node-or-XY )
+
+    // typedef std::pair< const SMDS_MeshNode*, gp_XYZ > TNodeOrXY; // node-or-XY
+    // typedef std::vector< TNodeOrXY* >                 TFaceConn; // face connectivity
+    // std::vector< TFaceConn >                    newFacesVec;     // connectivity of all faces
+    // std::map< const SMDS_MeshNode*, TNodeOrXY > srcNode2tgtNXY;  // src node -> node-or-XY
+
+    // TAssocTool::TNodeNodeMap::iterator                                       srcN_tgtN;
+    // std::map< const SMDS_MeshNode*, TNodeOrXY >::iterator                    srcN_tgtNXY;
+    // std::pair< std::map< const SMDS_MeshNode*, TNodeOrXY >::iterator, bool > n2n_isNew;
+    // TNodeOrXY nullNXY( (SMDS_MeshNode*)NULL, gp_XYZ(0,0,0) );
+
+    // SMESHDS_SubMesh* srcSubDS = srcMeshDS->MeshElements( srcFace );
+    // newFacesVec.resize( srcSubDS->NbElements() );
+    // int iFaceSrc = 0;
+
+    // SMDS_ElemIteratorPtr elemIt = srcSubDS->GetElements();
+    // while ( elemIt->more() ) // loop on all mesh faces on srcFace
+    // {
+    //   const SMDS_MeshElement* elem = elemIt->next();
+    //   TFaceConn& tgtNodes = newFacesVec[ iFaceSrc++ ];
+
+    //   const int nbN = elem->NbCornerNodes();
+    //   tgtNodes.resize( nbN );
+    //   for ( int i = 0; i < nbN; ++i ) // loop on nodes of the source element
+    //   {
+    //     const SMDS_MeshNode* srcNode = elem->GetNode(i);
+    //     n2n_isNew = srcNode2tgtNXY.insert( make_pair( srcNode, nullNXY ));
+    //     TNodeOrXY & tgtNodeOrXY = n2n_isNew.first->second;
+    //     if ( n2n_isNew.second ) // new src node encounters
+    //     {
+    //       srcN_tgtN = src2tgtNodes.find( srcNode );
+    //       if ( srcN_tgtN != src2tgtNodes.end() )
+    //       {
+    //         tgtNodeOrXY.first = srcN_tgtN->second; // tgt node exists
+    //       }
+    //       else
+    //       {
+    //         // find XY of src node within the quadrilateral srcFace
+    //         if ( !block.ComputeParameters( SMESH_TNodeXYZ( srcNode ),
+    //                                        tgtNodeOrXY.second, srcFaceBID ))
+    //           return false;
+    //       }
+    //     }
+    //     tgtNodes[ i ] = & tgtNodeOrXY;
+    //   }
+    // }
+
+    // // as all XY are computed, create tgt nodes and faces
+
+    // SMESH_MesherHelper helper = *tgtWires[0]->FaceHelper();
+    // if ( is1DComputed )
+    //   helper.IsQuadraticSubMesh( tgtFace );
+    // else
+    //   helper.SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
+    // helper.SetElementsOnShape( true );
+    // Handle(Geom_Surface) tgtSurface = BRep_Tool::Surface( tgtFace );
+
+    // SMESH_MesherHelper srcHelper = *srcWires[0]->FaceHelper();
+
+    // vector< const SMDS_MeshNode* > tgtNodes;
+    // gp_XY uv;
+
+    // for ( size_t iFaceTgt = 0; iFaceTgt < newFacesVec.size(); ++iFaceTgt )
+    // {
+    //   TFaceConn& tgtConn = newFacesVec[ iFaceTgt ];
+    //   tgtNodes.resize( tgtConn.size() );
+    //   for ( size_t iN = 0; iN < tgtConn.size(); ++iN )
+    //   {
+    //     const SMDS_MeshNode* & tgtN = tgtConn[ iN ]->first;
+    //     if ( !tgtN ) // create a node
+    //     {
+    //       if ( !block.FaceUV( tgtFaceBID, tgtConn[iN]->second, uv ))
+    //         return false;
+    //       gp_Pnt p = tgtSurface->Value( uv.X(), uv.Y() );
+    //       tgtN = helper.AddNode( p.X(), p.Y(), p.Z(), uv.X(), uv.Y() );
+    //     }
+    //     tgtNodes[ tgtNodes.size() - iN - 1] = tgtN; // reversed orientation
+    //   }
+    //   switch ( tgtNodes.size() )
+    //   {
+    //   case 3: helper.AddFace(tgtNodes[0], tgtNodes[1], tgtNodes[2]); break;
+    //   case 4: helper.AddFace(tgtNodes[0], tgtNodes[1], tgtNodes[2], tgtNodes[3]); break;
+    //   default:
+    //     if ( tgtNodes.size() > 4 )
+    //       helper.AddPolygonalFace( tgtNodes );
+    //   }
+    // }
+    return false; //true;
+
+  } // bool projectQuads(...)
 
   //================================================================================
   /*!
@@ -931,7 +1510,7 @@ namespace {
   {
     SMESH_subMesh* faceSM = helper.GetMesh()->GetSubMesh( helper.GetSubShape() );
 
-    if ( helper.IsDistorted2D( faceSM, /*checkUV=*/false ))
+    //if ( helper.IsDistorted2D( faceSM, /*checkUV=*/true ))
     {
       SMESH_MeshEditor editor( helper.GetMesh() );
       SMESHDS_SubMesh* smDS = faceSM->GetSubMeshDS();
@@ -977,6 +1556,468 @@ namespace {
     return true;
   }
 
+  //=======================================================================
+  /*
+   * Set initial association of VERTEXes for the case of projection
+   * from a quadrangle FACE to a closed FACE, where opposite src EDGEs
+   * have different nb of segments
+   */
+  //=======================================================================
+
+  void initAssoc4Quad2Closed(const TopoDS_Shape&          tgtFace,
+                             SMESH_MesherHelper&          tgtHelper,
+                             const TopoDS_Shape&          srcFace,
+                             SMESH_Mesh*                  srcMesh,
+                             TAssocTool::TShapeShapeMap & assocMap)
+  {
+    if ( !tgtHelper.HasRealSeam() || srcFace.ShapeType() != TopAbs_FACE )
+      return; // no seam edge
+    list< TopoDS_Edge > tgtEdges, srcEdges;
+    list< int > tgtNbEW, srcNbEW;
+    int tgtNbW = SMESH_Block::GetOrderedEdges( TopoDS::Face( tgtFace ), tgtEdges, tgtNbEW );
+    int srcNbW = SMESH_Block::GetOrderedEdges( TopoDS::Face( srcFace ), srcEdges, srcNbEW );
+    if ( tgtNbW != 1 || srcNbW != 1 ||
+         tgtNbEW.front() != 4 || srcNbEW.front() != 4 )
+      return; // not quads
+
+    smIdType srcNbSeg[4];
+    list< TopoDS_Edge >::iterator edgeS = srcEdges.begin(), edgeT = tgtEdges.begin();
+    for ( int i = 0; edgeS != srcEdges.end(); ++i, ++edgeS )
+      if ( SMESHDS_SubMesh* sm = srcMesh->GetMeshDS()->MeshElements( *edgeS ))
+        srcNbSeg[ i ] = sm->NbNodes();
+      else
+        return; // not meshed
+    if ( srcNbSeg[0] == srcNbSeg[2] && srcNbSeg[1] == srcNbSeg[3] )
+      return; // same nb segments
+    if ( srcNbSeg[0] != srcNbSeg[2] && srcNbSeg[1] != srcNbSeg[3] )
+      return; // all different nb segments
+
+    edgeS = srcEdges.begin();
+    if ( srcNbSeg[0] != srcNbSeg[2] )
+      ++edgeS;
+    TAssocTool::InsertAssociation( tgtHelper.IthVertex( 0,*edgeT ),
+                                   tgtHelper.IthVertex( 0,*edgeS ), assocMap );
+    TAssocTool::InsertAssociation( tgtHelper.IthVertex( 1,*edgeT ),
+                                   tgtHelper.IthVertex( 1,*edgeS ), assocMap );
+  }
+
+  //================================================================================
+  /*!
+   * \brief Find sub-shape association such that corresponding VERTEXes of
+   *        two corresponding FACEs lie on lines parallel to thePiercingLine
+   */
+  //================================================================================
+
+  bool findSubShapeAssociationByPiercing( const TopoDS_Face&          theTgtFace,
+                                          SMESH_Mesh *                /*theTgtMesh*/,
+                                          const TopoDS_Shape&         theSrcShape,
+                                          SMESH_Mesh*                 theSrcMesh,
+                                          TAssocTool::TShapeShapeMap& theShape2ShapeMap,
+                                          Handle(Geom_Line) &         thePiercingLine )
+  {
+    list< TopoDS_Edge > tgtEdges, srcEdges;
+    list< int > tgtNbEW, srcNbEW;
+    int tgtNbW = SMESH_Block::GetOrderedEdges( TopoDS::Face( theTgtFace ), tgtEdges, tgtNbEW );
+
+    TopTools_IndexedMapOfShape tgtVV, srcVV;
+    for ( const TopoDS_Edge& tgtEdge : tgtEdges )
+      tgtVV.Add( SMESH_MesherHelper::IthVertex( 0, tgtEdge ));
+    // if ( tgtVV.Size() < 2 )
+    //   return false;
+
+    const int       nbVV = tgtVV.Size();
+    const gp_Pnt   tgtP0 = BRep_Tool::Pnt( TopoDS::Vertex( tgtVV( 1 )));
+    double minVertexDist = Precision::Infinite(), assocTol;
+    gp_Lin      piercingLine;
+    TopoDS_Face assocSrcFace;
+    double      tol;
+
+    for ( TopExp_Explorer faceExp( theSrcShape, TopAbs_FACE ); faceExp.More(); faceExp.Next())
+    {
+      const TopoDS_Face& srcFace = TopoDS::Face( faceExp.Current() );
+
+      int srcNbW = SMESH_Block::GetOrderedEdges( srcFace, srcEdges, srcNbEW );
+      if ( tgtNbW != srcNbW )
+        continue;
+
+      srcVV.Clear( false );
+      for ( const TopoDS_Edge& srcEdge : srcEdges )
+        srcVV.Add( SMESH_MesherHelper::IthVertex( 0, srcEdge ));
+      if ( srcVV.Extent() != tgtVV.Extent() )
+        continue;
+
+      // make srcFace computed
+      SMESH_subMesh* srcFaceSM = theSrcMesh->GetSubMesh( srcFace );
+      if ( !TAssocTool::MakeComputed( srcFaceSM ))
+        continue;
+
+      // compute tolerance
+      double sumLen = 0, nbEdges = 0;
+      for ( const TopoDS_Edge& srcEdge : srcEdges )
+      {
+        SMESH_subMesh* srcSM = theSrcMesh->GetSubMesh( srcEdge );
+        if ( !srcSM->GetSubMeshDS() )
+          continue;
+        SMDS_ElemIteratorPtr edgeIt = srcSM->GetSubMeshDS()->GetElements();
+        while ( edgeIt->more() )
+        {
+          const SMDS_MeshElement* edge = edgeIt->next();
+          sumLen += SMESH_NodeXYZ( edge->GetNode( 0 )).Distance( edge->GetNode( 1 ));
+          nbEdges += 1;
+        }
+      }
+      if ( nbEdges == 0 )
+        continue;
+
+      tol = 0.1 * sumLen / nbEdges;
+
+      // try to find corresponding VERTEXes
+
+      gp_Lin line;
+      double vertexDist;
+      for ( int iSrcV0 = 1; iSrcV0 <= srcVV.Size(); ++iSrcV0 )
+      {
+        const gp_Pnt srcP0 = BRep_Tool::Pnt( TopoDS::Vertex( srcVV( iSrcV0 )));
+        try {
+          line.SetDirection( gp_Vec( srcP0, tgtP0 ));
+        }
+        catch (...) {
+          continue;
+        }
+        bool correspond;
+        for ( int iDir : { -1, 1 }) // move connected VERTEX forward and backward
+        {
+          correspond = true;
+          vertexDist = 0;
+          int iTgtV = 0, iSrcV = iSrcV0 - 1;
+          for ( int i = 1; i < tgtVV.Size() &&   correspond; ++i )
+          {
+            iTgtV = ( iTgtV + 1           ) % nbVV;
+            iSrcV = ( iSrcV + iDir + nbVV ) % nbVV;
+            gp_Pnt tgtP = BRep_Tool::Pnt( TopoDS::Vertex( tgtVV( iTgtV + 1 )));
+            gp_Pnt srcP = BRep_Tool::Pnt( TopoDS::Vertex( srcVV( iSrcV + 1 )));
+            line.SetLocation( tgtP );
+            correspond = ( line.SquareDistance( srcP ) < tol * tol );
+            vertexDist += tgtP.SquareDistance( srcP );
+          }
+          if ( correspond )
+            break;
+        }
+        if ( correspond )
+        {
+          if ( vertexDist < minVertexDist )
+          {
+            minVertexDist = vertexDist;
+            piercingLine    = line;
+            assocSrcFace  = srcFace;
+            assocTol      = tol;
+          }
+          break;
+        }
+      }
+      continue;
+
+    } // loop on src FACEs
+
+    if ( Precision::IsInfinite( minVertexDist ))
+      return false; // no correspondence found
+
+    thePiercingLine = new Geom_Line( piercingLine );
+
+    // fill theShape2ShapeMap
+
+    TAssocTool::InsertAssociation( theTgtFace, assocSrcFace, theShape2ShapeMap );
+
+    for ( const TopoDS_Shape& tgtV : tgtVV ) // fill theShape2ShapeMap with VERTEXes
+    {
+      gp_Pnt tgtP = BRep_Tool::Pnt( TopoDS::Vertex( tgtV ));
+      piercingLine.SetLocation( tgtP );
+      bool found = false;
+      for ( const TopoDS_Shape& srcV : srcVV )
+      {
+        gp_Pnt srcP = BRep_Tool::Pnt( TopoDS::Vertex( srcV ));
+        if ( piercingLine.SquareDistance( srcP ) < assocTol * assocTol )
+        {
+          TAssocTool::InsertAssociation( tgtV, srcV, theShape2ShapeMap );
+          found = true;
+          break;
+        }
+      }
+      if ( !found )
+        return false;
+    }
+
+    TopoDS_Vertex vvT[2], vvS[2], vvMapped[2];
+    for ( const TopoDS_Edge& tgtEdge : tgtEdges ) // fill theShape2ShapeMap with EDGEs
+    {
+      if ( SMESH_Algo::isDegenerated( tgtEdge ))
+        continue;
+
+      TopExp::Vertices( tgtEdge, vvT[0], vvT[1], true );
+      if ( !theShape2ShapeMap.IsBound( vvT[0] ) ||
+           !theShape2ShapeMap.IsBound( vvT[1] ))
+        return false;
+
+      vvMapped[0] = TopoDS::Vertex( theShape2ShapeMap( vvT[0] ));
+      vvMapped[1] = TopoDS::Vertex( theShape2ShapeMap( vvT[1] ));
+
+      bool found = false;
+      for ( TopExp_Explorer eExp( assocSrcFace, TopAbs_EDGE ); eExp.More(); eExp.Next())
+      {
+        TopoDS_Edge srcEdge = TopoDS::Edge( eExp.Current() );
+        TopExp::Vertices( srcEdge, vvS[0], vvS[1], true );
+        found = (( vvMapped[0].IsSame( vvS[0] ) && vvMapped[1].IsSame( vvS[1] )) ||
+                 ( vvMapped[0].IsSame( vvS[1] ) && vvMapped[1].IsSame( vvS[0] )));
+
+        if ( found && nbVV < 3 )
+        {
+          BRepAdaptor_Curve tgtCurve( tgtEdge );
+          gp_Pnt tgtP = tgtCurve.Value( 0.5 * ( tgtCurve.FirstParameter() +
+                                                tgtCurve.LastParameter() ));
+          thePiercingLine->SetLocation( tgtP );
+
+          double f,l;
+          Handle(Geom_Curve) srcCurve = BRep_Tool::Curve( srcEdge, f,l );
+          if ( srcCurve.IsNull() )
+          {
+            found = false;
+            continue;
+          }
+          GeomAPI_ExtremaCurveCurve extrema( thePiercingLine, srcCurve );
+          if ( !extrema.Extrema().IsDone() ||
+               extrema.Extrema().IsParallel() ||
+               extrema.NbExtrema() == 0 ||
+               extrema.LowerDistance() > tol )
+            found = false;
+        }
+        if ( found )
+        {
+          if ( !vvMapped[0].IsSame( vvS[0] ))
+            srcEdge.Reverse();
+          TAssocTool::InsertAssociation( tgtEdge, srcEdge, theShape2ShapeMap );
+          break;
+        }
+      }
+      if ( !found )
+        return false;
+    }
+
+    return true;
+
+  } // findSubShapeAssociationByPiercing()
+
+    //================================================================================
+  /*!
+   * \brief Project by piercing theTgtFace by lines parallel to thePiercingLine
+   */
+  //================================================================================
+
+  bool projectByPiercing(Handle(Geom_Line)                  thePiercingLine,
+                         const TopoDS_Face&                 theTgtFace,
+                         const TopoDS_Face&                 theSrcFace,
+                         const TSideVector&                 theTgtWires,
+                         const TSideVector&                 theSrcWires,
+                         const TAssocTool::TShapeShapeMap&  theShape2ShapeMap,
+                         TAssocTool::TNodeNodeMap&          theSrc2tgtNodes,
+                         const bool                         theIs1DComputed)
+  {
+    SMESH_Mesh * tgtMesh = theTgtWires[0]->GetMesh();
+    SMESH_Mesh * srcMesh = theSrcWires[0]->GetMesh();
+
+    if ( thePiercingLine.IsNull() )
+    {
+      // try to set thePiercingLine by VERTEX association of theShape2ShapeMap
+
+      const double tol = 0.1 * theSrcWires[0]->Length() / theSrcWires[0]->NbSegments();
+
+      for ( TopExp_Explorer vExp( theTgtFace, TopAbs_VERTEX ); vExp.More(); vExp.Next() )
+      {
+        const TopoDS_Vertex & tgtV = TopoDS::Vertex( vExp.Current() );
+        const TopoDS_Vertex & srcV = TopoDS::Vertex( theShape2ShapeMap( tgtV ));
+        gp_Pnt tgtP = BRep_Tool::Pnt( tgtV );
+        gp_Pnt srcP = BRep_Tool::Pnt( srcV );
+        if ( thePiercingLine.IsNull() ) // set thePiercingLine
+        {
+          gp_Lin line;
+          try {
+            line.SetDirection( gp_Vec( srcP, tgtP ));
+            line.SetLocation( tgtP );
+            thePiercingLine = new Geom_Line( line );
+          }
+          catch ( ... )
+          {
+            continue;
+          }
+        }
+        else // check thePiercingLine
+        {
+          thePiercingLine->SetLocation( tgtP );
+          if ( thePiercingLine->Lin().SquareDistance( srcP ) > tol * tol )
+            return false;
+        }
+      }
+
+      for ( TopExp_Explorer eExp( theTgtFace, TopAbs_EDGE ); eExp.More(); eExp.Next() )
+      {
+        BRepAdaptor_Curve tgtCurve( TopoDS::Edge( eExp.Current() ));
+        gp_Pnt tgtP = tgtCurve.Value( 0.5 * ( tgtCurve.FirstParameter() +
+                                              tgtCurve.LastParameter() ));
+        thePiercingLine->SetLocation( tgtP );
+
+        double f,l;
+        TopoDS_Edge srcEdge = TopoDS::Edge( theShape2ShapeMap( eExp.Current() ));
+        Handle(Geom_Curve) srcCurve = BRep_Tool::Curve( srcEdge, f,l );
+        if ( srcCurve.IsNull() )
+          continue;
+        GeomAPI_ExtremaCurveCurve extrema( thePiercingLine, srcCurve,
+                                           -Precision::Infinite(), Precision::Infinite(), f, l );
+        if ( !extrema.Extrema().IsDone() ||
+             extrema.Extrema().IsParallel() ||
+             extrema.NbExtrema() == 0 ||
+             extrema.LowerDistance() > tol )
+          return false;
+      }
+    } // if ( thePiercingLine.IsNull() )
+
+    SMESHDS_SubMesh* srcSubDS = srcMesh->GetMeshDS()->MeshElements( theSrcFace );
+
+    SMESH_MesherHelper* helper = theTgtWires[0]->FaceHelper();
+    if ( theIs1DComputed )
+      helper->IsQuadraticSubMesh( theTgtFace );
+    else
+      helper->SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
+    helper->SetElementsOnShape( true );
+    SMESHDS_Mesh* tgtMeshDS = tgtMesh->GetMeshDS();
+
+    Handle(Geom_Surface)             tgtSurface = BRep_Tool::Surface( theTgtFace );
+#if OCC_VERSION_LARGE < 0x07070000
+    Handle(GeomAdaptor_HSurface) tgtSurfAdaptor = new GeomAdaptor_HSurface( tgtSurface );
+    Handle(GeomAdaptor_HCurve)    piercingCurve = new GeomAdaptor_HCurve( thePiercingLine );
+#else
+    Handle(GeomAdaptor_Surface) tgtSurfAdaptor = new GeomAdaptor_Surface( tgtSurface );
+    Handle(GeomAdaptor_Curve)    piercingCurve = new GeomAdaptor_Curve( thePiercingLine );
+#endif
+    IntCurveSurface_HInter intersect;
+
+    SMESH_MesherHelper* srcHelper = theSrcWires[0]->FaceHelper();
+
+    const SMDS_MeshNode* nullNode = 0;
+    TAssocTool::TNodeNodeMap::iterator srcN_tgtN;
+    vector< const SMDS_MeshNode* > tgtNodes;
+
+    SMDS_ElemIteratorPtr elemIt = srcSubDS->GetElements();
+    while ( elemIt->more() ) // loop on all mesh faces on srcFace
+    {
+      const SMDS_MeshElement* elem = elemIt->next();
+      const int nbN = elem->NbCornerNodes();
+      tgtNodes.resize( nbN );
+      for ( int i = 0; i < nbN; ++i ) // loop on nodes of the source element
+      {
+        const SMDS_MeshNode* srcNode = elem->GetNode(i);
+        srcN_tgtN = theSrc2tgtNodes.insert( make_pair( srcNode, nullNode )).first;
+        if ( srcN_tgtN->second == nullNode )
+        {
+          // create a new node
+          thePiercingLine->SetLocation( SMESH_NodeXYZ( srcNode ));
+          intersect.Perform( piercingCurve, tgtSurfAdaptor );
+          bool pierced = ( intersect.IsDone() && intersect.NbPoints() > 0 );
+          double U, V;
+          const SMDS_MeshNode* n = nullNode;
+          if ( pierced )
+          {
+            double W, minW = Precision::Infinite();
+            gp_Pnt tgtP;
+            for ( int iInt = 1; iInt <= intersect.NbPoints(); ++iInt )
+            {
+              W = intersect.Point( iInt ).W();
+              if ( 0 < W && W < minW )
+              {
+                U    = intersect.Point( iInt ).U();
+                V    = intersect.Point( iInt ).V();
+                tgtP = intersect.Point( iInt ).Pnt();
+                minW = W;
+              }
+            }
+            n = tgtMeshDS->AddNode( tgtP.X(), tgtP.Y(), tgtP.Z() );
+          }
+
+          SMDS_TypeOfPosition shapeType = srcNode->GetPosition()->GetTypeOfPosition();
+          TopoDS_Shape        srcShape;
+          if ( shapeType != SMDS_TOP_FACE )
+          {
+            srcShape = srcHelper->GetSubShapeByNode( srcNode, srcHelper->GetMeshDS() );
+            if ( !theShape2ShapeMap.IsBound( srcShape, /*isSrc=*/true ))
+            {
+              if ( n )  // INTERNAL shape w/o corresponding target shape (3D_mesh_Extrusion_02/E0)
+                shapeType = SMDS_TOP_FACE;
+              else
+                return false;
+            }
+          }
+
+          switch ( shapeType )
+          {
+          case SMDS_TOP_FACE: {
+            if ( !n )
+              return false;
+            tgtMeshDS->SetNodeOnFace( n, helper->GetSubShapeID(), U, V );
+            break;
+          }
+          case SMDS_TOP_EDGE: {
+            TopoDS_Edge  tgtEdge = TopoDS::Edge( theShape2ShapeMap( srcShape, /*isSrc=*/true ));
+            if ( n )
+            {
+              U = Precision::Infinite();
+              helper->CheckNodeU( tgtEdge, n, U, Precision::PConfusion());
+            }
+            else
+            {
+              Handle(Geom_Curve) tgtCurve = BRep_Tool::Curve( tgtEdge, U,V );
+              if ( tgtCurve.IsNull() )
+                return false;
+              GeomAPI_ExtremaCurveCurve extrema( thePiercingLine, tgtCurve );
+              if ( !extrema.Extrema().IsDone() ||
+                   extrema.Extrema().IsParallel() ||
+                   extrema.NbExtrema() == 0 )
+                return false;
+              gp_Pnt pOnLine, pOnEdge;
+              extrema.NearestPoints( pOnLine, pOnEdge );
+              extrema.LowerDistanceParameters( V, U );
+              n = tgtMeshDS->AddNode( pOnEdge.X(), pOnEdge.Y(), pOnEdge.Z() );
+            }
+            tgtMeshDS->SetNodeOnEdge( n, tgtEdge, U );
+            break;
+          }
+          case SMDS_TOP_VERTEX: {
+            TopoDS_Shape tgtV = theShape2ShapeMap( srcShape, /*isSrc=*/true );
+            if ( !n )
+            {
+              gp_Pnt tgtP = BRep_Tool::Pnt( TopoDS::Vertex( tgtV ));
+              n = tgtMeshDS->AddNode( tgtP.X(), tgtP.Y(), tgtP.Z() );
+            }
+            tgtMeshDS->SetNodeOnVertex( n, TopoDS::Vertex( tgtV ));
+            break;
+          }
+          default:;
+          }
+          srcN_tgtN->second = n;
+        }
+        tgtNodes[i] = srcN_tgtN->second;
+      }
+      // create a new face (with reversed orientation)
+      switch ( nbN )
+      {
+      case 3: helper->AddFace(tgtNodes[0], tgtNodes[2], tgtNodes[1]); break;
+      case 4: helper->AddFace(tgtNodes[0], tgtNodes[3], tgtNodes[2], tgtNodes[1]); break;
+      }
+    }  // loop on all mesh faces on srcFace
+
+    return true;
+
+  } // projectByPiercing()
+
+
+
 } // namespace
 
 
@@ -989,7 +2030,6 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
 {
   _src2tgtNodes.clear();
 
-  MESSAGE("Projection_2D Compute");
   if ( !_sourceHypo )
     return false;
 
@@ -999,6 +2039,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     srcMesh = tgtMesh;
 
   SMESHDS_Mesh * meshDS = theMesh.GetMeshDS();
+  SMESH_MesherHelper helper( theMesh );
 
   // ---------------------------
   // Make sub-shapes association
@@ -1007,22 +2048,35 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
   TopoDS_Face   tgtFace = TopoDS::Face( theShape.Oriented(TopAbs_FORWARD));
   TopoDS_Shape srcShape = _sourceHypo->GetSourceFace().Oriented(TopAbs_FORWARD);
 
+  helper.SetSubShape( tgtFace );
+
   TAssocTool::TShapeShapeMap shape2ShapeMap;
   TAssocTool::InitVertexAssociation( _sourceHypo, shape2ShapeMap );
+  if ( shape2ShapeMap.IsEmpty() )
+    initAssoc4Quad2Closed( tgtFace, helper, srcShape, srcMesh, shape2ShapeMap );
+
+  Handle(Geom_Line) piercingLine;
+  bool piercingTried = false;
+
   if ( !TAssocTool::FindSubShapeAssociation( tgtFace, tgtMesh, srcShape, srcMesh,
                                              shape2ShapeMap)  ||
        !shape2ShapeMap.IsBound( tgtFace ))
   {
-    if ( srcShape.ShapeType() == TopAbs_FACE )
+    piercingTried = true;
+    if ( !findSubShapeAssociationByPiercing( tgtFace, tgtMesh, srcShape, srcMesh,
+                                             shape2ShapeMap, piercingLine ))
     {
-      int nbE1 = SMESH_MesherHelper::Count( tgtFace, TopAbs_EDGE, /*ignoreSame=*/true );
-      int nbE2 = SMESH_MesherHelper::Count( srcShape, TopAbs_EDGE, /*ignoreSame=*/true );
-      if ( nbE1 != nbE2 )
-        return error(COMPERR_BAD_SHAPE,
-                     SMESH_Comment("Different number of edges in source and target faces: ")
-                     << nbE2 << " and " << nbE1 );
+      if ( srcShape.ShapeType() == TopAbs_FACE )
+      {
+        int nbE1 = helper.Count( tgtFace, TopAbs_EDGE, /*ignoreSame=*/true );
+        int nbE2 = helper.Count( srcShape, TopAbs_EDGE, /*ignoreSame=*/true );
+        if ( nbE1 != nbE2 )
+          return error(COMPERR_BAD_SHAPE,
+                       SMESH_Comment("Different number of edges in source and target faces: ")
+                       << nbE2 << " and " << nbE1 );
+      }
+      return error(COMPERR_BAD_SHAPE,"Topology of source and target faces seems different" );
     }
-    return error(COMPERR_BAD_SHAPE,"Topology of source and target faces seems different" );
   }
   TopoDS_Face srcFace = TopoDS::Face( shape2ShapeMap( tgtFace ).Oriented(TopAbs_FORWARD));
 
@@ -1052,13 +2106,20 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
   // get ordered src and tgt EDGEs
   TSideVector srcWires, tgtWires;
   bool is1DComputed = false; // if any tgt EDGE is meshed
-  TError err = getWires( tgtFace, srcFace, tgtMesh, srcMesh,
+  TError err = getWires( tgtFace, srcFace, tgtMesh, srcMesh, &helper,
                          shape2ShapeMap, srcWires, tgtWires, _src2tgtNodes, is1DComputed );
   if ( err && !err->IsOK() )
     return error( err );
 
   bool projDone = false;
 
+  if ( !projDone && !piercingLine.IsNull() )
+  {
+    // project by piercing tgtFace by lines parallel to piercingLine
+    projDone = projectByPiercing( piercingLine, tgtFace, srcFace, tgtWires, srcWires,
+                                  shape2ShapeMap, _src2tgtNodes, is1DComputed );
+    piercingTried = true;
+  }
   if ( !projDone )
   {
     // try to project from the same face with different location
@@ -1069,11 +2130,20 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
   {
     // projection in case if the faces are similar in 2D space
     projDone = projectBy2DSimilarity( tgtFace, srcFace, tgtWires, srcWires,
-                                      shape2ShapeMap, _src2tgtNodes, is1DComputed);
+                                      shape2ShapeMap, _src2tgtNodes, is1DComputed );
+  }
+  if ( !projDone )
+  {
+    // projection in case of quadrilateral faces
+    projDone = projectQuads( tgtFace, srcFace, tgtWires, srcWires,
+                             shape2ShapeMap, _src2tgtNodes, is1DComputed);
+  }
+  if ( !projDone && !piercingTried )
+  {
+    // project by piercing tgtFace by lines parallel to piercingLine
+    projDone = projectByPiercing( piercingLine, tgtFace, srcFace, tgtWires, srcWires,
+                                  shape2ShapeMap, _src2tgtNodes, is1DComputed );
   }
-
-  SMESH_MesherHelper helper( theMesh );
-  helper.SetSubShape( tgtFace );
 
   // it will remove mesh built on edges and vertices in failure case
   MeshCleaner cleaner( tgtSubMesh );
@@ -1082,26 +2152,28 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
   {
     _src2tgtNodes.clear();
     // --------------------
-    // Prepare to mapping 
+    // Prepare to mapping
     // --------------------
 
     // Check if node projection to a face is needed
     Bnd_B2d uvBox;
     SMDS_ElemIteratorPtr faceIt = srcSubMesh->GetSubMeshDS()->GetElements();
-    int nbFaceNodes = 0;
-    for ( ; nbFaceNodes < 3 && faceIt->more();  ) {
+    set< const SMDS_MeshNode* > faceNodes;
+    for ( ; faceNodes.size() < 3 && faceIt->more();  ) {
       const SMDS_MeshElement* face = faceIt->next();
       SMDS_ElemIteratorPtr nodeIt = face->nodesIterator();
       while ( nodeIt->more() ) {
         const SMDS_MeshNode* node = static_cast<const SMDS_MeshNode*>( nodeIt->next() );
-        if ( node->GetPosition()->GetTypeOfPosition() == SMDS_TOP_FACE ) {
-          nbFaceNodes++;
+        if ( node->GetPosition()->GetTypeOfPosition() == SMDS_TOP_FACE &&
+             faceNodes.insert( node ).second )
           uvBox.Add( helper.GetNodeUV( srcFace, node ));
-        }
       }
     }
-    const bool toProjectNodes =
-      ( nbFaceNodes > 0 && ( uvBox.IsVoid() || uvBox.SquareExtent() < DBL_MIN ));
+    bool toProjectNodes = false;
+    if ( faceNodes.size() == 1 )
+      toProjectNodes = ( uvBox.IsVoid() || uvBox.CornerMin().IsEqual( gp_XY(0,0), 1e-12 ));
+    else if ( faceNodes.size() > 1 )
+      toProjectNodes = ( uvBox.IsVoid() || uvBox.SquareExtent() < DBL_MIN );
 
     // Find the corresponding source and target vertex
     // and <theReverse> flag needed to call mapper.Apply()
@@ -1109,13 +2181,10 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     TopoDS_Vertex srcV1, tgtV1;
     bool reverse = false;
 
-    if ( _sourceHypo->HasVertexAssociation() ) {
-      srcV1 = _sourceHypo->GetSourceVertex(1);
-      tgtV1 = _sourceHypo->GetTargetVertex(1);
-    } else {
-      srcV1 = TopoDS::Vertex( TopExp_Explorer( srcFace, TopAbs_VERTEX ).Current() );
-      tgtV1 = TopoDS::Vertex( shape2ShapeMap( srcV1, /*isSrc=*/true ));
-    }
+    TopExp_Explorer vSrcExp( srcFace, TopAbs_VERTEX );
+    srcV1 = TopoDS::Vertex( vSrcExp.Current() );
+    tgtV1 = TopoDS::Vertex( shape2ShapeMap( srcV1, /*isSrc=*/true ));
+
     list< TopoDS_Edge > tgtEdges, srcEdges;
     list< int > nbEdgesInWires;
     SMESH_Block::GetOrderedEdges( tgtFace, tgtEdges, nbEdgesInWires, tgtV1 );
@@ -1126,29 +2195,94 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
       TopoDS_Edge srcE1 = srcEdges.front(), tgtE1 = tgtEdges.front();
       TopoDS_Shape srcE1bis = shape2ShapeMap( tgtE1 );
       reverse = ( ! srcE1.IsSame( srcE1bis ));
-      if ( reverse &&
-           _sourceHypo->HasVertexAssociation() &&
+      if ( ( reverse || srcE1.Orientation() != srcE1bis.Orientation() ) &&
            nbEdgesInWires.front() > 2 &&
            helper.IsRealSeam( tgtEdges.front() ))
       {
+        if ( srcE1.Orientation() != srcE1bis.Orientation() )
+          reverse = true;
         // projection to a face with seam EDGE; pb is that GetOrderedEdges()
         // always puts a seam EDGE first (if possible) and as a result
         // we can't use only theReverse flag to correctly associate source
         // and target faces in the mapper. Thus we select srcV1 so that
         // GetOrderedEdges() to return EDGEs in a needed order
-        list< TopoDS_Edge >::iterator edge = srcEdges.begin();
-        for ( ; edge != srcEdges.end(); ++edge ) {
-          if ( srcE1bis.IsSame( *edge )) {
-            srcV1 = helper.IthVertex( 0, *edge );
-            break;
+        TopoDS_Face tgtFaceBis = tgtFace;
+        TopTools_MapOfShape checkedVMap( tgtEdges.size() );
+        checkedVMap.Add ( srcV1 );
+        for ( vSrcExp.Next(); vSrcExp.More(); )
+        {
+          tgtFaceBis.Reverse();
+          tgtEdges.clear();
+          SMESH_Block::GetOrderedEdges( tgtFaceBis, tgtEdges, nbEdgesInWires, tgtV1 );
+          bool ok = true;
+          list< TopoDS_Edge >::iterator edgeS = srcEdges.begin(), edgeT = tgtEdges.begin();
+          for ( ; edgeS != srcEdges.end() && ok ; ++edgeS, ++edgeT )
+            ok = edgeT->IsSame( shape2ShapeMap( *edgeS, /*isSrc=*/true ));
+          if ( ok )
+            break; // FOUND!
+
+          reverse = !reverse;
+          if ( reverse )
+          {
+            vSrcExp.Next();
+            while ( vSrcExp.More() && !checkedVMap.Add( vSrcExp.Current() ))
+              vSrcExp.Next();
+          }
+          else
+          {
+            srcV1 = TopoDS::Vertex( vSrcExp.Current() );
+            tgtV1 = TopoDS::Vertex( shape2ShapeMap( srcV1, /*isSrc=*/true ));
+            srcEdges.clear();
+            SMESH_Block::GetOrderedEdges( srcFace, srcEdges, nbEdgesInWires, srcV1 );
+          }
+        }
+      }
+      // for the case: project to a closed face from a non-closed face w/o vertex assoc;
+      // avoid projecting to a seam from two EDGEs with different nb nodes on them
+      // ( test mesh_Projection_2D_01/B1 )
+      if ( !_sourceHypo->HasVertexAssociation() &&
+           nbEdgesInWires.front() > 2 &&
+           helper.IsRealSeam( tgtEdges.front() ))
+      {
+        TopoDS_Shape srcEdge1 = shape2ShapeMap( tgtEdges.front() );
+        list< TopoDS_Edge >::iterator srcEdge2 =
+          std::find( srcEdges.begin(), srcEdges.end(), srcEdge1);
+        list< TopoDS_Edge >::iterator srcEdge3 =
+          std::find( srcEdges.begin(), srcEdges.end(), srcEdge1.Reversed());
+        if ( srcEdge2 == srcEdges.end() || srcEdge3 == srcEdges.end() ) // srcEdge1 is not a seam
+        {
+          // find srcEdge2 which also will be projected to tgtEdges.front()
+          for ( srcEdge2 = srcEdges.begin(); srcEdge2 != srcEdges.end(); ++srcEdge2 )
+            if ( !srcEdge1.IsSame( *srcEdge2 ) &&
+                 tgtEdges.front().IsSame( shape2ShapeMap( *srcEdge2, /*isSrc=*/true )))
+              break;
+          // compare nb nodes on srcEdge1 and srcEdge2
+          if ( srcEdge2 != srcEdges.end() )
+          {
+            smIdType nbN1 = 0, nbN2 = 0;
+            if ( SMESHDS_SubMesh* sm = srcMesh->GetMeshDS()->MeshElements( srcEdge1 ))
+              nbN1 = sm->NbNodes();
+            if ( SMESHDS_SubMesh* sm = srcMesh->GetMeshDS()->MeshElements( *srcEdge2 ))
+              nbN2 = sm->NbNodes();
+            if ( nbN1 != nbN2 )
+              srcV1 = helper.IthVertex( 1, srcEdges.front() );
           }
         }
       }
     }
-    else if ( nbEdgesInWires.front() == 1 )
+    else if ( nbEdgesInWires.front() == 1 ) // a sole edge in a wire
     {
-      // TODO::Compare orientation of curves in a sole edge
-      //RETURN_BAD_RESULT("Not implemented case");
+      TopoDS_Edge srcE1 = srcEdges.front(), tgtE1 = tgtEdges.front();
+      for ( size_t iW = 0; iW < srcWires.size(); ++iW )
+      {
+        StdMeshers_FaceSidePtr srcWire = srcWires[iW];
+        for ( int iE = 0; iE < srcWire->NbEdges(); ++iE )
+          if ( srcE1.IsSame( srcWire->Edge( iE )))
+          {
+            reverse = ( tgtE1.Orientation() != tgtWires[iW]->Edge( iE ).Orientation() );
+            break;
+          }
+      }
     }
     else
     {
@@ -1157,7 +2291,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
 
     // Load pattern from the source face
     SMESH_Pattern mapper;
-    mapper.Load( srcMesh, srcFace, toProjectNodes, srcV1 );
+    mapper.Load( srcMesh, srcFace, toProjectNodes, srcV1, /*keepNodes=*/true );
     if ( mapper.GetErrorCode() != SMESH_Pattern::ERR_OK )
       return error(COMPERR_BAD_INPUT_MESH,"Can't load mesh pattern from the source face");
 
@@ -1168,8 +2302,11 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     // Compute mesh on a target face
 
     mapper.Apply( tgtFace, tgtV1, reverse );
-    if ( mapper.GetErrorCode() != SMESH_Pattern::ERR_OK )
+    if ( mapper.GetErrorCode() != SMESH_Pattern::ERR_OK ) {
+      // std::ofstream file("/tmp/Pattern.smp" );
+      // mapper.Save( file );
       return error("Can't apply source mesh pattern to the face");
+    }
 
     // Create the mesh
 
@@ -1178,6 +2315,18 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     if ( mapper.GetErrorCode() != SMESH_Pattern::ERR_OK )
       return error("Can't make mesh by source mesh pattern");
 
+    // fill _src2tgtNodes
+    std::vector< const SMDS_MeshNode* > *srcNodes, *tgtNodes;
+    mapper.GetInOutNodes( srcNodes, tgtNodes );
+    size_t nbN = std::min( srcNodes->size(), tgtNodes->size() );
+    for ( size_t i = 0; i < nbN; ++i )
+      if ( (*srcNodes)[i] && (*tgtNodes)[i] )
+        _src2tgtNodes.insert( make_pair( (*srcNodes)[i], (*tgtNodes)[i] ));
+
+
+  } // end of projection using Pattern mapping
+
+  {
     // -------------------------------------------------------------------------
     // mapper doesn't take care of nodes already existing on edges and vertices,
     // so we must merge nodes created by it with existing ones
@@ -1217,7 +2366,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
         continue; // do not treat sm of degen VERTEX
       }
 
-      // Sort new and old nodes of a submesh separately
+      // Sort new and old nodes of a sub-mesh separately
 
       bool isSeam = helper.IsRealSeam( sm->GetId() );
 
@@ -1228,7 +2377,9 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
 
       // mapper changed, no more "mapper puts on a seam edge nodes from 2 edges"
       if ( isSeam && ! getBoundaryNodes ( sm, tgtFace, u2nodesOnSeam, seamNodes ))
-        ;//RETURN_BAD_RESULT("getBoundaryNodes() failed");
+      {
+        //RETURN_BAD_RESULT("getBoundaryNodes() failed");
+      }
 
       SMDS_NodeIteratorPtr nIt = smDS->GetNodes();
       while ( nIt->more() )
@@ -1253,8 +2404,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
           break;
         }
         case  SMDS_TOP_EDGE:   {
-          const SMDS_EdgePosition* pos =
-            static_cast<const SMDS_EdgePosition*>(node->GetPosition());
+          SMDS_EdgePositionPtr pos = node->GetPosition();
           pos2nodes.insert( make_pair( pos->GetUParameter(), node ));
           break;
         }
@@ -1272,7 +2422,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
         if ( u2nodesMaps[ NEW_NODES ].size() > 0 &&
              u2nodesMaps[ OLD_NODES ].size() > 0 )
         {
-          u_oldNode = u2nodesMaps[ OLD_NODES ].begin(); 
+          u_oldNode = u2nodesMaps[ OLD_NODES ].begin();
           newEnd    = u2nodesMaps[ OLD_NODES ].end();
           for ( ; u_oldNode != newEnd; ++u_oldNode )
             SMESH_Algo::addBadInputElement( u_oldNode->second );
@@ -1287,8 +2437,8 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
              u2nodesOnSeam.size()            > 0 &&
              seam.ShapeType() == TopAbs_EDGE )
         {
-          int nbE1 = SMESH_MesherHelper::Count( tgtFace, TopAbs_EDGE, /*ignoreSame=*/true );
-          int nbE2 = SMESH_MesherHelper::Count( srcFace, TopAbs_EDGE, /*ignoreSame=*/true );
+          int nbE1 = helper.Count( tgtFace, TopAbs_EDGE, /*ignoreSame=*/true );
+          int nbE2 = helper.Count( srcFace, TopAbs_EDGE, /*ignoreSame=*/true );
           if ( nbE1 != nbE2 ) // 2 EDGEs are mapped to a seam EDGE
           {
             // find the 2 EDGEs of srcFace
@@ -1305,7 +2455,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
 
       // Make groups of nodes to merge
 
-      u_oldNode = u2nodesMaps[ OLD_NODES ].begin(); 
+      u_oldNode = u2nodesMaps[ OLD_NODES ].begin();
       u_newNode = u2nodesMaps[ NEW_NODES ].begin();
       newEnd    = u2nodesMaps[ NEW_NODES ].end();
       u_newOnSeam = u2nodesOnSeam.begin();
@@ -1331,9 +2481,9 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     // Merge
 
     SMESH_MeshEditor editor( tgtMesh );
-    int nbFaceBeforeMerge = tgtSubMesh->GetSubMeshDS()->NbElements();
+    smIdType nbFaceBeforeMerge = tgtSubMesh->GetSubMeshDS()->NbElements();
     editor.MergeNodes( groupsOfNodes );
-    int nbFaceAtferMerge = tgtSubMesh->GetSubMeshDS()->NbElements();
+    smIdType nbFaceAtferMerge = tgtSubMesh->GetSubMeshDS()->NbElements();
     if ( nbFaceBeforeMerge != nbFaceAtferMerge && !helper.HasDegeneratedEdges() )
       return error(COMPERR_BAD_INPUT_MESH, "Probably invalid node parameters on geom faces");
 
@@ -1341,6 +2491,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     // The mapper can't create quadratic elements, so convert if needed
     // ----------------------------------------------------------------
 
+    SMDS_ElemIteratorPtr faceIt;
     faceIt         = srcSubMesh->GetSubMeshDS()->GetElements();
     bool srcIsQuad = faceIt->next()->IsQuadratic();
     faceIt         = tgtSubMesh->GetSubMeshDS()->GetElements();
@@ -1354,19 +2505,26 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
 
       editor.ConvertToQuadratic(/*theForce3d=*/false, tgtFaces, false);
     }
-
-  } // end of projection using Pattern mapping
+  } // end of coincident nodes and quadratic elements treatment
 
 
   if ( !projDone || is1DComputed )
     // ----------------------------------------------------------------
     // The mapper can create distorted faces by placing nodes out of the FACE
-    // boundary, also bad face can be created if EDGEs already discretized
+    // boundary, also bad faces can be created if EDGEs already discretized
     // --> fix bad faces by smoothing
     // ----------------------------------------------------------------
-    if ( !fixDistortedFaces( helper, tgtWires ))
-      return error("Invalid mesh generated");
-
+    if ( helper.IsDistorted2D( tgtSubMesh, /*checkUV=*/false, &helper ))
+    {
+      TAssocTool::Morph morph( srcWires );
+      morph.Perform( helper, tgtWires, helper.GetSurface( tgtFace ),
+                     _src2tgtNodes, /*moveAll=*/true );
+      if(SALOME::VerbosityActivated())
+        cout << "StdMeshers_Projection_2D: Projection mesh IsDistorted2D() ==> do morph" << endl;
+
+      if ( !fixDistortedFaces( helper, tgtWires )) // smooth and check
+        return error("Invalid mesh generated");
+    }
   // ---------------------------
   // Check elements orientation
   // ---------------------------
@@ -1420,7 +2578,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
 
 //=======================================================================
 //function : Evaluate
-//purpose  : 
+//purpose  :
 //=======================================================================
 
 bool StdMeshers_Projection_2D::Evaluate(SMESH_Mesh&         theMesh,
@@ -1455,7 +2613,7 @@ bool StdMeshers_Projection_2D::Evaluate(SMESH_Mesh&         theMesh,
   // Assure that mesh on a source Face is computed/evaluated
   // -------------------------------------------------------
 
-  std::vector<int> aVec;
+  std::vector<smIdType> aVec;
 
   SMESH_subMesh* srcSubMesh = srcMesh->GetSubMesh( srcFace );
   if ( srcSubMesh->IsMeshComputed() )