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bos #20256: [CEA 18523] Porting SMESH to int 64 bits
[modules/smesh.git] / src / StdMeshers / StdMeshers_Projection_2D.cxx
index b0118c7199c8020693cc5056f2a5f1ccc69ac7d6..bbc874cf9da73bf50d8dbb7a52403027ba958744 100644 (file)
@@ -1,4 +1,4 @@
-// Copyright (C) 2007-2014  CEA/DEN, EDF R&D, OPEN CASCADE
+// Copyright (C) 2007-2021  CEA/DEN, EDF R&D, OPEN CASCADE
 //
 // Copyright (C) 2003-2007  OPEN CASCADE, EADS/CCR, LIP6, CEA/DEN,
 // CEDRAT, EDF R&D, LEG, PRINCIPIA R&D, BUREAU VERITAS
@@ -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 "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_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 <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_HCurve.hxx>
+#include <GeomAdaptor_HSurface.hxx>
+#include <GeomAdaptor_Surface.hxx>
+#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");
@@ -89,7 +118,7 @@ StdMeshers_Projection_2D::~StdMeshers_Projection_2D()
 
 //=======================================================================
 //function : CheckHypothesis
-//purpose  : 
+//purpose  :
 //=======================================================================
 
 bool StdMeshers_Projection_2D::CheckHypothesis(SMESH_Mesh&                          theMesh,
@@ -194,7 +223,7 @@ namespace {
    */
   //================================================================================
 
-  bool isOldNode( const SMDS_MeshNode* node/*, const bool is1DComputed*/ )
+  bool isOldNode( const SMDS_MeshNode* node )
   {
     // old nodes are shared by edges and new ones are shared
     // only by faces created by mapper
@@ -253,7 +282,7 @@ 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
@@ -262,7 +291,7 @@ 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)
   {
@@ -356,8 +385,7 @@ 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 );
       }
@@ -374,227 +402,296 @@ namespace {
 
   //================================================================================
   /*!
-   * \brief Preform projection in case if tgtFace.IsPartner( srcFace ) and in case
-   * if projection by transformation is possible
+   * \brief Check if two consecutive EDGEs are connected in 2D
+   *  \param [in] E1 - a well oriented non-seam EDGE
+   *  \param [in] E2 - a possibly well oriented seam EDGE
+   *  \param [in] F - a FACE
+   *  \return bool - result
    */
   //================================================================================
 
-  bool projectPartner(const TopoDS_Face&                tgtFace,
-                      const TopoDS_Face&                srcFace,
-                      SMESH_Mesh *                      tgtMesh,
-                      SMESH_Mesh *                      srcMesh,
-                      const TAssocTool::TShapeShapeMap& shape2ShapeMap)
+  bool are2dConnected( const TopoDS_Edge & E1,
+                       const TopoDS_Edge & E2,
+                       const TopoDS_Face & F )
   {
-    SMESHDS_Mesh* tgtMeshDS = tgtMesh->GetMeshDS();
-    SMESHDS_Mesh* srcMeshDS = srcMesh->GetMeshDS();
+    double f,l;
+    Handle(Geom2d_Curve) c1 = BRep_Tool::CurveOnSurface( E1, F, f, l );
+    gp_Pnt2d uvFirst1 = c1->Value( f );
+    gp_Pnt2d uvLast1  = c1->Value( l );
 
-    const double tol = 1.e-7 * srcMeshDS->getMaxDim();
+    Handle(Geom2d_Curve) c2 = BRep_Tool::CurveOnSurface( E2, F, f, l );
+    gp_Pnt2d uvFirst2 = c2->Value( E2.Orientation() == TopAbs_REVERSED ? l : f );
+    double tol2 = Max( Precision::PConfusion() * Precision::PConfusion(),
+                       1e-5 * uvLast1.SquareDistance( uvFirst1 ));
 
-    gp_Trsf trsf; // transformation to get location of target nodes from source ones
-    if ( tgtFace.IsPartner( srcFace ))
-    {
-      gp_Trsf srcTrsf = srcFace.Location();
-      gp_Trsf tgtTrsf = tgtFace.Location();
-      trsf = srcTrsf.Inverted() * tgtTrsf;
-    }
-    else
+    return (( uvFirst2.SquareDistance( uvFirst1 ) < tol2 ) ||
+            ( uvFirst2.SquareDistance( uvLast1  ) < tol2 ));
+  }
+
+  //================================================================================
+  /*!
+   * \brief Compose TSideVector for both FACEs keeping matching order of EDGEs
+   *        and fill src2tgtNodes map
+   */
+  //================================================================================
+
+  TError getWires(const TopoDS_Face&                 tgtFace,
+                  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)
+  {
+    src2tgtNodes.clear();
+
+    // get ordered src EDGEs
+    TError err;
+    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 )
     {
-      // Try to find the transformation
-
-      // make any local coord systems of src and tgt faces
-      vector<gp_Pnt> srcPP, tgtPP; // 3 points on face boundaries to make axes of CS
-      int tgtNbVert = SMESH_MesherHelper::Count( tgtFace, TopAbs_VERTEX, /*ignoreSame=*/true );
-      int srcNbVert = SMESH_MesherHelper::Count( srcFace, TopAbs_VERTEX, /*ignoreSame=*/true );
-      SMESH_subMesh *         srcSM = srcMesh->GetSubMesh( srcFace );
-      SMESH_subMeshIteratorPtr smIt = srcSM->getDependsOnIterator(/*includeSelf=*/false,false);
-      srcSM = smIt->next(); // sm of a vertex
-      while ( smIt->more() && srcPP.size() < 3 )
+      StdMeshers_FaceSidePtr srcWire = srcWires[iW];
+
+      list< TopoDS_Edge > tgtEdges;
+      TopTools_IndexedMapOfShape edgeMap; // to detect seam edges
+      for ( int iE = 0; iE < srcWire->NbEdges(); ++iE )
       {
-        srcSM = smIt->next();
-        SMESHDS_SubMesh* srcSmds = srcSM->GetSubMeshDS();
-        if ( !srcSmds ) continue;
-        SMDS_NodeIteratorPtr nIt = srcSmds->GetNodes();
-        while ( nIt->more() )
+        TopoDS_Edge     srcE = srcWire->Edge( iE );
+        TopoDS_Edge     tgtE = TopoDS::Edge( shape2ShapeMap( srcE, /*isSrc=*/true));
+        TopoDS_Shape srcEbis = shape2ShapeMap( tgtE, /*isSrc=*/false );
+        if ( srcE.Orientation() != srcEbis.Orientation() )
+          tgtE.Reverse();
+        // reverse a seam edge encountered for the second time
+        const int index = edgeMap.Add( tgtE );
+        if ( index < edgeMap.Extent() ) // E is a seam
         {
-          SMESH_TNodeXYZ p ( nIt->next());
-          bool pOK = false;
-          switch ( srcPP.size() )
+          // check which of edges to reverse, E or one already being in tgtEdges
+          if ( are2dConnected( tgtEdges.back(), tgtE, tgtFace ))
           {
-          case 0: pOK = true; break;
-
-          case 1: pOK = ( srcPP[0].SquareDistance( p ) > 10*tol ); break;
-            
-          case 2:
-            {
-              gp_Vec p0p1( srcPP[0], srcPP[1] ), p0p( srcPP[0], p );
-              // pOK = !p0p1.IsParallel( p0p, tol );
-              pOK = !p0p1.IsParallel( p0p, 3.14/20 ); // angle min 18 degrees
-              break;
-            }
+            list< TopoDS_Edge >::iterator eIt = tgtEdges.begin();
+            std::advance( eIt, index-1 );
+            if ( are2dConnected( tgtEdges.back(), *eIt, tgtFace ))
+              eIt->Reverse();
           }
-          if ( !pOK )
-            continue;
-
-          // find corresponding point on target shape
-          pOK = false;
-          gp_Pnt tgtP;
-          const TopoDS_Shape& tgtShape = shape2ShapeMap( srcSM->GetSubShape(), /*isSrc=*/true );
-          if ( tgtShape.ShapeType() == TopAbs_VERTEX )
+          else
           {
-            tgtP = BRep_Tool::Pnt( TopoDS::Vertex( tgtShape ));
-            if ( srcNbVert == tgtNbVert || tgtPP.empty() )
-              pOK = true;
-            else
-              pOK = (( tgtP.Distance( tgtPP[0] ) > tol*tol ) &&
-                     ( tgtPP.size() == 1 || tgtP.Distance( tgtPP[1] ) > tol*tol ));
-            //cout << "V - nS " << p._node->GetID() << " - nT " << SMESH_Algo::VertexNode(TopoDS::Vertex( tgtShape),tgtMeshDS)->GetID() << endl;
+            tgtE.Reverse();
           }
-          else if ( tgtPP.size() > 0 )
+        }
+        if ( srcWire->NbEdges() == 1 && tgtMesh == srcMesh ) // circle
+        {
+          // try to verify ori by propagation
+          pair<int,TopoDS_Edge> nE =
+            StdMeshers_ProjectionUtils::GetPropagationEdge( srcMesh, tgtE, srcE );
+          if ( !nE.second.IsNull() )
+            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
+
+      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 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 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() )
           {
-            if ( SMESHDS_SubMesh* tgtSmds = tgtMeshDS->MeshElements( tgtShape ))
+            vector< const SMDS_MeshNode* >::iterator tn = tgtNodes.begin();
+            //if ( srcWire->Edge(iE).Orientation() == tgtWire->Edge(iE).Orientation() )
             {
-              double srcDist = srcPP[0].Distance( p );
-              double eTol = BRep_Tool::Tolerance( TopoDS::Edge( tgtShape ));
-              if (eTol < tol) eTol = tol;
-              SMDS_NodeIteratorPtr nItT = tgtSmds->GetNodes();
-              while ( nItT->more() && !pOK )
-              {
-                const SMDS_MeshNode* n = nItT->next();
-                tgtP = SMESH_TNodeXYZ( n );
-                pOK = ( fabs( srcDist - tgtPP[0].Distance( tgtP )) < 2*eTol );
-                //cout << "E - nS " << p._node->GetID() << " - nT " << n->GetID()<< " OK - " << pOK<< " " << fabs( srcDist - tgtPP[0].Distance( tgtP ))<< " tol " << eTol<< endl;
-              }
+              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;
           }
-          if ( !pOK )
-            continue;
-
-          srcPP.push_back( p );
-          tgtPP.push_back( tgtP );
         }
-      }
-      if ( srcPP.size() != 3 )
-        return false;
+      } // loop on EDGEs of a WIRE
 
-      // make transformation
-      gp_Trsf fromTgtCS, toSrcCS; // from/to global CS
-      gp_Ax2 srcCS( srcPP[0], gp_Vec( srcPP[0], srcPP[1] ), gp_Vec( srcPP[0], srcPP[2]));
-      gp_Ax2 tgtCS( tgtPP[0], gp_Vec( tgtPP[0], tgtPP[1] ), gp_Vec( tgtPP[0], tgtPP[2]));
-      toSrcCS  .SetTransformation( gp_Ax3( srcCS ));
-      fromTgtCS.SetTransformation( gp_Ax3( tgtCS ));
-      fromTgtCS.Invert();
+    } // loop on WIREs
 
-      trsf = fromTgtCS * toSrcCS;
-    }
-
-    // Fill map of src to tgt nodes with nodes on edges
-
-    map<const SMDS_MeshNode* , const SMDS_MeshNode*> src2tgtNodes;
-    map<const SMDS_MeshNode* , const SMDS_MeshNode*>::iterator srcN_tgtN;
+    return TError();
+  }
 
-    bool tgtEdgesMeshed = false;
-    for ( TopExp_Explorer srcExp( srcFace, TopAbs_EDGE); srcExp.More(); srcExp.Next() )
-    {
-      const TopoDS_Shape& srcEdge = srcExp.Current();
-      const TopoDS_Shape& tgtEdge = shape2ShapeMap( srcEdge, /*isSrc=*/true );
-      tgtEdgesMeshed != tgtMesh->GetSubMesh( tgtEdge )->IsEmpty();
+  //================================================================================
+  /*!
+   * \brief Perform projection in case if tgtFace.IsPartner( srcFace ) and in case
+   * if projection by 3D transformation is possible
+   */
+  //================================================================================
 
-      if ( srcMesh->GetSubMesh( srcEdge )->IsEmpty() ||
-           tgtMesh->GetSubMesh( tgtEdge )->IsEmpty() )
-        continue;
+  bool projectPartner(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();
+    SMESH_MesherHelper* helper = tgtWires[0]->FaceHelper();
 
-      map< double, const SMDS_MeshNode* > srcNodes, tgtNodes;
-      if (( ! SMESH_Algo::GetSortedNodesOnEdge( srcMeshDS,
-                                                TopoDS::Edge( srcEdge ),
-                                                /*ignoreMediumNodes = */true,
-                                                srcNodes ))
-           ||
-          ( ! SMESH_Algo::GetSortedNodesOnEdge( tgtMeshDS,
-                                                TopoDS::Edge( tgtEdge ),
-                                                /*ignoreMediumNodes = */true,
-                                                tgtNodes ))
-           ||
-          (( srcNodes.size() != tgtNodes.size() ) && tgtNodes.size() > 0 )
-          )
-        return false;
+    const double tol = 1.e-7 * srcMeshDS->getMaxDim();
 
-      if ( !tgtEdge.IsPartner( srcEdge ))
-      {
-        if ( tgtNodes.empty() )
-          return false;
-        // check that transformation is OK by three nodes
-        gp_Pnt p0S = SMESH_TNodeXYZ( (srcNodes.begin())  ->second);
-        gp_Pnt p1S = SMESH_TNodeXYZ( (srcNodes.rbegin()) ->second);
-        gp_Pnt p2S = SMESH_TNodeXYZ( (++srcNodes.begin())->second);
-
-        gp_Pnt p0T = SMESH_TNodeXYZ( (tgtNodes.begin())  ->second);
-        gp_Pnt p1T = SMESH_TNodeXYZ( (tgtNodes.rbegin()) ->second);
-        gp_Pnt p2T = SMESH_TNodeXYZ( (++tgtNodes.begin())->second);
-
-        // transform source points, they must coincide with target ones
-        if ( p0T.SquareDistance( p0S.Transformed( trsf )) > tol ||
-             p1T.SquareDistance( p1S.Transformed( trsf )) > tol ||
-             p2T.SquareDistance( p2S.Transformed( trsf )) > tol )
-        {
-          //cout << "KO trsf, 3 dist: "
-          //<< p0T.SquareDistance( p0S.Transformed( trsf ))<< ", "
-          //<< p1T.SquareDistance( p1S.Transformed( trsf ))<< ", "
-          //<< p2T.SquareDistance( p2S.Transformed( trsf ))<< ", "<<endl;
-          return false;
-        }
-      }
-      if ( !tgtNodes.empty() )
+    // transformation to get location of target nodes from source ones
+    StdMeshers_ProjectionUtils::TrsfFinder3D trsf;
+    bool trsfIsOK = false;
+    if ( tgtFace.IsPartner( srcFace ))
+    {
+      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() );
+      trsfIsOK = ( tgtP.Distance( trsf.Transform( srcP )) < tol );
+      if ( !trsfIsOK )
       {
-        map< double, const SMDS_MeshNode* >::iterator u_tn = tgtNodes.begin();
-        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 ));
+        trsf.Set( tgtTrsf.Inverted().Multiplied( srcTrsf ));
+        trsfIsOK = ( tgtP.Distance( trsf.Transform( srcP )) < tol );
       }
     }
-    // check nodes on VERTEXes for a case of not meshes EDGEs
-    for ( TopExp_Explorer srcExp( srcFace, TopAbs_VERTEX); srcExp.More(); srcExp.Next() )
+    if ( !trsfIsOK )
     {
-      const TopoDS_Shape&  srcV = srcExp.Current();
-      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 );
-      if ( !srcN )
-        continue;
-      if ( !tgtN || tgtV.ShapeType() != TopAbs_VERTEX )
-        return false;
-
-      if ( !tgtV.IsPartner( srcV ))
+      // Try to find the 3D transformation
+
+      const int totNbSeg = 50;
+      vector< gp_XYZ > srcPnts, tgtPnts;
+      srcPnts.reserve( totNbSeg );
+      tgtPnts.reserve( totNbSeg );
+      gp_XYZ srcBC( 0,0,0 ), tgtBC( 0,0,0 );
+      for ( size_t iW = 0; iW < srcWires.size(); ++iW )
       {
-        // check that transformation is OK by three nodes
-        gp_Pnt p0S = SMESH_TNodeXYZ( srcN );
-        gp_Pnt p0T = SMESH_TNodeXYZ( tgtN );
-        if ( p0T.SquareDistance( p0S.Transformed( trsf )) > tol )
+        const double minSegLen = srcWires[iW]->Length() / totNbSeg;
+        for ( int iE = 0; iE < srcWires[iW]->NbEdges(); ++iE )
         {
-          return false;
+          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;
+          double tgtDu = ( tgtWires[iW]->LastParameter( iE )- tgtU ) / nbSeg;
+          for ( size_t i = 0; i < nbSeg; ++i  )
+          {
+            srcPnts.push_back( srcWires[iW]->Value3d( srcU ).XYZ() );
+            tgtPnts.push_back( tgtWires[iW]->Value3d( tgtU ).XYZ() );
+            srcU += srcDu;
+            tgtU += tgtDu;
+            srcBC += srcPnts.back();
+            tgtBC += tgtPnts.back();
+          }
         }
       }
-      src2tgtNodes.insert( make_pair( srcN, tgtN ));
-    }
+      if ( !trsf.Solve( srcPnts, tgtPnts ))
+        return false;
+
+      // check trsf
 
+      const int nbTestPnt = 20;
+      const size_t  iStep = Max( 1, int( srcPnts.size() / nbTestPnt ));
+      // check boundary
+      gp_Pnt trsfTgt = trsf.Transform( srcBC / srcPnts.size() );
+      trsfIsOK = ( trsfTgt.SquareDistance( tgtBC / tgtPnts.size() ) < tol*tol );
+      for ( size_t i = 0; ( i < srcPnts.size() && trsfIsOK ); i += iStep )
+      {
+        gp_Pnt trsfTgt = trsf.Transform( srcPnts[i] );
+        trsfIsOK = ( trsfTgt.SquareDistance( tgtPnts[i] ) < tol*tol );
+      }
+      // check an in-FACE point
+      if ( trsfIsOK )
+      {
+        BRepAdaptor_Surface srcSurf( srcFace );
+        gp_Pnt srcP =
+          srcSurf.Value( 0.321 * ( srcSurf.FirstUParameter() + srcSurf.LastUParameter() ),
+                         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 );
+        if ( !loc.IsIdentity() )
+          tgtTrsfP.Transform( loc.Transformation().Inverted() );
+        proj.Perform( tgtTrsfP );
+        trsfIsOK = ( proj.IsDone() &&
+                     proj.NbPoints() > 0 &&
+                     proj.LowerDistance() < tol );
+      }
+      if ( !trsfIsOK )
+        return false;
+    }
 
     // Make new faces
 
     // prepare the helper to adding quadratic elements if necessary
-    SMESH_MesherHelper helper( *tgtMesh );
-    helper.SetSubShape( tgtFace );
-    helper.IsQuadraticSubMesh( tgtFace );
+    helper->IsQuadraticSubMesh( tgtFace );
 
     SMESHDS_SubMesh* srcSubDS = srcMeshDS->MeshElements( srcFace );
-    if ( !tgtEdgesMeshed && srcSubDS->NbElements() )
-      helper.SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
+    if ( !is1DComputed && srcSubDS->NbElements() )
+      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;
 
     // indices of nodes to create properly oriented faces
-    bool isReverse = ( trsf.Form() != gp_Identity );
+    bool isReverse = ( !trsf.IsIdentity() );
     int tri1 = 1, tri2 = 2, quad1 = 1, quad3 = 3;
     if ( isReverse )
       std::swap( tri1, tri2 ), std::swap( quad1, quad3 );
@@ -606,7 +703,7 @@ namespace {
       const SMDS_MeshElement* elem = elemIt->next();
       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);
@@ -614,23 +711,42 @@ namespace {
         if ( srcN_tgtN->second == nullNode )
         {
           // create a new node
-          gp_Pnt tgtP = gp_Pnt( SMESH_TNodeXYZ( srcNode )).Transformed( trsf );
-          SMDS_MeshNode* n = helper.AddNode( tgtP.X(), tgtP.Y(), tgtP.Z() );
+          gp_Pnt tgtP = trsf.Transform( SMESH_TNodeXYZ( srcNode ));
+          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:
@@ -646,14 +762,14 @@ 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 );
       }
     }
 
@@ -661,6 +777,8 @@ namespace {
 
     if ( !tgtFace.IsPartner( srcFace ) )
     {
+      helper->ToFixNodeParameters( true );
+
       int nbOkPos = 0;
       const double tol2d = 1e-12;
       srcN_tgtN = src2tgtNodes.begin();
@@ -671,22 +789,20 @@ namespace {
         {
         case SMDS_TOP_FACE:
         {
-          gp_XY uv = helper.GetNodeUV( tgtFace, n ), uvBis = uv;
-          if (( helper.CheckNodeUV( tgtFace, n, uv, tol )) &&
-              (( uv - uvBis ).SquareModulus() < tol2d )    &&
-              ( ++nbOkPos > 10 ))
-            return true;
+          if ( nbOkPos > 10 ) break;
+          gp_XY uv = helper->GetNodeUV( tgtFace, n ), uvBis = uv;
+          if (( helper->CheckNodeUV( tgtFace, n, uv, tol )) &&
+              (( uv - uvBis ).SquareModulus() < tol2d ))
+            ++nbOkPos;
           else
-            nbOkPos = 0;
+            nbOkPos = -((int) src2tgtNodes.size() );
           break;
         }
         case SMDS_TOP_EDGE:
         {
-          const TopoDS_Edge & tgtE = TopoDS::Edge( tgtMeshDS->IndexToShape( n->getshapeId() ));
-          double u = helper.GetNodeU( tgtE, n ), uBis = u;
-          if (( !helper.CheckNodeU( tgtE, n, u, tol )) ||
-              (( u - uBis ) < tol2d ))
-            nbOkPos = 0;
+          // const TopoDS_Edge & tgtE = TopoDS::Edge( tgtMeshDS->IndexToShape( n->getshapeId() ));
+          // edgeHelper.SetSubShape( tgtE );
+          // edgeHelper.GetNodeU( tgtE, n, 0, &toCheck );
           break;
         }
         default:;
@@ -700,93 +816,27 @@ namespace {
 
   //================================================================================
   /*!
-   * \brief Check if two consecutive EDGEs are connected in 2D
-   *  \param [in] E1 - a well oriented non-seam EDGE
-   *  \param [in] E2 - a possibly well oriented seam EDGE
-   *  \param [in] F - a FACE
-   *  \return bool - result
+   * \brief Perform projection in case if the faces are similar in 2D space
    */
   //================================================================================
 
-  bool are2dConnected( const TopoDS_Edge & E1,
-                       const TopoDS_Edge & E2,
-                       const TopoDS_Face & F )
+  bool projectBy2DSimilarity(const TopoDS_Face&                 tgtFace,
+                             const TopoDS_Face&                 srcFace,
+                             const TSideVector&                 tgtWires,
+                             const TSideVector&                 srcWires,
+                             const TAssocTool::TShapeShapeMap&  shape2ShapeMap,
+                             TAssocTool::TNodeNodeMap&          src2tgtNodes,
+                             const bool                         is1DComputed)
   {
-    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 );
+    SMESH_Mesh * tgtMesh = tgtWires[0]->GetMesh();
+    SMESH_Mesh * srcMesh = srcWires[0]->GetMesh();
 
-    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 );
+    // WARNING: we can have problems if the FACE is symmetrical in 2D,
+    // then the projection can be mirrored relating to what is expected
 
-    return (( uvLast1.SquareDistance( uvFirst2 ) < tol2 ) ||
-            ( uvLast1.SquareDistance( uvLast2 ) < tol2 ));
-  }
+    // 1) Find 2D transformation
 
-  //================================================================================
-  /*!
-   * \brief Preform projection in case if the faces are similar in 2D space
-   */
-  //================================================================================
-
-  bool projectBy2DSimilarity(const TopoDS_Face&                tgtFace,
-                             const TopoDS_Face&                srcFace,
-                             SMESH_Mesh *                      tgtMesh,
-                             SMESH_Mesh *                      srcMesh,
-                             const TAssocTool::TShapeShapeMap& shape2ShapeMap,
-                             const bool                        is1DComputed)
-  {
-    // 1) Preparation
-
-    // get ordered src EDGEs
-    TError err;
-    TSideVector srcWires =
-      StdMeshers_FaceSide::GetFaceWires( srcFace, *srcMesh,/*ignoreMediumNodes = */false, err);
-    if ( err && !err->IsOK() )
-      return false;
-
-    // make corresponding sequence of tgt EDGEs
-    TSideVector tgtWires( srcWires.size() );
-    for ( size_t iW = 0; iW < srcWires.size(); ++iW )
-    {
-      list< TopoDS_Edge > tgtEdges;
-      StdMeshers_FaceSidePtr srcWire = srcWires[iW];
-      TopTools_IndexedMapOfShape edgeMap; // to detect seam edges
-      for ( int iE = 0; iE < srcWire->NbEdges(); ++iE )
-      {
-        TopoDS_Edge E = TopoDS::Edge( shape2ShapeMap( srcWire->Edge( iE ), /*isSrc=*/true));
-        // reverse a seam edge encountered for the second time
-        const int index = edgeMap.Add( E );
-        if ( index < edgeMap.Extent() ) // E is a seam
-        {
-          // check which of edges to reverse, E or one already being in tgtEdges
-          if ( are2dConnected( tgtEdges.back(), E, tgtFace ))
-          {
-            list< TopoDS_Edge >::iterator eIt = tgtEdges.begin();
-            std::advance( eIt, index-1 );
-            eIt->Reverse();
-          }
-          else
-          {
-            E.Reverse();
-          }
-        }
-        tgtEdges.push_back( E );
-      }
-      tgtWires[ iW ].reset( new StdMeshers_FaceSide( tgtFace, tgtEdges, tgtMesh,
-                                                     /*theIsForward = */ true,
-                                                     /*theIgnoreMediumNodes = */false));
-      if ( is1DComputed &&
-           srcWires[iW]->GetUVPtStruct().size() !=
-           tgtWires[iW]->GetUVPtStruct().size())
-        return false;
-    }
-
-    // 2) Find transformation
-
-    gp_Trsf2d trsf;
+    StdMeshers_ProjectionUtils::TrsfFinder2D trsf;
     {
       // get 2 pairs of corresponding UVs
       gp_Pnt2d srcP0 = srcWires[0]->Value2d(0.0);
@@ -801,67 +851,79 @@ namespace {
       toSrcCS  .SetTransformation( srcCS );
       fromTgtCS.SetTransformation( tgtCS );
       fromTgtCS.Invert();
-
-      trsf = fromTgtCS * toSrcCS;
+      trsf.Set( fromTgtCS * toSrcCS );
 
       // check transformation
+      bool trsfIsOK = true;
       const double tol = 1e-5 * gp_Vec2d( srcP0, srcP1 ).Magnitude();
-      for ( double u = 0.12; u < 1.; u += 0.1 )
+      for ( double u = 0.12; ( u < 1. && trsfIsOK ); u += 0.1 )
       {
-        gp_Pnt2d srcUV = srcWires[0]->Value2d( u );
-        gp_Pnt2d tgtUV = tgtWires[0]->Value2d( u );
-        gp_Pnt2d tgtUV2 = srcUV.Transformed( trsf );
-        if ( tgtUV.Distance( tgtUV2 ) > tol )
-          return false;
+        gp_Pnt2d srcUV  = srcWires[0]->Value2d( u );
+        gp_Pnt2d tgtUV  = tgtWires[0]->Value2d( u );
+        gp_Pnt2d tgtUV2 = trsf.Transform( srcUV );
+        trsfIsOK = ( tgtUV.Distance( tgtUV2 ) < tol );
       }
-    }
 
-    // 3) Projection
+      // Find trsf using a least-square approximation
+      if ( !trsfIsOK )
+      {
+        // find trsf
+        const int totNbSeg = 50;
+        vector< gp_XY > srcPnts, tgtPnts;
+        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 )
+          {
+            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;
+            double tgtDu = ( tgtWires[iW]->LastParameter( iE )- tgtU ) / nbSeg;
+            for ( size_t i = 0; i < nbSeg; ++i, srcU += srcDu, tgtU += tgtDu  )
+            {
+              srcPnts.push_back( srcWires[iW]->Value2d( srcU ).XY() );
+              tgtPnts.push_back( tgtWires[iW]->Value2d( tgtU ).XY() );
+            }
+          }
+        }
+        if ( !trsf.Solve( srcPnts, tgtPnts ))
+          return false;
 
-    typedef map<const SMDS_MeshNode* , const SMDS_MeshNode*, TIDCompare> TN2NMap;
-    TN2NMap src2tgtNodes;
-    TN2NMap::iterator srcN_tgtN;
+        // check trsf
 
-    // fill src2tgtNodes in with nodes on EDGEs
-    for ( unsigned iW = 0; iW < srcWires.size(); ++iW )
-      if ( is1DComputed )
-      {
-        const vector<UVPtStruct>& srcUVs = srcWires[iW]->GetUVPtStruct();
-        const vector<UVPtStruct>& tgtUVs = tgtWires[iW]->GetUVPtStruct();
-        for ( unsigned i = 0; i < srcUVs.size(); ++i )
-          src2tgtNodes.insert( make_pair( srcUVs[i].node, tgtUVs[i].node ));
-      }
-      else
-      {
-        for ( int iE = 0; iE < srcWires[iW]->NbEdges(); ++iE )
+        trsfIsOK = true;
+        const int nbTestPnt = 10;
+        const size_t  iStep = Max( 1, int( srcPnts.size() / nbTestPnt ));
+        for ( size_t i = 0; ( i < srcPnts.size() && trsfIsOK ); i += iStep )
         {
-          TopoDS_Vertex srcV = srcWires[iW]->FirstVertex(iE);
-          TopoDS_Vertex tgtV = tgtWires[iW]->FirstVertex(iE);
-          const SMDS_MeshNode* srcNode = SMESH_Algo::VertexNode( srcV, srcMesh->GetMeshDS() );
-          const SMDS_MeshNode* tgtNode = SMESH_Algo::VertexNode( tgtV, tgtMesh->GetMeshDS() );
-          if ( tgtNode && srcNode )
-            src2tgtNodes.insert( make_pair( srcNode, tgtNode ));
+          gp_Pnt2d trsfTgt = trsf.Transform( srcPnts[i] );
+          trsfIsOK = ( trsfTgt.Distance( tgtPnts[i] ) < tol );
         }
+        if ( !trsfIsOK )
+          return false;
       }
+    } // "Find transformation" block
 
-    // make elements
+    // 2) Projection
 
     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;
 
     SMDS_ElemIteratorPtr elemIt = srcSubDS->GetElements();
     vector< const SMDS_MeshNode* > tgtNodes;
@@ -869,7 +931,7 @@ 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
       {
@@ -878,32 +940,32 @@ 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 tgtUV = srcUV.Transformed( trsf );
-          gp_Pnt   tgtP  = tgtSurface->Value( tgtUV.X(), tgtUV.Y() );
+          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 ));
-            tgtMeshDS->SetNodeOnEdge( n, TopoDS::Edge( tgtEdge ));
-            double U = srcHelper.GetNodeU( TopoDS::Edge( srcEdge ), srcNode );
-            helper.CheckNodeU( tgtEdge, n, U, Precision::PConfusion());
-            n->SetPosition(SMDS_PositionPtr(new SMDS_EdgePosition( U )));
+            double U = Precision::Infinite();
+            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;
         }
@@ -912,25 +974,693 @@ 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;
+  }
+
+  //================================================================================
+  /*!
+   * \brief Perform projection in case of quadrilateral faces
+   */
+  //================================================================================
+
+  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[0]->NbEdges() != 4 )
+    //   return false;
+    // 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(...)
+
+  //================================================================================
+  /*!
+   * \brief Fix bad faces by smoothing
+   */
+  //================================================================================
+
+  bool fixDistortedFaces( SMESH_MesherHelper& helper,
+                          TSideVector&        tgtWires )
+  {
+    SMESH_subMesh* faceSM = helper.GetMesh()->GetSubMesh( helper.GetSubShape() );
+
+    //if ( helper.IsDistorted2D( faceSM, /*checkUV=*/true ))
+    {
+      SMESH_MeshEditor editor( helper.GetMesh() );
+      SMESHDS_SubMesh* smDS = faceSM->GetSubMeshDS();
+      const TopoDS_Face&  F = TopoDS::Face( faceSM->GetSubShape() );
+
+      TIDSortedElemSet faces;
+      SMDS_ElemIteratorPtr faceIt = smDS->GetElements();
+      for ( faceIt = smDS->GetElements(); faceIt->more(); )
+        faces.insert( faces.end(), faceIt->next() );
+
+      // choose smoothing algo
+      //SMESH_MeshEditor:: SmoothMethod algo = SMESH_MeshEditor::CENTROIDAL;
+      bool isConcaveBoundary = false;
+      for ( size_t iW = 0; iW < tgtWires.size() && !isConcaveBoundary; ++iW )
+      {
+        TopoDS_Edge prevEdge = tgtWires[iW]->Edge( tgtWires[iW]->NbEdges() - 1 );
+        for ( int iE = 0; iE < tgtWires[iW]->NbEdges() && !isConcaveBoundary; ++iE )
+        {
+          double angle = helper.GetAngle( prevEdge, tgtWires[iW]->Edge( iE ),
+                                          F,        tgtWires[iW]->FirstVertex( iE ));
+          isConcaveBoundary = ( angle < -5. * M_PI / 180. );
+
+          prevEdge = tgtWires[iW]->Edge( iE );
+        }
+      }
+      SMESH_MeshEditor:: SmoothMethod algo =
+        isConcaveBoundary ? SMESH_MeshEditor::CENTROIDAL : SMESH_MeshEditor::LAPLACIAN;
+
+      // smooth in 2D or 3D?
+      TopLoc_Location loc;
+      Handle(Geom_Surface) surface = BRep_Tool::Surface( F, loc );
+      bool isPlanar = GeomLib_IsPlanarSurface( surface ).IsPlanar();
+
+      // smoothing
+      set<const SMDS_MeshNode*> fixedNodes;
+      editor.Smooth( faces, fixedNodes, algo, /*nbIterations=*/ 10,
+                     /*theTgtAspectRatio=*/1.0, /*the2D=*/!isPlanar);
+
+      helper.ToFixNodeParameters( true );
+
+      return !helper.IsDistorted2D( faceSM, /*checkUV=*/true );
     }
     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 );
+    Handle(GeomAdaptor_HSurface) tgtSurfAdaptor = new GeomAdaptor_HSurface( tgtSurface );
+    Handle(GeomAdaptor_HCurve)    piercingCurve = new GeomAdaptor_HCurve( thePiercingLine );
+    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()
+
 
-  } // bool projectBy2DSimilarity(...)
 
 } // namespace
 
 
 //=======================================================================
 //function : Compute
-//purpose  : 
+//purpose  :
 //=======================================================================
 
 bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape& theShape)
 {
-  MESSAGE("Projection_2D Compute");
+  _src2tgtNodes.clear();
+
   if ( !_sourceHypo )
     return false;
 
@@ -940,6 +1670,7 @@ 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
@@ -948,22 +1679,35 @@ 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));
 
@@ -990,56 +1734,78 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
   // Projection
   // ===========
 
-  // find out if EDGEs are meshed or not
-  bool is1DComputed = false;
-  SMESH_subMeshIteratorPtr smIt = tgtSubMesh->getDependsOnIterator(/*includeSelf=*/false,
-                                                                   /*complexShapeFirst=*/true);
-  while ( smIt->more() && !is1DComputed )
-  {
-    SMESH_subMesh* sm = smIt->next();
-    if ( sm->GetSubShape().ShapeType() == TopAbs_EDGE )
-      is1DComputed = sm->IsMeshComputed();
-  }
+  // 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, &helper,
+                         shape2ShapeMap, srcWires, tgtWires, _src2tgtNodes, is1DComputed );
+  if ( err && !err->IsOK() )
+    return error( err );
 
-  bool done = false;
+  bool projDone = false;
 
-  if ( !done )
+  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
-    done = projectPartner( tgtFace, srcFace, tgtMesh, srcMesh, shape2ShapeMap );
+    projDone = projectPartner( tgtFace, srcFace, tgtWires, srcWires,
+                               shape2ShapeMap, _src2tgtNodes, is1DComputed );
   }
-  if ( !done )
+  if ( !projDone )
   {
     // projection in case if the faces are similar in 2D space
-    done = projectBy2DSimilarity( tgtFace, srcFace, tgtMesh, srcMesh, shape2ShapeMap, is1DComputed);
+    projDone = projectBy2DSimilarity( tgtFace, srcFace, tgtWires, srcWires,
+                                      shape2ShapeMap, _src2tgtNodes, is1DComputed );
+  }
+  if ( !projDone )
+  {
+    // projection in case of quadrilateral faces
+    // NOT IMPLEMENTED, returns false
+    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 );
 
-  if ( !done )
+  if ( !projDone )
   {
+    _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()
@@ -1047,13 +1813,10 @@ 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 );
@@ -1064,29 +1827,94 @@ 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
     {
@@ -1095,19 +1923,22 @@ 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");
 
     // --------------------
-    // Perform 2D mapping 
+    // Perform 2D mapping
     // --------------------
 
     // 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
 
@@ -1116,13 +1947,21 @@ 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");
 
-    // it will remove mesh built by pattern mapper on edges and vertices
-    // in failure case
-    MeshCleaner cleaner( tgtSubMesh );
+    // 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 
+    // so we must merge nodes created by it with existing ones
     // -------------------------------------------------------------------------
 
     SMESH_MeshEditor::TListOfListOfNodes groupsOfNodes;
@@ -1130,7 +1969,8 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     // Make groups of nodes to merge
 
     // loop on EDGE and VERTEX sub-meshes of a target FACE
-    smIt = tgtSubMesh->getDependsOnIterator(/*includeSelf=*/false,/*complexShapeFirst=*/false);
+    SMESH_subMeshIteratorPtr smIt = tgtSubMesh->getDependsOnIterator(/*includeSelf=*/false,
+                                                                     /*complexShapeFirst=*/false);
     while ( smIt->more() )
     {
       SMESH_subMesh*     sm = smIt->next();
@@ -1138,7 +1978,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
       if ( !smDS || smDS->NbNodes() == 0 )
         continue;
       //if ( !is1DComputed && sm->GetSubShape().ShapeType() == TopAbs_EDGE )
-      //break;
+      //  break;
 
       if ( helper.IsDegenShape( sm->GetId() ) ) // to merge all nodes on degenerated
       {
@@ -1158,7 +1998,7 @@ 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() );
 
@@ -1169,7 +2009,9 @@ 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() )
@@ -1194,8 +2036,7 @@ 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;
         }
@@ -1213,7 +2054,7 @@ 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 );
@@ -1228,8 +2069,8 @@ 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
@@ -1246,7 +2087,7 @@ 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();
@@ -1272,9 +2113,9 @@ 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");
 
@@ -1282,6 +2123,7 @@ 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();
@@ -1295,12 +2137,24 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
 
       editor.ConvertToQuadratic(/*theForce3d=*/false, tgtFaces, false);
     }
+  } // end of coincident nodes and quadratic elements treatment
 
-    cleaner.Release(); // not to remove mesh
-
-  } // end of projection using Pattern mapping
 
+  if ( !projDone || is1DComputed )
+    // ----------------------------------------------------------------
+    // The mapper can create distorted faces by placing nodes out of the FACE
+    // boundary, also bad faces can be created if EDGEs already discretized
+    // --> fix bad faces by smoothing
+    // ----------------------------------------------------------------
+    if ( helper.IsDistorted2D( tgtSubMesh, /*checkUV=*/false, &helper ))
+    {
+      TAssocTool::Morph morph( srcWires );
+      morph.Perform( helper, tgtWires, helper.GetSurface( tgtFace ),
+                     _src2tgtNodes, /*moveAll=*/true );
 
+      if ( !fixDistortedFaces( helper, tgtWires ))
+        return error("Invalid mesh generated");
+    }
   // ---------------------------
   // Check elements orientation
   // ---------------------------
@@ -1346,13 +2200,15 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     }
   }
 
+  cleaner.Release(); // not to remove mesh
+
   return true;
 }
 
 
 //=======================================================================
 //function : Evaluate
-//purpose  : 
+//purpose  :
 //=======================================================================
 
 bool StdMeshers_Projection_2D::Evaluate(SMESH_Mesh&         theMesh,
@@ -1387,7 +2243,7 @@ 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() )