Salome HOME
Re-fix regression of SALOME_TESTS/Grids/smesh/3D_mesh_Extrusion_01/B2
[modules/smesh.git] / src / StdMeshers / StdMeshers_Projection_2D.cxx
index 6bb6adc1fa94d0693d7d55fbf7bf1679d003fc12..8413288b8913ee001ac109dd0d310f5bb5a9a4b5 100644 (file)
@@ -1,4 +1,4 @@
-// Copyright (C) 2007-2013  CEA/DEN, EDF R&D, OPEN CASCADE
+// Copyright (C) 2007-2016  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
@@ -6,7 +6,7 @@
 // This library is free software; you can redistribute it and/or
 // modify it under the terms of the GNU Lesser General Public
 // License as published by the Free Software Foundation; either
-// version 2.1 of the License.
+// version 2.1 of the License, or (at your option) any later version.
 //
 // This library is distributed in the hope that it will be useful,
 // but WITHOUT ANY WARRANTY; without even the implied warranty of
 #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_MesherHelper.hxx"
 #include "SMESH_Pattern.hxx"
 #include "SMESH_subMesh.hxx"
 #include "SMESH_subMeshEventListener.hxx"
 
-#include "utilities.h"
+#include <utilities.h>
 
+#include <BRepAdaptor_Surface.hxx>
+#include <BRepMesh_Delaun.hxx>
 #include <BRep_Tool.hxx>
 #include <Bnd_B2d.hxx>
+#include <GeomAPI_ProjectPointOnSurf.hxx>
+#include <GeomLib_IsPlanarSurface.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;
@@ -139,6 +148,7 @@ bool StdMeshers_Projection_2D::CheckHypothesis(SMESH_Mesh&
            !SMESH_MesherHelper::IsSubShape( edge, _sourceHypo->GetSourceFace() ))
       {
         theStatus = HYP_BAD_PARAMETER;
+        error("Invalid source vertices");
         SCRUTE((edge.IsNull()));
         SCRUTE((SMESH_MesherHelper::IsSubShape( edge, srcMesh )));
         SCRUTE((SMESH_MesherHelper::IsSubShape( edge, _sourceHypo->GetSourceFace() )));
@@ -151,6 +161,7 @@ bool StdMeshers_Projection_2D::CheckHypothesis(SMESH_Mesh&
         if ( edge.IsNull() || !SMESH_MesherHelper::IsSubShape( edge, tgtMesh ))
         {
           theStatus = HYP_BAD_PARAMETER;
+          error("Invalid target vertices");
           SCRUTE((edge.IsNull()));
           SCRUTE((SMESH_MesherHelper::IsSubShape( edge, tgtMesh )));
         }
@@ -159,6 +170,7 @@ bool StdMeshers_Projection_2D::CheckHypothesis(SMESH_Mesh&
                   !SMESH_MesherHelper::IsSubShape( edge, theShape ))
         {
           theStatus = HYP_BAD_PARAMETER;
+          error("Invalid target vertices");
           SCRUTE((SMESH_MesherHelper::IsSubShape( edge, theShape )));
         }
       }
@@ -168,6 +180,7 @@ bool StdMeshers_Projection_2D::CheckHypothesis(SMESH_Mesh&
          ( srcMesh == tgtMesh && theShape == _sourceHypo->GetSourceFace() ))
     {
       theStatus = HYP_BAD_PARAMETER;
+      error("Invalid source face");
       SCRUTE((SMESH_MesherHelper::IsSubShape( _sourceHypo->GetSourceFace(), srcMesh )));
       SCRUTE((srcMesh == tgtMesh));
       SCRUTE(( theShape == _sourceHypo->GetSourceFace() ));
@@ -190,7 +203,7 @@ 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
@@ -249,7 +262,7 @@ 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
@@ -370,189 +383,289 @@ 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 )
   {
-    MESSAGE("projectPartner");
-    const double tol = 1.e-7*srcMesh->GetMeshDS()->getMaxDim();
+    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 );
+
+    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 ));
+
+    return (( uvFirst2.SquareDistance( uvFirst1 ) < tol2 ) ||
+            ( uvFirst2.SquareDistance( uvLast1  ) < tol2 ));
+  }
 
-    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
+  //================================================================================
+  /*!
+   * \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,
+                  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;
+
+    SMESH_MesherHelper srcHelper( *srcMesh );
+    srcHelper.SetSubShape( srcFace );
+
+    // 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),tgtMesh->GetMeshDS())->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));
+      StdMeshers_FaceSidePtr tgtWire = tgtWires[ iW ];
+
+      // Fill map of src to tgt nodes with nodes on edges
+
+      for ( int iE = 0; iE < srcWire->NbEdges(); ++iE )
+      {
+        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);
+          StdMeshers_FaceSide tgtEdge( tgtFace, tgtWire->Edge(iE), tgtMesh, isFwd, skipMedium);
+          
+          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 = tgtMesh->GetMeshDS()->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;
-    }
+    return TError();
+  }
 
-    // Fill map of src to tgt nodes with nodes on edges
+  //================================================================================
+  /*!
+   * \brief Preform projection in case if tgtFace.IsPartner( srcFace ) and in case
+   * if projection by 3D transformation is possible
+   */
+  //================================================================================
 
-    map<const SMDS_MeshNode* , const SMDS_MeshNode*> src2tgtNodes;
-    map<const SMDS_MeshNode* , const SMDS_MeshNode*>::iterator srcN_tgtN;
+  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( *tgtMesh );
 
-    for ( TopExp_Explorer srcEdge( srcFace, TopAbs_EDGE); srcEdge.More(); srcEdge.Next() )
-    {
-      const TopoDS_Shape& tgtEdge = shape2ShapeMap( srcEdge.Current(), /*isSrc=*/true );
-
-      map< double, const SMDS_MeshNode* > srcNodes, tgtNodes;
-      if ( !SMESH_Algo::GetSortedNodesOnEdge( srcMesh->GetMeshDS(),
-                                              TopoDS::Edge( srcEdge.Current() ),
-                                              /*ignoreMediumNodes = */true,
-                                              srcNodes )
-           ||
-           !SMESH_Algo::GetSortedNodesOnEdge( tgtMesh->GetMeshDS(),
-                                              TopoDS::Edge( tgtEdge ),
-                                              /*ignoreMediumNodes = */true,
-                                              tgtNodes )
-           ||
-           srcNodes.size() != tgtNodes.size())
-        return false;
+    const double tol = 1.e-7 * srcMeshDS->getMaxDim();
 
-      if ( !tgtEdge.IsPartner( srcEdge.Current() ))
+    // 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 )
+      {
+        trsf.Set( tgtTrsf.Inverted().Multiplied( srcTrsf ));
+        trsfIsOK = ( tgtP.Distance( trsf.Transform( srcP )) < tol );
+      }
+    }
+    if ( !trsfIsOK )
+    {
+      // 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( (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 )
+        const double minSegLen = srcWires[iW]->Length() / totNbSeg;
+        for ( int iE = 0; iE < srcWires[iW]->NbEdges(); ++iE )
         {
-          //cout << "KO trsf, 3 dist: "
-          //<< p0T.SquareDistance( p0S.Transformed( trsf ))<< ", "
-          //<< p1T.SquareDistance( p1S.Transformed( trsf ))<< ", "
-          //<< p2T.SquareDistance( p2S.Transformed( trsf ))<< ", "<<endl;
-          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();
+          }
         }
       }
+      if ( !trsf.Solve( srcPnts, tgtPnts ))
+        return false;
 
-      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 ));
+      // 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.SetSubShape( tgtFace );
     helper.IsQuadraticSubMesh( tgtFace );
-    helper.SetElementsOnShape( true );
+
+    SMESHDS_SubMesh* srcSubDS = srcMeshDS->MeshElements( srcFace );
+    if ( !is1DComputed && srcSubDS->NbElements() )
+      helper.SetIsQuadratic( srcSubDS->GetElements()->next()->IsQuadratic() );
 
     SMESH_MesherHelper srcHelper( *srcMesh );
     srcHelper.SetSubShape( srcFace );
 
     const SMDS_MeshNode* nullNode = 0;
+    TAssocTool::TNodeNodeMap::iterator srcN_tgtN;
 
     // indices of nodes to create properly oriented faces
+    bool isReverse = ( !trsf.IsIdentity() );
     int tri1 = 1, tri2 = 2, quad1 = 1, quad3 = 3;
-    if ( trsf.Form() != gp_Identity )
+    if ( isReverse )
       std::swap( tri1, tri2 ), std::swap( quad1, quad3 );
 
-    SMESHDS_SubMesh* srcSubDS = srcMesh->GetMeshDS()->MeshElements( srcFace );
     SMDS_ElemIteratorPtr elemIt = srcSubDS->GetElements();
     vector< const SMDS_MeshNode* > tgtNodes;
     while ( elemIt->more() ) // loop on all mesh faces on srcFace
@@ -560,6 +673,7 @@ namespace {
       const SMDS_MeshElement* elem = elemIt->next();
       const int nbN = elem->NbCornerNodes(); 
       tgtNodes.resize( nbN );
+      helper.SetElementsOnShape( false );
       for ( int i = 0; i < nbN; ++i ) // loop on nodes of the source element
       {
         const SMDS_MeshNode* srcNode = elem->GetNode(i);
@@ -567,23 +681,89 @@ namespace {
         if ( srcN_tgtN->second == nullNode )
         {
           // create a new node
-          gp_Pnt tgtP = gp_Pnt(srcNode->X(),srcNode->Y(),srcNode->Z()).Transformed( trsf );
+          gp_Pnt tgtP = trsf.Transform( SMESH_TNodeXYZ( srcNode ));
           SMDS_MeshNode* n = helper.AddNode( tgtP.X(), tgtP.Y(), tgtP.Z() );
           srcN_tgtN->second = n;
-
-          gp_Pnt2d srcUV = srcHelper.GetNodeUV( srcFace, srcNode,
-                                                elem->GetNode( helper.WrapIndex(i+1,nbN)));
-          n->SetPosition( new SMDS_FacePosition( srcUV.X(), srcUV.Y() ));
+          switch ( srcNode->GetPosition()->GetTypeOfPosition() )
+          {
+          case SMDS_TOP_FACE:
+          {
+            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 );
+            break;
+          }
+          case SMDS_TOP_VERTEX:
+          {
+            const TopoDS_Shape & srcV = srcMeshDS->IndexToShape( srcNode->getshapeId() );
+            const TopoDS_Shape & tgtV = shape2ShapeMap( srcV, /*isSrc=*/true );
+            tgtMeshDS->SetNodeOnVertex( n, TopoDS::Vertex( tgtV ));
+            break;
+          }
+          default:;
+          }
         }
         tgtNodes[i] = srcN_tgtN->second;
       }
       // create a new face
+      helper.SetElementsOnShape( true );
       switch ( nbN )
       {
       case 3: helper.AddFace(tgtNodes[0], tgtNodes[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 );
       }
     }
+
+    // check node positions
+
+    if ( !tgtFace.IsPartner( srcFace ) )
+    {
+      SMESH_MesherHelper edgeHelper( *tgtMesh );
+      edgeHelper.ToFixNodeParameters( true );
+      helper.ToFixNodeParameters( true );
+
+      int nbOkPos = 0;
+      bool toCheck = true;
+      const double tol2d = 1e-12;
+      srcN_tgtN = src2tgtNodes.begin();
+      for ( ; srcN_tgtN != src2tgtNodes.end(); ++srcN_tgtN )
+      {
+        const SMDS_MeshNode* n = srcN_tgtN->second;
+        switch ( n->GetPosition()->GetTypeOfPosition() )
+        {
+        case SMDS_TOP_FACE:
+        {
+          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 = -((int) src2tgtNodes.size() );
+          break;
+        }
+        case SMDS_TOP_EDGE:
+        {
+          const TopoDS_Edge & tgtE = TopoDS::Edge( tgtMeshDS->IndexToShape( n->getshapeId() ));
+          edgeHelper.SetSubShape( tgtE );
+          edgeHelper.GetNodeU( tgtE, n, 0, &toCheck );
+          break;
+        }
+        default:;
+        }
+      }
+    }
+
     return true;
 
   } //   bool projectPartner()
@@ -594,50 +774,23 @@ namespace {
    */
   //================================================================================
 
-  bool projectBy2DSimilarity(const TopoDS_Face&                tgtFace,
-                             const TopoDS_Face&                srcFace,
-                             SMESH_Mesh *                      tgtMesh,
-                             SMESH_Mesh *                      srcMesh,
-                             const TAssocTool::TShapeShapeMap& shape2ShapeMap,
-                             const bool                        is1DComputed)
+  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)
   {
-    // 1) Preparation
+    SMESH_Mesh * tgtMesh = tgtWires[0]->GetMesh();
+    SMESH_Mesh * srcMesh = srcWires[0]->GetMesh();
 
-    // get ordered src EDGEs
-    TError err;
-    TSideVector srcWires =
-      StdMeshers_FaceSide::GetFaceWires( srcFace, *srcMesh,/*ignoreMediumNodes = */false, err);
-    if ( err && !err->IsOK() )
-      return false;
+    // WARNING: we can have problems if the FACE is symmetrical in 2D,
+    // then the projection can be mirrored relating to what is expected
 
-    // make corresponding sequence of tgt EDGEs
-    TSideVector tgtWires( srcWires.size() );
-    for ( unsigned 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 )
-      {
-        tgtEdges.push_back( TopoDS::Edge( shape2ShapeMap( srcWire->Edge( iE ), /*isSrc=*/true)));
-        // reverse a seam edge encountered for the second time
-        const int oldExtent = edgeMap.Extent();
-        edgeMap.Add( tgtEdges.back() );
-        if ( oldExtent == edgeMap.Extent() )
-          tgtEdges.back().Reverse();
-      }
-      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
+    // 1) Find 2D transformation
 
-    gp_Trsf2d trsf;
+    StdMeshers_ProjectionUtils::TrsfFinder2D trsf;
     {
       // get 2 pairs of corresponding UVs
       gp_Pnt2d srcP0 = srcWires[0]->Value2d(0.0);
@@ -652,50 +805,63 @@ 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 );
 
@@ -713,6 +879,7 @@ namespace {
     srcHelper.SetSubShape( srcFace );
 
     const SMDS_MeshNode* nullNode = 0;
+    TAssocTool::TNodeNodeMap::iterator srcN_tgtN;
 
     SMDS_ElemIteratorPtr elemIt = srcSubDS->GetElements();
     vector< const SMDS_MeshNode* > tgtNodes;
@@ -731,8 +898,8 @@ namespace {
           // 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   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() )
           {
@@ -743,10 +910,9 @@ namespace {
           case SMDS_TOP_EDGE: {
             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 );
+            double U = Precision::Infinite();
             helper.CheckNodeU( tgtEdge, n, U, Precision::PConfusion());
-            n->SetPosition(SMDS_PositionPtr(new SMDS_EdgePosition( U )));
+            tgtMeshDS->SetNodeOnEdge( n, TopoDS::Edge( tgtEdge ), U );
             break;
           }
           case SMDS_TOP_VERTEX: {
@@ -755,6 +921,7 @@ namespace {
             tgtMeshDS->SetNodeOnVertex( n, TopoDS::Vertex( tgtV ));
             break;
           }
+          default:;
           }
           srcN_tgtN->second = n;
         }
@@ -766,22 +933,513 @@ namespace {
       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 Preform 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 withing 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( *tgtMesh );
+    // helper.SetSubShape( tgtFace );
+    // 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( *srcMesh );
+    // srcHelper.SetSubShape( srcFace );
+
+    // 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;
+  }
+
+  typedef list< pair< const SMDS_MeshNode*, const BRepMesh_Triangle* > > TNodeTriaList;
+
+  //================================================================================
+  /*!
+   * \brief Add in-FACE nodes surrounding a given node to a queue
+   */
+  //================================================================================
+
+  void addCloseNodes( const SMDS_MeshNode*     srcNode,
+                      const BRepMesh_Triangle* bmTria,
+                      const int                srcFaceID,
+                      TNodeTriaList &          noTriQueue )
+  {
+    // find in-FACE nodes
+    SMDS_ElemIteratorPtr elems = srcNode->GetInverseElementIterator(SMDSAbs_Face);
+    while ( elems->more() )
+    {
+      const SMDS_MeshElement* elem = elems->next();
+      if ( elem->getshapeId() == srcFaceID )
+      {
+        for ( int i = 0, nb = elem->NbNodes(); i < nb; ++i )
+        {
+          const SMDS_MeshNode* n = elem->GetNode( i );
+          if ( !n->isMarked() )
+            noTriQueue.push_back( make_pair( n, bmTria ));
+        }
+      }
+    }
+  }
+
+  //================================================================================
+  /*!
+   * \brief Find a delauney triangle containing a given 2D point and return
+   *        barycentric coordinates within the found triangle
+   */
+  //================================================================================
+
+  const BRepMesh_Triangle* findTriangle( const gp_XY&                            uv,
+                                         const BRepMesh_Triangle*                bmTria,
+                                         Handle(BRepMesh_DataStructureOfDelaun)& triaDS,
+                                         double                                  bc[3] )
+  {
+    int   nodeIDs[3];
+    gp_XY nodeUVs[3];
+    int   linkIDs[3];
+    Standard_Boolean ori[3];
+
+    while ( bmTria )
+    {
+      // check bmTria
+
+      triaDS->ElementNodes( *bmTria, nodeIDs );
+      nodeUVs[0] = triaDS->GetNode( nodeIDs[0] ).Coord();
+      nodeUVs[1] = triaDS->GetNode( nodeIDs[1] ).Coord();
+      nodeUVs[2] = triaDS->GetNode( nodeIDs[2] ).Coord();
+
+      SMESH_MeshAlgos::GetBarycentricCoords( uv,
+                                             nodeUVs[0], nodeUVs[1], nodeUVs[2],
+                                             bc[0], bc[1] );
+      if ( bc[0] >= 0 && bc[1] >= 0 && bc[0] + bc[1] <= 1 )
+      {
+        bc[2] = 1 - bc[0] - bc[1];
+        return bmTria;
+      }
+
+      // look for a neighbor triangle, which is adjacent to a link intersected
+      // by a segment( triangle center -> uv )
+
+      gp_XY gc = ( nodeUVs[0] + nodeUVs[1] + nodeUVs[2] ) / 3.;
+      gp_XY seg = uv - gc;
+
+      bmTria->Edges( linkIDs, ori );
+      int triaID = triaDS->IndexOf( *bmTria );
+      bmTria = 0;
+
+      for ( int i = 0; i < 3; ++i )
+      {
+        const BRepMesh_PairOfIndex & triIDs = triaDS->ElementsConnectedTo( linkIDs[i] );
+        if ( triIDs.Extent() < 2 )
+          continue; // no neighbor triangle
+
+        // check if a link intersects gc2uv
+        const BRepMesh_Edge & link = triaDS->GetLink( linkIDs[i] );
+        const BRepMesh_Vertex & n1 = triaDS->GetNode( link.FirstNode() );
+        const BRepMesh_Vertex & n2 = triaDS->GetNode( link.LastNode() );
+        gp_XY uv1 = n1.Coord();
+        gp_XY lin = n2.Coord() - uv1; // link direction
+
+        double crossSegLin = seg ^ lin;
+        if ( Abs( crossSegLin ) < std::numeric_limits<double>::min() )
+          continue; // parallel
+
+        double uSeg = ( uv1 - gc ) ^ lin / crossSegLin;
+        if ( 0. <= uSeg && uSeg <= 1. )
+        {
+          bmTria = & triaDS->GetElement( triIDs.Index( 1 + ( triIDs.Index(1) == triaID )));
+          break;
+        }
+      }
+    }
+    return bmTria;
+  }
+
+  //================================================================================
+  /*!
+   * \brief Morph mesh on the target face to lie within FACE boundary w/o distortion
+   *
+   * algo:
+   * - make a CDT on the src FACE
+   * - find a triangle containing a src node and get its barycentric coordinates
+   * - move the node to a point with the same barycentric coordinates in a corresponding
+   *   tgt triangle
+   */
+  //================================================================================
+
+  bool morph( SMESH_MesherHelper&             tgtHelper,
+              const TopoDS_Face&              tgtFace,
+              const TopoDS_Face&              srcFace,
+              const TSideVector&              tgtWires,
+              const TSideVector&              srcWires,
+              const TAssocTool::TNodeNodeMap& src2tgtNodes )
+  {
+    if ( srcWires.size() != tgtWires.size() ) return false;
+
+    // count boundary points
+    int iP = 1, nbP = 0;
+    for ( size_t iW = 0; iW < srcWires.size(); ++iW )
+      nbP += srcWires[iW]->NbPoints() - 1; // 1st and last points coincide
+
+    // fill boundary points
+    BRepMesh::Array1OfVertexOfDelaun srcVert( 1, 1 + nbP ), tgtVert( 1, 1 + nbP );
+    vector< const SMDS_MeshNode* > bndSrcNodes( nbP + 1 ); bndSrcNodes[0] = 0;
+    BRepMesh_Vertex v( 0, 0, BRepMesh_Frontier );
+    for ( size_t iW = 0; iW < srcWires.size(); ++iW )
+    {
+      const UVPtStructVec& srcPnt = srcWires[iW]->GetUVPtStruct();
+      const UVPtStructVec& tgtPnt = tgtWires[iW]->GetUVPtStruct();
+      if ( srcPnt.size() != tgtPnt.size() ) return false;
+
+      for ( int i = 0, nb = srcPnt.size() - 1;  i < nb;  ++i, ++iP )
+      {
+        bndSrcNodes[ iP ]  = srcPnt[i].node;
+        srcPnt[i].node->setIsMarked( true );
+
+        v.ChangeCoord() = srcPnt[i].UV();
+        srcVert( iP )   = v;
+        v.ChangeCoord() = tgtPnt[i].UV();
+        tgtVert( iP )   = v;
+      }
     }
+    // triangulate the srcFace in 2D
+    BRepMesh_Delaun delauney( srcVert );
+    Handle(BRepMesh_DataStructureOfDelaun) triaDS = delauney.Result();
+
+    Handle(ShapeAnalysis_Surface) tgtSurface = tgtHelper.GetSurface( tgtFace );
+    SMESHDS_Mesh* srcMesh = srcWires[0]->GetMesh()->GetMeshDS();
+    SMESHDS_Mesh* tgtMesh = tgtHelper.GetMeshDS();
+    const SMDS_MeshNode *srcNode, *tgtNode;
+    const BRepMesh_Triangle *bmTria;
+
+    // un-mark internal src nodes; later we will mark moved nodes
+    SMDS_NodeIteratorPtr nIt = srcMesh->MeshElements( srcFace )->GetNodes();
+    if ( !nIt || !nIt->more() ) return true;
+    while ( nIt->more() )
+      ( srcNode = nIt->next() )->setIsMarked( false );
+
+    // initialize a queue of nodes with starting triangles
+    const int srcFaceID = srcNode->getshapeId();
+    TNodeTriaList noTriQueue;
+    size_t iBndSrcN = 1;
+    for ( ; iBndSrcN < bndSrcNodes.size() &&  noTriQueue.empty();  ++iBndSrcN )
+    {
+      // get a triangle
+      const BRepMesh::ListOfInteger & linkIds = triaDS->LinksConnectedTo( iBndSrcN );
+      const BRepMesh_PairOfIndex &    triaIds = triaDS->ElementsConnectedTo( linkIds.First() );
+      const BRepMesh_Triangle&           tria = triaDS->GetElement( triaIds.Index(1) );
+
+      addCloseNodes( bndSrcNodes[ iBndSrcN ], &tria, srcFaceID, noTriQueue );
+    }
+
+    // Move tgt nodes
+
+    double bc[3]; // barycentric coordinates
+    int    nodeIDs[3];
+    bool   checkUV = true;
+    const SMDS_FacePosition* pos;
+
+    while ( !noTriQueue.empty() )
+    {
+      srcNode = noTriQueue.front().first;
+      bmTria  = noTriQueue.front().second;
+      noTriQueue.pop_front();
+      if ( srcNode->isMarked() )
+        continue;
+      srcNode->setIsMarked( true );
+
+      // find a delauney triangle containing the src node
+      gp_XY uv = tgtHelper.GetNodeUV( srcFace, srcNode, NULL, &checkUV );
+      bmTria = findTriangle( uv, bmTria, triaDS, bc );
+      if ( !bmTria )
+        continue;
+
+      // compute new coordinates for a corresponding tgt node
+      gp_XY uvNew( 0., 0. ), nodeUV;
+      triaDS->ElementNodes( *bmTria, nodeIDs );
+      for ( int i = 0; i < 3; ++i )
+        uvNew += bc[i] * tgtVert( nodeIDs[i]).Coord();
+      gp_Pnt xyz = tgtSurface->Value( uvNew );
+
+      // find and move tgt node
+      TAssocTool::TNodeNodeMap::const_iterator n2n = src2tgtNodes.find( srcNode );
+      if ( n2n == src2tgtNodes.end() ) continue;
+      tgtNode = n2n->second;
+      tgtMesh->MoveNode( tgtNode, xyz.X(), xyz.Y(), xyz.Z() );
+
+      if (( pos = dynamic_cast< const SMDS_FacePosition* >( tgtNode->GetPosition() )))
+        const_cast<SMDS_FacePosition*>( pos )->SetParameters( uvNew.X(), uvNew.Y() );
+
+      addCloseNodes( srcNode, bmTria, srcFaceID, noTriQueue );
+
+      // assure that all src nodes are visited
+      for ( ; iBndSrcN < bndSrcNodes.size() &&  noTriQueue.empty();  ++iBndSrcN )
+      {
+        const BRepMesh::ListOfInteger & linkIds = triaDS->LinksConnectedTo( iBndSrcN );
+        const BRepMesh_PairOfIndex &    triaIds = triaDS->ElementsConnectedTo( linkIds.First() );
+        const BRepMesh_Triangle&           tria = triaDS->GetElement( triaIds.Index(1) );
+        addCloseNodes( bndSrcNodes[ iBndSrcN ], &tria, srcFaceID, noTriQueue );
+      }
+    }
+
     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
+   */
+  //=======================================================================
 
-  } // bool projectBy2DSimilarity(...)
+  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
+
+    int 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 );
+  }
 
 } // 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;
 
@@ -791,6 +1449,7 @@ 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
@@ -799,16 +1458,20 @@ 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 );
   if ( !TAssocTool::FindSubShapeAssociation( tgtFace, tgtMesh, srcShape, srcMesh,
                                              shape2ShapeMap)  ||
        !shape2ShapeMap.IsBound( tgtFace ))
   {
     if ( srcShape.ShapeType() == TopAbs_FACE )
     {
-      int nbE1 = SMESH_MesherHelper::Count( tgtFace, TopAbs_EDGE, /*ignoreSame=*/true );
-      int nbE2 = SMESH_MesherHelper::Count( srcShape, TopAbs_EDGE, /*ignoreSame=*/true );
+      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: ")
@@ -841,35 +1504,42 @@ 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,
+                         shape2ShapeMap, srcWires, tgtWires, _src2tgtNodes, is1DComputed );
+  if ( err && !err->IsOK() )
+    return error( err );
 
-  bool done = false;
+  bool projDone = false;
 
-  if ( !done )
+  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);
   }
 
-  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 
     // --------------------
@@ -877,20 +1547,22 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     // 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()
@@ -898,13 +1570,10 @@ 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 );
@@ -916,7 +1585,7 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
       TopoDS_Shape srcE1bis = shape2ShapeMap( tgtE1 );
       reverse = ( ! srcE1.IsSame( srcE1bis ));
       if ( reverse &&
-           _sourceHypo->HasVertexAssociation() &&
+           //_sourceHypo->HasVertexAssociation() &&
            nbEdgesInWires.front() > 2 &&
            helper.IsRealSeam( tgtEdges.front() ))
       {
@@ -925,19 +1594,83 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
         // 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() )
+          {
+            int 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
     {
@@ -946,19 +1679,22 @@ 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
 
@@ -967,13 +1703,21 @@ 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;
@@ -981,7 +1725,8 @@ 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();
@@ -989,7 +1734,7 @@ 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
       {
@@ -1009,7 +1754,7 @@ 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() );
 
@@ -1018,9 +1763,9 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
       map< double, const SMDS_MeshNode* >::iterator u_oldNode, u_newNode, u_newOnSeam, newEnd;
       set< const SMDS_MeshNode* > seamNodes;
 
-      // mapper puts on a seam edge nodes from 2 edges
+      // 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() )
@@ -1079,8 +1824,8 @@ 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
@@ -1133,6 +1878,7 @@ 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();
@@ -1146,12 +1892,22 @@ 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 face can be created if EDGEs already discretized
+    // --> fix bad faces by smoothing
+    // ----------------------------------------------------------------
+    if ( helper.IsDistorted2D( tgtSubMesh, /*checkUV=*/false ))
+    {
+      morph( helper, tgtFace, srcFace, tgtWires, srcWires, _src2tgtNodes );
 
+      if ( !fixDistortedFaces( helper, tgtWires ))
+        return error("Invalid mesh generated");
+    }
   // ---------------------------
   // Check elements orientation
   // ---------------------------
@@ -1197,6 +1953,8 @@ bool StdMeshers_Projection_2D::Compute(SMESH_Mesh& theMesh, const TopoDS_Shape&
     }
   }
 
+  cleaner.Release(); // not to remove mesh
+
   return true;
 }