Salome HOME
Merge from V6_main 12/11/2012
[modules/smesh.git] / src / StdMeshers / StdMeshers_Quadrangle_2D.cxx
index 8aa83e935233528e0cc0528b82ebcc0446b34302..d75a5aac2de8c7be2bd8f4387197e17d9199ae3f 100644 (file)
@@ -1,4 +1,4 @@
-// Copyright (C) 2007-2011  CEA/DEN, EDF R&D, OPEN CASCADE
+// Copyright (C) 2007-2012  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
 
 #include "StdMeshers_Quadrangle_2D.hxx"
 
-#include "StdMeshers_FaceSide.hxx"
-
-#include "StdMeshers_QuadrangleParams.hxx"
-
+#include "SMDS_EdgePosition.hxx"
+#include "SMDS_FacePosition.hxx"
+#include "SMDS_MeshElement.hxx"
+#include "SMDS_MeshNode.hxx"
+#include "SMESH_Block.hxx"
+#include "SMESH_Comment.hxx"
 #include "SMESH_Gen.hxx"
 #include "SMESH_Mesh.hxx"
-#include "SMESH_subMesh.hxx"
 #include "SMESH_MesherHelper.hxx"
-#include "SMESH_Block.hxx"
-#include "SMESH_Comment.hxx"
-
-#include "SMDS_MeshElement.hxx"
-#include "SMDS_MeshNode.hxx"
-#include "SMDS_EdgePosition.hxx"
-#include "SMDS_FacePosition.hxx"
+#include "SMESH_subMesh.hxx"
+#include "StdMeshers_FaceSide.hxx"
+#include "StdMeshers_QuadrangleParams.hxx"
+#include "StdMeshers_ViscousLayers2D.hxx"
 
 #include <BRep_Tool.hxx>
 #include <Geom_Surface.hxx>
@@ -79,7 +77,8 @@ typedef SMESH_Comment TComm;
 
 StdMeshers_Quadrangle_2D::StdMeshers_Quadrangle_2D (int hypId, int studyId,
                                                     SMESH_Gen* gen)
-     : SMESH_2D_Algo(hypId, studyId, gen)
+  : SMESH_2D_Algo(hypId, studyId, gen),
+    myHelper( 0 )
 {
   MESSAGE("StdMeshers_Quadrangle_2D::StdMeshers_Quadrangle_2D");
   _name = "Quadrangle_2D";
@@ -87,7 +86,7 @@ StdMeshers_Quadrangle_2D::StdMeshers_Quadrangle_2D (int hypId, int studyId,
   _compatibleHypothesis.push_back("QuadrangleParams");
   _compatibleHypothesis.push_back("QuadranglePreference");
   _compatibleHypothesis.push_back("TrianglePreference");
-  myHelper = 0;
+  _compatibleHypothesis.push_back("ViscousLayers2D");
 }
 
 //=============================================================================
@@ -193,11 +192,11 @@ bool StdMeshers_Quadrangle_2D::CheckHypothesis
  */
 //=============================================================================
 
-bool StdMeshers_Quadrangle_2D::Compute (SMESH_Mesh& aMesh,
-                                        const TopoDS_Shape& aShape)// throw (SALOME_Exception)
+bool StdMeshers_Quadrangle_2D::Compute (SMESH_Mesh&         aMesh,
+                                        const TopoDS_Shape& aShape)
 {
-  // PAL14921. Enable catching std::bad_alloc and Standard_OutOfMemory outside
-  //Unexpect aCatchSalomeException);
+  const TopoDS_Face& F = TopoDS::Face(aShape);
+  Handle(Geom_Surface) S = BRep_Tool::Surface(F);
 
   SMESHDS_Mesh * meshDS = aMesh.GetMeshDS();
   aMesh.GetSubMesh(aShape);
@@ -205,6 +204,10 @@ bool StdMeshers_Quadrangle_2D::Compute (SMESH_Mesh& aMesh,
   SMESH_MesherHelper helper (aMesh);
   myHelper = &helper;
 
+  myProxyMesh = StdMeshers_ViscousLayers2D::Compute( aMesh, F );
+  if ( !myProxyMesh )
+    return false;
+
   _quadraticMesh = myHelper->IsQuadraticSubMesh(aShape);
   myNeedSmooth = false;
 
@@ -263,9 +266,6 @@ bool StdMeshers_Quadrangle_2D::Compute (SMESH_Mesh& aMesh,
   int nbhoriz  = Min(nbdown, nbup);
   int nbvertic = Min(nbright, nbleft);
 
-  const TopoDS_Face& F = TopoDS::Face(aShape);
-  Handle(Geom_Surface) S = BRep_Tool::Surface(F);
-
   // internal mesh nodes
   int i, j, geomFaceID = meshDS->ShapeToIndex(F);
   for (i = 1; i < nbhoriz - 1; i++) {
@@ -307,10 +307,10 @@ bool StdMeshers_Quadrangle_2D::Compute (SMESH_Mesh& aMesh,
   for (i = ilow; i < iup; i++) {
     for (j = jlow; j < jup; j++) {
       const SMDS_MeshNode *a, *b, *c, *d;
-      a = quad->uv_grid[j * nbhoriz + i].node;
-      b = quad->uv_grid[j * nbhoriz + i + 1].node;
+      a = quad->uv_grid[j       * nbhoriz + i    ].node;
+      b = quad->uv_grid[j       * nbhoriz + i + 1].node;
       c = quad->uv_grid[(j + 1) * nbhoriz + i + 1].node;
-      d = quad->uv_grid[(j + 1) * nbhoriz + i].node;
+      d = quad->uv_grid[(j + 1) * nbhoriz + i    ].node;
       SMDS_MeshFace* face = myHelper->AddFace(a, b, c, d);
       if (face) {
         meshDS->SetMeshElementOnShape(face, geomFaceID);
@@ -831,9 +831,12 @@ FaceQuadStruct* StdMeshers_Quadrangle_2D::CheckNbEdges(SMESH_Mesh &         aMes
         }
         if (!E1.IsNull() && !E2.IsNull() && !E3.IsNull())
         {
-          quad->side.push_back(new StdMeshers_FaceSide(F, E1, &aMesh, true, ignoreMediumNodes));
-          quad->side.push_back(new StdMeshers_FaceSide(F, E2, &aMesh, true, ignoreMediumNodes));
-          quad->side.push_back(new StdMeshers_FaceSide(F, E3, &aMesh, false,ignoreMediumNodes));
+          quad->side.push_back(new StdMeshers_FaceSide(F, E1, &aMesh, true,
+                                                       ignoreMediumNodes, myProxyMesh));
+          quad->side.push_back(new StdMeshers_FaceSide(F, E2, &aMesh, true,
+                                                       ignoreMediumNodes, myProxyMesh));
+          quad->side.push_back(new StdMeshers_FaceSide(F, E3, &aMesh, false,
+                                                       ignoreMediumNodes, myProxyMesh));
           const vector<UVPtStruct>& UVPSleft  = quad->side[0]->GetUVPtStruct(true,0);
           /*  vector<UVPtStruct>& UVPStop   = */quad->side[1]->GetUVPtStruct(false,1);
           /*  vector<UVPtStruct>& UVPSright = */quad->side[2]->GetUVPtStruct(true,1);
@@ -856,8 +859,8 @@ FaceQuadStruct* StdMeshers_Quadrangle_2D::CheckNbEdges(SMESH_Mesh &         aMes
   else if (nbEdgesInWire.front() == 4) // exactly 4 edges
   {
     for (; edgeIt != edges.end(); ++edgeIt, nbSides++)
-      quad->side.push_back(new StdMeshers_FaceSide(F, *edgeIt, &aMesh,
-                                                    nbSides<TOP_SIDE, ignoreMediumNodes));
+      quad->side.push_back(new StdMeshers_FaceSide(F, *edgeIt, &aMesh, nbSides < TOP_SIDE,
+                                                   ignoreMediumNodes, myProxyMesh));
   }
   else if (nbEdgesInWire.front() > 4) // more than 4 edges - try to unite some
   {
@@ -883,8 +886,8 @@ FaceQuadStruct* StdMeshers_Quadrangle_2D::CheckNbEdges(SMESH_Mesh &         aMes
       if ( sideEdges.size() == 1 && BRep_Tool::Degenerated( sideEdges.front() ))
         degenSides.push_back( nbSides );
 
-      quad->side.push_back(new StdMeshers_FaceSide(F, sideEdges, &aMesh,
-                                                    nbSides<TOP_SIDE, ignoreMediumNodes));
+      quad->side.push_back(new StdMeshers_FaceSide(F, sideEdges, &aMesh, nbSides < TOP_SIDE,
+                                                   ignoreMediumNodes, myProxyMesh));
       ++nbSides;
     }
     if ( !degenSides.empty() && nbSides - degenSides.size() == 4 )
@@ -895,9 +898,9 @@ FaceQuadStruct* StdMeshers_Quadrangle_2D::CheckNbEdges(SMESH_Mesh &         aMes
 
       for ( int i = degenSides.size()-1; i > -1; --i )
       {
-        StdMeshers_FaceSide * & degenSide = quad->side[ degenSides[ i ]];
+        StdMeshers_FaceSide* degenSide = quad->side[ degenSides[ i ]];
         delete degenSide;
-        quad->side.erase( vector<StdMeshers_FaceSide*>::iterator( & degenSide ));
+        quad->side.erase( quad->side.begin() + degenSides[ i ] );
       }
       for ( unsigned i = TOP_SIDE; i < quad->side.size(); ++i )
         quad->side[i]->Reverse();
@@ -935,7 +938,8 @@ FaceQuadStruct* StdMeshers_Quadrangle_2D::CheckNbEdges(SMESH_Mesh &         aMes
           }
         }
         quad->side.push_back(new StdMeshers_FaceSide(F, sideEdges, &aMesh,
-                                                      nbSides<TOP_SIDE, ignoreMediumNodes));
+                                                     nbSides < TOP_SIDE,
+                                                     ignoreMediumNodes, myProxyMesh));
         ++nbSides;
       }
     }
@@ -1265,37 +1269,29 @@ bool StdMeshers_Quadrangle_2D::SetNormalizedGrid (SMESH_Mesh & aMesh,
   if ( myNeedSmooth )
     UpdateDegenUV( quad );
 
-  // nodes Id on "in" edges
-  if (! quad->isEdgeOut[0]) {
-    int j = 0;
-    for (int i = 0; i < nbhoriz; i++) { // down
-      int ij = j * nbhoriz + i;
-      uv_grid[ij].node = uv_e0[i].node;
-    }
+  // copy data of face boundary
+  /*if (! quad->isEdgeOut[0])*/ {
+    const int j = 0;
+    for (int i = 0; i < nbhoriz; i++)       // down
+      uv_grid[ j * nbhoriz + i ] = uv_e0[i];
   }
-  if (! quad->isEdgeOut[1]) {
-    int i = nbhoriz - 1;
-    for (int j = 0; j < nbvertic; j++) { // right
-      int ij = j * nbhoriz + i;
-      uv_grid[ij].node = uv_e1[j].node;
-    }
+  /*if (! quad->isEdgeOut[1])*/ {
+    const int i = nbhoriz - 1;
+    for (int j = 0; j < nbvertic; j++)      // right
+      uv_grid[ j * nbhoriz + i ] = uv_e1[j];
   }
-  if (! quad->isEdgeOut[2]) {
-    int j = nbvertic - 1;
-    for (int i = 0; i < nbhoriz; i++) { // up
-      int ij = j * nbhoriz + i;
-      uv_grid[ij].node = uv_e2[i].node;
-    }
+  /*if (! quad->isEdgeOut[2])*/ {
+    const int j = nbvertic - 1;
+    for (int i = 0; i < nbhoriz; i++)       // up
+      uv_grid[ j * nbhoriz + i ] = uv_e2[i];
   }
-  if (! quad->isEdgeOut[3]) {
+  /*if (! quad->isEdgeOut[3])*/ {
     int i = 0;
-    for (int j = 0; j < nbvertic; j++) { // left
-      int ij = j * nbhoriz + i;
-      uv_grid[ij].node = uv_e3[j].node;
-    }
+    for (int j = 0; j < nbvertic; j++)      // left
+      uv_grid[ j * nbhoriz + i ] = uv_e3[j];
   }
 
-  // normalized 2d values on grid
+  // normalized 2d parameters on grid
   for (int i = 0; i < nbhoriz; i++) {
     for (int j = 0; j < nbvertic; j++) {
       int ij = j * nbhoriz + i;
@@ -1316,26 +1312,23 @@ bool StdMeshers_Quadrangle_2D::SetNormalizedGrid (SMESH_Mesh & aMesh,
   }
 
   // 4 --- projection on 2d domain (u,v)
-  gp_UV a0(uv_e0.front().u, uv_e0.front().v);
-  gp_UV a1(uv_e0.back().u,  uv_e0.back().v);
-  gp_UV a2(uv_e2.back().u,  uv_e2.back().v);
-  gp_UV a3(uv_e2.front().u, uv_e2.front().v);
+  gp_UV a0 (uv_e0.front().u, uv_e0.front().v);
+  gp_UV a1 (uv_e0.back().u,  uv_e0.back().v );
+  gp_UV a2 (uv_e2.back().u,  uv_e2.back().v );
+  gp_UV a3 (uv_e2.front().u, uv_e2.front().v);
+
+  for (int i = 0; i < nbhoriz; i++)
+  {
+    gp_UV p0( uv_e0[i].u, uv_e0[i].v );
+    gp_UV p2( uv_e2[i].u, uv_e2[i].v );
+    for (int j = 0; j < nbvertic; j++)
+    {
+      gp_UV p1( uv_e1[j].u, uv_e1[j].v );
+      gp_UV p3( uv_e3[j].u, uv_e3[j].v );
 
-  for (int i = 0; i < nbhoriz; i++) {
-    for (int j = 0; j < nbvertic; j++) {
       int ij = j * nbhoriz + i;
       double x = uv_grid[ij].x;
       double y = uv_grid[ij].y;
-      double param_0 = uv_e0[0].normParam + x * (uv_e0.back().normParam - uv_e0[0].normParam); // sud
-      double param_2 = uv_e2[0].normParam + x * (uv_e2.back().normParam - uv_e2[0].normParam); // nord
-      double param_1 = uv_e1[0].normParam + y * (uv_e1.back().normParam - uv_e1[0].normParam); // est
-      double param_3 = uv_e3[0].normParam + y * (uv_e3.back().normParam - uv_e3[0].normParam); // ouest
-
-      //MESSAGE("params "<<param_0<<" "<<param_1<<" "<<param_2<<" "<<param_3);
-      gp_UV p0 = quad->side[0]->Value2d(param_0).XY();
-      gp_UV p1 = quad->side[1]->Value2d(param_1).XY();
-      gp_UV p2 = quad->side[2]->Value2d(param_2).XY();
-      gp_UV p3 = quad->side[3]->Value2d(param_3).XY();
 
       gp_UV uv = CalcUV(x,y, a0,a1,a2,a3, p0,p1,p2,p3);
 
@@ -1353,7 +1346,8 @@ bool StdMeshers_Quadrangle_2D::SetNormalizedGrid (SMESH_Mesh & aMesh,
 
 static void ShiftQuad(FaceQuadStruct* quad, const int num, bool)
 {
-  StdMeshers_FaceSide* side[4] = { quad->side[0], quad->side[1], quad->side[2], quad->side[3] };
+  StdMeshers_FaceSide* side[4] = { quad->side[0], quad->side[1],
+                                   quad->side[2], quad->side[3] };
   for (int i = BOTTOM_SIDE; i < NB_SIDES; ++i) {
     int id = (i + num) % NB_SIDES;
     bool wasForward = (i < TOP_SIDE);
@@ -1374,23 +1368,18 @@ static gp_UV CalcUV(double x0, double x1, double y0, double y1,
                     const gp_UV& a0, const gp_UV& a1,
                     const gp_UV& a2, const gp_UV& a3)
 {
-  const vector<UVPtStruct>& uv_eb = quad->side[0]->GetUVPtStruct(true,0);
-  const vector<UVPtStruct>& uv_er = quad->side[1]->GetUVPtStruct(false,1);
-  const vector<UVPtStruct>& uv_et = quad->side[2]->GetUVPtStruct(true,1);
-  const vector<UVPtStruct>& uv_el = quad->side[3]->GetUVPtStruct(false,0);
+  // const vector<UVPtStruct>& uv_eb = quad->side[0]->GetUVPtStruct(true,0);
+  // const vector<UVPtStruct>& uv_er = quad->side[1]->GetUVPtStruct(false,1);
+  // const vector<UVPtStruct>& uv_et = quad->side[2]->GetUVPtStruct(true,1);
+  // const vector<UVPtStruct>& uv_el = quad->side[3]->GetUVPtStruct(false,0);
 
   double x = (x0 + y0 * (x1 - x0)) / (1 - (y1 - y0) * (x1 - x0));
   double y = y0 + x * (y1 - y0);
 
-  double param_b = uv_eb[0].normParam + x * (uv_eb.back().normParam - uv_eb[0].normParam);
-  double param_t = uv_et[0].normParam + x * (uv_et.back().normParam - uv_et[0].normParam);
-  double param_r = uv_er[0].normParam + y * (uv_er.back().normParam - uv_er[0].normParam);
-  double param_l = uv_el[0].normParam + y * (uv_el.back().normParam - uv_el[0].normParam);
-
-  gp_UV p0 = quad->side[BOTTOM_SIDE]->Value2d(param_b).XY();
-  gp_UV p1 = quad->side[RIGHT_SIDE ]->Value2d(param_r).XY();
-  gp_UV p2 = quad->side[TOP_SIDE   ]->Value2d(param_t).XY();
-  gp_UV p3 = quad->side[LEFT_SIDE  ]->Value2d(param_l).XY();
+  gp_UV p0 = quad->side[BOTTOM_SIDE]->Value2d(x).XY();
+  gp_UV p1 = quad->side[RIGHT_SIDE ]->Value2d(y).XY();
+  gp_UV p2 = quad->side[TOP_SIDE   ]->Value2d(x).XY();
+  gp_UV p3 = quad->side[LEFT_SIDE  ]->Value2d(y).XY();
 
   gp_UV uv = CalcUV(x,y, a0,a1,a2,a3, p0,p1,p2,p3);
 
@@ -2152,6 +2141,183 @@ void StdMeshers_Quadrangle_2D::SplitQuad(SMESHDS_Mesh *theMeshDS,
   }
 }
 
+namespace
+{
+  enum uvPos { UV_A0, UV_A1, UV_A2, UV_A3, UV_B, UV_R, UV_T, UV_L, UV_SIZE };
+
+  inline  SMDS_MeshNode* makeNode( UVPtStruct &         uvPt,
+                                   const double         y,
+                                   FaceQuadStruct*      quad,
+                                   const gp_UV*         UVs,
+                                   SMESH_MesherHelper*  helper,
+                                   Handle(Geom_Surface) S)
+  {
+    const vector<UVPtStruct>& uv_eb = quad->side[BOTTOM_SIDE]->GetUVPtStruct();
+    const vector<UVPtStruct>& uv_et = quad->side[TOP_SIDE   ]->GetUVPtStruct();
+    double rBot = ( uv_eb.size() - 1 ) * uvPt.normParam;
+    double rTop = ( uv_et.size() - 1 ) * uvPt.normParam;
+    int iBot = int( rBot );
+    int iTop = int( rTop );
+    double xBot = uv_eb[ iBot ].normParam + ( rBot - iBot ) * ( uv_eb[ iBot+1 ].normParam - uv_eb[ iBot ].normParam );
+    double xTop = uv_et[ iTop ].normParam + ( rTop - iTop ) * ( uv_et[ iTop+1 ].normParam - uv_et[ iTop ].normParam );
+    double x = xBot + y * ( xTop - xBot );
+    
+    gp_UV uv = CalcUV(/*x,y=*/x, y,
+                      /*a0,...=*/UVs[UV_A0], UVs[UV_A1], UVs[UV_A2], UVs[UV_A3],
+                      /*p0=*/quad->side[BOTTOM_SIDE]->Value2d( x ).XY(),
+                      /*p1=*/UVs[ UV_R ],
+                      /*p2=*/quad->side[TOP_SIDE   ]->Value2d( x ).XY(),
+                      /*p3=*/UVs[ UV_L ]);
+    gp_Pnt P = S->Value( uv.X(), uv.Y() );
+    uvPt.u = uv.X();
+    uvPt.v = uv.Y();
+    return helper->AddNode(P.X(), P.Y(), P.Z(), 0, uv.X(), uv.Y() );
+  }
+
+  void reduce42( const vector<UVPtStruct>& curr_base,
+                 vector<UVPtStruct>&       next_base,
+                 const int                 j,
+                 int &                     next_base_len,
+                 FaceQuadStruct*           quad,
+                 gp_UV*                    UVs,
+                 const double              y,
+                 SMESH_MesherHelper*       helper,
+                 Handle(Geom_Surface)&     S)
+  {
+    // add one "HH": nodes a,b,c,d,e and faces 1,2,3,4,5,6
+    //
+    //  .-----a-----b i + 1
+    //  |\ 5  | 6  /|
+    //  | \   |   / |
+    //  |  c--d--e  |
+    //  |1 |2 |3 |4 |
+    //  |  |  |  |  |
+    //  .--.--.--.--. i
+    //
+    //  j     j+2   j+4
+
+    // a (i + 1, j + 2)
+    const SMDS_MeshNode*& Na = next_base[ ++next_base_len ].node;
+    if ( !Na )
+      Na = makeNode( next_base[ next_base_len ], y, quad, UVs, helper, S );
+
+    // b (i + 1, j + 4)
+    const SMDS_MeshNode*& Nb = next_base[ ++next_base_len ].node;
+    if ( !Nb )
+      Nb = makeNode( next_base[ next_base_len ], y, quad, UVs, helper, S );
+
+    // c
+    double u = (curr_base[j + 2].u + next_base[next_base_len - 2].u) / 2.0;
+    double v = (curr_base[j + 2].v + next_base[next_base_len - 2].v) / 2.0;
+    gp_Pnt P = S->Value(u,v);
+    SMDS_MeshNode* Nc = helper->AddNode(P.X(), P.Y(), P.Z(), 0, u, v);
+
+    // d
+    u = (curr_base[j + 2].u + next_base[next_base_len - 1].u) / 2.0;
+    v = (curr_base[j + 2].v + next_base[next_base_len - 1].v) / 2.0;
+    P = S->Value(u,v);
+    SMDS_MeshNode* Nd = helper->AddNode(P.X(), P.Y(), P.Z(), 0, u, v);
+
+    // e
+    u = (curr_base[j + 2].u + next_base[next_base_len].u) / 2.0;
+    v = (curr_base[j + 2].v + next_base[next_base_len].v) / 2.0;
+    P = S->Value(u,v);
+    SMDS_MeshNode* Ne = helper->AddNode(P.X(), P.Y(), P.Z(), 0, u, v);
+
+    // Faces
+    helper->AddFace(curr_base[j + 0].node,
+                    curr_base[j + 1].node, Nc,
+                    next_base[next_base_len - 2].node);
+
+    helper->AddFace(curr_base[j + 1].node,
+                    curr_base[j + 2].node, Nd, Nc);
+
+    helper->AddFace(curr_base[j + 2].node,
+                    curr_base[j + 3].node, Ne, Nd);
+
+    helper->AddFace(curr_base[j + 3].node,
+                    curr_base[j + 4].node, Nb, Ne);
+
+    helper->AddFace(Nc, Nd, Na, next_base[next_base_len - 2].node);
+
+    helper->AddFace(Nd, Ne, Nb, Na);
+  }
+
+  void reduce31( const vector<UVPtStruct>& curr_base,
+                 vector<UVPtStruct>&       next_base,
+                 const int                 j,
+                 int &                     next_base_len,
+                 FaceQuadStruct*           quad,
+                 gp_UV*                    UVs,
+                 const double              y,
+                 SMESH_MesherHelper*       helper,
+                 Handle(Geom_Surface)&     S)
+  {
+    // add one "H": nodes b,c,e and faces 1,2,4,5
+    //
+    //  .---------b i + 1
+    //  |\   5   /|
+    //  | \     / |
+    //  |  c---e  |
+    //  |1 |2  |4 |
+    //  |  |   |  |
+    //  .--.---.--. i
+    //
+    //  j j+1 j+2 j+3
+
+    // b (i + 1, j + 3)
+    const SMDS_MeshNode*& Nb = next_base[ ++next_base_len ].node;
+    if ( !Nb )
+      Nb = makeNode( next_base[ next_base_len ], y, quad, UVs, helper, S );
+
+    // c and e
+    double u1 = (curr_base[ j   ].u + next_base[ next_base_len-1 ].u ) / 2.0;
+    double u2 = (curr_base[ j+3 ].u + next_base[ next_base_len   ].u ) / 2.0;
+    double u3 = (u2 - u1) / 3.0;
+    //
+    double v1 = (curr_base[ j   ].v + next_base[ next_base_len-1 ].v ) / 2.0;
+    double v2 = (curr_base[ j+3 ].v + next_base[ next_base_len   ].v ) / 2.0;
+    double v3 = (v2 - v1) / 3.0;
+    // c
+    double u = u1 + u3;
+    double v = v1 + v3;
+    gp_Pnt P = S->Value(u,v);
+    SMDS_MeshNode* Nc = helper->AddNode( P.X(), P.Y(), P.Z(), 0, u, v );
+    // e
+    u = u1 + u3 + u3;
+    v = v1 + v3 + v3;
+    P = S->Value(u,v);
+    SMDS_MeshNode* Ne = helper->AddNode( P.X(), P.Y(), P.Z(), 0, u, v );
+
+    // Faces
+    // 1
+    helper->AddFace( curr_base[ j + 0 ].node,
+                     curr_base[ j + 1 ].node,
+                     Nc,
+                     next_base[ next_base_len - 1 ].node);
+    // 2
+    helper->AddFace( curr_base[ j + 1 ].node,
+                     curr_base[ j + 2 ].node, Ne, Nc);
+    // 4
+    helper->AddFace( curr_base[ j + 2 ].node,
+                     curr_base[ j + 3 ].node, Nb, Ne);
+    // 5
+    helper->AddFace(Nc, Ne, Nb,
+                    next_base[ next_base_len - 1 ].node);
+  }
+
+  typedef void (* PReduceFunction) ( const vector<UVPtStruct>& curr_base,
+                                     vector<UVPtStruct>&       next_base,
+                                     const int                 j,
+                                     int &                     next_base_len,
+                                     FaceQuadStruct*           quad,
+                                     gp_UV*                    UVs,
+                                     const double              y,
+                                     SMESH_MesherHelper*       helper,
+                                     Handle(Geom_Surface)&     S);
+
+} // namespace
+
 //=======================================================================
 /*!
  *  Implementation of Reduced algorithm (meshing with quadrangles only)
@@ -2171,7 +2337,7 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
   int nt = quad->side[2]->NbPoints();
   int nl = quad->side[3]->NbPoints();
 
-  //  Simple Reduce 8->6->4->2 (3 steps)      Multiple Reduce 8->2 (1 step)
+  //  Simple Reduce 10->8->6->4 (3 steps)     Multiple Reduce 10->4 (1 step)
   //
   //  .-----.-----.-----.-----.               .-----.-----.-----.-----.
   //  |    / \    |    / \    |               |    / \    |    / \    |
@@ -2218,9 +2384,9 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
     int nrows = nr1 - 1;
     int ncol_top = nt1 - 1;
     int ncol_bot = nb1 - 1;
-    // maximum number of bottom elements for "tree" simple reduce 3->1
-    int max_tree31 = ncol_top * pow(3.0, nrows);
-    if (ncol_bot > max_tree31)
+    // number of rows needed to reduce ncol_bot to ncol_top using simple 3->1 "tree" (see below)
+    int nrows_tree31 = int( log( (double)(ncol_bot / ncol_top) ) / log((double) 3 )); // = log x base 3
+    if ( nrows < nrows_tree31 )
       MultipleReduce = true;
   }
 
@@ -2256,7 +2422,7 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
     nl = quad->side[3]->NbPoints();
     dh = abs(nb-nt);
     dv = abs(nr-nl);
-    int nbh  = Max(nb,nt);
+    int nbh = Max(nb,nt);
     int nbv = Max(nr,nl);
     int addh = 0;
     int addv = 0;
@@ -2330,7 +2496,7 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
     gp_XY a3 (uv_et.front().u, uv_et.front().v);
 
     int nnn = Min(nr,nl);
-    // auxilary sequence of XY for creation nodes
+    // auxilary sequence of XY for creation of nodes
     // in the bottom part of central domain
     // it's length must be == nbv-nnn-1
     TColgp_SequenceOfXY UVL;
@@ -2380,7 +2546,7 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
         for (j=1; j<nl; j++) {
             SMDS_MeshFace* F =
               myHelper->AddFace(NodesL.Value(i,j), NodesL.Value(i+1,j),
-                              NodesL.Value(i+1,j+1), NodesL.Value(i,j+1));
+                                NodesL.Value(i+1,j+1), NodesL.Value(i,j+1));
             if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
         }
       }
@@ -2435,7 +2601,7 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
         for (j=1; j<nr; j++) {
             SMDS_MeshFace* F =
               myHelper->AddFace(NodesR.Value(i,j), NodesR.Value(i+1,j),
-                              NodesR.Value(i+1,j+1), NodesR.Value(i,j+1));
+                                NodesR.Value(i+1,j+1), NodesR.Value(i,j+1));
             if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
         }
       }
@@ -2532,26 +2698,31 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
     nr = quad->side[1]->NbPoints();
     nt = quad->side[2]->NbPoints();
     nl = quad->side[3]->NbPoints();
+
     // number of rows and columns
     int nrows = nr - 1; // and also == nl - 1
     int ncol_top = nt - 1;
     int ncol_bot = nb - 1;
     int npair_top = ncol_top / 2;
     // maximum number of bottom elements for "linear" simple reduce 4->2
-    int max_lin = ncol_top + npair_top * 2 * nrows;
-    // maximum number of bottom elements for "linear" simple reduce 4->2
+    int max_lin42 = ncol_top + npair_top * 2 * nrows;
+    // maximum number of bottom elements for "linear" simple reduce 3->1
     int max_lin31 = ncol_top + ncol_top * 2 * nrows;
     // maximum number of bottom elements for "tree" simple reduce 4->2
-    int max_tree42 = npair_top * pow(2.0, nrows + 1);
-    if (ncol_top > npair_top * 2) {
-      int delta = ncol_bot - max_tree42;
-      for (int irow = 1; irow < nrows; irow++) {
-        int nfour = delta / 4;
-        delta -= nfour * 2;
+    int max_tree42 = 0;
+    // number of rows needed to reduce ncol_bot to ncol_top using simple 4->2 "tree"
+    int nrows_tree42 = int( log( (double)(ncol_bot / ncol_top) )/log((double)2)  ); // needed to avoid overflow at pow(2) while computing max_tree42
+    if (nrows_tree42 < nrows) {
+      max_tree42 = npair_top * pow(2.0, nrows + 1);
+      if ( ncol_top > npair_top * 2 ) {
+        int delta = ncol_bot - max_tree42;
+        for (int irow = 1; irow < nrows; irow++) {
+          int nfour = delta / 4;
+          delta -= nfour * 2;
+        }
+        if (delta <= (ncol_top - npair_top * 2))
+          max_tree42 = ncol_bot;
       }
-      if (delta <= (ncol_top - npair_top * 2))
-        max_tree42 = ncol_bot;
     }
     // maximum number of bottom elements for "tree" simple reduce 3->1
     //int max_tree31 = ncol_top * pow(3.0, nrows);
@@ -2559,7 +2730,8 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
     bool is_lin_42 = false;
     bool is_tree_31 = false;
     bool is_tree_42 = false;
-    if (ncol_bot > max_lin) {
+    int max_lin = max_lin42;
+    if (ncol_bot > max_lin42) {
       if (ncol_bot <= max_lin31) {
         is_lin_31 = true;
         max_lin = max_lin31;
@@ -2595,53 +2767,184 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
     if (uv_eb.size() != nb || uv_er.size() != nr || uv_et.size() != nt || uv_el.size() != nl)
       return error(COMPERR_BAD_INPUT_MESH);
 
-    // arrays for normalized params
-    TColStd_SequenceOfReal npb, npr, npt, npl;
-    for (j = 0; j < nb; j++) {
-      npb.Append(uv_eb[j].normParam);
-    }
-    for (i = 0; i < nr; i++) {
-      npr.Append(uv_er[i].normParam);
-    }
-    for (j = 0; j < nt; j++) {
-      npt.Append(uv_et[j].normParam);
-    }
-    for (i = 0; i < nl; i++) {
-      npl.Append(uv_el[i].normParam);
-    }
+    myHelper->SetElementsOnShape( true );
 
-    // We will ajust new points to this grid
-    if (!SetNormalizedGrid(aMesh, aShape, quad))
-      return false;
+    gp_UV uv[ UV_SIZE ];
+    uv[ UV_A0 ].SetCoord( uv_eb.front().u, uv_eb.front().v);
+    uv[ UV_A1 ].SetCoord( uv_eb.back().u,  uv_eb.back().v );
+    uv[ UV_A2 ].SetCoord( uv_et.back().u,  uv_et.back().v );
+    uv[ UV_A3 ].SetCoord( uv_et.front().u, uv_et.front().v);
 
-    // TODO ???
-    gp_XY a0 (uv_eb.front().u, uv_eb.front().v);
-    gp_XY a1 (uv_eb.back().u,  uv_eb.back().v);
-    gp_XY a2 (uv_et.back().u,  uv_et.back().v);
-    gp_XY a3 (uv_et.front().u, uv_et.front().v);
-    //=========================================================
+    vector<UVPtStruct> curr_base = uv_eb, next_base;
 
-    TColStd_SequenceOfInteger curr_base, next_base;
-    TColStd_SequenceOfReal curr_par_u, curr_par_v;
-    TColStd_SequenceOfReal next_par_u, next_par_v;
-    StdMeshers_Array2OfNode NodesBRD (1,nb, 1,nr);
-    for (j = 1; j <= nb; j++) {
-      NodesBRD.SetValue(j, 1, uv_eb[j - 1].node); // bottom
-      curr_base.Append(j);
-      next_base.Append(-1);
-      curr_par_u.Append(uv_eb[j-1].u);
-      curr_par_v.Append(uv_eb[j-1].v);
-      next_par_u.Append(0.);
-      next_par_v.Append(0.);
-    }
-    for (j = 1; j <= nt; j++) {
-      NodesBRD.SetValue(j, nr, uv_et[j - 1].node); // top
-    }
+    UVPtStruct nullUVPtStruct; nullUVPtStruct.node = 0;
 
     int curr_base_len = nb;
     int next_base_len = 0;
 
-    if (is_tree_42) {
+    if ( true )
+    { // ------------------------------------------------------------------
+      // New algorithm implemented by request of IPAL22856
+      // "2D quadrangle mesher of reduced type works wrong"
+      // http://bugtracker.opencascade.com/show_bug.cgi?id=22856
+
+      // the algorithm is following: all reduces are centred in horizontal
+      // direction and are distributed among all rows
+
+      if (ncol_bot > max_tree42) {
+        is_lin_31 = true;
+      }
+      else {
+        if ((ncol_top/3)*3 == ncol_top ) {
+          is_lin_31 = true;
+        }
+        else {
+          is_lin_42 = true;
+        }
+      }
+
+      const int col_top_size  = is_lin_42 ? 2 : 1;
+      const int col_base_size = is_lin_42 ? 4 : 3;
+
+      // Compute nb of "columns" (like in "linear" simple reducing) in all rows
+
+      vector<int> nb_col_by_row;
+
+      int delta_all = nb - nt;
+      int delta_one_col = nrows * 2;
+      int nb_col = delta_all / delta_one_col;
+      int remainder = delta_all - nb_col * delta_one_col;
+      if (remainder > 0) {
+        nb_col++;
+      }
+      if ( nb_col * col_top_size >= nt ) // == "tree" reducing situation
+      {
+        // top row is full (all elements reduced), add "columns" one by one
+        // in rows below until all bottom elements are reduced
+        nb_col = ( nt - 1 ) / col_top_size;
+        nb_col_by_row.resize( nrows, nb_col );
+        int nbrows_not_full = nrows - 1;
+        int cur_top_size = nt - 1;
+        remainder = delta_all - nb_col * delta_one_col;
+        while ( remainder > 0 )
+        {
+          delta_one_col = nbrows_not_full * 2;
+          int nb_col_add = remainder / delta_one_col;
+          cur_top_size += 2 * nb_col_by_row[ nbrows_not_full ];
+          int nb_col_free = cur_top_size / col_top_size - nb_col_by_row[ nbrows_not_full-1 ];
+          if ( nb_col_add > nb_col_free )
+            nb_col_add = nb_col_free;
+          for ( int irow = 0; irow < nbrows_not_full; ++irow )
+            nb_col_by_row[ irow ] += nb_col_add;
+          nbrows_not_full --;
+          remainder -=  nb_col_add * delta_one_col;
+        }
+      }
+      else // == "linear" reducing situation
+      {
+        nb_col_by_row.resize( nrows, nb_col );
+        if (remainder > 0)
+          for ( int irow = remainder / 2; irow < nrows; ++irow )
+            nb_col_by_row[ irow ]--;
+      }
+
+      // Make elements
+
+      PReduceFunction reduceFunction = & ( is_lin_42 ? reduce42 : reduce31 );
+
+      const int reduce_grp_size = is_lin_42 ? 4 : 3;
+
+      for (i = 1; i < nr; i++) // layer by layer
+      {
+        nb_col = nb_col_by_row[ i-1 ];
+        int nb_next = curr_base_len - nb_col * 2;
+        if (nb_next < nt) nb_next = nt;
+
+        const double y = uv_el[ i ].normParam;
+
+        if ( i + 1 == nr ) // top
+        {
+          next_base = uv_et;
+        }
+        else
+        {
+          next_base.clear();
+          next_base.resize( nb_next, nullUVPtStruct );
+          next_base.front() = uv_el[i];
+          next_base.back()  = uv_er[i];
+
+          // compute normalized param u
+          double du = 1. / ( nb_next - 1 );
+          next_base[0].normParam = 0.;
+          for ( j = 1; j < nb_next; ++j )
+            next_base[j].normParam = next_base[j-1].normParam + du;
+        }
+        uv[ UV_L ].SetCoord( next_base.front().u, next_base.front().v );
+        uv[ UV_R ].SetCoord( next_base.back().u,  next_base.back().v );
+
+        int free_left = ( curr_base_len - 1 - nb_col * col_base_size ) / 2;
+        int free_middle = curr_base_len - 1 - nb_col * col_base_size - 2 * free_left;
+
+        // not reduced left elements
+        for (j = 0; j < free_left; j++)
+        {
+          // f (i + 1, j + 1)
+          const SMDS_MeshNode*& Nf = next_base[++next_base_len].node;
+          if ( !Nf )
+            Nf = makeNode( next_base[ next_base_len ], y, quad, uv, myHelper, S );
+
+          myHelper->AddFace(curr_base[ j ].node,
+                            curr_base[ j+1 ].node,
+                            Nf,
+                            next_base[ next_base_len-1 ].node);
+        }
+
+        for (int icol = 1; icol <= nb_col; icol++)
+        {
+          // add "H"
+          reduceFunction( curr_base, next_base, j, next_base_len, quad, uv, y, myHelper, S );
+
+          j += reduce_grp_size;
+
+          // elements in the middle of "columns" added for symmetry
+          if ( free_middle > 0 && ( nb_col % 2 == 0 ) && icol == nb_col / 2 )
+          {
+            for (int imiddle = 1; imiddle <= free_middle; imiddle++) {
+              // f (i + 1, j + imiddle)
+              const SMDS_MeshNode*& Nf = next_base[++next_base_len].node;
+              if ( !Nf )
+                Nf = makeNode( next_base[ next_base_len ], y, quad, uv, myHelper, S );
+
+              myHelper->AddFace(curr_base[ j-1+imiddle ].node,
+                                curr_base[ j  +imiddle ].node,
+                                Nf,
+                                next_base[ next_base_len-1 ].node);
+            }
+            j += free_middle;
+          }
+        }
+
+        // not reduced right elements
+        for (; j < curr_base_len-1; j++) {
+          // f (i + 1, j + 1)
+          const SMDS_MeshNode*& Nf = next_base[++next_base_len].node;
+          if ( !Nf )
+            Nf = makeNode( next_base[ next_base_len ], y, quad, uv, myHelper, S );
+
+          myHelper->AddFace(curr_base[ j ].node,
+                            curr_base[ j+1 ].node,
+                            Nf,
+                            next_base[ next_base_len-1 ].node);
+        }
+
+        curr_base_len = next_base_len + 1;
+        next_base_len = 0;
+        curr_base.swap( next_base );
+      }
+
+    }
+    else if ( is_tree_42 || is_tree_31 )
+    {
       // "tree" simple reduce "42": 2->4->8->16->32->...
       //
       //  .-------------------------------.-------------------------------. nr
@@ -2663,236 +2966,6 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
       //  .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. 1
       //  1                               j                               nb
 
-      for (i = 1; i < nr; i++) { // layer by layer
-        // left
-        NodesBRD.SetValue(1, i+1, uv_el[i].node);
-        next_base.SetValue(++next_base_len, 1);
-        // right
-        NodesBRD.SetValue(nb, i+1, uv_er[i].node);
-
-        next_par_u.SetValue(next_base_len, uv_el[i].u);
-        next_par_v.SetValue(next_base_len, uv_el[i].v);
-
-        // to stop reducing, if number of nodes reaches nt
-        int delta = curr_base_len - nt;
-
-        //double du = uv_er[i].u - uv_el[i].u;
-        //double dv = uv_er[i].v - uv_el[i].v;
-
-        // to calculate normalized parameter, we must know number of points in next layer
-        int nb_four = (curr_base_len - 1) / 4;
-        int nb_next = nb_four*2 + (curr_base_len - nb_four*4);
-        if (nb_next < nt) nb_next = nt;
-
-        for (j = 1; j + 4 <= curr_base_len && delta > 0; j += 4, delta -= 2) {
-          // add one "HH": nodes a,b,c,d,e and faces 1,2,3,4,5,6
-          //
-          //  .-----a-----b i + 1
-          //  |\ 5  | 6  /|
-          //  | \   |   / |
-          //  |  c--d--e  |
-          //  |1 |2 |3 |4 |
-          //  |  |  |  |  |
-          //  .--.--.--.--. i
-          //
-          //  j     j+2   j+4
-
-          double u,v;
-
-          // a (i + 1, j + 2)
-          const SMDS_MeshNode* Na;
-          next_base_len++;
-          next_base.SetValue(next_base_len, curr_base.Value(j + 2));
-          if (i + 1 == nr) { // top
-            Na = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Na);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else {
-            //double norm_par = double(next_base_len - 1)/double(nb_next - 1);
-            //u = uv_el[i].u + du * norm_par;
-            //v = uv_el[i].v + dv * norm_par;
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            //u = uv_el[i].u + du*npb.Value(curr_base.Value(j + 2));
-            //v = uv_el[i].v + dv*npb.Value(curr_base.Value(j + 2));
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Na1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Na1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Na1);
-            Na = Na1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-
-          // b (i + 1, j + 4)
-          const SMDS_MeshNode* Nb;
-          next_base_len++;
-          next_base.SetValue(next_base_len, curr_base.Value(j + 4));
-          if (i + 1 == nr) { // top
-            Nb = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nb);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else if (j + 4 == curr_base_len) { // right
-            Nb = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-            u = uv_er[i].u;
-            v = uv_er[i].v;
-          }
-          else {
-            //double norm_par = double(next_base_len - 1)/double(nb_next - 1);
-            //u = uv_el[i].u + du * norm_par;
-            //v = uv_el[i].v + dv * norm_par;
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            //u = uv_el[i].u + du*npb.Value(curr_base.Value(j + 4));
-            //v = uv_el[i].v + dv*npb.Value(curr_base.Value(j + 4));
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nb1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nb1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nb1);
-            Nb = Nb1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-
-          // c
-          u = (curr_par_u.Value(j + 2) + next_par_u.Value(next_base_len - 2)) / 2.0;
-          v = (curr_par_v.Value(j + 2) + next_par_v.Value(next_base_len - 2)) / 2.0;
-          gp_Pnt P = S->Value(u,v);
-          SMDS_MeshNode* Nc = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Nc, geomFaceID, u, v);
-
-          // d
-          u = (curr_par_u.Value(j + 2) + next_par_u.Value(next_base_len - 1)) / 2.0;
-          v = (curr_par_v.Value(j + 2) + next_par_v.Value(next_base_len - 1)) / 2.0;
-          P = S->Value(u,v);
-          SMDS_MeshNode* Nd = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Nd, geomFaceID, u, v);
-
-          // e
-          u = (curr_par_u.Value(j + 2) + next_par_u.Value(next_base_len)) / 2.0;
-          v = (curr_par_v.Value(j + 2) + next_par_v.Value(next_base_len)) / 2.0;
-          P = S->Value(u,v);
-          SMDS_MeshNode* Ne = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Ne, geomFaceID, u, v);
-
-          // Faces
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 0), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              Nc,
-                                              NodesBRD.Value(next_base.Value(next_base_len - 2), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-
-          SMDS_MeshFace* F2 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(curr_base.Value(j + 2), i),
-                                              Nd, Nc);
-          if (F2) meshDS->SetMeshElementOnShape(F2, geomFaceID);
-
-          SMDS_MeshFace* F3 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 2), i),
-                                              NodesBRD.Value(curr_base.Value(j + 3), i),
-                                              Ne, Nd);
-          if (F3) meshDS->SetMeshElementOnShape(F3, geomFaceID);
-
-          SMDS_MeshFace* F4 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 3), i),
-                                              NodesBRD.Value(curr_base.Value(j + 4), i),
-                                              Nb, Ne);
-          if (F4) meshDS->SetMeshElementOnShape(F4, geomFaceID);
-
-          SMDS_MeshFace* F5 = myHelper->AddFace(Nc, Nd, Na,
-                                              NodesBRD.Value(next_base.Value(next_base_len - 2), i + 1));
-          if (F5) meshDS->SetMeshElementOnShape(F5, geomFaceID);
-
-          SMDS_MeshFace* F6 = myHelper->AddFace(Nd, Ne, Nb, Na);
-          if (F6) meshDS->SetMeshElementOnShape(F6, geomFaceID);
-        }
-
-        // not reduced side elements (if any)
-        for (; j < curr_base_len; j++) {
-          // f (i + 1, j + 1)
-          const SMDS_MeshNode* Nf;
-          double u,v;
-          next_base.SetValue(++next_base_len, curr_base.Value(j + 1));
-          if (i + 1 == nr) { // top
-            Nf = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else if (j + 1 == curr_base_len) { // right
-            Nf = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-            u = uv_er[i].u;
-            v = uv_er[i].v;
-          }
-          else {
-            //double norm_par = double(next_base_len - 1)/double(nb_next - 1);
-            //u = uv_el[i].u + du * norm_par;
-            //v = uv_el[i].v + dv * norm_par;
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            //u = uv_el[i].u + du*npb.Value(curr_base.Value(j + 1));
-            //v = uv_el[i].v + dv*npb.Value(curr_base.Value(j + 1));
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nf1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nf1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf1);
-            Nf = Nf1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(next_base.Value(next_base_len), i + 1),
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-        }
-
-        curr_base_len = next_base_len;
-        curr_base = next_base;
-        curr_par_u = next_par_u;
-        curr_par_v = next_par_v;
-        next_base_len = 0;
-      }
-    } // end "tree" simple reduce "42"
-    else if (is_tree_31) {
       // "tree" simple reduce "31": 1->3->9->27->...
       //
       //  .-----------------------------------------------------. nr
@@ -2910,178 +2983,84 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
       //  .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. 1
       //  1                          j                          nb
 
-      for (i = 1; i < nr; i++) { // layer by layer
-        // left
-        NodesBRD.SetValue(1, i+1, uv_el[i].node);
-        next_base.SetValue(++next_base_len, 1);
-        // right
-        NodesBRD.SetValue(nb, i+1, uv_er[i].node);
+      PReduceFunction reduceFunction = & ( is_tree_42 ? reduce42 : reduce31 );
 
-        next_par_u.SetValue(next_base_len, uv_el[i].u);
-        next_par_v.SetValue(next_base_len, uv_el[i].v);
+      const int reduce_grp_size = is_tree_42 ? 4 : 3;
 
+      for (i = 1; i < nr; i++) // layer by layer
+      {
         // to stop reducing, if number of nodes reaches nt
         int delta = curr_base_len - nt;
 
         // to calculate normalized parameter, we must know number of points in next layer
-        int nb_three = (curr_base_len - 1) / 3;
-        int nb_next = nb_three + (curr_base_len - nb_three*3);
+        int nb_reduce_groups = (curr_base_len - 1) / reduce_grp_size;
+        int nb_next = nb_reduce_groups * (reduce_grp_size-2) + (curr_base_len - nb_reduce_groups*reduce_grp_size);
         if (nb_next < nt) nb_next = nt;
 
-        for (j = 1; j + 3 <= curr_base_len && delta > 0; j += 3, delta -= 2) {
-          // add one "H": nodes b,c,e and faces 1,2,4,5
-          //
-          //  .---------b i + 1
-          //  |\   5   /|
-          //  | \     / |
-          //  |  c---e  |
-          //  |1 |2  |4 |
-          //  |  |   |  |
-          //  .--.---.--. i
-          //
-          //  j j+1 j+2 j+3
-
-          double u,v;
-
-          // b (i + 1, j + 3)
-          const SMDS_MeshNode* Nb;
-          next_base_len++;
-          next_base.SetValue(next_base_len, curr_base.Value(j + 3));
-          if (i + 1 == nr) { // top
-            Nb = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nb);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else if (j + 3 == curr_base_len) { // right
-            Nb = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-            u = uv_er[i].u;
-            v = uv_er[i].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nb1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nb1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nb1);
-            Nb = Nb1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-
-          // c and e
-          double u1 = (curr_par_u.Value(j) + next_par_u.Value(next_base_len - 1)) / 2.0;
-          double u2 = (curr_par_u.Value(j + 3) + next_par_u.Value(next_base_len)) / 2.0;
-          double u3 = (u2 - u1) / 3.0;
-
-          double v1 = (curr_par_v.Value(j) + next_par_v.Value(next_base_len - 1)) / 2.0;
-          double v2 = (curr_par_v.Value(j + 3) + next_par_v.Value(next_base_len)) / 2.0;
-          double v3 = (v2 - v1) / 3.0;
-
-          // c
-          u = u1 + u3;
-          v = v1 + v3;
-          gp_Pnt P = S->Value(u,v);
-          SMDS_MeshNode* Nc = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Nc, geomFaceID, u, v);
-
-          // e
-          u = u1 + u3 + u3;
-          v = v1 + v3 + v3;
-          P = S->Value(u,v);
-          SMDS_MeshNode* Ne = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Ne, geomFaceID, u, v);
-
-          // Faces
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 0), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              Nc,
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-
-          SMDS_MeshFace* F2 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(curr_base.Value(j + 2), i),
-                                              Ne, Nc);
-          if (F2) meshDS->SetMeshElementOnShape(F2, geomFaceID);
-
-          SMDS_MeshFace* F4 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 2), i),
-                                              NodesBRD.Value(curr_base.Value(j + 3), i),
-                                              Nb, Ne);
-          if (F4) meshDS->SetMeshElementOnShape(F4, geomFaceID);
-
-          SMDS_MeshFace* F5 = myHelper->AddFace(Nc, Ne, Nb,
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F5) meshDS->SetMeshElementOnShape(F5, geomFaceID);
+        const double y = uv_el[ i ].normParam;
+
+        if ( i + 1 == nr ) // top
+        {
+          next_base = uv_et;
+        }
+        else
+        {
+          next_base.clear();
+          next_base.resize( nb_next, nullUVPtStruct );
+          next_base.front() = uv_el[i];
+          next_base.back()  = uv_er[i];
+
+          // compute normalized param u
+          double du = 1. / ( nb_next - 1 );
+          next_base[0].normParam = 0.;
+          for ( j = 1; j < nb_next; ++j )
+            next_base[j].normParam = next_base[j-1].normParam + du;
+        }
+        uv[ UV_L ].SetCoord( next_base.front().u, next_base.front().v );
+        uv[ UV_R ].SetCoord( next_base.back().u,  next_base.back().v );
+
+        for (j = 0; j+reduce_grp_size < curr_base_len && delta > 0; j+=reduce_grp_size, delta-=2)
+        {
+          reduceFunction( curr_base, next_base, j, next_base_len, quad, uv, y, myHelper, S );
         }
 
         // not reduced side elements (if any)
-        for (; j < curr_base_len; j++) {
+        for (; j < curr_base_len-1; j++)
+        {
           // f (i + 1, j + 1)
-          const SMDS_MeshNode* Nf;
-          double u,v;
-          next_base.SetValue(++next_base_len, curr_base.Value(j + 1));
-          if (i + 1 == nr) { // top
-            Nf = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else if (j + 1 == curr_base_len) { // right
-            Nf = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-            u = uv_er[i].u;
-            v = uv_er[i].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nf1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nf1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf1);
-            Nf = Nf1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(next_base.Value(next_base_len), i + 1),
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-        }
-
-        curr_base_len = next_base_len;
-        curr_base = next_base;
-        curr_par_u = next_par_u;
-        curr_par_v = next_par_v;
+          const SMDS_MeshNode*& Nf = next_base[++next_base_len].node;
+          if ( !Nf )
+            Nf = makeNode( next_base[ next_base_len ], y, quad, uv, myHelper, S );
+          
+          myHelper->AddFace(curr_base[ j ].node,
+                            curr_base[ j+1 ].node,
+                            Nf,
+                            next_base[ next_base_len-1 ].node);
+        }
+        curr_base_len = next_base_len + 1;
         next_base_len = 0;
+        curr_base.swap( next_base );
       }
-    } // end "tree" simple reduce "31"
-    else if (is_lin_42) {
+    } // end "tree" simple reduce
+
+    else if ( is_lin_42 || is_lin_31 ) {
+      // "linear" simple reduce "31": 2->6->10->14
+      //
+      //  .-----------------------------.-----------------------------. nr
+      //  |     \                 /     |     \                 /     |
+      //  |         .---------.         |         .---------.         |
+      //  |         |         |         |         |         |         |
+      //  .---------.---------.---------.---------.---------.---------.
+      //  |        / \       / \        |        / \       / \        |
+      //  |       /   .-----.   \       |       /   .-----.   \       | i
+      //  |      /    |     |    \      |      /    |     |    \      |
+      //  .-----.-----.-----.-----.-----.-----.-----.-----.-----.-----.
+      //  |    /     / \   / \     \    |    /     / \   / \     \    |
+      //  |   /     /   .-.   \     \   |   /     /   .-.   \     \   |
+      //  |  /     /   /   \   \     \  |  /     /   /   \   \     \  |
+      //  .--.----.---.-----.---.-----.-.--.----.---.-----.---.-----.-. 1
+      //  1                             j                             nb
+
       // "linear" simple reduce "42": 4->8->12->16
       //
       //  .---------------.---------------.---------------.---------------. nr
@@ -3117,7 +3096,8 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
       if (remainder > 0) {
         nb_col++;
       }
-      int free_left = ((nt - 1) - nb_col * 2) / 2;
+      const int col_top_size = is_lin_42 ? 2 : 1;
+      int free_left = ((nt - 1) - nb_col * col_top_size) / 2;
       free_left += nr - 2;
       int free_middle = (nr - 2) * 2;
       if (remainder > 0 && nb_col == 1) {
@@ -3134,17 +3114,12 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
       //int free_left = 2;
       //int free_middle = 4;
 
-      for (i = 1; i < nr; i++, free_middle -= 2, free_left -= 1) { // layer by layer
-        // left
-        NodesBRD.SetValue(1, i+1, uv_el[i].node);
-        next_base.SetValue(++next_base_len, 1);
-        // right
-        NodesBRD.SetValue(nb, i+1, uv_er[i].node);
+      PReduceFunction reduceFunction = & ( is_lin_42 ? reduce42 : reduce31 );
 
-        // left
-        next_par_u.SetValue(next_base_len, uv_el[i].u);
-        next_par_v.SetValue(next_base_len, uv_el[i].v);
+      const int reduce_grp_size = is_lin_42 ? 4 : 3;
 
+      for (i = 1; i < nr; i++, free_middle -= 2, free_left -= 1) // layer by layer
+      {
         // to calculate normalized parameter, we must know number of points in next layer
         int nb_next = curr_base_len - nb_col * 2;
         if (remainder > 0 && i > remainder / 2)
@@ -3152,399 +3127,40 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
           nb_next += 2;
         if (nb_next < nt) nb_next = nt;
 
-        // not reduced left elements
-        for (j = 1; j <= free_left; j++) {
-          // f (i + 1, j + 1)
-          const SMDS_MeshNode* Nf;
-          double u,v;
-          next_base.SetValue(++next_base_len, curr_base.Value(j + 1));
-          if (i + 1 == nr) { // top
-            Nf = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nf1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nf1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf1);
-            Nf = Nf1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(next_base.Value(next_base_len), i + 1),
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-        }
-
-        for (int icol = 1; icol <= nb_col; icol++) {
-
-          if (remainder > 0 && icol == nb_col && i > remainder / 2)
-            // stop short "column"
-            break;
-
-          // add one "HH": nodes a,b,c,d,e and faces 1,2,3,4,5,6
-          //
-          //  .-----a-----b i + 1
-          //  |\ 5  | 6  /|
-          //  | \   |   / |
-          //  |  c--d--e  |
-          //  |1 |2 |3 |4 |
-          //  |  |  |  |  |
-          //  .--.--.--.--. i
-          //
-          //  j     j+2   j+4
-
-          double u,v;
-
-          // a (i + 1, j + 2)
-          const SMDS_MeshNode* Na;
-          next_base_len++;
-          next_base.SetValue(next_base_len, curr_base.Value(j + 2));
-          if (i + 1 == nr) { // top
-            Na = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Na);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Na1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Na1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Na1);
-            Na = Na1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-
-          // b (i + 1, j + 4)
-          const SMDS_MeshNode* Nb;
-          next_base_len++;
-          next_base.SetValue(next_base_len, curr_base.Value(j + 4));
-          if (i + 1 == nr) { // top
-            Nb = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nb);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else if (j + 4 == curr_base_len) { // right
-            Nb = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-            u = uv_er[i].u;
-            v = uv_er[i].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nb1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nb1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nb1);
-            Nb = Nb1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-
-          // c
-          u = (curr_par_u.Value(j + 2) + next_par_u.Value(next_base_len - 2)) / 2.0;
-          v = (curr_par_v.Value(j + 2) + next_par_v.Value(next_base_len - 2)) / 2.0;
-          gp_Pnt P = S->Value(u,v);
-          SMDS_MeshNode* Nc = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Nc, geomFaceID, u, v);
-
-          // d
-          u = (curr_par_u.Value(j + 2) + next_par_u.Value(next_base_len - 1)) / 2.0;
-          v = (curr_par_v.Value(j + 2) + next_par_v.Value(next_base_len - 1)) / 2.0;
-          P = S->Value(u,v);
-          SMDS_MeshNode* Nd = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Nd, geomFaceID, u, v);
-
-          // e
-          u = (curr_par_u.Value(j + 2) + next_par_u.Value(next_base_len)) / 2.0;
-          v = (curr_par_v.Value(j + 2) + next_par_v.Value(next_base_len)) / 2.0;
-          P = S->Value(u,v);
-          SMDS_MeshNode* Ne = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Ne, geomFaceID, u, v);
-
-          // Faces
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 0), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              Nc,
-                                              NodesBRD.Value(next_base.Value(next_base_len - 2), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-
-          SMDS_MeshFace* F2 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(curr_base.Value(j + 2), i),
-                                              Nd, Nc);
-          if (F2) meshDS->SetMeshElementOnShape(F2, geomFaceID);
-
-          SMDS_MeshFace* F3 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 2), i),
-                                              NodesBRD.Value(curr_base.Value(j + 3), i),
-                                              Ne, Nd);
-          if (F3) meshDS->SetMeshElementOnShape(F3, geomFaceID);
-
-          SMDS_MeshFace* F4 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 3), i),
-                                              NodesBRD.Value(curr_base.Value(j + 4), i),
-                                              Nb, Ne);
-          if (F4) meshDS->SetMeshElementOnShape(F4, geomFaceID);
-
-          SMDS_MeshFace* F5 = myHelper->AddFace(Nc, Nd, Na,
-                                              NodesBRD.Value(next_base.Value(next_base_len - 2), i + 1));
-          if (F5) meshDS->SetMeshElementOnShape(F5, geomFaceID);
-
-          SMDS_MeshFace* F6 = myHelper->AddFace(Nd, Ne, Nb, Na);
-          if (F6) meshDS->SetMeshElementOnShape(F6, geomFaceID);
-
-          j += 4;
-
-          // not reduced middle elements
-          if (icol < nb_col) {
-            if (remainder > 0 && icol == nb_col - 1 && i > remainder / 2)
-              // pass middle elements before stopped short "column"
-              break;
-
-            int free_add = free_middle;
-            if (remainder > 0 && icol == nb_col - 1)
-              // next "column" is short
-              free_add -= (nr - 1) - (remainder / 2);
+        const double y = uv_el[ i ].normParam;
 
-            for (int imiddle = 1; imiddle <= free_add; imiddle++) {
-              // f (i + 1, j + imiddle)
-              const SMDS_MeshNode* Nf;
-              double u,v;
-              next_base.SetValue(++next_base_len, curr_base.Value(j + imiddle));
-              if (i + 1 == nr) { // top
-                Nf = uv_et[next_base_len - 1].node;
-                NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf);
-                u = uv_et[next_base_len - 1].u;
-                v = uv_et[next_base_len - 1].v;
-              }
-              else if (j + imiddle == curr_base_len) { // right
-                Nf = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-                u = uv_er[i].u;
-                v = uv_er[i].v;
-              }
-              else {
-                {
-                  double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-                  int nearest_node_j = (int)rel;
-                  rel -= nearest_node_j;
-                  int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-                  double u1 = quad->uv_grid[ij].u;
-                  double v1 = quad->uv_grid[ij].v;
-                  double u2 = quad->uv_grid[ij + 1].u;
-                  double v2 = quad->uv_grid[ij + 1].v;
-                  double duj = (u2 - u1) * rel;
-                  double dvj = (v2 - v1) * rel;
-                  u = u1 + duj;
-                  v = v1 + dvj;
-                }
-                gp_Pnt P = S->Value(u,v);
-                SMDS_MeshNode* Nf1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-                meshDS->SetNodeOnFace(Nf1, geomFaceID, u, v);
-                NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf1);
-                Nf = Nf1;
-              }
-              next_par_u.SetValue(next_base_len, u);
-              next_par_v.SetValue(next_base_len, v);
-              SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j - 1 + imiddle), i),
-                                                  NodesBRD.Value(curr_base.Value(j + imiddle), i),
-                                                  NodesBRD.Value(next_base.Value(next_base_len), i + 1),
-                                                  NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-              if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-            }
-            j += free_add;
-          }
+        if ( i + 1 == nr ) // top
+        {
+          next_base = uv_et;
         }
-
-        // not reduced right elements
-        for (; j < curr_base_len; j++) {
-          // f (i + 1, j + 1)
-          const SMDS_MeshNode* Nf;
-          double u,v;
-          next_base.SetValue(++next_base_len, curr_base.Value(j + 1));
-          if (i + 1 == nr) { // top
-            Nf = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else if (j + 1 == curr_base_len) { // right
-            Nf = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-            u = uv_er[i].u;
-            v = uv_er[i].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nf1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nf1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf1);
-            Nf = Nf1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(next_base.Value(next_base_len), i + 1),
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-        }
-
-        curr_base_len = next_base_len;
-        curr_base = next_base;
-        curr_par_u = next_par_u;
-        curr_par_v = next_par_v;
-        next_base_len = 0;
-      }
-    } // end "linear" simple reduce "42"
-    else if (is_lin_31) {
-      // "linear" simple reduce "31": 2->6->10->14
-      //
-      //  .-----------------------------.-----------------------------. nr
-      //  |     \                 /     |     \                 /     |
-      //  |         .---------.         |         .---------.         |
-      //  |         |         |         |         |         |         |
-      //  .---------.---------.---------.---------.---------.---------.
-      //  |        / \       / \        |        / \       / \        |
-      //  |       /   .-----.   \       |       /   .-----.   \       | i
-      //  |      /    |     |    \      |      /    |     |    \      |
-      //  .-----.-----.-----.-----.-----.-----.-----.-----.-----.-----.
-      //  |    /     / \   / \     \    |    /     / \   / \     \    |
-      //  |   /     /   .-.   \     \   |   /     /   .-.   \     \   |
-      //  |  /     /   /   \   \     \  |  /     /   /   \   \     \  |
-      //  .--.----.---.-----.---.-----.-.--.----.---.-----.---.-----.-. 1
-      //  1                             j                             nb
-
-      int delta_all = nb - nt;
-      int delta_one_col = (nr - 1) * 2;
-      int nb_col = delta_all / delta_one_col;
-      int remainder = delta_all - nb_col * delta_one_col;
-      if (remainder > 0) {
-        nb_col++;
-      }
-      int free_left = ((nt - 1) - nb_col) / 2;
-      free_left += nr - 2;
-      int free_middle = (nr - 2) * 2;
-      if (remainder > 0 && nb_col == 1) {
-        int nb_rows_short_col = remainder / 2;
-        int nb_rows_thrown = (nr - 1) - nb_rows_short_col;
-        free_left -= nb_rows_thrown;
-      }
-
-      for (i = 1; i < nr; i++, free_middle -= 2, free_left -= 1) { // layer by layer
-        // left
-        NodesBRD.SetValue(1, i+1, uv_el[i].node);
-        next_base.SetValue(++next_base_len, 1);
-        // right
-        NodesBRD.SetValue(nb, i+1, uv_er[i].node);
-
-        // left
-        next_par_u.SetValue(next_base_len, uv_el[i].u);
-        next_par_v.SetValue(next_base_len, uv_el[i].v);
-
-        // to calculate normalized parameter, we must know number of points in next layer
-        int nb_next = curr_base_len - nb_col * 2;
-        if (remainder > 0 && i > remainder / 2)
-          // take into account short "column"
-          nb_next += 2;
-        if (nb_next < nt) nb_next = nt;
+        else
+        {
+          next_base.clear();
+          next_base.resize( nb_next, nullUVPtStruct );
+          next_base.front() = uv_el[i];
+          next_base.back()  = uv_er[i];
+
+          // compute normalized param u
+          double du = 1. / ( nb_next - 1 );
+          next_base[0].normParam = 0.;
+          for ( j = 1; j < nb_next; ++j )
+            next_base[j].normParam = next_base[j-1].normParam + du;
+        }
+        uv[ UV_L ].SetCoord( next_base.front().u, next_base.front().v );
+        uv[ UV_R ].SetCoord( next_base.back().u,  next_base.back().v );
 
         // not reduced left elements
-        for (j = 1; j <= free_left; j++) {
+        for (j = 0; j < free_left; j++)
+        {
           // f (i + 1, j + 1)
-          const SMDS_MeshNode* Nf;
-          double u,v;
-          next_base.SetValue(++next_base_len, curr_base.Value(j + 1));
-          if (i + 1 == nr) { // top
-            Nf = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nf1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nf1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf1);
-            Nf = Nf1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(next_base.Value(next_base_len), i + 1),
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
+          const SMDS_MeshNode*& Nf = next_base[++next_base_len].node;
+          if ( !Nf )
+            Nf = makeNode( next_base[ next_base_len ], y, quad, uv, myHelper, S );
+
+          myHelper->AddFace(curr_base[ j ].node,
+                            curr_base[ j+1 ].node,
+                            Nf,
+                            next_base[ next_base_len-1 ].node);
         }
 
         for (int icol = 1; icol <= nb_col; icol++) {
@@ -3553,104 +3169,10 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
             // stop short "column"
             break;
 
-          // add one "H": nodes b,c,e and faces 1,2,4,5
-          //
-          //  .---------b i + 1
-          //  |\   5   /|
-          //  | \     / |
-          //  |  c---e  |
-          //  |1 |2  |4 |
-          //  |  |   |  |
-          //  .--.---.--. i
-          //
-          //  j j+1 j+2 j+3
-
-          double u,v;
-
-          // b (i + 1, j + 3)
-          const SMDS_MeshNode* Nb;
-          next_base_len++;
-          next_base.SetValue(next_base_len, curr_base.Value(j + 3));
-          if (i + 1 == nr) { // top
-            Nb = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nb);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else if (j + 3 == curr_base_len) { // right
-            Nb = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-            u = uv_er[i].u;
-            v = uv_er[i].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nb1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nb1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nb1);
-            Nb = Nb1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-
-          // c and d
-          double u1 = (curr_par_u.Value(j) + next_par_u.Value(next_base_len - 1)) / 2.0;
-          double u2 = (curr_par_u.Value(j + 3) + next_par_u.Value(next_base_len)) / 2.0;
-          double u3 = (u2 - u1) / 3.0;
-
-          double v1 = (curr_par_v.Value(j) + next_par_v.Value(next_base_len - 1)) / 2.0;
-          double v2 = (curr_par_v.Value(j + 3) + next_par_v.Value(next_base_len)) / 2.0;
-          double v3 = (v2 - v1) / 3.0;
-
-          // c
-          u = u1 + u3;
-          v = v1 + v3;
-          gp_Pnt P = S->Value(u,v);
-          SMDS_MeshNode* Nc = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Nc, geomFaceID, u, v);
-
-          // e
-          u = u1 + u3 + u3;
-          v = v1 + v3 + v3;
-          P = S->Value(u,v);
-          SMDS_MeshNode* Ne = meshDS->AddNode(P.X(), P.Y(), P.Z());
-          meshDS->SetNodeOnFace(Ne, geomFaceID, u, v);
-
-          // Faces
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 0), i),
-                                              NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              Nc,
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-
-          SMDS_MeshFace* F2 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 1), i),
-                                              NodesBRD.Value(curr_base.Value(j + 2), i),
-                                              Ne, Nc);
-          if (F2) meshDS->SetMeshElementOnShape(F2, geomFaceID);
-
-          SMDS_MeshFace* F4 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j + 2), i),
-                                              NodesBRD.Value(curr_base.Value(j + 3), i),
-                                              Nb, Ne);
-          if (F4) meshDS->SetMeshElementOnShape(F4, geomFaceID);
-
-          SMDS_MeshFace* F5 = myHelper->AddFace(Nc, Ne, Nb,
-                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F5) meshDS->SetMeshElementOnShape(F5, geomFaceID);
-
-          j += 3;
+          // add "H"
+          reduceFunction( curr_base, next_base, j, next_base_len, quad, uv, y, myHelper, S );
+
+          j += reduce_grp_size;
 
           // not reduced middle elements
           if (icol < nb_col) {
@@ -3665,108 +3187,41 @@ bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
 
             for (int imiddle = 1; imiddle <= free_add; imiddle++) {
               // f (i + 1, j + imiddle)
-              const SMDS_MeshNode* Nf;
-              double u,v;
-              next_base.SetValue(++next_base_len, curr_base.Value(j + imiddle));
-              if (i + 1 == nr) { // top
-                Nf = uv_et[next_base_len - 1].node;
-                NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf);
-                u = uv_et[next_base_len - 1].u;
-                v = uv_et[next_base_len - 1].v;
-              }
-              else if (j + imiddle == curr_base_len) { // right
-                Nf = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-                u = uv_er[i].u;
-                v = uv_er[i].v;
-              }
-              else {
-                {
-                  double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-                  int nearest_node_j = (int)rel;
-                  rel -= nearest_node_j;
-                  int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-                  double u1 = quad->uv_grid[ij].u;
-                  double v1 = quad->uv_grid[ij].v;
-                  double u2 = quad->uv_grid[ij + 1].u;
-                  double v2 = quad->uv_grid[ij + 1].v;
-                  double duj = (u2 - u1) * rel;
-                  double dvj = (v2 - v1) * rel;
-                  u = u1 + duj;
-                  v = v1 + dvj;
-                }
-                gp_Pnt P = S->Value(u,v);
-                SMDS_MeshNode* Nf1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-                meshDS->SetNodeOnFace(Nf1, geomFaceID, u, v);
-                NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf1);
-                Nf = Nf1;
-              }
-              next_par_u.SetValue(next_base_len, u);
-              next_par_v.SetValue(next_base_len, v);
-              SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j - 1 + imiddle), i),
-                                                  NodesBRD.Value(curr_base.Value(j + imiddle), i),
-                                                  NodesBRD.Value(next_base.Value(next_base_len), i + 1),
-                                                  NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-              if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
+              const SMDS_MeshNode*& Nf = next_base[++next_base_len].node;
+              if ( !Nf )
+                Nf = makeNode( next_base[ next_base_len ], y, quad, uv, myHelper, S );
+
+              myHelper->AddFace(curr_base[ j-1+imiddle ].node,
+                                curr_base[ j  +imiddle ].node,
+                                Nf,
+                                next_base[ next_base_len-1 ].node);
             }
             j += free_add;
           }
         }
 
         // not reduced right elements
-        for (; j < curr_base_len; j++) {
+        for (; j < curr_base_len-1; j++) {
           // f (i + 1, j + 1)
-          const SMDS_MeshNode* Nf;
-          double u,v;
-          next_base.SetValue(++next_base_len, curr_base.Value(j + 1));
-          if (i + 1 == nr) { // top
-            Nf = uv_et[next_base_len - 1].node;
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf);
-            u = uv_et[next_base_len - 1].u;
-            v = uv_et[next_base_len - 1].v;
-          }
-          else if (j + 1 == curr_base_len) { // right
-            Nf = NodesBRD.Value(next_base.Value(next_base_len), i + 1);
-            u = uv_er[i].u;
-            v = uv_er[i].v;
-          }
-          else {
-            {
-              double rel = double(next_base_len - 1) * double(nt - 1) / double(nb_next - 1) + 1;
-              int nearest_node_j = (int)rel;
-              rel -= nearest_node_j;
-              int ij = (i + 1 - 1) * nt + (nearest_node_j - 1);
-              double u1 = quad->uv_grid[ij].u;
-              double v1 = quad->uv_grid[ij].v;
-              double u2 = quad->uv_grid[ij + 1].u;
-              double v2 = quad->uv_grid[ij + 1].v;
-              double duj = (u2 - u1) * rel;
-              double dvj = (v2 - v1) * rel;
-              u = u1 + duj;
-              v = v1 + dvj;
-            }
-            gp_Pnt P = S->Value(u,v);
-            SMDS_MeshNode* Nf1 = meshDS->AddNode(P.X(), P.Y(), P.Z());
-            meshDS->SetNodeOnFace(Nf1, geomFaceID, u, v);
-            NodesBRD.SetValue(next_base.Value(next_base_len), i + 1, Nf1);
-            Nf = Nf1;
-          }
-          next_par_u.SetValue(next_base_len, u);
-          next_par_v.SetValue(next_base_len, v);
-          SMDS_MeshFace* F1 = myHelper->AddFace(NodesBRD.Value(curr_base.Value(j), i),
-                                                NodesBRD.Value(curr_base.Value(j + 1), i),
-                                                NodesBRD.Value(next_base.Value(next_base_len), i + 1),
-                                                NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
-          if (F1) meshDS->SetMeshElementOnShape(F1, geomFaceID);
-        }
-
-        curr_base_len = next_base_len;
-        curr_base = next_base;
-        curr_par_u = next_par_u;
-        curr_par_v = next_par_v;
+          const SMDS_MeshNode*& Nf = next_base[++next_base_len].node;
+          if ( !Nf )
+            Nf = makeNode( next_base[ next_base_len ], y, quad, uv, myHelper, S );
+
+          myHelper->AddFace(curr_base[ j ].node,
+                            curr_base[ j+1 ].node,
+                            Nf,
+                            next_base[ next_base_len-1 ].node);
+        }
+
+        curr_base_len = next_base_len + 1;
         next_base_len = 0;
+        curr_base.swap( next_base );
       }
-    } // end "linear" simple reduce "31"
+
+    } // end "linear" simple reduce
+
     else {
+      return false;
     }
   } // end Simple Reduce implementation