smesh/src/StdMeshers/StdMeshers_Quadrangle_2D.cxx

//  Copyright (C) 2007-2010  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
//
//  This library is free software; you can redistribute it and/or
//  modify it under the terms of the GNU Lesser General Public
//  License as published by the Free Software Foundation; either
//  version 2.1 of the License.
//
//  This library is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
//  Lesser General Public License for more details.
//
//  You should have received a copy of the GNU Lesser General Public
//  License along with this library; if not, write to the Free Software
//  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA
//
//  See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com

//  File   : StdMeshers_Quadrangle_2D.cxx
//  Author : Paul RASCLE, EDF
//  Module : SMESH

#include "StdMeshers_Quadrangle_2D.hxx"

#include "StdMeshers_FaceSide.hxx"

#include "StdMeshers_QuadrangleParams.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 <BRep_Tool.hxx>
#include <Geom_Surface.hxx>
#include <NCollection_DefineArray2.hxx>
#include <Precision.hxx>
#include <TColStd_SequenceOfReal.hxx>
#include <TColStd_SequenceOfInteger.hxx>
#include <TColgp_SequenceOfXY.hxx>
#include <TopExp.hxx>
#include <TopExp_Explorer.hxx>
#include <TopTools_ListIteratorOfListOfShape.hxx>
#include <TopTools_MapOfShape.hxx>
#include <TopoDS.hxx>

#include "utilities.h"
#include "Utils_ExceptHandlers.hxx"

#ifndef StdMeshers_Array2OfNode_HeaderFile
#define StdMeshers_Array2OfNode_HeaderFile
typedef const SMDS_MeshNode* SMDS_MeshNodePtr;
DEFINE_BASECOLLECTION (StdMeshers_BaseCollectionNodePtr, SMDS_MeshNodePtr)
DEFINE_ARRAY2(StdMeshers_Array2OfNode,
              StdMeshers_BaseCollectionNodePtr, SMDS_MeshNodePtr)
#endif

using namespace std;

typedef gp_XY gp_UV;
typedef SMESH_Comment TComm;

//=============================================================================
/*!
 *  
 */
//=============================================================================

StdMeshers_Quadrangle_2D::StdMeshers_Quadrangle_2D (int hypId, int studyId,
                                                    SMESH_Gen* gen)
     : SMESH_2D_Algo(hypId, studyId, gen)
{
  MESSAGE("StdMeshers_Quadrangle_2D::StdMeshers_Quadrangle_2D");
  _name = "Quadrangle_2D";
  _shapeType = (1 << TopAbs_FACE);
  _compatibleHypothesis.push_back("QuadrangleParams");
  _compatibleHypothesis.push_back("QuadranglePreference");
  _compatibleHypothesis.push_back("TrianglePreference");
  myTool = 0;
}

//=============================================================================
/*!
 *  
 */
//=============================================================================

StdMeshers_Quadrangle_2D::~StdMeshers_Quadrangle_2D()
{
  MESSAGE("StdMeshers_Quadrangle_2D::~StdMeshers_Quadrangle_2D");
}

//=============================================================================
/*!
 *  
 */
//=============================================================================

bool StdMeshers_Quadrangle_2D::CheckHypothesis
                         (SMESH_Mesh&                          aMesh,
                          const TopoDS_Shape&                  aShape,
                          SMESH_Hypothesis::Hypothesis_Status& aStatus)
{
  bool isOk = true;
  aStatus = SMESH_Hypothesis::HYP_OK;

  const list <const SMESHDS_Hypothesis * >& hyps =
    GetUsedHypothesis(aMesh, aShape, false);
  const SMESHDS_Hypothesis * aHyp = 0;

  myTriaVertexID = -1;
  myQuadType = QUAD_STANDARD;
  myQuadranglePreference = false;
  myTrianglePreference = false;

  bool isFirstParams = true;

  // First assigned hypothesis (if any) is processed now
  if (hyps.size() > 0) {
    aHyp = hyps.front();
    if (strcmp("QuadrangleParams", aHyp->GetName()) == 0) {
      const StdMeshers_QuadrangleParams* aHyp1 = 
        (const StdMeshers_QuadrangleParams*)aHyp;
      myTriaVertexID = aHyp1->GetTriaVertex();
      myQuadType = aHyp1->GetQuadType();
      if (myQuadType == QUAD_QUADRANGLE_PREF ||
          myQuadType == QUAD_QUADRANGLE_PREF_REVERSED)
        myQuadranglePreference = true;
      else if (myQuadType == QUAD_TRIANGLE_PREF)
        myTrianglePreference = true;
    }
    else if (strcmp("QuadranglePreference", aHyp->GetName()) == 0) {
      isFirstParams = false;
      myQuadranglePreference = true;
    }
    else if (strcmp("TrianglePreference", aHyp->GetName()) == 0){
      isFirstParams = false;
      myTrianglePreference = true; 
    }
    else {
      isFirstParams = false;
    }
  }

  // Second(last) assigned hypothesis (if any) is processed now
  if (hyps.size() > 1) {
    aHyp = hyps.back();
    if (isFirstParams) {
      if (strcmp("QuadranglePreference", aHyp->GetName()) == 0) {
        myQuadranglePreference = true;
        myTrianglePreference = false; 
        myQuadType = QUAD_STANDARD;
      }
      else if (strcmp("TrianglePreference", aHyp->GetName()) == 0){
        myQuadranglePreference = false;
        myTrianglePreference = true; 
        myQuadType = QUAD_STANDARD;
      }
    }
    else {
      const StdMeshers_QuadrangleParams* aHyp2 = 
        (const StdMeshers_QuadrangleParams*)aHyp;
      myTriaVertexID = aHyp2->GetTriaVertex();

      if (!myQuadranglePreference && !myTrianglePreference) { // priority of hypos
        myQuadType = aHyp2->GetQuadType();
        if (myQuadType == QUAD_QUADRANGLE_PREF ||
            myQuadType == QUAD_QUADRANGLE_PREF_REVERSED)
          myQuadranglePreference = true;
        else if (myQuadType == QUAD_TRIANGLE_PREF)
          myTrianglePreference = true;
      }
    }
  }

  return isOk;
}

//=============================================================================
/*!
 *  
 */
//=============================================================================

bool StdMeshers_Quadrangle_2D::Compute (SMESH_Mesh& aMesh,
                                        const TopoDS_Shape& aShape)// throw (SALOME_Exception)
{
  // PAL14921. Enable catching std::bad_alloc and Standard_OutOfMemory outside
  //Unexpect aCatchSalomeException);

  SMESHDS_Mesh * meshDS = aMesh.GetMeshDS();
  aMesh.GetSubMesh(aShape);

  SMESH_MesherHelper helper (aMesh);
  myTool = &helper;

  _quadraticMesh = myTool->IsQuadraticSubMesh(aShape);

  FaceQuadStruct *quad = CheckNbEdges(aMesh, aShape);
  std::auto_ptr<FaceQuadStruct> quadDeleter (quad); // to delete quad at exit from Compute()
  if (!quad)
    return false;

  if (myQuadranglePreference) {
    int n1 = quad->side[0]->NbPoints();
    int n2 = quad->side[1]->NbPoints();
    int n3 = quad->side[2]->NbPoints();
    int n4 = quad->side[3]->NbPoints();
    int nfull = n1+n2+n3+n4;
    int ntmp = nfull/2;
    ntmp = ntmp*2;
    if (nfull == ntmp && ((n1 != n3) || (n2 != n4))) {
      // special path for using only quandrangle faces
      bool ok = ComputeQuadPref(aMesh, aShape, quad);
      return ok;
    }
  }
  else if (myQuadType == QUAD_REDUCED) {
    int n1 = quad->side[0]->NbPoints();
    int n2 = quad->side[1]->NbPoints();
    int n3 = quad->side[2]->NbPoints();
    int n4 = quad->side[3]->NbPoints();
    int n13 = n1 - n3;
    int n24 = n2 - n4;
    int n13tmp = n13/2; n13tmp = n13tmp*2;
    int n24tmp = n24/2; n24tmp = n24tmp*2;
    if ((n1 == n3 && n2 != n4 && n24tmp == n24) ||
        (n2 == n4 && n1 != n3 && n13tmp == n13)) {
      bool ok = ComputeReduced(aMesh, aShape, quad);
      return ok;
    }
  }

  // set normalized grid on unit square in parametric domain
  
  if (!SetNormalizedGrid(aMesh, aShape, quad))
    return false;

  // --- compute 3D values on points, store points & quadrangles

  int nbdown  = quad->side[0]->NbPoints();
  int nbup    = quad->side[2]->NbPoints();

  int nbright = quad->side[1]->NbPoints();
  int nbleft  = quad->side[3]->NbPoints();

  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++) {
    for (j = 1; j < nbvertic - 1; j++) {
      int ij = j * nbhoriz + i;
      double u = quad->uv_grid[ij].u;
      double v = quad->uv_grid[ij].v;
      gp_Pnt P = S->Value(u, v);
      SMDS_MeshNode * node = meshDS->AddNode(P.X(), P.Y(), P.Z());
      meshDS->SetNodeOnFace(node, geomFaceID, u, v);
      quad->uv_grid[ij].node = node;
    }
  }
  
  // mesh faces

  //             [2]
  //      --.--.--.--.--.--  nbvertic
  //     |                 | ^
  //     |                 | ^
  // [3] |                 | ^ j  [1]
  //     |                 | ^
  //     |                 | ^
  //      ---.----.----.---  0
  //     0 > > > > > > > > nbhoriz
  //              i
  //             [0]
  
  i = 0;
  int ilow = 0;
  int iup = nbhoriz - 1;
  if (quad->isEdgeOut[3]) { ilow++; } else { if (quad->isEdgeOut[1]) iup--; }
  
  int jlow = 0;
  int jup = nbvertic - 1;
  if (quad->isEdgeOut[0]) { jlow++; } else { if (quad->isEdgeOut[2]) jup--; }
  
  // regular quadrangles
  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;
      c = quad->uv_grid[(j + 1) * nbhoriz + i + 1].node;
      d = quad->uv_grid[(j + 1) * nbhoriz + i].node;
      SMDS_MeshFace* face = myTool->AddFace(a, b, c, d);
      if (face) {
        meshDS->SetMeshElementOnShape(face, geomFaceID);
      }
    }
  }

  const vector<UVPtStruct>& uv_e0 = quad->side[0]->GetUVPtStruct(true,0);
  const vector<UVPtStruct>& uv_e1 = quad->side[1]->GetUVPtStruct(false,1);
  const vector<UVPtStruct>& uv_e2 = quad->side[2]->GetUVPtStruct(true,1);
  const vector<UVPtStruct>& uv_e3 = quad->side[3]->GetUVPtStruct(false,0);

  if (uv_e0.empty() || uv_e1.empty() || uv_e2.empty() || uv_e3.empty())
    return error(COMPERR_BAD_INPUT_MESH);

  double eps = Precision::Confusion();

  // Boundary quadrangles
  
  if (quad->isEdgeOut[0]) {
    // Down edge is out
    // 
    // |___|___|___|___|___|___|
    // |   |   |   |   |   |   |
    // |___|___|___|___|___|___|
    // |   |   |   |   |   |   |
    // |___|___|___|___|___|___| __ first row of the regular grid
    // .  .  .  .  .  .  .  .  . __ down edge nodes
    // 
    // >->->->->->->->->->->->-> -- direction of processing
      
    int g = 0; // number of last processed node in the regular grid
    
    // number of last node of the down edge to be processed
    int stop = nbdown - 1;
    // if right edge is out, we will stop at a node, previous to the last one
    if (quad->isEdgeOut[1]) stop--;
    
    // for each node of the down edge find nearest node
    // in the first row of the regular grid and link them
    for (i = 0; i < stop; i++) {
      const SMDS_MeshNode *a, *b, *c, *d;
      a = uv_e0[i].node;
      b = uv_e0[i + 1].node;
      gp_Pnt pb (b->X(), b->Y(), b->Z());
      
      // find node c in the regular grid, which will be linked with node b
      int near = g;
      if (i == stop - 1) {
        // right bound reached, link with the rightmost node
        near = iup;
        c = quad->uv_grid[nbhoriz + iup].node;
      }
      else {
        // find in the grid node c, nearest to the b
        double mind = RealLast();
        for (int k = g; k <= iup; k++) {
          
          const SMDS_MeshNode *nk;
          if (k < ilow) // this can be, if left edge is out
            nk = uv_e3[1].node; // get node from the left edge
          else
            nk = quad->uv_grid[nbhoriz + k].node; // get one of middle nodes

          gp_Pnt pnk (nk->X(), nk->Y(), nk->Z());
          double dist = pb.Distance(pnk);
          if (dist < mind - eps) {
            c = nk;
            near = k;
            mind = dist;
          } else {
            break;
          }
        }
      }

      if (near == g) { // make triangle
        SMDS_MeshFace* face = myTool->AddFace(a, b, c);
        if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
      }
      else { // make quadrangle
        if (near - 1 < ilow)
          d = uv_e3[1].node;
        else
          d = quad->uv_grid[nbhoriz + near - 1].node;
        //SMDS_MeshFace* face = meshDS->AddFace(a, b, c, d);
        
        if (!myTrianglePreference){
          SMDS_MeshFace* face = myTool->AddFace(a, b, c, d);
          if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
        }
        else {
          SplitQuad(meshDS, geomFaceID, a, b, c, d);
        }

        // if node d is not at position g - make additional triangles
        if (near - 1 > g) {
          for (int k = near - 1; k > g; k--) {
            c = quad->uv_grid[nbhoriz + k].node;
            if (k - 1 < ilow)
              d = uv_e3[1].node;
            else
              d = quad->uv_grid[nbhoriz + k - 1].node;
            SMDS_MeshFace* face = myTool->AddFace(a, c, d);
            if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
          }
        }
        g = near;
      }
    }
  } else {
    if (quad->isEdgeOut[2]) {
      // Up edge is out
      // 
      // <-<-<-<-<-<-<-<-<-<-<-<-< -- direction of processing
      // 
      // .  .  .  .  .  .  .  .  . __ up edge nodes
      //  ___ ___ ___ ___ ___ ___  __ first row of the regular grid
      // |   |   |   |   |   |   |
      // |___|___|___|___|___|___|
      // |   |   |   |   |   |   |
      // |___|___|___|___|___|___|
      // |   |   |   |   |   |   |

      int g = nbhoriz - 1; // last processed node in the regular grid

      int stop = 0;
      // if left edge is out, we will stop at a second node
      if (quad->isEdgeOut[3]) stop++;

      // for each node of the up edge find nearest node
      // in the first row of the regular grid and link them
      for (i = nbup - 1; i > stop; i--) {
        const SMDS_MeshNode *a, *b, *c, *d;
        a = uv_e2[i].node;
        b = uv_e2[i - 1].node;
        gp_Pnt pb (b->X(), b->Y(), b->Z());

        // find node c in the grid, which will be linked with node b
        int near = g;
        if (i == stop + 1) { // left bound reached, link with the leftmost node
          c = quad->uv_grid[nbhoriz*(nbvertic - 2) + ilow].node;
          near = ilow;
        } else {
          // find node c in the grid, nearest to the b
          double mind = RealLast();
          for (int k = g; k >= ilow; k--) {
            const SMDS_MeshNode *nk;
            if (k > iup)
              nk = uv_e1[nbright - 2].node;
            else
              nk = quad->uv_grid[nbhoriz*(nbvertic - 2) + k].node;
            gp_Pnt pnk (nk->X(), nk->Y(), nk->Z());
            double dist = pb.Distance(pnk);
            if (dist < mind - eps) {
              c = nk;
              near = k;
              mind = dist;
            } else {
              break;
            }
          }
        }

        if (near == g) { // make triangle
          SMDS_MeshFace* face = myTool->AddFace(a, b, c);
          if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
        }
        else { // make quadrangle
          if (near + 1 > iup)
            d = uv_e1[nbright - 2].node;
          else
            d = quad->uv_grid[nbhoriz*(nbvertic - 2) + near + 1].node;
          //SMDS_MeshFace* face = meshDS->AddFace(a, b, c, d);
          if (!myTrianglePreference){
            SMDS_MeshFace* face = myTool->AddFace(a, b, c, d);
            if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
          }
          else {
            SplitQuad(meshDS, geomFaceID, a, b, c, d);
          }

          if (near + 1 < g) { // if d not is at g - make additional triangles
            for (int k = near + 1; k < g; k++) {
              c = quad->uv_grid[nbhoriz*(nbvertic - 2) + k].node;
              if (k + 1 > iup)
                d = uv_e1[nbright - 2].node;
              else
                d = quad->uv_grid[nbhoriz*(nbvertic - 2) + k + 1].node;
              SMDS_MeshFace* face = myTool->AddFace(a, c, d);
              if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
            }
          }
          g = near;
        }
      }
    }
  }

  // right or left boundary quadrangles
  if (quad->isEdgeOut[1]) {
//    MESSAGE("right edge is out");
    int g = 0; // last processed node in the grid
    int stop = nbright - 1;
    if (quad->isEdgeOut[2]) stop--;
    for (i = 0; i < stop; i++) {
      const SMDS_MeshNode *a, *b, *c, *d;
      a = uv_e1[i].node;
      b = uv_e1[i + 1].node;
      gp_Pnt pb (b->X(), b->Y(), b->Z());

      // find node c in the grid, nearest to the b
      int near = g;
      if (i == stop - 1) { // up bondary reached
        c = quad->uv_grid[nbhoriz*(jup + 1) - 2].node;
        near = jup;
      } else {
        double mind = RealLast();
        for (int k = g; k <= jup; k++) {
          const SMDS_MeshNode *nk;
          if (k < jlow)
            nk = uv_e0[nbdown - 2].node;
          else
            nk = quad->uv_grid[nbhoriz*(k + 1) - 2].node;
          gp_Pnt pnk (nk->X(), nk->Y(), nk->Z());
          double dist = pb.Distance(pnk);
          if (dist < mind - eps) {
            c = nk;
            near = k;
            mind = dist;
          } else {
            break;
          }
        }
      }

      if (near == g) { // make triangle
        SMDS_MeshFace* face = myTool->AddFace(a, b, c);
        if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
      }
      else { // make quadrangle
        if (near - 1 < jlow)
          d = uv_e0[nbdown - 2].node;
        else
          d = quad->uv_grid[nbhoriz*near - 2].node;
        //SMDS_MeshFace* face = meshDS->AddFace(a, b, c, d);

        if (!myTrianglePreference){
          SMDS_MeshFace* face = myTool->AddFace(a, b, c, d);
          if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
        }
        else {
          SplitQuad(meshDS, geomFaceID, a, b, c, d);
        }

        if (near - 1 > g) { // if d not is at g - make additional triangles
          for (int k = near - 1; k > g; k--) {
            c = quad->uv_grid[nbhoriz*(k + 1) - 2].node;
            if (k - 1 < jlow)
              d = uv_e0[nbdown - 2].node;
            else
              d = quad->uv_grid[nbhoriz*k - 2].node;
            SMDS_MeshFace* face = myTool->AddFace(a, c, d);
            if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
          }
        }
        g = near;
      }
    }
  } else {
    if (quad->isEdgeOut[3]) {
//      MESSAGE("left edge is out");
      int g = nbvertic - 1; // last processed node in the grid
      int stop = 0;
      if (quad->isEdgeOut[0]) stop++;
      for (i = nbleft - 1; i > stop; i--) {
        const SMDS_MeshNode *a, *b, *c, *d;
        a = uv_e3[i].node;
        b = uv_e3[i - 1].node;
        gp_Pnt pb (b->X(), b->Y(), b->Z());

        // find node c in the grid, nearest to the b
        int near = g;
        if (i == stop + 1) { // down bondary reached
          c = quad->uv_grid[nbhoriz*jlow + 1].node;
          near = jlow;
        } else {
          double mind = RealLast();
          for (int k = g; k >= jlow; k--) {
            const SMDS_MeshNode *nk;
            if (k > jup)
              nk = uv_e2[1].node;
            else
              nk = quad->uv_grid[nbhoriz*k + 1].node;
            gp_Pnt pnk (nk->X(), nk->Y(), nk->Z());
            double dist = pb.Distance(pnk);
            if (dist < mind - eps) {
              c = nk;
              near = k;
              mind = dist;
            } else {
              break;
            }
          }
        }

        if (near == g) { // make triangle
          SMDS_MeshFace* face = myTool->AddFace(a, b, c);
          if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
        }
        else { // make quadrangle
          if (near + 1 > jup)
            d = uv_e2[1].node;
          else
            d = quad->uv_grid[nbhoriz*(near + 1) + 1].node;
          //SMDS_MeshFace* face = meshDS->AddFace(a, b, c, d);
          if (!myTrianglePreference){
            SMDS_MeshFace* face = myTool->AddFace(a, b, c, d);
            if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
          }
          else {
            SplitQuad(meshDS, geomFaceID, a, b, c, d);
          }

          if (near + 1 < g) { // if d not is at g - make additional triangles
            for (int k = near + 1; k < g; k++) {
              c = quad->uv_grid[nbhoriz*k + 1].node;
              if (k + 1 > jup)
                d = uv_e2[1].node;
              else
                d = quad->uv_grid[nbhoriz*(k + 1) + 1].node;
              SMDS_MeshFace* face = myTool->AddFace(a, c, d);
              if (face) meshDS->SetMeshElementOnShape(face, geomFaceID);
            }
          }
          g = near;
        }
      }
    }
  }

  bool isOk = true;
  return isOk;
}


//=============================================================================
/*!
 *  Evaluate
 */
//=============================================================================

bool StdMeshers_Quadrangle_2D::Evaluate(SMESH_Mesh& aMesh,
                                        const TopoDS_Shape& aShape,
                                        MapShapeNbElems& aResMap)

{
  aMesh.GetSubMesh(aShape);

  std::vector<int> aNbNodes(4);
  bool IsQuadratic = false;
  if (!CheckNbEdgesForEvaluate(aMesh, aShape, aResMap, aNbNodes, IsQuadratic)) {
    std::vector<int> aResVec(SMDSEntity_Last);
    for (int i=SMDSEntity_Node; i<SMDSEntity_Last; i++) aResVec[i] = 0;
    SMESH_subMesh * sm = aMesh.GetSubMesh(aShape);
    aResMap.insert(std::make_pair(sm,aResVec));
    SMESH_ComputeErrorPtr& smError = sm->GetComputeError();
    smError.reset(new SMESH_ComputeError(COMPERR_ALGO_FAILED,"Submesh can not be evaluated",this));
    return false;
  }

  if (myQuadranglePreference) {
    int n1 = aNbNodes[0];
    int n2 = aNbNodes[1];
    int n3 = aNbNodes[2];
    int n4 = aNbNodes[3];
    int nfull = n1+n2+n3+n4;
    int ntmp = nfull/2;
    ntmp = ntmp*2;
    if (nfull==ntmp && ((n1!=n3) || (n2!=n4))) {
      // special path for using only quandrangle faces
      return EvaluateQuadPref(aMesh, aShape, aNbNodes, aResMap, IsQuadratic);
      //return true;
    }
  }

  int nbdown  = aNbNodes[0];
  int nbup    = aNbNodes[2];

  int nbright = aNbNodes[1];
  int nbleft  = aNbNodes[3];

  int nbhoriz  = Min(nbdown, nbup);
  int nbvertic = Min(nbright, nbleft);

  int dh = Max(nbdown, nbup) - nbhoriz;
  int dv = Max(nbright, nbleft) - nbvertic;

  //int kdh = 0;
  //if (dh>0) kdh = 1;
  //int kdv = 0;
  //if (dv>0) kdv = 1;

  int nbNodes = (nbhoriz-2)*(nbvertic-2);
  //int nbFaces3 = dh + dv + kdh*(nbvertic-1)*2 + kdv*(nbhoriz-1)*2;
  int nbFaces3 = dh + dv;
  //if (kdh==1 && kdv==1) nbFaces3 -= 2;
  //if (dh>0 && dv>0) nbFaces3 -= 2;
  //int nbFaces4 = (nbhoriz-1-kdh)*(nbvertic-1-kdv);
  int nbFaces4 = (nbhoriz-1)*(nbvertic-1);

  std::vector<int> aVec(SMDSEntity_Last);
  for (int i=SMDSEntity_Node; i<SMDSEntity_Last; i++) aVec[i] = 0;
  if (IsQuadratic) {
    aVec[SMDSEntity_Quad_Triangle] = nbFaces3;
    aVec[SMDSEntity_Quad_Quadrangle] = nbFaces4;
    int nbbndedges = nbdown + nbup + nbright + nbleft -4;
    int nbintedges = (nbFaces4*4 + nbFaces3*3 - nbbndedges) / 2;
    aVec[SMDSEntity_Node] = nbNodes + nbintedges;
    if (aNbNodes.size()==5) {
      aVec[SMDSEntity_Quad_Triangle] = nbFaces3 + aNbNodes[3] -1;
      aVec[SMDSEntity_Quad_Quadrangle] = nbFaces4 - aNbNodes[3] +1;
    }
  }
  else {
    aVec[SMDSEntity_Node] = nbNodes;
    aVec[SMDSEntity_Triangle] = nbFaces3;
    aVec[SMDSEntity_Quadrangle] = nbFaces4;
    if (aNbNodes.size()==5) {
      aVec[SMDSEntity_Triangle] = nbFaces3 + aNbNodes[3] - 1;
      aVec[SMDSEntity_Quadrangle] = nbFaces4 - aNbNodes[3] + 1;
    }
  }
  SMESH_subMesh * sm = aMesh.GetSubMesh(aShape);
  aResMap.insert(std::make_pair(sm,aVec));

  return true;
}


//================================================================================
/*!
 * \brief Return true if only two given edges meat at their common vertex
 */
//================================================================================

static bool twoEdgesMeatAtVertex(const TopoDS_Edge& e1,
                                 const TopoDS_Edge& e2,
                                 SMESH_Mesh &       mesh)
{
  TopoDS_Vertex v;
  if (!TopExp::CommonVertex(e1, e2, v))
    return false;
  TopTools_ListIteratorOfListOfShape ancestIt(mesh.GetAncestors(v));
  for (; ancestIt.More() ; ancestIt.Next())
    if (ancestIt.Value().ShapeType() == TopAbs_EDGE)
      if (!e1.IsSame(ancestIt.Value()) && !e2.IsSame(ancestIt.Value()))
        return false;
  return true;
}

//=============================================================================
/*!
 *  
 */
//=============================================================================

FaceQuadStruct* StdMeshers_Quadrangle_2D::CheckNbEdges(SMESH_Mesh &         aMesh,
                                                       const TopoDS_Shape & aShape)
  //throw(SALOME_Exception)
{
  TopoDS_Face F = TopoDS::Face(aShape);
  if ( F.Orientation() >= TopAbs_INTERNAL ) F.Orientation( TopAbs_FORWARD );
  const bool ignoreMediumNodes = _quadraticMesh;

  // verify 1 wire only, with 4 edges
  TopoDS_Vertex V;
  list< TopoDS_Edge > edges;
  list< int > nbEdgesInWire;
  int nbWire = SMESH_Block::GetOrderedEdges (F, V, edges, nbEdgesInWire);
  if (nbWire != 1) {
    error(COMPERR_BAD_SHAPE, TComm("Wrong number of wires: ") << nbWire);
    return 0;
  }
  FaceQuadStruct* quad = new FaceQuadStruct;
  quad->uv_grid = 0;
  quad->side.reserve(nbEdgesInWire.front());
  quad->face = F;

  int nbSides = 0;
  list< TopoDS_Edge >::iterator edgeIt = edges.begin();
  if (nbEdgesInWire.front() == 3) // exactly 3 edges
  {
    SMESH_Comment comment;
    SMESHDS_Mesh* meshDS = aMesh.GetMeshDS();
    if (myTriaVertexID == -1)
    {
      comment << "No Base vertex parameter provided for a trilateral geometrical face";
    }
    else
    {
      TopoDS_Vertex V = TopoDS::Vertex(meshDS->IndexToShape(myTriaVertexID));
      if (!V.IsNull()) {
        TopoDS_Edge E1,E2,E3;
        for (; edgeIt != edges.end(); ++edgeIt) {
          TopoDS_Edge E =  *edgeIt;
          TopoDS_Vertex VF, VL;
          TopExp::Vertices(E, VF, VL, true);
          if (VF.IsSame(V))
            E1 = E;
          else if (VL.IsSame(V))
            E3 = E;
          else
            E2 = E;
        }
        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));
          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);
          const SMDS_MeshNode* aNode = UVPSleft[0].node;
          gp_Pnt2d aPnt2d(UVPSleft[0].u, UVPSleft[0].v);
          quad->side.push_back(new StdMeshers_FaceSide(aNode, aPnt2d, quad->side[1]));
          return quad;
        }
      }
      comment << "Invalid Base vertex parameter: " << myTriaVertexID << " is not among [";
      TopTools_MapOfShape vMap;
      for (TopExp_Explorer v(aShape, TopAbs_VERTEX); v.More(); v.Next())
        if (vMap.Add(v.Current()))
          comment << meshDS->ShapeToIndex(v.Current()) << (vMap.Extent()==3 ? "]" : ", ");
    }
    error(comment);
    delete quad;
    return quad = 0;
  }
  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));
  }
  else if (nbEdgesInWire.front() > 4) { // more than 4 edges - try to unite some
    list< TopoDS_Edge > sideEdges;
    while (!edges.empty()) {
      sideEdges.clear();
      sideEdges.splice(sideEdges.end(), edges, edges.begin()); // edges.front() -> sideEdges.end()
      bool sameSide = true;
      while (!edges.empty() && sameSide) {
        sameSide = SMESH_Algo::IsContinuous(sideEdges.back(), edges.front());
        if (sameSide)
          sideEdges.splice(sideEdges.end(), edges, edges.begin());
      }
      if (nbSides == 0) { // go backward from the first edge
        sameSide = true;
        while (!edges.empty() && sameSide) {
          sameSide = SMESH_Algo::IsContinuous(sideEdges.front(), edges.back());
          if (sameSide)
            sideEdges.splice(sideEdges.begin(), edges, --edges.end());
        }
      }
      quad->side.push_back(new StdMeshers_FaceSide(F, sideEdges, &aMesh,
                                                    nbSides<TOP_SIDE, ignoreMediumNodes));
      ++nbSides;
    }
    // issue 20222. Try to unite only edges shared by two same faces
    if (nbSides < 4) {
      // delete found sides
      { FaceQuadStruct cleaner(*quad); }
      quad->side.clear();
      quad->side.reserve(nbEdgesInWire.front());
      nbSides = 0;

      SMESH_Block::GetOrderedEdges (F, V, edges, nbEdgesInWire);
      while (!edges.empty()) {
        sideEdges.clear();
        sideEdges.splice(sideEdges.end(), edges, edges.begin());
        bool sameSide = true;
        while (!edges.empty() && sameSide) {
          sameSide =
            SMESH_Algo::IsContinuous(sideEdges.back(), edges.front()) &&
            twoEdgesMeatAtVertex(sideEdges.back(), edges.front(), aMesh);
          if (sameSide)
            sideEdges.splice(sideEdges.end(), edges, edges.begin());
        }
        if (nbSides == 0) { // go backward from the first edge
          sameSide = true;
          while (!edges.empty() && sameSide) {
            sameSide =
              SMESH_Algo::IsContinuous(sideEdges.front(), edges.back()) &&
              twoEdgesMeatAtVertex(sideEdges.front(), edges.back(), aMesh);
            if (sameSide)
              sideEdges.splice(sideEdges.begin(), edges, --edges.end());
          }
        }
        quad->side.push_back(new StdMeshers_FaceSide(F, sideEdges, &aMesh,
                                                      nbSides<TOP_SIDE, ignoreMediumNodes));
        ++nbSides;
      }
    }
  }
  if (nbSides != 4) {
#ifdef _DEBUG_
    MESSAGE ("StdMeshers_Quadrangle_2D. Edge IDs of " << nbSides << " sides:\n");
    for (int i = 0; i < nbSides; ++i) {
      MESSAGE (" (");
      for (int e = 0; e < quad->side[i]->NbEdges(); ++e)
        MESSAGE (myTool->GetMeshDS()->ShapeToIndex(quad->side[i]->Edge(e)) << " ");
      MESSAGE (")\n");
    }
    //cout << endl;
#endif
    if (!nbSides)
      nbSides = nbEdgesInWire.front();
    error(COMPERR_BAD_SHAPE, TComm("Face must have 4 sides but not ") << nbSides);
    delete quad;
    quad = 0;
  }

  return quad;
}


//=============================================================================
/*!
 *  
 */
//=============================================================================

bool StdMeshers_Quadrangle_2D::CheckNbEdgesForEvaluate(SMESH_Mesh& aMesh,
                                                       const TopoDS_Shape & aShape,
                                                       MapShapeNbElems& aResMap,
                                                       std::vector<int>& aNbNodes,
                                                       bool& IsQuadratic)

{
  const TopoDS_Face & F = TopoDS::Face(aShape);

  // verify 1 wire only, with 4 edges
  TopoDS_Vertex V;
  list< TopoDS_Edge > edges;
  list< int > nbEdgesInWire;
  int nbWire = SMESH_Block::GetOrderedEdges (F, V, edges, nbEdgesInWire);
  if (nbWire != 1) {
    return false;
  }

  aNbNodes.resize(4);

  int nbSides = 0;
  list< TopoDS_Edge >::iterator edgeIt = edges.begin();
  SMESH_subMesh * sm = aMesh.GetSubMesh(*edgeIt);
  MapShapeNbElemsItr anIt = aResMap.find(sm);
  if (anIt==aResMap.end()) {
    return false;
  }
  std::vector<int> aVec = (*anIt).second;
  IsQuadratic = (aVec[SMDSEntity_Quad_Edge] > aVec[SMDSEntity_Edge]);
  if (nbEdgesInWire.front() == 3) { // exactly 3 edges
    if (myTriaVertexID>0) {
      SMESHDS_Mesh* meshDS = aMesh.GetMeshDS();
      TopoDS_Vertex V = TopoDS::Vertex(meshDS->IndexToShape(myTriaVertexID));
      if (!V.IsNull()) {
        TopoDS_Edge E1,E2,E3;
        for (; edgeIt != edges.end(); ++edgeIt) {
          TopoDS_Edge E =  TopoDS::Edge(*edgeIt);
          TopoDS_Vertex VF, VL;
          TopExp::Vertices(E, VF, VL, true);
          if (VF.IsSame(V))
            E1 = E;
          else if (VL.IsSame(V))
            E3 = E;
          else
            E2 = E;
        }
        SMESH_subMesh * sm = aMesh.GetSubMesh(E1);
        MapShapeNbElemsItr anIt = aResMap.find(sm);
        if (anIt==aResMap.end()) return false;
        std::vector<int> aVec = (*anIt).second;
        if (IsQuadratic)
          aNbNodes[0] = (aVec[SMDSEntity_Node]-1)/2 + 2;
        else
          aNbNodes[0] = aVec[SMDSEntity_Node] + 2;
        sm = aMesh.GetSubMesh(E2);
        anIt = aResMap.find(sm);
        if (anIt==aResMap.end()) return false;
        aVec = (*anIt).second;
        if (IsQuadratic)
          aNbNodes[1] = (aVec[SMDSEntity_Node]-1)/2 + 2;
        else
          aNbNodes[1] = aVec[SMDSEntity_Node] + 2;
        sm = aMesh.GetSubMesh(E3);
        anIt = aResMap.find(sm);
        if (anIt==aResMap.end()) return false;
        aVec = (*anIt).second;
        if (IsQuadratic)
          aNbNodes[2] = (aVec[SMDSEntity_Node]-1)/2 + 2;
        else
          aNbNodes[2] = aVec[SMDSEntity_Node] + 2;
        aNbNodes[3] = aNbNodes[1];
        aNbNodes.resize(5);
        nbSides = 4;
      }
    }
  }
  if (nbEdgesInWire.front() == 4) { // exactly 4 edges
    for (; edgeIt != edges.end(); edgeIt++) {
      SMESH_subMesh * sm = aMesh.GetSubMesh(*edgeIt);
      MapShapeNbElemsItr anIt = aResMap.find(sm);
      if (anIt==aResMap.end()) {
        return false;
      }
      std::vector<int> aVec = (*anIt).second;
      if (IsQuadratic)
        aNbNodes[nbSides] = (aVec[SMDSEntity_Node]-1)/2 + 2;
      else
        aNbNodes[nbSides] = aVec[SMDSEntity_Node] + 2;
      nbSides++;
    }
  }
  else if (nbEdgesInWire.front() > 4) { // more than 4 edges - try to unite some
    list< TopoDS_Edge > sideEdges;
    while (!edges.empty()) {
      sideEdges.clear();
      sideEdges.splice(sideEdges.end(), edges, edges.begin()); // edges.front() -> sideEdges.end()
      bool sameSide = true;
      while (!edges.empty() && sameSide) {
        sameSide = SMESH_Algo::IsContinuous(sideEdges.back(), edges.front());
        if (sameSide)
          sideEdges.splice(sideEdges.end(), edges, edges.begin());
      }
      if (nbSides == 0) { // go backward from the first edge
        sameSide = true;
        while (!edges.empty() && sameSide) {
          sameSide = SMESH_Algo::IsContinuous(sideEdges.front(), edges.back());
          if (sameSide)
            sideEdges.splice(sideEdges.begin(), edges, --edges.end());
        }
      }
      list<TopoDS_Edge>::iterator ite = sideEdges.begin();
      aNbNodes[nbSides] = 1;
      for (; ite!=sideEdges.end(); ite++) {
        SMESH_subMesh * sm = aMesh.GetSubMesh(*ite);
        MapShapeNbElemsItr anIt = aResMap.find(sm);
        if (anIt==aResMap.end()) {
          return false;
        }
        std::vector<int> aVec = (*anIt).second;
        if (IsQuadratic)
          aNbNodes[nbSides] += (aVec[SMDSEntity_Node]-1)/2 + 1;
        else
          aNbNodes[nbSides] += aVec[SMDSEntity_Node] + 1;
      }
      ++nbSides;
    }
    // issue 20222. Try to unite only edges shared by two same faces
    if (nbSides < 4) {
      nbSides = 0;
      SMESH_Block::GetOrderedEdges (F, V, edges, nbEdgesInWire);
      while (!edges.empty()) {
        sideEdges.clear();
        sideEdges.splice(sideEdges.end(), edges, edges.begin());
        bool sameSide = true;
        while (!edges.empty() && sameSide) {
          sameSide =
            SMESH_Algo::IsContinuous(sideEdges.back(), edges.front()) &&
            twoEdgesMeatAtVertex(sideEdges.back(), edges.front(), aMesh);
          if (sameSide)
            sideEdges.splice(sideEdges.end(), edges, edges.begin());
        }
        if (nbSides == 0) { // go backward from the first edge
          sameSide = true;
          while (!edges.empty() && sameSide) {
            sameSide =
              SMESH_Algo::IsContinuous(sideEdges.front(), edges.back()) &&
              twoEdgesMeatAtVertex(sideEdges.front(), edges.back(), aMesh);
            if (sameSide)
              sideEdges.splice(sideEdges.begin(), edges, --edges.end());
          }
        }
        list<TopoDS_Edge>::iterator ite = sideEdges.begin();
        aNbNodes[nbSides] = 1;
        for (; ite!=sideEdges.end(); ite++) {
          SMESH_subMesh * sm = aMesh.GetSubMesh(*ite);
          MapShapeNbElemsItr anIt = aResMap.find(sm);
          if (anIt==aResMap.end()) {
            return false;
          }
          std::vector<int> aVec = (*anIt).second;
          if (IsQuadratic)
            aNbNodes[nbSides] += (aVec[SMDSEntity_Node]-1)/2 + 1;
          else
            aNbNodes[nbSides] += aVec[SMDSEntity_Node] + 1;
        }
        ++nbSides;
      }
    }
  }
  if (nbSides != 4) {
    if (!nbSides)
      nbSides = nbEdgesInWire.front();
    error(COMPERR_BAD_SHAPE, TComm("Face must have 4 sides but not ") << nbSides);
    return false;
  }

  return true;
}


//=============================================================================
/*!
 *  CheckAnd2Dcompute
 */
//=============================================================================

FaceQuadStruct *StdMeshers_Quadrangle_2D::CheckAnd2Dcompute
                           (SMESH_Mesh &         aMesh,
                            const TopoDS_Shape & aShape,
                            const bool           CreateQuadratic) //throw(SALOME_Exception)
{
  _quadraticMesh = CreateQuadratic;

  FaceQuadStruct *quad = CheckNbEdges(aMesh, aShape);

  if (!quad) return 0;

  // set normalized grid on unit square in parametric domain
  bool stat = SetNormalizedGrid(aMesh, aShape, quad);
  if (!stat) {
    if (quad) delete quad;
    quad = 0;
  }

  return quad;
}

//=============================================================================
/*!
 *  
 */
//=============================================================================

faceQuadStruct::~faceQuadStruct()
{
  for (int i = 0; i < side.size(); i++) {
    if (side[i])     delete side[i];
  }
  if (uv_grid)       delete [] uv_grid;
}

namespace {
  inline const vector<UVPtStruct>& GetUVPtStructIn(FaceQuadStruct* quad, int i, int nbSeg)
  {
    bool   isXConst   = (i == BOTTOM_SIDE || i == TOP_SIDE);
    double constValue = (i == BOTTOM_SIDE || i == LEFT_SIDE) ? 0 : 1;
    return
      quad->isEdgeOut[i] ?
      quad->side[i]->SimulateUVPtStruct(nbSeg,isXConst,constValue) :
      quad->side[i]->GetUVPtStruct(isXConst,constValue);
  }
  inline gp_UV CalcUV(double x, double y,
                      const gp_UV& a0,const gp_UV& a1,const gp_UV& a2,const gp_UV& a3,
                      const gp_UV& p0,const gp_UV& p1,const gp_UV& p2,const gp_UV& p3)
  {
    return
      ((1 - y) * p0 + x * p1 + y * p2 + (1 - x) * p3 ) -
      ((1 - x) * (1 - y) * a0 + x * (1 - y) * a1 + x * y * a2 + (1 - x) * y * a3);
  }
}

//=============================================================================
/*!
 *  
 */
//=============================================================================

bool StdMeshers_Quadrangle_2D::SetNormalizedGrid (SMESH_Mesh & aMesh,
                                                  const TopoDS_Shape& aShape,
                                                  FaceQuadStruct* & quad) //throw (SALOME_Exception)
{
  // Algorithme décrit dans "Génération automatique de maillages"
  // P.L. GEORGE, MASSON, § 6.4.1 p. 84-85
  // traitement dans le domaine paramétrique 2d u,v
  // transport - projection sur le carré unité

//  MESSAGE("StdMeshers_Quadrangle_2D::SetNormalizedGrid");
//  const TopoDS_Face& F = TopoDS::Face(aShape);

  // 1 --- find orientation of the 4 edges, by test on extrema

  //      max             min                    0     x1     1
  //     |<----north-2-------^                a3 -------------> a2
  //     |                   |                   ^1          1^
  //    west-3            east-1 =right          |            |
  //     |                   |         ==>       |            |
  //  y0 |                   | y1                |            |
  //     |                   |                   |0          0|
  //     v----south-0-------->                a0 -------------> a1
  //      min             max                    0     x0     1
  //             =down
  //

  // 3 --- 2D normalized values on unit square [0..1][0..1]

  int nbhoriz  = Min(quad->side[0]->NbPoints(), quad->side[2]->NbPoints());
  int nbvertic = Min(quad->side[1]->NbPoints(), quad->side[3]->NbPoints());

  quad->isEdgeOut[0] = (quad->side[0]->NbPoints() > quad->side[2]->NbPoints());
  quad->isEdgeOut[1] = (quad->side[1]->NbPoints() > quad->side[3]->NbPoints());
  quad->isEdgeOut[2] = (quad->side[2]->NbPoints() > quad->side[0]->NbPoints());
  quad->isEdgeOut[3] = (quad->side[3]->NbPoints() > quad->side[1]->NbPoints());

  UVPtStruct *uv_grid = quad->uv_grid = new UVPtStruct[nbvertic * nbhoriz];

  const vector<UVPtStruct>& uv_e0 = GetUVPtStructIn(quad, 0, nbhoriz - 1);
  const vector<UVPtStruct>& uv_e1 = GetUVPtStructIn(quad, 1, nbvertic - 1);
  const vector<UVPtStruct>& uv_e2 = GetUVPtStructIn(quad, 2, nbhoriz - 1);
  const vector<UVPtStruct>& uv_e3 = GetUVPtStructIn(quad, 3, nbvertic - 1);

  if (uv_e0.empty() || uv_e1.empty() || uv_e2.empty() || uv_e3.empty())
    //return error("Can't find nodes on sides");
    return error(COMPERR_BAD_INPUT_MESH);

  // 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;
    }
  }
  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[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[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;
    }
  }

  // normalized 2d values on grid
  for (int i = 0; i < nbhoriz; i++) {
    for (int j = 0; j < nbvertic; j++) {
      int ij = j * nbhoriz + i;
      // --- droite i cste : x = x0 + y(x1-x0)
      double x0 = uv_e0[i].normParam;   // bas - sud
      double x1 = uv_e2[i].normParam;   // haut - nord
      // --- droite j cste : y = y0 + x(y1-y0)
      double y0 = uv_e3[j].normParam;   // gauche-ouest
      double y1 = uv_e1[j].normParam;   // droite - est
      // --- intersection : x=x0+(y0+x(y1-y0))(x1-x0)
      double x = (x0 + y0 * (x1 - x0)) / (1 - (y1 - y0) * (x1 - x0));
      double y = y0 + x * (y1 - y0);
      uv_grid[ij].x = x;
      uv_grid[ij].y = y;
      //MESSAGE("-xy-01 "<<x0<<" "<<x1<<" "<<y0<<" "<<y1);
      //MESSAGE("-xy-norm "<<i<<" "<<j<<" "<<x<<" "<<y);
    }
  }

  // 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);

  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);

      uv_grid[ij].u = uv.X();
      uv_grid[ij].v = uv.Y();
    }
  }
  return true;
}

//=======================================================================
//function : ShiftQuad
//purpose  : auxilary function for ComputeQuadPref
//=======================================================================

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] };
  for (int i = BOTTOM_SIDE; i < NB_SIDES; ++i) {
    int id = (i + num) % NB_SIDES;
    bool wasForward = (i < TOP_SIDE);
    bool newForward = (id < TOP_SIDE);
    if (wasForward != newForward)
      side[ i ]->Reverse();
    quad->side[ id ] = side[ i ];
  }
}

//=======================================================================
//function : CalcUV
//purpose  : auxilary function for ComputeQuadPref
//=======================================================================

static gp_UV CalcUV(double x0, double x1, double y0, double y1,
                    FaceQuadStruct* quad,
                    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);

  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 uv = CalcUV(x,y, a0,a1,a2,a3, p0,p1,p2,p3);

  return uv;
}

//=======================================================================
//function : CalcUV2
//purpose  : auxilary function for ComputeQuadPref
//=======================================================================

static gp_UV CalcUV2(double x, double y,
                     FaceQuadStruct* quad,
                     const gp_UV& a0, const gp_UV& a1,
                     const gp_UV& a2, const gp_UV& a3)
{
  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);

  return uv;
}


//=======================================================================
/*!
 * Create only quandrangle faces
 */
//=======================================================================

bool StdMeshers_Quadrangle_2D::ComputeQuadPref (SMESH_Mesh &        aMesh,
                                                const TopoDS_Shape& aShape,
                                                FaceQuadStruct*     quad)
{
  // Auxilary key in order to keep old variant
  // of meshing after implementation new variant
  // for bug 0016220 from Mantis.
  bool OldVersion = false;
  if (myQuadType == QUAD_QUADRANGLE_PREF_REVERSED)
    OldVersion = true;

  SMESHDS_Mesh * meshDS = aMesh.GetMeshDS();
  const TopoDS_Face& F = TopoDS::Face(aShape);
  Handle(Geom_Surface) S = BRep_Tool::Surface(F);
  bool WisF = true;
  int i,j,geomFaceID = meshDS->ShapeToIndex(F);

  int nb = quad->side[0]->NbPoints();
  int nr = quad->side[1]->NbPoints();
  int nt = quad->side[2]->NbPoints();
  int nl = quad->side[3]->NbPoints();
  int dh = abs(nb-nt);
  int dv = abs(nr-nl);

  if (dh>=dv) {
    if (nt>nb) {
      // it is a base case => not shift quad but me be replacement is need
      ShiftQuad(quad,0,WisF);
    }
    else {
      // we have to shift quad on 2
      ShiftQuad(quad,2,WisF);
    }
  }
  else {
    if (nr>nl) {
      // we have to shift quad on 1
      ShiftQuad(quad,1,WisF);
    }
    else {
      // we have to shift quad on 3
      ShiftQuad(quad,3,WisF);
    }
  }

  nb = quad->side[0]->NbPoints();
  nr = quad->side[1]->NbPoints();
  nt = quad->side[2]->NbPoints();
  nl = quad->side[3]->NbPoints();
  dh = abs(nb-nt);
  dv = abs(nr-nl);
  int nbh  = Max(nb,nt);
  int nbv = Max(nr,nl);
  int addh = 0;
  int addv = 0;

  // ----------- Old version ---------------
  // orientation of face and 3 main domain for future faces
  //       0   top    1
  //      1------------1
  //       |   |  |   |
  //       |   |  |   |
  //       | L |  | R |
  //  left |   |  |   | rigth
  //       |  /    \  |
  //       | /  C   \ |
  //       |/        \|
  //      0------------0
  //       0  bottom  1

  // ----------- New version ---------------
  // orientation of face and 3 main domain for future faces
  //       0   top    1
  //      1------------1
  //       |  |____|  |
  //       |  /    \  |
  //       | /  C   \ |
  //  left |/________\| rigth
  //       |          |
  //       |          |
  //       |          |
  //      0------------0
  //       0  bottom  1

  if (dh>dv) {
    addv = (dh-dv)/2;
    nbv = nbv + addv;
  }
  else { // dv>=dh
    addh = (dv-dh)/2;
    nbh = nbh + addh;
  }

  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);

  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
  //cout<<"Dump B:"<<endl;
  TColStd_SequenceOfReal npb, npr, npt, npl;
  for (i=0; i<nb; i++) {
    npb.Append(uv_eb[i].normParam);
    //cout<<"i="<<i<<" par="<<uv_eb[i].normParam<<" npar="<<uv_eb[i].normParam;
    //const SMDS_MeshNode* N = uv_eb[i].node;
    //cout<<" node("<<N->X()<<","<<N->Y()<<","<<N->Z()<<")"<<endl;
  }
  for (i=0; i<nr; i++) {
    npr.Append(uv_er[i].normParam);
  }
  for (i=0; i<nt; i++) {
    npt.Append(uv_et[i].normParam);
  }
  for (i=0; i<nl; i++) {
    npl.Append(uv_el[i].normParam);
  }

  int dl,dr;
  if (OldVersion) {
    // add some params to right and left after the first param
    // insert to right
    dr = nbv - nr;
    double dpr = (npr.Value(2) - npr.Value(1))/(dr+1);
    for (i=1; i<=dr; i++) {
      npr.InsertAfter(1,npr.Value(2)-dpr);
    }
    // insert to left
    dl = nbv - nl;
    dpr = (npl.Value(2) - npl.Value(1))/(dl+1);
    for (i=1; i<=dl; i++) {
      npl.InsertAfter(1,npl.Value(2)-dpr);
    }
  }
  //cout<<"npb:";
  //for (i=1; i<=npb.Length(); i++) {
  //  cout<<" "<<npb.Value(i);
  //}
  //cout<<endl;
  
  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);
  //cout<<" a0("<<a0.X()<<","<<a0.Y()<<")"<<" a1("<<a1.X()<<","<<a1.Y()<<")"
  //    <<" a2("<<a2.X()<<","<<a2.Y()<<")"<<" a3("<<a3.X()<<","<<a3.Y()<<")"<<endl;

  int nnn = Min(nr,nl);
  // auxilary sequence of XY for creation nodes
  // in the bottom part of central domain
  // Length of UVL and UVR must be == nbv-nnn
  TColgp_SequenceOfXY UVL, UVR, UVT;

  if (OldVersion) {
    // step1: create faces for left domain
    StdMeshers_Array2OfNode NodesL(1,dl+1,1,nl);
    // add left nodes
    for (j=1; j<=nl; j++)
      NodesL.SetValue(1,j,uv_el[j-1].node);
    if (dl>0) {
      // add top nodes
      for (i=1; i<=dl; i++) 
        NodesL.SetValue(i+1,nl,uv_et[i].node);
      // create and add needed nodes
      TColgp_SequenceOfXY UVtmp;
      for (i=1; i<=dl; i++) {
        double x0 = npt.Value(i+1);
        double x1 = x0;
        // diagonal node
        double y0 = npl.Value(i+1);
        double y1 = npr.Value(i+1);
        gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
        gp_Pnt P = S->Value(UV.X(),UV.Y());
        SMDS_MeshNode * N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
        NodesL.SetValue(i+1,1,N);
        if (UVL.Length()<nbv-nnn) UVL.Append(UV);
        // internal nodes
        for (j=2; j<nl; j++) {
          double y0 = npl.Value(dl+j);
          double y1 = npr.Value(dl+j);
          gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
          gp_Pnt P = S->Value(UV.X(),UV.Y());
          SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
          meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
          NodesL.SetValue(i+1,j,N);
          if (i==dl) UVtmp.Append(UV);
        }
      }
      for (i=1; i<=UVtmp.Length() && UVL.Length()<nbv-nnn; i++) {
        UVL.Append(UVtmp.Value(i));
      }
      //cout<<"Dump NodesL:"<<endl;
      //for (i=1; i<=dl+1; i++) {
      //  cout<<"i="<<i;
      //  for (j=1; j<=nl; j++) {
      //    cout<<" ("<<NodesL.Value(i,j)->X()<<","<<NodesL.Value(i,j)->Y()<<","<<NodesL.Value(i,j)->Z()<<")";
      //  }
      //  cout<<endl;
      //}
      // create faces
      for (i=1; i<=dl; i++) {
        for (j=1; j<nl; j++) {
          if (WisF) {
            SMDS_MeshFace* F =
              myTool->AddFace(NodesL.Value(i,j), NodesL.Value(i+1,j),
                              NodesL.Value(i+1,j+1), NodesL.Value(i,j+1));
            if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
          }
          else {
            SMDS_MeshFace* F =
              myTool->AddFace(NodesL.Value(i,j), NodesL.Value(i,j+1),
                              NodesL.Value(i+1,j+1), NodesL.Value(i+1,j));
            if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
          }
        }
      }
    }
    else {
      // fill UVL using c2d
      for (i=1; i<npl.Length() && UVL.Length()<nbv-nnn; i++) {
        UVL.Append(gp_UV (uv_el[i].u, uv_el[i].v));
      }
    }
    
    // step2: create faces for right domain
    StdMeshers_Array2OfNode NodesR(1,dr+1,1,nr);
    // add right nodes
    for (j=1; j<=nr; j++) 
      NodesR.SetValue(1,j,uv_er[nr-j].node);
    if (dr>0) {
      // add top nodes
      for (i=1; i<=dr; i++) 
        NodesR.SetValue(i+1,1,uv_et[nt-1-i].node);
      // create and add needed nodes
      TColgp_SequenceOfXY UVtmp;
      for (i=1; i<=dr; i++) {
        double x0 = npt.Value(nt-i);
        double x1 = x0;
        // diagonal node
        double y0 = npl.Value(i+1);
        double y1 = npr.Value(i+1);
        gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
        gp_Pnt P = S->Value(UV.X(),UV.Y());
        SMDS_MeshNode * N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
        NodesR.SetValue(i+1,nr,N);
        if (UVR.Length()<nbv-nnn) UVR.Append(UV);
        // internal nodes
        for (j=2; j<nr; j++) {
          double y0 = npl.Value(nbv-j+1);
          double y1 = npr.Value(nbv-j+1);
          gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
          gp_Pnt P = S->Value(UV.X(),UV.Y());
          SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
          meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
          NodesR.SetValue(i+1,j,N);
          if (i==dr) UVtmp.Prepend(UV);
        }
      }
      for (i=1; i<=UVtmp.Length() && UVR.Length()<nbv-nnn; i++) {
        UVR.Append(UVtmp.Value(i));
      }
      // create faces
      for (i=1; i<=dr; i++) {
        for (j=1; j<nr; j++) {
          if (WisF) {
            SMDS_MeshFace* F =
              myTool->AddFace(NodesR.Value(i,j), NodesR.Value(i+1,j),
                              NodesR.Value(i+1,j+1), NodesR.Value(i,j+1));
            if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
          }
          else {
            SMDS_MeshFace* F =
              myTool->AddFace(NodesR.Value(i,j), NodesR.Value(i,j+1),
                              NodesR.Value(i+1,j+1), NodesR.Value(i+1,j));
            if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
          }
        }
      }
    }
    else {
      // fill UVR using c2d
      for (i=1; i<npr.Length() && UVR.Length()<nbv-nnn; i++) {
        UVR.Append(gp_UV(uv_er[i].u, uv_er[i].v));
      }
    }
    
    // step3: create faces for central domain
    StdMeshers_Array2OfNode NodesC(1,nb,1,nbv);
    // add first line using NodesL
    for (i=1; i<=dl+1; i++)
      NodesC.SetValue(1,i,NodesL(i,1));
    for (i=2; i<=nl; i++)
      NodesC.SetValue(1,dl+i,NodesL(dl+1,i));
    // add last line using NodesR
    for (i=1; i<=dr+1; i++)
      NodesC.SetValue(nb,i,NodesR(i,nr));
    for (i=1; i<nr; i++)
      NodesC.SetValue(nb,dr+i+1,NodesR(dr+1,nr-i));
    // add top nodes (last columns)
    for (i=dl+2; i<nbh-dr; i++) 
      NodesC.SetValue(i-dl,nbv,uv_et[i-1].node);
    // add bottom nodes (first columns)
    for (i=2; i<nb; i++)
      NodesC.SetValue(i,1,uv_eb[i-1].node);
    
    // create and add needed nodes
    // add linear layers
    for (i=2; i<nb; i++) {
      double x0 = npt.Value(dl+i);
      double x1 = x0;
      for (j=1; j<nnn; j++) {
        double y0 = npl.Value(nbv-nnn+j);
        double y1 = npr.Value(nbv-nnn+j);
        gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
        gp_Pnt P = S->Value(UV.X(),UV.Y());
        SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
        NodesC.SetValue(i,nbv-nnn+j,N);
        if ( j==1 )
          UVT.Append( UV );
      }
    }
    // add diagonal layers
    //cout<<"UVL.Length()="<<UVL.Length()<<" UVR.Length()="<<UVR.Length()<<endl;
    //cout<<"Dump UVL:"<<endl;
    //for (i=1; i<=UVL.Length(); i++) {
    //  cout<<" ("<<UVL.Value(i).X()<<","<<UVL.Value(i).Y()<<")";
    //}
    //cout<<endl;
    gp_UV A2 = UVR.Value(nbv-nnn);
    gp_UV A3 = UVL.Value(nbv-nnn);
    for (i=1; i<nbv-nnn; i++) {
      gp_UV p1 = UVR.Value(i);
      gp_UV p3 = UVL.Value(i);
      double y = i / double(nbv-nnn);
      for (j=2; j<nb; j++) {
        double x = npb.Value(j);
        gp_UV p0( uv_eb[j-1].u, uv_eb[j-1].v );
        gp_UV p2 = UVT.Value( j-1 );
        gp_UV UV = CalcUV(x, y, a0, a1, A2, A3, p0,p1,p2,p3 );
        gp_Pnt P = S->Value(UV.X(),UV.Y());
        SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, UV.X(),UV.Y());
        NodesC.SetValue(j,i+1,N);
      }
    }
    // create faces
    for (i=1; i<nb; i++) {
      for (j=1; j<nbv; j++) {
        if (WisF) {
          SMDS_MeshFace* F =
            myTool->AddFace(NodesC.Value(i,j), NodesC.Value(i+1,j),
                            NodesC.Value(i+1,j+1), NodesC.Value(i,j+1));
          if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
        }
        else {
          SMDS_MeshFace* F =
            myTool->AddFace(NodesC.Value(i,j), NodesC.Value(i,j+1),
                            NodesC.Value(i+1,j+1), NodesC.Value(i+1,j));
          if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
        }
      }
    }
  }

  else { // New version (!OldVersion)
    // step1: create faces for bottom rectangle domain
    StdMeshers_Array2OfNode NodesBRD(1,nb,1,nnn-1);
    // fill UVL and UVR using c2d
    for (j=0; j<nb; j++) {
      NodesBRD.SetValue(j+1,1,uv_eb[j].node);
    }
    for (i=1; i<nnn-1; i++) {
      NodesBRD.SetValue(1,i+1,uv_el[i].node);
      NodesBRD.SetValue(nb,i+1,uv_er[i].node);
      for (j=2; j<nb; j++) {
        double x = npb.Value(j);
        double y = (1-x) * npl.Value(i+1) + x * npr.Value(i+1);
        gp_UV UV = CalcUV2(x, y, quad, a0, a1, a2, a3);
        gp_Pnt P = S->Value(UV.X(),UV.Y());
        SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, UV.X(),UV.Y());
        NodesBRD.SetValue(j,i+1,N);
      }
    }
    for (j=1; j<nnn-1; j++) {
      for (i=1; i<nb; i++) {
        if (WisF) {
          SMDS_MeshFace* F =
            myTool->AddFace(NodesBRD.Value(i,j), NodesBRD.Value(i+1,j),
                            NodesBRD.Value(i+1,j+1), NodesBRD.Value(i,j+1));
          if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
        }
        else {
          SMDS_MeshFace* F =
            myTool->AddFace(NodesBRD.Value(i,j), NodesBRD.Value(i,j+1),
                            NodesBRD.Value(i+1,j+1), NodesBRD.Value(i+1,j));
          if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
        }
      }
    }
    int drl = abs(nr-nl);
    // create faces for region C
    StdMeshers_Array2OfNode NodesC(1,nb,1,drl+1+addv);
    // add nodes from previous region
    for (j=1; j<=nb; j++) {
      NodesC.SetValue(j,1,NodesBRD.Value(j,nnn-1));
    }
    if ((drl+addv) > 0) {
      int n1,n2;
      if (nr>nl) {
        n1 = 1;
        n2 = drl + 1;
        TColgp_SequenceOfXY UVtmp;
        double drparam = npr.Value(nr) - npr.Value(nnn-1);
        double dlparam = npl.Value(nnn) - npl.Value(nnn-1);
        double y0,y1;
        for (i=1; i<=drl; i++) {
          // add existed nodes from right edge
          NodesC.SetValue(nb,i+1,uv_er[nnn+i-2].node);
          //double dtparam = npt.Value(i+1);
          y1 = npr.Value(nnn+i-1); // param on right edge
          double dpar = (y1 - npr.Value(nnn-1))/drparam;
          y0 = npl.Value(nnn-1) + dpar*dlparam; // param on left edge
          double dy = y1 - y0;
          for (j=1; j<nb; j++) {
            double x = npt.Value(i+1) + npb.Value(j)*(1-npt.Value(i+1));
            double y = y0 + dy*x;
            gp_UV UV = CalcUV2(x, y, quad, a0, a1, a2, a3);
            gp_Pnt P = S->Value(UV.X(),UV.Y());
            SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
            meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
            NodesC.SetValue(j,i+1,N);
          }
        }
        double dy0 = (1-y0)/(addv+1);
        double dy1 = (1-y1)/(addv+1);
        for (i=1; i<=addv; i++) {
          double yy0 = y0 + dy0*i;
          double yy1 = y1 + dy1*i;
          double dyy = yy1 - yy0;
          for (j=1; j<=nb; j++) {
            double x = npt.Value(i+1+drl) + 
              npb.Value(j) * (npt.Value(nt-i) - npt.Value(i+1+drl));
            double y = yy0 + dyy*x;
            gp_UV UV = CalcUV2(x, y, quad, a0, a1, a2, a3);
            gp_Pnt P = S->Value(UV.X(),UV.Y());
            SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
            meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
            NodesC.SetValue(j,i+drl+1,N);
          }
        }
      }
      else { // nr<nl
        n2 = 1;
        n1 = drl + 1;
        TColgp_SequenceOfXY UVtmp;
        double dlparam = npl.Value(nl) - npl.Value(nnn-1);
        double drparam = npr.Value(nnn) - npr.Value(nnn-1);
        double y0 = npl.Value(nnn-1);
        double y1 = npr.Value(nnn-1);
        for (i=1; i<=drl; i++) {
          // add existed nodes from right edge
          NodesC.SetValue(1,i+1,uv_el[nnn+i-2].node);
          y0 = npl.Value(nnn+i-1); // param on left edge
          double dpar = (y0 - npl.Value(nnn-1))/dlparam;
          y1 = npr.Value(nnn-1) + dpar*drparam; // param on right edge
          double dy = y1 - y0;
          for (j=2; j<=nb; j++) {
            double x = npb.Value(j)*npt.Value(nt-i);
            double y = y0 + dy*x;
            gp_UV UV = CalcUV2(x, y, quad, a0, a1, a2, a3);
            gp_Pnt P = S->Value(UV.X(),UV.Y());
            SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
            meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
            NodesC.SetValue(j,i+1,N);
          }
        }
        double dy0 = (1-y0)/(addv+1);
        double dy1 = (1-y1)/(addv+1);
        for (i=1; i<=addv; i++) {
          double yy0 = y0 + dy0*i;
          double yy1 = y1 + dy1*i;
          double dyy = yy1 - yy0;
          for (j=1; j<=nb; j++) {
            double x = npt.Value(i+1) + 
              npb.Value(j) * (npt.Value(nt-i-drl) - npt.Value(i+1));
            double y = yy0 + dyy*x;
            gp_UV UV = CalcUV2(x, y, quad, a0, a1, a2, a3);
            gp_Pnt P = S->Value(UV.X(),UV.Y());
            SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
            meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
            NodesC.SetValue(j,i+drl+1,N);
          }
        }
      }
      // create faces
      for (j=1; j<=drl+addv; j++) {
        for (i=1; i<nb; i++) {
          if (WisF) {
            SMDS_MeshFace* F =
              myTool->AddFace(NodesC.Value(i,j), NodesC.Value(i+1,j),
                              NodesC.Value(i+1,j+1), NodesC.Value(i,j+1));
            if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
          }
          else {
            SMDS_MeshFace* F =
              myTool->AddFace(NodesC.Value(i,j), NodesC.Value(i,j+1),
                              NodesC.Value(i+1,j+1), NodesC.Value(i+1,j));
            if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
          }
        }
      } // end nr<nl

      StdMeshers_Array2OfNode NodesLast(1,nt,1,2);
      for (i=1; i<=nt; i++) {
        NodesLast.SetValue(i,2,uv_et[i-1].node);
      }
      int nnn=0;
      for (i=n1; i<drl+addv+1; i++) {
        nnn++;
        NodesLast.SetValue(nnn,1,NodesC.Value(1,i));
      }
      for (i=1; i<=nb; i++) {
        nnn++;
        NodesLast.SetValue(nnn,1,NodesC.Value(i,drl+addv+1));
      }
      for (i=drl+addv; i>=n2; i--) {
        nnn++;
        NodesLast.SetValue(nnn,1,NodesC.Value(nb,i));
      }
      for (i=1; i<nt; i++) {
        if (WisF) {
          SMDS_MeshFace* F =
            myTool->AddFace(NodesLast.Value(i,1), NodesLast.Value(i+1,1),
                            NodesLast.Value(i+1,2), NodesLast.Value(i,2));
          if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
        }
        else {
          SMDS_MeshFace* F =
            myTool->AddFace(NodesLast.Value(i,1), NodesLast.Value(i,2),
                            NodesLast.Value(i+1,2), NodesLast.Value(i+1,2));
          if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
        }
      }
    } // if ((drl+addv) > 0)

  } // end new version implementation

  bool isOk = true;
  return isOk;
}


//=======================================================================
/*!
 * Evaluate only quandrangle faces
 */
//=======================================================================

bool StdMeshers_Quadrangle_2D::EvaluateQuadPref(SMESH_Mesh &        aMesh,
                                                const TopoDS_Shape& aShape,
                                                std::vector<int>& aNbNodes,
                                                MapShapeNbElems& aResMap,
                                                bool IsQuadratic)
{
  // Auxilary key in order to keep old variant
  // of meshing after implementation new variant
  // for bug 0016220 from Mantis.
  bool OldVersion = false;
  if (myQuadType == QUAD_QUADRANGLE_PREF_REVERSED)
    OldVersion = true;

  const TopoDS_Face& F = TopoDS::Face(aShape);
  Handle(Geom_Surface) S = BRep_Tool::Surface(F);

  int nb = aNbNodes[0];
  int nr = aNbNodes[1];
  int nt = aNbNodes[2];
  int nl = aNbNodes[3];
  int dh = abs(nb-nt);
  int dv = abs(nr-nl);

  if (dh>=dv) {
    if (nt>nb) {
      // it is a base case => not shift 
    }
    else {
      // we have to shift on 2
      nb = aNbNodes[2];
      nr = aNbNodes[3];
      nt = aNbNodes[0];
      nl = aNbNodes[1];
    }
  }
  else {
    if (nr>nl) {
      // we have to shift quad on 1
      nb = aNbNodes[3];
      nr = aNbNodes[0];
      nt = aNbNodes[1];
      nl = aNbNodes[2];
    }
    else {
      // we have to shift quad on 3
      nb = aNbNodes[1];
      nr = aNbNodes[2];
      nt = aNbNodes[3];
      nl = aNbNodes[0];
    }
  }

  dh = abs(nb-nt);
  dv = abs(nr-nl);
  int nbh  = Max(nb,nt);
  int nbv = Max(nr,nl);
  int addh = 0;
  int addv = 0;

  if (dh>dv) {
    addv = (dh-dv)/2;
    nbv = nbv + addv;
  }
  else { // dv>=dh
    addh = (dv-dh)/2;
    nbh = nbh + addh;
  }

  int dl,dr;
  if (OldVersion) {
    // add some params to right and left after the first param
    // insert to right
    dr = nbv - nr;
    // insert to left
    dl = nbv - nl;
  }
  
  int nnn = Min(nr,nl);

  int nbNodes = 0;
  int nbFaces = 0;
  if (OldVersion) {
    // step1: create faces for left domain
    if (dl>0) {
      nbNodes += dl*(nl-1);
      nbFaces += dl*(nl-1);
    }
    // step2: create faces for right domain
    if (dr>0) {
      nbNodes += dr*(nr-1);
      nbFaces += dr*(nr-1);
    }
    // step3: create faces for central domain
    nbNodes += (nb-2)*(nnn-1) + (nbv-nnn-1)*(nb-2);
    nbFaces += (nb-1)*(nbv-1);
  }
  else { // New version (!OldVersion)
    nbNodes += (nnn-2)*(nb-2);
    nbFaces += (nnn-2)*(nb-1);
    int drl = abs(nr-nl);
    nbNodes += drl*(nb-1) + addv*nb;
    nbFaces += (drl+addv)*(nb-1) + (nt-1);
  } // end new version implementation

  std::vector<int> aVec(SMDSEntity_Last);
  for (int i=SMDSEntity_Node; i<SMDSEntity_Last; i++) aVec[i] = 0;
  if (IsQuadratic) {
    aVec[SMDSEntity_Quad_Quadrangle] = nbFaces;
    aVec[SMDSEntity_Node] = nbNodes + nbFaces*4;
    if (aNbNodes.size()==5) {
      aVec[SMDSEntity_Quad_Triangle] = aNbNodes[3] - 1;
      aVec[SMDSEntity_Quad_Quadrangle] = nbFaces - aNbNodes[3] + 1;
    }
  }
  else {
    aVec[SMDSEntity_Node] = nbNodes;
    aVec[SMDSEntity_Quadrangle] = nbFaces;
    if (aNbNodes.size()==5) {
      aVec[SMDSEntity_Triangle] = aNbNodes[3] - 1;
      aVec[SMDSEntity_Quadrangle] = nbFaces - aNbNodes[3] + 1;
    }
  }
  SMESH_subMesh * sm = aMesh.GetSubMesh(aShape);
  aResMap.insert(std::make_pair(sm,aVec));

  return true;
}


//=============================================================================
/*! Split quadrangle in to 2 triangles by smallest diagonal
 *   
 */
//=============================================================================
void StdMeshers_Quadrangle_2D::SplitQuad(SMESHDS_Mesh *theMeshDS,
                                         int theFaceID,
                                         const SMDS_MeshNode* theNode1,
                                         const SMDS_MeshNode* theNode2,
                                         const SMDS_MeshNode* theNode3,
                                         const SMDS_MeshNode* theNode4)
{
  gp_Pnt a(theNode1->X(),theNode1->Y(),theNode1->Z());
  gp_Pnt b(theNode2->X(),theNode2->Y(),theNode2->Z());
  gp_Pnt c(theNode3->X(),theNode3->Y(),theNode3->Z());
  gp_Pnt d(theNode4->X(),theNode4->Y(),theNode4->Z());
  SMDS_MeshFace* face;
  if (a.Distance(c) > b.Distance(d)){
    face = myTool->AddFace(theNode2, theNode4 , theNode1);
    if (face) theMeshDS->SetMeshElementOnShape(face, theFaceID);
    face = myTool->AddFace(theNode2, theNode3, theNode4);
    if (face) theMeshDS->SetMeshElementOnShape(face, theFaceID);

  }
  else{
    face = myTool->AddFace(theNode1, theNode2 ,theNode3);
    if (face) theMeshDS->SetMeshElementOnShape(face, theFaceID);
    face = myTool->AddFace(theNode1, theNode3, theNode4);
    if (face) theMeshDS->SetMeshElementOnShape(face, theFaceID);
  }
}

//=======================================================================
/*!
 *  Implementation of Reduced algorithm (meshing with quadrangles only)
 */
//=======================================================================
bool StdMeshers_Quadrangle_2D::ComputeReduced (SMESH_Mesh &        aMesh,
                                               const TopoDS_Shape& aShape,
                                               FaceQuadStruct*     quad)
{
  SMESHDS_Mesh * meshDS = aMesh.GetMeshDS();
  const TopoDS_Face& F = TopoDS::Face(aShape);
  Handle(Geom_Surface) S = BRep_Tool::Surface(F);
  int i,j,geomFaceID = meshDS->ShapeToIndex(F);

  int nb = quad->side[0]->NbPoints();
  int nr = quad->side[1]->NbPoints();
  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)
  //
  //  .-----.-----.-----.-----.               .-----.-----.-----.-----.
  //  |    / \    |    / \    |               |    / \    |    / \    |
  //  |   /    .--.--.    \   |               |    / \    |    / \    |
  //  |   /   /   |   \   \   |               |   /  .----.----.  \   |
  //  .---.---.---.---.---.---.               |   / / \   |   / \ \   |
  //  |   /  / \  |  / \  \   |               |   / / \   |   / \ \   |
  //  |  /  /   .-.-.   \  \  |               |  / /  .---.---.  \ \  |
  //  |  /  /  /  |  \  \  \  |               |  / / / \  |  / \ \ \  |
  //  .--.--.--.--.--.--.--.--.               |  / / /  \ | /  \ \ \  |
  //  |  / /  / \ | / \  \ \  |               | / / /   .-.-.   \ \ \ |
  //  | / /  /  .-.-.  \  \ \ |               | / / /  /  |  \  \ \ \ |
  //  | / / /  /  |  \  \ \ \ |               | / / /  /  |  \  \ \ \ |
  //  .-.-.-.--.--.--.--.-.-.-.               .-.-.-.--.--.--.--.-.-.-.

  bool MultipleReduce = false;
  {
    int nb1 = nb;
    int nr1 = nr;
    int nt1 = nt;
    int nl1 = nl;

    if (nr == nl) {
      if (nb < nt) {
        nt1 = nb;
        nb1 = nt;
      }
    }
    else if (nb == nt) {
      nl1 = nb; // and == nt
      nr1 = nb; // and == nt
      if (nl < nr) {
        nt1 = nl;
        nb1 = nr;
      }
      else {
        nt1 = nr;
        nb1 = nl;
      }
    }
    else {
      return false;
    }

    // number of rows and columns
    int nrows = nr1 - 1; // and also == nl1 - 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)
      MultipleReduce = true;
  }

  if (MultipleReduce) { // == ComputeQuadPref QUAD_QUADRANGLE_PREF_REVERSED
    //==================================================
    int dh = abs(nb-nt);
    int dv = abs(nr-nl);

    if (dh >= dv) {
      if (nt > nb) {
        // it is a base case => not shift quad but may be replacement is need
        ShiftQuad(quad,0,true);
      }
      else {
        // we have to shift quad on 2
        ShiftQuad(quad,2,true);
      }
    }
    else {
      if (nr > nl) {
        // we have to shift quad on 1
        ShiftQuad(quad,1,true);
      }
      else {
        // we have to shift quad on 3
        ShiftQuad(quad,3,true);
      }
    }

    nb = quad->side[0]->NbPoints();
    nr = quad->side[1]->NbPoints();
    nt = quad->side[2]->NbPoints();
    nl = quad->side[3]->NbPoints();
    dh = abs(nb-nt);
    dv = abs(nr-nl);
    int nbh  = Max(nb,nt);
    int nbv = Max(nr,nl);
    int addh = 0;
    int addv = 0;

    if (dh>dv) {
      addv = (dh-dv)/2;
      nbv = nbv + addv;
    }
    else { // dv>=dh
      addh = (dv-dh)/2;
      nbh = nbh + addh;
    }

    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);

    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);
    }

    int dl,dr;
    // orientation of face and 3 main domain for future faces
    //       0   top    1
    //      1------------1
    //       |   |  |   |
    //       |   |  |   |
    //       | L |  | R |
    //  left |   |  |   | rigth
    //       |  /    \  |
    //       | /  C   \ |
    //       |/        \|
    //      0------------0
    //       0  bottom  1

    // add some params to right and left after the first param
    // insert to right
    dr = nbv - nr;
    double dpr = (npr.Value(2) - npr.Value(1))/(dr+1);
    for (i=1; i<=dr; i++) {
      npr.InsertAfter(1,npr.Value(2)-dpr);
    }
    // insert to left
    dl = nbv - nl;
    dpr = (npl.Value(2) - npl.Value(1))/(dl+1);
    for (i=1; i<=dl; i++) {
      npl.InsertAfter(1,npl.Value(2)-dpr);
    }
  
    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);

    int nnn = Min(nr,nl);
    // auxilary sequence of XY for creation nodes
    // in the bottom part of central domain
    // it's length must be == nbv-nnn-1
    TColgp_SequenceOfXY UVL;
    TColgp_SequenceOfXY UVR;
    //==================================================

    // step1: create faces for left domain
    StdMeshers_Array2OfNode NodesL(1,dl+1,1,nl);
    // add left nodes
    for (j=1; j<=nl; j++)
      NodesL.SetValue(1,j,uv_el[j-1].node);
    if (dl>0) {
      // add top nodes
      for (i=1; i<=dl; i++) 
        NodesL.SetValue(i+1,nl,uv_et[i].node);
      // create and add needed nodes
      TColgp_SequenceOfXY UVtmp;
      for (i=1; i<=dl; i++) {
        double x0 = npt.Value(i+1);
        double x1 = x0;
        // diagonal node
        double y0 = npl.Value(i+1);
        double y1 = npr.Value(i+1);
        gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
        gp_Pnt P = S->Value(UV.X(),UV.Y());
        SMDS_MeshNode * N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
        NodesL.SetValue(i+1,1,N);
        if (UVL.Length()<nbv-nnn-1) UVL.Append(UV);
        // internal nodes
        for (j=2; j<nl; j++) {
          double y0 = npl.Value(dl+j);
          double y1 = npr.Value(dl+j);
          gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
          gp_Pnt P = S->Value(UV.X(),UV.Y());
          SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
          meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
          NodesL.SetValue(i+1,j,N);
          if (i==dl) UVtmp.Append(UV);
        }
      }
      for (i=1; i<=UVtmp.Length() && UVL.Length()<nbv-nnn-1; i++) {
        UVL.Append(UVtmp.Value(i));
      }
      // create faces
      for (i=1; i<=dl; i++) {
        for (j=1; j<nl; j++) {
            SMDS_MeshFace* F =
              myTool->AddFace(NodesL.Value(i,j), NodesL.Value(i+1,j),
                              NodesL.Value(i+1,j+1), NodesL.Value(i,j+1));
            if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
        }
      }
    }
    else {
      // fill UVL using c2d
      for (i=1; i<npl.Length() && UVL.Length()<nbv-nnn-1; i++) {
        UVL.Append(gp_UV (uv_el[i].u, uv_el[i].v));
      }
    }
    
    // step2: create faces for right domain
    StdMeshers_Array2OfNode NodesR(1,dr+1,1,nr);
    // add right nodes
    for (j=1; j<=nr; j++) 
      NodesR.SetValue(1,j,uv_er[nr-j].node);
    if (dr>0) {
      // add top nodes
      for (i=1; i<=dr; i++) 
        NodesR.SetValue(i+1,1,uv_et[nt-1-i].node);
      // create and add needed nodes
      TColgp_SequenceOfXY UVtmp;
      for (i=1; i<=dr; i++) {
        double x0 = npt.Value(nt-i);
        double x1 = x0;
        // diagonal node
        double y0 = npl.Value(i+1);
        double y1 = npr.Value(i+1);
        gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
        gp_Pnt P = S->Value(UV.X(),UV.Y());
        SMDS_MeshNode * N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
        NodesR.SetValue(i+1,nr,N);
        if (UVR.Length()<nbv-nnn-1) UVR.Append(UV);
        // internal nodes
        for (j=2; j<nr; j++) {
          double y0 = npl.Value(nbv-j+1);
          double y1 = npr.Value(nbv-j+1);
          gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
          gp_Pnt P = S->Value(UV.X(),UV.Y());
          SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
          meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
          NodesR.SetValue(i+1,j,N);
          if (i==dr) UVtmp.Prepend(UV);
        }
      }
      for (i=1; i<=UVtmp.Length() && UVR.Length()<nbv-nnn-1; i++) {
        UVR.Append(UVtmp.Value(i));
      }
      // create faces
      for (i=1; i<=dr; i++) {
        for (j=1; j<nr; j++) {
            SMDS_MeshFace* F =
              myTool->AddFace(NodesR.Value(i,j), NodesR.Value(i+1,j),
                              NodesR.Value(i+1,j+1), NodesR.Value(i,j+1));
            if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
        }
      }
    }
    else {
      // fill UVR using c2d
      for (i=1; i<npr.Length() && UVR.Length()<nbv-nnn-1; i++) {
        UVR.Append(gp_UV(uv_er[i].u, uv_er[i].v));
      }
    }
    
    // step3: create faces for central domain
    StdMeshers_Array2OfNode NodesC(1,nb,1,nbv);
    // add first line using NodesL
    for (i=1; i<=dl+1; i++)
      NodesC.SetValue(1,i,NodesL(i,1));
    for (i=2; i<=nl; i++)
      NodesC.SetValue(1,dl+i,NodesL(dl+1,i));
    // add last line using NodesR
    for (i=1; i<=dr+1; i++)
      NodesC.SetValue(nb,i,NodesR(i,nr));
    for (i=1; i<nr; i++)
      NodesC.SetValue(nb,dr+i+1,NodesR(dr+1,nr-i));
    // add top nodes (last columns)
    for (i=dl+2; i<nbh-dr; i++) 
      NodesC.SetValue(i-dl,nbv,uv_et[i-1].node);
    // add bottom nodes (first columns)
    for (i=2; i<nb; i++)
      NodesC.SetValue(i,1,uv_eb[i-1].node);
    
    // create and add needed nodes
    // add linear layers
    for (i=2; i<nb; i++) {
      double x0 = npt.Value(dl+i);
      double x1 = x0;
      for (j=1; j<nnn; j++) {
        double y0 = npl.Value(nbv-nnn+j);
        double y1 = npr.Value(nbv-nnn+j);
        gp_UV UV = CalcUV(x0, x1, y0, y1, quad, a0, a1, a2, a3);
        gp_Pnt P = S->Value(UV.X(),UV.Y());
        SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, UV.X(), UV.Y());
        NodesC.SetValue(i,nbv-nnn+j,N);
      }
    }
    // add diagonal layers
    for (i=1; i<nbv-nnn; i++) {
      double du = UVR.Value(i).X() - UVL.Value(i).X();
      double dv = UVR.Value(i).Y() - UVL.Value(i).Y();
      for (j=2; j<nb; j++) {
        double u = UVL.Value(i).X() + du*npb.Value(j);
        double v = UVL.Value(i).Y() + dv*npb.Value(j);
        gp_Pnt P = S->Value(u,v);
        SMDS_MeshNode* N = meshDS->AddNode(P.X(), P.Y(), P.Z());
        meshDS->SetNodeOnFace(N, geomFaceID, u, v);
        NodesC.SetValue(j,i+1,N);
      }
    }
    // create faces
    for (i=1; i<nb; i++) {
      for (j=1; j<nbv; j++) {
          SMDS_MeshFace* F =
            myTool->AddFace(NodesC.Value(i,j), NodesC.Value(i+1,j),
                            NodesC.Value(i+1,j+1), NodesC.Value(i,j+1));
          if (F) meshDS->SetMeshElementOnShape(F, geomFaceID);
      }
    }
    // TODO ???
  } // end Multiple Reduce implementation
  else { // Simple Reduce (!MultipleReduce)
    //=========================================================
    if (nr == nl) {
      if (nt < nb) {
        // it is a base case => not shift quad
        //ShiftQuad(quad,0,true);
      }
      else {
        // we have to shift quad on 2
        ShiftQuad(quad,2,true);
      }
    }
    else {
      if (nl > nr) {
        // we have to shift quad on 1
        ShiftQuad(quad,1,true);
      }
      else {
        // we have to shift quad on 3
        ShiftQuad(quad,3,true);
      }
    }

    nb = quad->side[0]->NbPoints();
    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_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;
      }
      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);
    bool is_lin_31 = false;
    bool is_lin_42 = false;
    bool is_tree_31 = false;
    bool is_tree_42 = false;
    if (ncol_bot > max_lin) {
      if (ncol_bot <= max_lin31) {
        is_lin_31 = true;
        max_lin = max_lin31;
      }
    }
    else {
      // if ncol_bot is a 3*n or not 2*n
      if ((ncol_bot/3)*3 == ncol_bot || (ncol_bot/2)*2 != ncol_bot) {
        is_lin_31 = true;
        max_lin = max_lin31;
      }
      else {
        is_lin_42 = true;
      }
    }
    if (ncol_bot > max_lin) { // not "linear"
      is_tree_31 = (ncol_bot > max_tree42);
      if (ncol_bot <= max_tree42) {
        if ((ncol_bot/3)*3 == ncol_bot || (ncol_bot/2)*2 != ncol_bot) {
          is_tree_31 = true;
        }
        else {
          is_tree_42 = true;
        }
      }
    }

    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);

    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);
    }

    // We will ajust new points to this grid
    if (!SetNormalizedGrid(aMesh, aShape, quad))
      return false;

    // 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);
    //=========================================================

    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
    }

    int curr_base_len = nb;
    int next_base_len = 0;

    if (is_tree_42) {
      // "tree" simple reduce "42": 2->4->8->16->32->...
      //
      //  .-------------------------------.-------------------------------. nr
      //  |    \                          |                          /    |
      //  |         \     .---------------.---------------.     /         |
      //  |               |               |               |               |
      //  .---------------.---------------.---------------.---------------.
      //  | \             |             / | \             |             / |
      //  |     \ .-------.-------. /     |     \ .-------.-------. /     |
      //  |       |       |       |       |       |       |       |       |
      //  .-------.-------.-------.-------.-------.-------.-------.-------. i
      //  |\      |      /|\      |      /|\      |      /|\      |      /|
      //  |  \.---.---./  |  \.---.---./  |  \.---.---./  |  \.---.---./  |
      //  |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
      //  .---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.
      //  |\  |  /|\  |  /|\  |  /|\  |  /|\  |  /|\  |  /|\  |  /|\  |  /|
      //  | .-.-. | .-.-. | .-.-. | .-.-. | .-.-. | .-.-. | .-.-. | .-.-. |
      //  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
      //  .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. 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 = myTool->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 = myTool->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 = myTool->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 = myTool->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 = myTool->AddFace(Nc, Nd, Na,
                                              NodesBRD.Value(next_base.Value(next_base_len - 2), i + 1));
          if (F5) meshDS->SetMeshElementOnShape(F5, geomFaceID);

          SMDS_MeshFace* F6 = myTool->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 = myTool->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
      //  |        \                                   /        |
      //  |                 .-----------------.                 |
      //  |                 |                 |                 |
      //  .-----------------.-----------------.-----------------.
      //  |   \         /   |   \         /   |   \         /   |
      //  |     .-----.     |     .-----.     |     .-----.     | i
      //  |     |     |     |     |     |     |     |     |     |
      //  .-----.-----.-----.-----.-----.-----.-----.-----.-----.
      //  |\   /|\   /|\   /|\   /|\   /|\   /|\   /|\   /|\   /|
      //  | .-. | .-. | .-. | .-. | .-. | .-. | .-. | .-. | .-. |
      //  | | | | | | | | | | | | | | | | | | | | | | | | | | | |
      //  .-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-. 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;

        // 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);
        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 = myTool->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 = myTool->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 = myTool->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 = myTool->AddFace(Nc, Ne, Nb,
                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
          if (F5) meshDS->SetMeshElementOnShape(F5, 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 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 = myTool->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 "31"
    else if (is_lin_42) {
      // "linear" simple reduce "42": 4->8->12->16
      //
      //  .---------------.---------------.---------------.---------------. nr
      //  | \             |             / | \             |             / |
      //  |     \ .-------.-------. /     |     \ .-------.-------. /     |
      //  |       |       |       |       |       |       |       |       |
      //  .-------.-------.-------.-------.-------.-------.-------.-------.
      //  |      / \      |      / \      |      / \      |      / \      |
      //  |     /   \.----.----./   \     |     /   \.----.----./   \     | i
      //  |     /    |    |    |    \     |     /    |    |    |    \     |
      //  .-----.----.----.----.----.-----.-----.----.----.----.----.-----.
      //  |     /   / \   |  /  \   \     |     /   / \   |  /  \   \     |
      //  |    /   /    .-.-.    \   \    |    /   /    .-.-.    \   \    |
      //  |   /   /    /  |  \    \   \   |   /   /    /  |  \    \   \   |
      //  .---.---.---.---.---.---.---.---.---.---.---.---.---.---.---.---. 1
      //  1                               j                               nb

      // nt = 5, nb = 7, nr = 4
      //int delta_all = 2;
      //int delta_one_col = 6;
      //int nb_col = 0;
      //int remainder = 2;
      //if (remainder > 0) nb_col++;
      //nb_col = 1;
      //int free_left = 1;
      //free_left += 2;
      //int free_middle = 4;

      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) / 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;
      }

      // nt = 5, nb = 17, nr = 4
      //int delta_all = 12;
      //int delta_one_col = 6;
      //int nb_col = 2;
      //int remainder = 0;
      //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);

        // 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;

        // 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 = myTool->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 = myTool->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 = myTool->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 = myTool->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 = myTool->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 = myTool->AddFace(Nc, Nd, Na,
                                              NodesBRD.Value(next_base.Value(next_base_len - 2), i + 1));
          if (F5) meshDS->SetMeshElementOnShape(F5, geomFaceID);

          SMDS_MeshFace* F6 = myTool->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);

            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 = myTool->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;
          }
        }

        // 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 = myTool->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;

        // 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 = myTool->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 "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 = myTool->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 = myTool->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 = myTool->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 = myTool->AddFace(Nc, Ne, Nb,
                                              NodesBRD.Value(next_base.Value(next_base_len - 1), i + 1));
          if (F5) meshDS->SetMeshElementOnShape(F5, geomFaceID);

          j += 3;

          // 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);

            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 = myTool->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;
          }
        }

        // 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 = myTool->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 "31"
    else {
    }
  } // end Simple Reduce implementation

  bool isOk = true;
  return isOk;
}