// Copyright (C) 2007-2014  CEA/DEN, EDF R&D, OPEN CASCADE
//
// 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, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// 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_ViscousLayers.cxx
// Created   : Wed Dec  1 15:15:34 2010
// Author    : Edward AGAPOV (eap)

#include "StdMeshers_ViscousLayers.hxx"

#include "SMDS_EdgePosition.hxx"
#include "SMDS_FaceOfNodes.hxx"
#include "SMDS_FacePosition.hxx"
#include "SMDS_MeshNode.hxx"
#include "SMDS_SetIterator.hxx"
#include "SMESHDS_Group.hxx"
#include "SMESHDS_Hypothesis.hxx"
#include "SMESH_Algo.hxx"
#include "SMESH_ComputeError.hxx"
#include "SMESH_ControlsDef.hxx"
#include "SMESH_Gen.hxx"
#include "SMESH_Group.hxx"
#include "SMESH_HypoFilter.hxx"
#include "SMESH_Mesh.hxx"
#include "SMESH_MeshAlgos.hxx"
#include "SMESH_MesherHelper.hxx"
#include "SMESH_ProxyMesh.hxx"
#include "SMESH_subMesh.hxx"
#include "SMESH_subMeshEventListener.hxx"
#include "StdMeshers_FaceSide.hxx"

#include <Adaptor3d_HSurface.hxx>
#include <BRepAdaptor_Curve2d.hxx>
#include <BRepAdaptor_Surface.hxx>
#include <BRepLProp_SLProps.hxx>
#include <BRep_Tool.hxx>
#include <Bnd_B2d.hxx>
#include <Bnd_B3d.hxx>
#include <ElCLib.hxx>
#include <GCPnts_AbscissaPoint.hxx>
#include <Geom2d_Circle.hxx>
#include <Geom2d_Line.hxx>
#include <Geom2d_TrimmedCurve.hxx>
#include <GeomAdaptor_Curve.hxx>
#include <GeomLib.hxx>
#include <Geom_Circle.hxx>
#include <Geom_Curve.hxx>
#include <Geom_Line.hxx>
#include <Geom_TrimmedCurve.hxx>
#include <Precision.hxx>
#include <Standard_ErrorHandler.hxx>
#include <Standard_Failure.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TopExp.hxx>
#include <TopExp_Explorer.hxx>
#include <TopTools_IndexedMapOfShape.hxx>
#include <TopTools_ListOfShape.hxx>
#include <TopTools_MapOfShape.hxx>
#include <TopoDS.hxx>
#include <TopoDS_Edge.hxx>
#include <TopoDS_Face.hxx>
#include <TopoDS_Vertex.hxx>
#include <gp_Ax1.hxx>
#include <gp_Cone.hxx>
#include <gp_Sphere.hxx>
#include <gp_Vec.hxx>
#include <gp_XY.hxx>

#include <list>
#include <string>
#include <cmath>
#include <limits>

#ifdef _DEBUG_
//#define __myDEBUG
//#define __NOT_INVALIDATE_BAD_SMOOTH
#endif

using namespace std;

//================================================================================
namespace VISCOUS_3D
{
  typedef int TGeomID;

  enum UIndex { U_TGT = 1, U_SRC, LEN_TGT };

  const double theMinSmoothCosin = 0.1;
  const double theSmoothThickToElemSizeRatio = 0.3;

  // what part of thickness is allowed till intersection
  // (defined by SALOME_TESTS/Grids/smesh/viscous_layers_00/A5)
  const double theThickToIntersection = 1.5;

  bool needSmoothing( double cosin, double tgtThick, double elemSize )
  {
    return cosin * tgtThick > theSmoothThickToElemSizeRatio * elemSize;
  }

  /*!
   * \brief SMESH_ProxyMesh computed by _ViscousBuilder for a SOLID.
   * It is stored in a SMESH_subMesh of the SOLID as SMESH_subMeshEventListenerData
   */
  struct _MeshOfSolid : public SMESH_ProxyMesh,
                        public SMESH_subMeshEventListenerData
  {
    bool                  _n2nMapComputed;
    SMESH_ComputeErrorPtr _warning;

    _MeshOfSolid( SMESH_Mesh* mesh)
      :SMESH_subMeshEventListenerData( /*isDeletable=*/true),_n2nMapComputed(false)
    {
      SMESH_ProxyMesh::setMesh( *mesh );
    }

    // returns submesh for a geom face
    SMESH_ProxyMesh::SubMesh* getFaceSubM(const TopoDS_Face& F, bool create=false)
    {
      TGeomID i = SMESH_ProxyMesh::shapeIndex(F);
      return create ? SMESH_ProxyMesh::getProxySubMesh(i) : findProxySubMesh(i);
    }
    void setNode2Node(const SMDS_MeshNode*                 srcNode,
                      const SMDS_MeshNode*                 proxyNode,
                      const SMESH_ProxyMesh::SubMesh* subMesh)
    {
      SMESH_ProxyMesh::setNode2Node( srcNode,proxyNode,subMesh);
    }
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Listener of events of 3D sub-meshes computed with viscous layers.
   * It is used to clear an inferior dim sub-meshes modified by viscous layers
   */
  class _ShrinkShapeListener : SMESH_subMeshEventListener
  {
    _ShrinkShapeListener()
      : SMESH_subMeshEventListener(/*isDeletable=*/false,
                                   "StdMeshers_ViscousLayers::_ShrinkShapeListener") {}
  public:
    static SMESH_subMeshEventListener* Get() { static _ShrinkShapeListener l; return &l; }
    virtual void ProcessEvent(const int                       event,
                              const int                       eventType,
                              SMESH_subMesh*                  solidSM,
                              SMESH_subMeshEventListenerData* data,
                              const SMESH_Hypothesis*         hyp)
    {
      if ( SMESH_subMesh::COMPUTE_EVENT == eventType && solidSM->IsEmpty() && data )
      {
        SMESH_subMeshEventListener::ProcessEvent(event,eventType,solidSM,data,hyp);
      }
    }
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Listener of events of 3D sub-meshes computed with viscous layers.
   * It is used to store data computed by _ViscousBuilder for a sub-mesh and to
   * delete the data as soon as it has been used
   */
  class _ViscousListener : SMESH_subMeshEventListener
  {
    _ViscousListener():
      SMESH_subMeshEventListener(/*isDeletable=*/false,
                                 "StdMeshers_ViscousLayers::_ViscousListener") {}
    static SMESH_subMeshEventListener* Get() { static _ViscousListener l; return &l; }
  public:
    virtual void ProcessEvent(const int                       event,
                              const int                       eventType,
                              SMESH_subMesh*                  subMesh,
                              SMESH_subMeshEventListenerData* data,
                              const SMESH_Hypothesis*         hyp)
    {
      if ( SMESH_subMesh::COMPUTE_EVENT       == eventType &&
           SMESH_subMesh::CHECK_COMPUTE_STATE != event)
      {
        // delete SMESH_ProxyMesh containing temporary faces
        subMesh->DeleteEventListener( this );
      }
    }
    // Finds or creates proxy mesh of the solid
    static _MeshOfSolid* GetSolidMesh(SMESH_Mesh*         mesh,
                                      const TopoDS_Shape& solid,
                                      bool                toCreate=false)
    {
      if ( !mesh ) return 0;
      SMESH_subMesh* sm = mesh->GetSubMesh(solid);
      _MeshOfSolid* data = (_MeshOfSolid*) sm->GetEventListenerData( Get() );
      if ( !data && toCreate )
      {
        data = new _MeshOfSolid(mesh);
        data->mySubMeshes.push_back( sm ); // to find SOLID by _MeshOfSolid
        sm->SetEventListener( Get(), data, sm );
      }
      return data;
    }
    // Removes proxy mesh of the solid
    static void RemoveSolidMesh(SMESH_Mesh* mesh, const TopoDS_Shape& solid)
    {
      mesh->GetSubMesh(solid)->DeleteEventListener( _ViscousListener::Get() );
    }
  };
  
  //================================================================================
  /*!
   * \brief sets a sub-mesh event listener to clear sub-meshes of sub-shapes of
   * the main shape when sub-mesh of the main shape is cleared,
   * for example to clear sub-meshes of FACEs when sub-mesh of a SOLID
   * is cleared
   */
  //================================================================================

  void ToClearSubWithMain( SMESH_subMesh* sub, const TopoDS_Shape& main)
  {
    SMESH_subMesh* mainSM = sub->GetFather()->GetSubMesh( main );
    SMESH_subMeshEventListenerData* data =
      mainSM->GetEventListenerData( _ShrinkShapeListener::Get());
    if ( data )
    {
      if ( find( data->mySubMeshes.begin(), data->mySubMeshes.end(), sub ) ==
           data->mySubMeshes.end())
        data->mySubMeshes.push_back( sub );
    }
    else
    {
      data = SMESH_subMeshEventListenerData::MakeData( /*dependent=*/sub );
      sub->SetEventListener( _ShrinkShapeListener::Get(), data, /*whereToListenTo=*/mainSM );
    }
  }
  struct _SolidData;
  //--------------------------------------------------------------------------------
  /*!
   * \brief Simplex (triangle or tetrahedron) based on 1 (tria) or 2 (tet) nodes of
   * _LayerEdge and 2 nodes of the mesh surface beening smoothed.
   * The class is used to check validity of face or volumes around a smoothed node;
   * it stores only 2 nodes as the other nodes are stored by _LayerEdge.
   */
  struct _Simplex
  {
    const SMDS_MeshNode *_nPrev, *_nNext; // nodes on a smoothed mesh surface
    const SMDS_MeshNode *_nOpp; // in 2D case, a node opposite to a smoothed node in QUAD
    _Simplex(const SMDS_MeshNode* nPrev=0,
             const SMDS_MeshNode* nNext=0,
             const SMDS_MeshNode* nOpp=0)
      : _nPrev(nPrev), _nNext(nNext), _nOpp(nOpp) {}
    bool IsForward(const SMDS_MeshNode* nSrc, const gp_XYZ* pntTgt, double& vol) const
    {
      const double M[3][3] =
        {{ _nNext->X() - nSrc->X(), _nNext->Y() - nSrc->Y(), _nNext->Z() - nSrc->Z() },
         { pntTgt->X() - nSrc->X(), pntTgt->Y() - nSrc->Y(), pntTgt->Z() - nSrc->Z() },
         { _nPrev->X() - nSrc->X(), _nPrev->Y() - nSrc->Y(), _nPrev->Z() - nSrc->Z() }};
      vol = ( + M[0][0]*M[1][1]*M[2][2]
              + M[0][1]*M[1][2]*M[2][0]
              + M[0][2]*M[1][0]*M[2][1]
              - M[0][0]*M[1][2]*M[2][1]
              - M[0][1]*M[1][0]*M[2][2]
              - M[0][2]*M[1][1]*M[2][0]);
      return vol > 1e-100;
    }
    bool IsForward(const gp_XY&         tgtUV,
                   const SMDS_MeshNode* smoothedNode,
                   const TopoDS_Face&   face,
                   SMESH_MesherHelper&  helper,
                   const double         refSign) const
    {
      gp_XY prevUV = helper.GetNodeUV( face, _nPrev, smoothedNode );
      gp_XY nextUV = helper.GetNodeUV( face, _nNext, smoothedNode );
      gp_Vec2d v1( tgtUV, prevUV ), v2( tgtUV, nextUV );
      double d = v1 ^ v2;
      return d*refSign > 1e-100;
    }
    bool IsNeighbour(const _Simplex& other) const
    {
      return _nPrev == other._nNext || _nNext == other._nPrev;
    }
    static void GetSimplices( const SMDS_MeshNode* node,
                              vector<_Simplex>&   simplices,
                              const set<TGeomID>& ingnoreShapes,
                              const _SolidData*   dataToCheckOri = 0,
                              const bool          toSort = false);
    static void SortSimplices(vector<_Simplex>& simplices);
  };
  //--------------------------------------------------------------------------------
  /*!
   * Structure used to take into account surface curvature while smoothing
   */
  struct _Curvature
  {
    double _r; // radius
    double _k; // factor to correct node smoothed position
    double _h2lenRatio; // avgNormProj / (2*avgDist)
  public:
    static _Curvature* New( double avgNormProj, double avgDist )
    {
      _Curvature* c = 0;
      if ( fabs( avgNormProj / avgDist ) > 1./200 )
      {
        c = new _Curvature;
        c->_r = avgDist * avgDist / avgNormProj;
        c->_k = avgDist * avgDist / c->_r / c->_r;
        //c->_k = avgNormProj / c->_r;
        c->_k *= ( c->_r < 0 ? 1/1.1 : 1.1 ); // not to be too restrictive
        c->_h2lenRatio = avgNormProj / ( avgDist + avgDist );
      }
      return c;
    }
    double lenDelta(double len) const { return _k * ( _r + len ); }
    double lenDeltaByDist(double dist) const { return dist * _h2lenRatio; }
  };
  //--------------------------------------------------------------------------------

  struct _2NearEdges;
  struct _LayerEdge;
  struct _EdgesOnShape;
  typedef map< const SMDS_MeshNode*, _LayerEdge*, TIDCompare > TNode2Edge;

  //--------------------------------------------------------------------------------
  /*!
   * \brief Edge normal to surface, connecting a node on solid surface (_nodes[0])
   * and a node of the most internal layer (_nodes.back())
   */
  struct _LayerEdge
  {
    typedef gp_XYZ (_LayerEdge::*PSmooFun)();

    vector< const SMDS_MeshNode*> _nodes;

    gp_XYZ              _normal; // to solid surface
    vector<gp_XYZ>      _pos; // points computed during inflation
    double              _len; // length achived with the last inflation step
    double              _cosin; // of angle (_normal ^ surface)
    double              _lenFactor; // to compute _len taking _cosin into account

    // face or edge w/o layer along or near which _LayerEdge is inflated
    //TopoDS_Shape*       _sWOL;
    // simplices connected to the source node (_nodes[0]);
    // used for smoothing and quality check of _LayerEdge's based on the FACE
    vector<_Simplex>    _simplices;
    PSmooFun            _smooFunction; // smoothing function
    // data for smoothing of _LayerEdge's based on the EDGE
    _2NearEdges*        _2neibors;

    _Curvature*         _curvature;
    // TODO:: detele _Curvature, _plnNorm

    void SetNewLength( double len, _EdgesOnShape& eos, SMESH_MesherHelper& helper );
    bool SetNewLength2d( Handle(Geom_Surface)& surface,
                         const TopoDS_Face&    F,
                         _EdgesOnShape&        eos,
                         SMESH_MesherHelper&   helper );
    void SetDataByNeighbors( const SMDS_MeshNode* n1,
                             const SMDS_MeshNode* n2,
                             const _EdgesOnShape& eos,
                             SMESH_MesherHelper&  helper);
    void InvalidateStep( int curStep, const _EdgesOnShape& eos, bool restoreLength=false );
    void ChooseSmooFunction(const set< TGeomID >& concaveVertices,
                            const TNode2Edge&     n2eMap);
    int  Smooth(const int step, const bool isConcaveFace, const bool findBest);
    bool SmoothOnEdge(Handle(Geom_Surface)& surface,
                      const TopoDS_Face&    F,
                      SMESH_MesherHelper&   helper);
    bool FindIntersection( SMESH_ElementSearcher&   searcher,
                           double &                 distance,
                           const double&            epsilon,
                           _EdgesOnShape&           eos,
                           const SMDS_MeshElement** face = 0);
    bool SegTriaInter( const gp_Ax1&        lastSegment,
                       const SMDS_MeshNode* n0,
                       const SMDS_MeshNode* n1,
                       const SMDS_MeshNode* n2,
                       double&              dist,
                       const double&        epsilon) const;
    gp_Ax1 LastSegment(double& segLen, _EdgesOnShape& eos) const;
    gp_XY  LastUV( const TopoDS_Face& F, _EdgesOnShape& eos ) const;
    bool   IsOnEdge() const { return _2neibors; }
    gp_XYZ Copy( _LayerEdge& other, _EdgesOnShape& eos, SMESH_MesherHelper& helper );
    void   SetCosin( double cosin );
    int    NbSteps() const { return _pos.size() - 1; } // nb inlation steps

    gp_XYZ smoothLaplacian();
    gp_XYZ smoothAngular();
    gp_XYZ smoothLengthWeighted();
    gp_XYZ smoothCentroidal();
    gp_XYZ smoothNefPolygon();

    enum { FUN_LAPLACIAN, FUN_LENWEIGHTED, FUN_CENTROIDAL, FUN_NEFPOLY, FUN_ANGULAR, FUN_NB };
    static const int theNbSmooFuns = FUN_NB;
    static PSmooFun _funs[theNbSmooFuns];
    static const char* _funNames[theNbSmooFuns+1];
    int smooFunID( PSmooFun fun=0) const;
  };
  _LayerEdge::PSmooFun _LayerEdge::_funs[theNbSmooFuns] = { &_LayerEdge::smoothLaplacian,
                                                            &_LayerEdge::smoothLengthWeighted,
                                                            &_LayerEdge::smoothCentroidal,
                                                            &_LayerEdge::smoothNefPolygon,
                                                            &_LayerEdge::smoothAngular };
  const char* _LayerEdge::_funNames[theNbSmooFuns+1] = { "Laplacian",
                                                         "LengthWeighted",
                                                         "Centroidal",
                                                         "NefPolygon",
                                                         "Angular",
                                                         "None"};
  struct _LayerEdgeCmp
  {
    bool operator () (const _LayerEdge* e1, const _LayerEdge* e2) const
    {
      const bool cmpNodes = ( e1 && e2 && e1->_nodes.size() && e2->_nodes.size() );
      return cmpNodes ? ( e1->_nodes[0]->GetID() < e2->_nodes[0]->GetID()) : ( e1 < e2 );
    }
  };
  //--------------------------------------------------------------------------------
  /*!
   * A 2D half plane used by _LayerEdge::smoothNefPolygon()
   */
  struct _halfPlane
  {
    gp_XY _pos, _dir, _inNorm;
    bool IsOut( const gp_XY p, const double tol ) const
    {
      return _inNorm * ( p - _pos ) < -tol;
    }
    bool FindInterestion( const _halfPlane& hp, gp_XY & intPnt )
    {
      const double eps = 1e-10;
      double D = _dir.Crossed( hp._dir );
      if ( fabs(D) < std::numeric_limits<double>::min())
        return false;
      gp_XY vec21 = _pos - hp._pos; 
      double u = hp._dir.Crossed( vec21 ) / D; 
      intPnt = _pos + _dir * u;
      return true;
    }
  };
  //--------------------------------------------------------------------------------
  /*!
   * Structure used to smooth a _LayerEdge based on an EDGE.
   */
  struct _2NearEdges
  {
    double               _wgt  [2]; // weights of _nodes
    _LayerEdge*          _edges[2];

     // normal to plane passing through _LayerEdge._normal and tangent of EDGE
    gp_XYZ*              _plnNorm;

    _2NearEdges() { _edges[0]=_edges[1]=0; _plnNorm = 0; }
    const SMDS_MeshNode* tgtNode(bool is2nd) {
      return _edges[is2nd] ? _edges[is2nd]->_nodes.back() : 0;
    }
    const SMDS_MeshNode* srcNode(bool is2nd) {
      return _edges[is2nd] ? _edges[is2nd]->_nodes[0] : 0;
    }
    void reverse() {
      std::swap( _wgt  [0], _wgt  [1] );
      std::swap( _edges[0], _edges[1] );
    }
  };


  //--------------------------------------------------------------------------------
  /*!
   * \brief Layers parameters got by averaging several hypotheses
   */
  struct AverageHyp
  {
    AverageHyp( const StdMeshers_ViscousLayers* hyp = 0 )
      :_nbLayers(0), _nbHyps(0), _thickness(0), _stretchFactor(0), _method(0)
    {
      Add( hyp );
    }
    void Add( const StdMeshers_ViscousLayers* hyp )
    {
      if ( hyp )
      {
        _nbHyps++;
        _nbLayers       = hyp->GetNumberLayers();
        //_thickness     += hyp->GetTotalThickness();
        _thickness      = Max( _thickness, hyp->GetTotalThickness() );
        _stretchFactor += hyp->GetStretchFactor();
        _method         = hyp->GetMethod();
      }
    }
    double GetTotalThickness() const { return _thickness; /*_nbHyps ? _thickness / _nbHyps : 0;*/ }
    double GetStretchFactor()  const { return _nbHyps ? _stretchFactor / _nbHyps : 0; }
    int    GetNumberLayers()   const { return _nbLayers; }
    int    GetMethod()         const { return _method; }

    bool   UseSurfaceNormal()  const
    { return _method == StdMeshers_ViscousLayers::SURF_OFFSET_SMOOTH; }
    bool   ToSmooth()          const
    { return _method == StdMeshers_ViscousLayers::SURF_OFFSET_SMOOTH; }
    bool   IsOffsetMethod()    const
    { return _method == StdMeshers_ViscousLayers::FACE_OFFSET; }

  private:
    int     _nbLayers, _nbHyps, _method;
    double  _thickness, _stretchFactor;
  };

  //--------------------------------------------------------------------------------
  /*!
   * \brief _LayerEdge's on a shape and other shape data
   */
  struct _EdgesOnShape
  {
    vector< _LayerEdge* > _edges;

    TopoDS_Shape          _shape;
    TGeomID               _shapeID;
    SMESH_subMesh *       _subMesh;
    // face or edge w/o layer along or near which _edges are inflated
    TopoDS_Shape          _sWOL;
    // averaged StdMeshers_ViscousLayers parameters
    AverageHyp            _hyp;
    bool                  _toSmooth;

    vector< gp_XYZ >      _faceNormals; // if _shape is FACE
    vector< _EdgesOnShape* > _faceEOS; // to get _faceNormals of adjacent FACEs

    TopAbs_ShapeEnum ShapeType() const
    { return _shape.IsNull() ? TopAbs_SHAPE : _shape.ShapeType(); }
    TopAbs_ShapeEnum SWOLType() const
    { return _sWOL.IsNull() ? TopAbs_SHAPE : _sWOL.ShapeType(); }
    bool             GetNormal( const SMDS_MeshElement* face, gp_Vec& norm );
  };

  //--------------------------------------------------------------------------------
  /*!
   * \brief Convex FACE whose radius of curvature is less than the thickness of 
   *        layers. It is used to detect distortion of prisms based on a convex
   *        FACE and to update normals to enable further increasing the thickness
   */
  struct _ConvexFace
  {
    TopoDS_Face                     _face;

    // edges whose _simplices are used to detect prism destorsion
    vector< _LayerEdge* >           _simplexTestEdges;

    // map a sub-shape to _SolidData::_edgesOnShape
    map< TGeomID, _EdgesOnShape* >  _subIdToEOS;

    bool                            _normalsFixed;

    bool GetCenterOfCurvature( _LayerEdge*         ledge,
                               BRepLProp_SLProps&  surfProp,
                               SMESH_MesherHelper& helper,
                               gp_Pnt &            center ) const;
    bool CheckPrisms() const;
  };

  //--------------------------------------------------------------------------------
  /*!
   * \brief Data of a SOLID
   */
  struct _SolidData
  {
    typedef const StdMeshers_ViscousLayers* THyp;
    TopoDS_Shape                    _solid;
    TGeomID                         _index; // SOLID id
    _MeshOfSolid*                   _proxyMesh;
    list< THyp >                    _hyps;
    list< TopoDS_Shape >            _hypShapes;
    map< TGeomID, THyp >            _face2hyp; // filled if _hyps.size() > 1
    set< TGeomID >                  _reversedFaceIds;
    set< TGeomID >                  _ignoreFaceIds; // WOL FACEs and FACEs of other SOLIDs

    double                          _stepSize, _stepSizeCoeff, _geomSize;
    const SMDS_MeshNode*            _stepSizeNodes[2];

    TNode2Edge                      _n2eMap; // nodes and _LayerEdge's based on them

    // map to find _n2eMap of another _SolidData by a shrink shape shared by two _SolidData's
    map< TGeomID, TNode2Edge* >     _s2neMap;
    // _LayerEdge's with underlying shapes
    vector< _EdgesOnShape >         _edgesOnShape;

    // key:   an id of shape (EDGE or VERTEX) shared by a FACE with
    //        layers and a FACE w/o layers
    // value: the shape (FACE or EDGE) to shrink mesh on.
    //       _LayerEdge's basing on nodes on key shape are inflated along the value shape
    map< TGeomID, TopoDS_Shape >     _shrinkShape2Shape;

    // Convex FACEs whose radius of curvature is less than the thickness of layers
    map< TGeomID, _ConvexFace >      _convexFaces;

    // shapes (EDGEs and VERTEXes) srink from which is forbidden due to collisions with
    // the adjacent SOLID
    set< TGeomID >                   _noShrinkShapes;

    int                              _nbShapesToSmooth;

    // <EDGE to smooth on> to <it's curve> -- for analytic smooth
    map< TGeomID,Handle(Geom_Curve)> _edge2curve;

    set< TGeomID >                   _concaveFaces;

    double                           _maxThickness; // of all _hyps
    double                           _minThickness; // of all _hyps

    double                           _epsilon; // precision for SegTriaInter()

    _SolidData(const TopoDS_Shape& s=TopoDS_Shape(),
               _MeshOfSolid*       m=0)
      :_solid(s), _proxyMesh(m) {}
    ~_SolidData();

    Handle(Geom_Curve) CurveForSmooth( const TopoDS_Edge&    E,
                                       _EdgesOnShape&        eos,
                                       SMESH_MesherHelper&   helper);

    void SortOnEdge( const TopoDS_Edge&     E,
                     vector< _LayerEdge* >& edges,
                     SMESH_MesherHelper&    helper);

    void Sort2NeiborsOnEdge( vector< _LayerEdge* >& edges );

    _ConvexFace* GetConvexFace( const TGeomID faceID )
    {
      map< TGeomID, _ConvexFace >::iterator id2face = _convexFaces.find( faceID );
      return id2face == _convexFaces.end() ? 0 : & id2face->second;
    }
    _EdgesOnShape* GetShapeEdges(const TGeomID       shapeID );
    _EdgesOnShape* GetShapeEdges(const TopoDS_Shape& shape );
    _EdgesOnShape* GetShapeEdges(const _LayerEdge*   edge )
    { return GetShapeEdges( edge->_nodes[0]->getshapeId() ); }

    void AddShapesToSmooth( const set< _EdgesOnShape* >& shape );

    void PrepareEdgesToSmoothOnFace( _EdgesOnShape* eof, bool substituteSrcNodes );
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Container of centers of curvature at nodes on an EDGE bounding _ConvexFace
   */
  struct _CentralCurveOnEdge
  {
    bool                  _isDegenerated;
    vector< gp_Pnt >      _curvaCenters;
    vector< _LayerEdge* > _ledges;
    vector< gp_XYZ >      _normals; // new normal for each of _ledges
    vector< double >      _segLength2;

    TopoDS_Edge           _edge;
    TopoDS_Face           _adjFace;
    bool                  _adjFaceToSmooth;

    void Append( const gp_Pnt& center, _LayerEdge* ledge )
    {
      if ( _curvaCenters.size() > 0 )
        _segLength2.push_back( center.SquareDistance( _curvaCenters.back() ));
      _curvaCenters.push_back( center );
      _ledges.push_back( ledge );
      _normals.push_back( ledge->_normal );
    }
    bool FindNewNormal( const gp_Pnt& center, gp_XYZ& newNormal );
    void SetShapes( const TopoDS_Edge&  edge,
                    const _ConvexFace&  convFace,
                    _SolidData&         data,
                    SMESH_MesherHelper& helper);
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Data of node on a shrinked FACE
   */
  struct _SmoothNode
  {
    const SMDS_MeshNode*         _node;
    vector<_Simplex>             _simplices; // for quality check

    enum SmoothType { LAPLACIAN, CENTROIDAL, ANGULAR, TFI };

    bool Smooth(int&                  badNb,
                Handle(Geom_Surface)& surface,
                SMESH_MesherHelper&   helper,
                const double          refSign,
                SmoothType            how,
                bool                  set3D);

    gp_XY computeAngularPos(vector<gp_XY>& uv,
                            const gp_XY&   uvToFix,
                            const double   refSign );
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Builder of viscous layers
   */
  class _ViscousBuilder
  {
  public:
    _ViscousBuilder();
    // does it's job
    SMESH_ComputeErrorPtr Compute(SMESH_Mesh&         mesh,
                                  const TopoDS_Shape& shape);
    // check validity of hypotheses
    SMESH_ComputeErrorPtr CheckHypotheses( SMESH_Mesh&         mesh,
                                           const TopoDS_Shape& shape );

    // restore event listeners used to clear an inferior dim sub-mesh modified by viscous layers
    void RestoreListeners();

    // computes SMESH_ProxyMesh::SubMesh::_n2n;
    bool MakeN2NMap( _MeshOfSolid* pm );

  private:

    bool findSolidsWithLayers();
    bool findFacesWithLayers(const bool onlyWith=false);
    void getIgnoreFaces(const TopoDS_Shape&             solid,
                        const StdMeshers_ViscousLayers* hyp,
                        const TopoDS_Shape&             hypShape,
                        set<TGeomID>&                   ignoreFaces);
    bool makeLayer(_SolidData& data);
    void setShapeData( _EdgesOnShape& eos, SMESH_subMesh* sm, _SolidData& data );
    bool setEdgeData(_LayerEdge& edge, _EdgesOnShape& eos, const set<TGeomID>& subIds,
                     SMESH_MesherHelper& helper, _SolidData& data);
    gp_XYZ getFaceNormal(const SMDS_MeshNode* n,
                         const TopoDS_Face&   face,
                         SMESH_MesherHelper&  helper,
                         bool&                isOK,
                         bool                 shiftInside=false);
    bool getFaceNormalAtSingularity(const gp_XY&        uv,
                                    const TopoDS_Face&  face,
                                    SMESH_MesherHelper& helper,
                                    gp_Dir&             normal );
    gp_XYZ getWeigthedNormal( const SMDS_MeshNode*             n,
                              std::pair< TopoDS_Face, gp_XYZ > fId2Normal[],
                              int                              nbFaces );
    bool findNeiborsOnEdge(const _LayerEdge*     edge,
                           const SMDS_MeshNode*& n1,
                           const SMDS_MeshNode*& n2,
                           _EdgesOnShape&        eos,
                           _SolidData&           data);
    void findSimplexTestEdges( _SolidData&                    data,
                               vector< vector<_LayerEdge*> >& edgesByGeom);
    void computeGeomSize( _SolidData& data );
    bool findShapesToSmooth( _SolidData& data);
    void limitStepSizeByCurvature( _SolidData&  data );
    void limitStepSize( _SolidData&             data,
                        const SMDS_MeshElement* face,
                        const _LayerEdge*       maxCosinEdge );
    void limitStepSize( _SolidData& data, const double minSize);
    bool inflate(_SolidData& data);
    bool smoothAndCheck(_SolidData& data, const int nbSteps, double & distToIntersection);
    bool smoothAnalyticEdge( _SolidData&           data,
                             _EdgesOnShape&        eos,
                             Handle(Geom_Surface)& surface,
                             const TopoDS_Face&    F,
                             SMESH_MesherHelper&   helper);
    bool updateNormals( _SolidData& data, SMESH_MesherHelper& helper, int stepNb );
    bool updateNormalsOfConvexFaces( _SolidData&         data,
                                     SMESH_MesherHelper& helper,
                                     int                 stepNb );
    bool refine(_SolidData& data);
    bool shrink();
    bool prepareEdgeToShrink( _LayerEdge& edge, _EdgesOnShape& eos,
                              SMESH_MesherHelper& helper,
                              const SMESHDS_SubMesh* faceSubMesh );
    void restoreNoShrink( _LayerEdge& edge ) const;
    void fixBadFaces(const TopoDS_Face&          F,
                     SMESH_MesherHelper&         helper,
                     const bool                  is2D,
                     const int                   step,
                     set<const SMDS_MeshNode*> * involvedNodes=NULL);
    bool addBoundaryElements();

    bool error( const string& text, int solidID=-1 );
    SMESHDS_Mesh* getMeshDS() const { return _mesh->GetMeshDS(); }

    // debug
    void makeGroupOfLE();

    SMESH_Mesh*           _mesh;
    SMESH_ComputeErrorPtr _error;

    vector< _SolidData >  _sdVec;
    int                   _tmpFaceID;
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Shrinker of nodes on the EDGE
   */
  class _Shrinker1D
  {
    TopoDS_Edge                   _geomEdge;
    vector<double>                _initU;
    vector<double>                _normPar;
    vector<const SMDS_MeshNode*>  _nodes;
    const _LayerEdge*             _edges[2];
    bool                          _done;
  public:
    void AddEdge( const _LayerEdge* e, _EdgesOnShape& eos, SMESH_MesherHelper& helper );
    void Compute(bool set3D, SMESH_MesherHelper& helper);
    void RestoreParams();
    void SwapSrcTgtNodes(SMESHDS_Mesh* mesh);
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Class of temporary mesh face.
   * We can't use SMDS_FaceOfNodes since it's impossible to set it's ID which is
   * needed because SMESH_ElementSearcher internaly uses set of elements sorted by ID
   */
  struct _TmpMeshFace : public SMDS_MeshElement
  {
    vector<const SMDS_MeshNode* > _nn;
    _TmpMeshFace( const vector<const SMDS_MeshNode*>& nodes, int id, int faceID=-1):
      SMDS_MeshElement(id), _nn(nodes) { setShapeId(faceID); }
    virtual const SMDS_MeshNode* GetNode(const int ind) const { return _nn[ind]; }
    virtual SMDSAbs_ElementType  GetType() const              { return SMDSAbs_Face; }
    virtual vtkIdType GetVtkType() const                      { return -1; }
    virtual SMDSAbs_EntityType   GetEntityType() const        { return SMDSEntity_Last; }
    virtual SMDSAbs_GeometryType GetGeomType() const
    { return _nn.size() == 3 ? SMDSGeom_TRIANGLE : SMDSGeom_QUADRANGLE; }
    virtual SMDS_ElemIteratorPtr elementsIterator(SMDSAbs_ElementType) const
    { return SMDS_ElemIteratorPtr( new SMDS_NodeVectorElemIterator( _nn.begin(), _nn.end()));}
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Class of temporary mesh face storing _LayerEdge it's based on
   */
  struct _TmpMeshFaceOnEdge : public _TmpMeshFace
  {
    _LayerEdge *_le1, *_le2;
    _TmpMeshFaceOnEdge( _LayerEdge* le1, _LayerEdge* le2, int ID ):
      _TmpMeshFace( vector<const SMDS_MeshNode*>(4), ID ), _le1(le1), _le2(le2)
    {
      _nn[0]=_le1->_nodes[0];
      _nn[1]=_le1->_nodes.back();
      _nn[2]=_le2->_nodes.back();
      _nn[3]=_le2->_nodes[0];
    }
  };
  //--------------------------------------------------------------------------------
  /*!
   * \brief Retriever of node coordinates either directly or from a surface by node UV.
   * \warning Location of a surface is ignored
   */
  struct _NodeCoordHelper
  {
    SMESH_MesherHelper&        _helper;
    const TopoDS_Face&         _face;
    Handle(Geom_Surface)       _surface;
    gp_XYZ (_NodeCoordHelper::* _fun)(const SMDS_MeshNode* n) const;

    _NodeCoordHelper(const TopoDS_Face& F, SMESH_MesherHelper& helper, bool is2D)
      : _helper( helper ), _face( F )
    {
      if ( is2D )
      {
        TopLoc_Location loc;
        _surface = BRep_Tool::Surface( _face, loc );
      }
      if ( _surface.IsNull() )
        _fun = & _NodeCoordHelper::direct;
      else
        _fun = & _NodeCoordHelper::byUV;
    }
    gp_XYZ operator()(const SMDS_MeshNode* n) const { return (this->*_fun)( n ); }

  private:
    gp_XYZ direct(const SMDS_MeshNode* n) const
    {
      return SMESH_TNodeXYZ( n );
    }
    gp_XYZ byUV  (const SMDS_MeshNode* n) const
    {
      gp_XY uv = _helper.GetNodeUV( _face, n );
      return _surface->Value( uv.X(), uv.Y() ).XYZ();
    }
  };

} // namespace VISCOUS_3D



//================================================================================
// StdMeshers_ViscousLayers hypothesis
//
StdMeshers_ViscousLayers::StdMeshers_ViscousLayers(int hypId, int studyId, SMESH_Gen* gen)
  :SMESH_Hypothesis(hypId, studyId, gen),
   _isToIgnoreShapes(1), _nbLayers(1), _thickness(1), _stretchFactor(1),
   _method( SURF_OFFSET_SMOOTH )
{
  _name = StdMeshers_ViscousLayers::GetHypType();
  _param_algo_dim = -3; // auxiliary hyp used by 3D algos
} // --------------------------------------------------------------------------------
void StdMeshers_ViscousLayers::SetBndShapes(const std::vector<int>& faceIds, bool toIgnore)
{
  if ( faceIds != _shapeIds )
    _shapeIds = faceIds, NotifySubMeshesHypothesisModification();
  if ( _isToIgnoreShapes != toIgnore )
    _isToIgnoreShapes = toIgnore, NotifySubMeshesHypothesisModification();
} // --------------------------------------------------------------------------------
void StdMeshers_ViscousLayers::SetTotalThickness(double thickness)
{
  if ( thickness != _thickness )
    _thickness = thickness, NotifySubMeshesHypothesisModification();
} // --------------------------------------------------------------------------------
void StdMeshers_ViscousLayers::SetNumberLayers(int nb)
{
  if ( _nbLayers != nb )
    _nbLayers = nb, NotifySubMeshesHypothesisModification();
} // --------------------------------------------------------------------------------
void StdMeshers_ViscousLayers::SetStretchFactor(double factor)
{
  if ( _stretchFactor != factor )
    _stretchFactor = factor, NotifySubMeshesHypothesisModification();
} // --------------------------------------------------------------------------------
void StdMeshers_ViscousLayers::SetMethod( ExtrusionMethod method )
{
  if ( _method != method )
    _method = method, NotifySubMeshesHypothesisModification();
} // --------------------------------------------------------------------------------
SMESH_ProxyMesh::Ptr
StdMeshers_ViscousLayers::Compute(SMESH_Mesh&         theMesh,
                                  const TopoDS_Shape& theShape,
                                  const bool          toMakeN2NMap) const
{
  using namespace VISCOUS_3D;
  _ViscousBuilder bulder;
  SMESH_ComputeErrorPtr err = bulder.Compute( theMesh, theShape );
  if ( err && !err->IsOK() )
    return SMESH_ProxyMesh::Ptr();

  vector<SMESH_ProxyMesh::Ptr> components;
  TopExp_Explorer exp( theShape, TopAbs_SOLID );
  for ( ; exp.More(); exp.Next() )
  {
    if ( _MeshOfSolid* pm =
         _ViscousListener::GetSolidMesh( &theMesh, exp.Current(), /*toCreate=*/false))
    {
      if ( toMakeN2NMap && !pm->_n2nMapComputed )
        if ( !bulder.MakeN2NMap( pm ))
          return SMESH_ProxyMesh::Ptr();
      components.push_back( SMESH_ProxyMesh::Ptr( pm ));
      pm->myIsDeletable = false; // it will de deleted by boost::shared_ptr

      if ( pm->_warning && !pm->_warning->IsOK() )
      {
        SMESH_subMesh* sm = theMesh.GetSubMesh( exp.Current() );
        SMESH_ComputeErrorPtr& smError = sm->GetComputeError();
        if ( !smError || smError->IsOK() )
          smError = pm->_warning;
      }
    }
    _ViscousListener::RemoveSolidMesh ( &theMesh, exp.Current() );
  }
  switch ( components.size() )
  {
  case 0: break;

  case 1: return components[0];

  default: return SMESH_ProxyMesh::Ptr( new SMESH_ProxyMesh( components ));
  }
  return SMESH_ProxyMesh::Ptr();
} // --------------------------------------------------------------------------------
std::ostream & StdMeshers_ViscousLayers::SaveTo(std::ostream & save)
{
  save << " " << _nbLayers
       << " " << _thickness
       << " " << _stretchFactor
       << " " << _shapeIds.size();
  for ( size_t i = 0; i < _shapeIds.size(); ++i )
    save << " " << _shapeIds[i];
  save << " " << !_isToIgnoreShapes; // negate to keep the behavior in old studies.
  save << " " << _method;
  return save;
} // --------------------------------------------------------------------------------
std::istream & StdMeshers_ViscousLayers::LoadFrom(std::istream & load)
{
  int nbFaces, faceID, shapeToTreat, method;
  load >> _nbLayers >> _thickness >> _stretchFactor >> nbFaces;
  while ( _shapeIds.size() < nbFaces && load >> faceID )
    _shapeIds.push_back( faceID );
  if ( load >> shapeToTreat ) {
    _isToIgnoreShapes = !shapeToTreat;
    if ( load >> method )
      _method = (ExtrusionMethod) method;
  }
  else {
    _isToIgnoreShapes = true; // old behavior
  }
  return load;
} // --------------------------------------------------------------------------------
bool StdMeshers_ViscousLayers::SetParametersByMesh(const SMESH_Mesh*   theMesh,
                                                   const TopoDS_Shape& theShape)
{
  // TODO
  return false;
} // --------------------------------------------------------------------------------
SMESH_ComputeErrorPtr
StdMeshers_ViscousLayers::CheckHypothesis(SMESH_Mesh&                          theMesh,
                                          const TopoDS_Shape&                  theShape,
                                          SMESH_Hypothesis::Hypothesis_Status& theStatus)
{
  VISCOUS_3D::_ViscousBuilder bulder;
  SMESH_ComputeErrorPtr err = bulder.CheckHypotheses( theMesh, theShape );
  if ( err && !err->IsOK() )
    theStatus = SMESH_Hypothesis::HYP_INCOMPAT_HYPS;
  else
    theStatus = SMESH_Hypothesis::HYP_OK;

  return err;
}
// --------------------------------------------------------------------------------
bool StdMeshers_ViscousLayers::IsShapeWithLayers(int shapeIndex) const
{
  bool isIn =
    ( std::find( _shapeIds.begin(), _shapeIds.end(), shapeIndex ) != _shapeIds.end() );
  return IsToIgnoreShapes() ? !isIn : isIn;
}
// END StdMeshers_ViscousLayers hypothesis
//================================================================================

namespace VISCOUS_3D
{
  gp_XYZ getEdgeDir( const TopoDS_Edge& E, const TopoDS_Vertex& fromV )
  {
    gp_Vec dir;
    double f,l;
    Handle(Geom_Curve) c = BRep_Tool::Curve( E, f, l );
    gp_Pnt p = BRep_Tool::Pnt( fromV );
    double distF = p.SquareDistance( c->Value( f ));
    double distL = p.SquareDistance( c->Value( l ));
    c->D1(( distF < distL ? f : l), p, dir );
    if ( distL < distF ) dir.Reverse();
    return dir.XYZ();
  }
  //--------------------------------------------------------------------------------
  gp_XYZ getEdgeDir( const TopoDS_Edge& E, const SMDS_MeshNode* atNode,
                     SMESH_MesherHelper& helper)
  {
    gp_Vec dir;
    double f,l; gp_Pnt p;
    Handle(Geom_Curve) c = BRep_Tool::Curve( E, f, l );
    if ( c.IsNull() ) return gp_XYZ( 1e100, 1e100, 1e100 );
    double u = helper.GetNodeU( E, atNode );
    c->D1( u, p, dir );
    return dir.XYZ();
  }
  //--------------------------------------------------------------------------------
  gp_XYZ getFaceDir( const TopoDS_Face& F, const TopoDS_Vertex& fromV,
                     const SMDS_MeshNode* node, SMESH_MesherHelper& helper, bool& ok,
                     double* cosin=0);
  //--------------------------------------------------------------------------------
  gp_XYZ getFaceDir( const TopoDS_Face& F, const TopoDS_Edge& fromE,
                     const SMDS_MeshNode* node, SMESH_MesherHelper& helper, bool& ok)
  {
    double f,l;
    Handle(Geom_Curve) c = BRep_Tool::Curve( fromE, f, l );
    if ( c.IsNull() )
    {
      TopoDS_Vertex v = helper.IthVertex( 0, fromE );
      return getFaceDir( F, v, node, helper, ok );
    }
    gp_XY uv = helper.GetNodeUV( F, node, 0, &ok );
    Handle(Geom_Surface) surface = BRep_Tool::Surface( F );
    gp_Pnt p; gp_Vec du, dv, norm;
    surface->D1( uv.X(),uv.Y(), p, du,dv );
    norm = du ^ dv;

    double u = helper.GetNodeU( fromE, node, 0, &ok );
    c->D1( u, p, du );
    TopAbs_Orientation o = helper.GetSubShapeOri( F.Oriented(TopAbs_FORWARD), fromE);
    if ( o == TopAbs_REVERSED )
      du.Reverse();

    gp_Vec dir = norm ^ du;

    if ( node->GetPosition()->GetTypeOfPosition() == SMDS_TOP_VERTEX &&
         helper.IsClosedEdge( fromE ))
    {
      if ( fabs(u-f) < fabs(u-l)) c->D1( l, p, dv );
      else                        c->D1( f, p, dv );
      if ( o == TopAbs_REVERSED )
        dv.Reverse();
      gp_Vec dir2 = norm ^ dv;
      dir = dir.Normalized() + dir2.Normalized();
    }
    return dir.XYZ();
  }
  //--------------------------------------------------------------------------------
  gp_XYZ getFaceDir( const TopoDS_Face& F, const TopoDS_Vertex& fromV,
                     const SMDS_MeshNode* node, SMESH_MesherHelper& helper,
                     bool& ok, double* cosin)
  {
    TopoDS_Face faceFrw = F;
    faceFrw.Orientation( TopAbs_FORWARD );
    double f,l; TopLoc_Location loc;
    TopoDS_Edge edges[2]; // sharing a vertex
    int nbEdges = 0;
    {
      TopoDS_Vertex VV[2];
      TopExp_Explorer exp( faceFrw, TopAbs_EDGE );
      for ( ; exp.More() && nbEdges < 2; exp.Next() )
      {
        const TopoDS_Edge& e = TopoDS::Edge( exp.Current() );
        if ( SMESH_Algo::isDegenerated( e )) continue;
        TopExp::Vertices( e, VV[0], VV[1], /*CumOri=*/true );
        if ( VV[1].IsSame( fromV )) {
          nbEdges += edges[ 0 ].IsNull();
          edges[ 0 ] = e;
        }
        else if ( VV[0].IsSame( fromV )) {
          nbEdges += edges[ 1 ].IsNull();
          edges[ 1 ] = e;
        }
      }
    }
    gp_XYZ dir(0,0,0), edgeDir[2];
    if ( nbEdges == 2 )
    {
      // get dirs of edges going fromV
      ok = true;
      for ( size_t i = 0; i < nbEdges && ok; ++i )
      {
        edgeDir[i] = getEdgeDir( edges[i], fromV );
        double size2 = edgeDir[i].SquareModulus();
        if (( ok = size2 > numeric_limits<double>::min() ))
          edgeDir[i] /= sqrt( size2 );
      }
      if ( !ok ) return dir;

      // get angle between the 2 edges
      gp_Vec faceNormal;
      double angle = helper.GetAngle( edges[0], edges[1], faceFrw, fromV, &faceNormal );
      if ( Abs( angle ) < 5 * M_PI/180 )
      {
        dir = ( faceNormal.XYZ() ^ edgeDir[0].Reversed()) + ( faceNormal.XYZ() ^ edgeDir[1] );
      }
      else
      {
        dir = edgeDir[0] + edgeDir[1];
        if ( angle < 0 )
          dir.Reverse();
      }
      if ( cosin ) {
        double angle = gp_Vec( edgeDir[0] ).Angle( dir );
        *cosin = Cos( angle );
      }
    }
    else if ( nbEdges == 1 )
    {
      dir = getFaceDir( faceFrw, edges[ edges[0].IsNull() ], node, helper, ok );
      if ( cosin ) *cosin = 1.;
    }
    else
    {
      ok = false;
    }

    return dir;
  }

  //================================================================================
  /*!
   * \brief Finds concave VERTEXes of a FACE
   */
  //================================================================================

  bool getConcaveVertices( const TopoDS_Face&  F,
                           SMESH_MesherHelper& helper,
                           set< TGeomID >*     vertices = 0)
  {
    // check angles at VERTEXes
    TError error;
    TSideVector wires = StdMeshers_FaceSide::GetFaceWires( F, *helper.GetMesh(), 0, error );
    for ( size_t iW = 0; iW < wires.size(); ++iW )
    {
      const int nbEdges = wires[iW]->NbEdges();
      if ( nbEdges < 2 && SMESH_Algo::isDegenerated( wires[iW]->Edge(0)))
        continue;
      for ( int iE1 = 0; iE1 < nbEdges; ++iE1 )
      {
        if ( SMESH_Algo::isDegenerated( wires[iW]->Edge( iE1 ))) continue;
        int iE2 = ( iE1 + 1 ) % nbEdges;
        while ( SMESH_Algo::isDegenerated( wires[iW]->Edge( iE2 )))
          iE2 = ( iE2 + 1 ) % nbEdges;
        TopoDS_Vertex V = wires[iW]->FirstVertex( iE2 );
        double angle = helper.GetAngle( wires[iW]->Edge( iE1 ),
                                        wires[iW]->Edge( iE2 ), F, V );
        if ( angle < -5. * M_PI / 180. )
        {
          if ( !vertices )
            return true;
          vertices->insert( helper.GetMeshDS()->ShapeToIndex( V ));
        }
      }
    }
    return vertices ? !vertices->empty() : false;
  }

  //================================================================================
  /*!
   * \brief Returns true if a FACE is bound by a concave EDGE
   */
  //================================================================================

  bool isConcave( const TopoDS_Face&  F,
                  SMESH_MesherHelper& helper,
                  set< TGeomID >*     vertices = 0 )
  {
    bool isConcv = false;
    // if ( helper.Count( F, TopAbs_WIRE, /*useMap=*/false) > 1 )
    //   return true;
    gp_Vec2d drv1, drv2;
    gp_Pnt2d p;
    TopExp_Explorer eExp( F.Oriented( TopAbs_FORWARD ), TopAbs_EDGE );
    for ( ; eExp.More(); eExp.Next() )
    {
      const TopoDS_Edge& E = TopoDS::Edge( eExp.Current() );
      if ( SMESH_Algo::isDegenerated( E )) continue;
      // check if 2D curve is concave
      BRepAdaptor_Curve2d curve( E, F );
      const int nbIntervals = curve.NbIntervals( GeomAbs_C2 );
      TColStd_Array1OfReal intervals(1, nbIntervals + 1 );
      curve.Intervals( intervals, GeomAbs_C2 );
      bool isConvex = true;
      for ( int i = 1; i <= nbIntervals && isConvex; ++i )
      {
        double u1 = intervals( i );
        double u2 = intervals( i+1 );
        curve.D2( 0.5*( u1+u2 ), p, drv1, drv2 );
        double cross = drv2 ^ drv1;
        if ( E.Orientation() == TopAbs_REVERSED )
          cross = -cross;
        isConvex = ( cross > 0.1 ); //-1e-9 );
      }
      if ( !isConvex )
      {
        //cout << "Concave FACE " << helper.GetMeshDS()->ShapeToIndex( F ) << endl;
        isConcv = true;
        if ( vertices )
          break;
        else
          return true;
      }
    }

    // check angles at VERTEXes
    if ( getConcaveVertices( F, helper, vertices ))
      isConcv = true;

    return isConcv;
  }

  //================================================================================
  /*!
   * \brief Computes mimimal distance of face in-FACE nodes from an EDGE
   *  \param [in] face - the mesh face to treat
   *  \param [in] nodeOnEdge - a node on the EDGE
   *  \param [out] faceSize - the computed distance
   *  \return bool - true if faceSize computed
   */
  //================================================================================

  bool getDistFromEdge( const SMDS_MeshElement* face,
                        const SMDS_MeshNode*    nodeOnEdge,
                        double &                faceSize )
  {
    faceSize = Precision::Infinite();
    bool done = false;

    int nbN  = face->NbCornerNodes();
    int iOnE = face->GetNodeIndex( nodeOnEdge );
    int iNext[2] = { SMESH_MesherHelper::WrapIndex( iOnE+1, nbN ),
                     SMESH_MesherHelper::WrapIndex( iOnE-1, nbN ) };
    const SMDS_MeshNode* nNext[2] = { face->GetNode( iNext[0] ),
                                      face->GetNode( iNext[1] ) };
    gp_XYZ segVec, segEnd = SMESH_TNodeXYZ( nodeOnEdge ); // segment on EDGE
    double segLen = -1.;
    // look for two neighbor not in-FACE nodes of face
    for ( int i = 0; i < 2; ++i )
    {
      if ( nNext[i]->GetPosition()->GetDim() != 2 &&
           nNext[i]->GetID() < nodeOnEdge->GetID() )
      {
        // look for an in-FACE node
        for ( int iN = 0; iN < nbN; ++iN )
        {
          if ( iN == iOnE || iN == iNext[i] )
            continue;
          SMESH_TNodeXYZ pInFace = face->GetNode( iN );
          gp_XYZ v = pInFace - segEnd;
          if ( segLen < 0 )
          {
            segVec = SMESH_TNodeXYZ( nNext[i] ) - segEnd;
            segLen = segVec.Modulus();
          }
          double distToSeg = v.Crossed( segVec ).Modulus() / segLen;
          faceSize = Min( faceSize, distToSeg );
          done = true;
        }
        segLen = -1;
      }
    }
    return done;
  }
  //================================================================================
  /*!
   * \brief Return direction of axis or revolution of a surface
   */
  //================================================================================

  bool getRovolutionAxis( const Adaptor3d_Surface& surface,
                          gp_Dir &                 axis )
  {
    switch ( surface.GetType() ) {
    case GeomAbs_Cone:
    {
      gp_Cone cone = surface.Cone();
      axis = cone.Axis().Direction();
      break;
    }
    case GeomAbs_Sphere:
    {
      gp_Sphere sphere = surface.Sphere();
      axis = sphere.Position().Direction();
      break;
    }
    case GeomAbs_SurfaceOfRevolution:
    {
      axis = surface.AxeOfRevolution().Direction();
      break;
    }
    //case GeomAbs_SurfaceOfExtrusion:
    case GeomAbs_OffsetSurface:
    {
      Handle(Adaptor3d_HSurface) base = surface.BasisSurface();
      return getRovolutionAxis( base->Surface(), axis );
    }
    default: return false;
    }
    return true;
  }

  //--------------------------------------------------------------------------------
  // DEBUG. Dump intermediate node positions into a python script
  // HOWTO use: run python commands written in a console to see
  //  construction steps of viscous layers
#ifdef __myDEBUG
  ofstream* py;
  int       theNbPyFunc;
  struct PyDump {
    PyDump(SMESH_Mesh& m) {
      int tag = 3 + m.GetId();
      const char* fname = "/tmp/viscous.py";
      cout << "execfile('"<<fname<<"')"<<endl;
      py = new ofstream(fname);
      *py << "import SMESH" << endl
          << "from salome.smesh import smeshBuilder" << endl
          << "smesh  = smeshBuilder.New(salome.myStudy)" << endl
          << "meshSO = smesh.GetCurrentStudy().FindObjectID('0:1:2:" << tag <<"')" << endl
          << "mesh   = smesh.Mesh( meshSO.GetObject() )"<<endl;
      theNbPyFunc = 0;
    }
    void Finish() {
      if (py) {
        *py << "mesh.GroupOnFilter(SMESH.VOLUME,'Viscous Prisms',"
          "smesh.GetFilter(SMESH.VOLUME,SMESH.FT_ElemGeomType,'=',SMESH.Geom_PENTA))"<<endl;
        *py << "mesh.GroupOnFilter(SMESH.VOLUME,'Neg Volumes',"
          "smesh.GetFilter(SMESH.VOLUME,SMESH.FT_Volume3D,'<',0))"<<endl;
      }
      delete py; py=0;
    }
    ~PyDump() { Finish(); cout << "NB FUNCTIONS: " << theNbPyFunc << endl; }
  };
#define dumpFunction(f) { _dumpFunction(f, __LINE__);}
#define dumpMove(n)     { _dumpMove(n, __LINE__);}
#define dumpMoveComm(n,txt) { _dumpMove(n, __LINE__, txt);}
#define dumpCmd(txt)    { _dumpCmd(txt, __LINE__);}
  void _dumpFunction(const string& fun, int ln)
  { if (py) *py<< "def "<<fun<<"(): # "<< ln <<endl; cout<<fun<<"()"<<endl; ++theNbPyFunc; }
  void _dumpMove(const SMDS_MeshNode* n, int ln, const char* txt="")
  { if (py) *py<< "  mesh.MoveNode( "<<n->GetID()<< ", "<< n->X()
               << ", "<<n->Y()<<", "<< n->Z()<< ")\t\t # "<< ln <<" "<< txt << endl; }
  void _dumpCmd(const string& txt, int ln)
  { if (py) *py<< "  "<<txt<<" # "<< ln <<endl; }
  void dumpFunctionEnd()
  { if (py) *py<< "  return"<< endl; }
  void dumpChangeNodes( const SMDS_MeshElement* f )
  { if (py) { *py<< "  mesh.ChangeElemNodes( " << f->GetID()<<", [";
      for ( int i=1; i < f->NbNodes(); ++i ) *py << f->GetNode(i-1)->GetID()<<", ";
      *py << f->GetNode( f->NbNodes()-1 )->GetID() << " ])"<< endl; }}
#define debugMsg( txt ) { cout << txt << " (line: " << __LINE__ << ")" << endl; }
#else
  struct PyDump { PyDump(SMESH_Mesh&) {} void Finish() {} };
#define dumpFunction(f) f
#define dumpMove(n)
#define dumpMoveComm(n,txt)
#define dumpCmd(txt)
#define dumpFunctionEnd()
#define dumpChangeNodes(f)
#define debugMsg( txt ) {}
#endif
}

using namespace VISCOUS_3D;

//================================================================================
/*!
 * \brief Constructor of _ViscousBuilder
 */
//================================================================================

_ViscousBuilder::_ViscousBuilder()
{
  _error = SMESH_ComputeError::New(COMPERR_OK);
  _tmpFaceID = 0;
}

//================================================================================
/*!
 * \brief Stores error description and returns false
 */
//================================================================================

bool _ViscousBuilder::error(const string& text, int solidId )
{
  const string prefix = string("Viscous layers builder: ");
  _error->myName    = COMPERR_ALGO_FAILED;
  _error->myComment = prefix + text;
  if ( _mesh )
  {
    SMESH_subMesh* sm = _mesh->GetSubMeshContaining( solidId );
    if ( !sm && !_sdVec.empty() )
      sm = _mesh->GetSubMeshContaining( solidId = _sdVec[0]._index );
    if ( sm && sm->GetSubShape().ShapeType() == TopAbs_SOLID )
    {
      SMESH_ComputeErrorPtr& smError = sm->GetComputeError();
      if ( smError && smError->myAlgo )
        _error->myAlgo = smError->myAlgo;
      smError = _error;
      sm->ComputeStateEngine( SMESH_subMesh::CHECK_COMPUTE_STATE );
    }
    // set KO to all solids
    for ( size_t i = 0; i < _sdVec.size(); ++i )
    {
      if ( _sdVec[i]._index == solidId )
        continue;
      sm = _mesh->GetSubMesh( _sdVec[i]._solid );
      if ( !sm->IsEmpty() )
        continue;
      SMESH_ComputeErrorPtr& smError = sm->GetComputeError();
      if ( !smError || smError->IsOK() )
      {
        smError = SMESH_ComputeError::New( COMPERR_ALGO_FAILED, prefix + "failed");
        sm->ComputeStateEngine( SMESH_subMesh::CHECK_COMPUTE_STATE );
      }
    }
  }
  makeGroupOfLE(); // debug

  return false;
}

//================================================================================
/*!
 * \brief At study restoration, restore event listeners used to clear an inferior
 *  dim sub-mesh modified by viscous layers
 */
//================================================================================

void _ViscousBuilder::RestoreListeners()
{
  // TODO
}

//================================================================================
/*!
 * \brief computes SMESH_ProxyMesh::SubMesh::_n2n
 */
//================================================================================

bool _ViscousBuilder::MakeN2NMap( _MeshOfSolid* pm )
{
  SMESH_subMesh* solidSM = pm->mySubMeshes.front();
  TopExp_Explorer fExp( solidSM->GetSubShape(), TopAbs_FACE );
  for ( ; fExp.More(); fExp.Next() )
  {
    SMESHDS_SubMesh* srcSmDS = pm->GetMeshDS()->MeshElements( fExp.Current() );
    const SMESH_ProxyMesh::SubMesh* prxSmDS = pm->GetProxySubMesh( fExp.Current() );

    if ( !srcSmDS || !prxSmDS || !srcSmDS->NbElements() || !prxSmDS->NbElements() )
      continue;
    if ( srcSmDS->GetElements()->next() == prxSmDS->GetElements()->next())
      continue;

    if ( srcSmDS->NbElements() != prxSmDS->NbElements() )
      return error( "Different nb elements in a source and a proxy sub-mesh", solidSM->GetId());

    SMDS_ElemIteratorPtr srcIt = srcSmDS->GetElements();
    SMDS_ElemIteratorPtr prxIt = prxSmDS->GetElements();
    while( prxIt->more() )
    {
      const SMDS_MeshElement* fSrc = srcIt->next();
      const SMDS_MeshElement* fPrx = prxIt->next();
      if ( fSrc->NbNodes() != fPrx->NbNodes())
        return error( "Different elements in a source and a proxy sub-mesh", solidSM->GetId());
      for ( int i = 0 ; i < fPrx->NbNodes(); ++i )
        pm->setNode2Node( fSrc->GetNode(i), fPrx->GetNode(i), prxSmDS );
    }
  }
  pm->_n2nMapComputed = true;
  return true;
}

//================================================================================
/*!
 * \brief Does its job
 */
//================================================================================

SMESH_ComputeErrorPtr _ViscousBuilder::Compute(SMESH_Mesh&         theMesh,
                                               const TopoDS_Shape& theShape)
{
  // TODO: set priority of solids during Gen::Compute()

  _mesh = & theMesh;

  // check if proxy mesh already computed
  TopExp_Explorer exp( theShape, TopAbs_SOLID );
  if ( !exp.More() )
    return error("No SOLID's in theShape"), _error;

  if ( _ViscousListener::GetSolidMesh( _mesh, exp.Current(), /*toCreate=*/false))
    return SMESH_ComputeErrorPtr(); // everything already computed

  PyDump debugDump( theMesh );

  // TODO: ignore already computed SOLIDs 
  if ( !findSolidsWithLayers())
    return _error;

  if ( !findFacesWithLayers() )
    return _error;

  for ( size_t i = 0; i < _sdVec.size(); ++i )
  {
    if ( ! makeLayer(_sdVec[i]) )
      return _error;

    if ( _sdVec[i]._n2eMap.size() == 0 )
      continue;
    
    if ( ! inflate(_sdVec[i]) )
      return _error;

    if ( ! refine(_sdVec[i]) )
      return _error;
  }
  if ( !shrink() )
    return _error;

  addBoundaryElements();

  makeGroupOfLE(); // debug
  debugDump.Finish();

  return _error;
}

//================================================================================
/*!
 * \brief Check validity of hypotheses
 */
//================================================================================

SMESH_ComputeErrorPtr _ViscousBuilder::CheckHypotheses( SMESH_Mesh&         mesh,
                                                        const TopoDS_Shape& shape )
{
  _mesh = & mesh;

  if ( _ViscousListener::GetSolidMesh( _mesh, shape, /*toCreate=*/false))
    return SMESH_ComputeErrorPtr(); // everything already computed


  findSolidsWithLayers();
  bool ok = findFacesWithLayers();

  // remove _MeshOfSolid's of _SolidData's
  for ( size_t i = 0; i < _sdVec.size(); ++i )
    _ViscousListener::RemoveSolidMesh( _mesh, _sdVec[i]._solid );

  if ( !ok )
    return _error;

  return SMESH_ComputeErrorPtr();
}

//================================================================================
/*!
 * \brief Finds SOLIDs to compute using viscous layers. Fills _sdVec
 */
//================================================================================

bool _ViscousBuilder::findSolidsWithLayers()
{
  // get all solids
  TopTools_IndexedMapOfShape allSolids;
  TopExp::MapShapes( _mesh->GetShapeToMesh(), TopAbs_SOLID, allSolids );
  _sdVec.reserve( allSolids.Extent());

  SMESH_Gen* gen = _mesh->GetGen();
  SMESH_HypoFilter filter;
  for ( int i = 1; i <= allSolids.Extent(); ++i )
  {
    // find StdMeshers_ViscousLayers hyp assigned to the i-th solid
    SMESH_Algo* algo = gen->GetAlgo( *_mesh, allSolids(i) );
    if ( !algo ) continue;
    // TODO: check if algo is hidden
    const list <const SMESHDS_Hypothesis *> & allHyps =
      algo->GetUsedHypothesis(*_mesh, allSolids(i), /*ignoreAuxiliary=*/false);
    _SolidData* soData = 0;
    list< const SMESHDS_Hypothesis *>::const_iterator hyp = allHyps.begin();
    const StdMeshers_ViscousLayers* viscHyp = 0;
    for ( ; hyp != allHyps.end(); ++hyp )
      if ( viscHyp = dynamic_cast<const StdMeshers_ViscousLayers*>( *hyp ))
      {
        TopoDS_Shape hypShape;
        filter.Init( filter.Is( viscHyp ));
        _mesh->GetHypothesis( allSolids(i), filter, true, &hypShape );

        if ( !soData )
        {
          _MeshOfSolid* proxyMesh = _ViscousListener::GetSolidMesh( _mesh,
                                                                    allSolids(i),
                                                                    /*toCreate=*/true);
          _sdVec.push_back( _SolidData( allSolids(i), proxyMesh ));
          soData = & _sdVec.back();
          soData->_index = getMeshDS()->ShapeToIndex( allSolids(i));
        }
        soData->_hyps.push_back( viscHyp );
        soData->_hypShapes.push_back( hypShape );
      }
  }
  if ( _sdVec.empty() )
    return error
      ( SMESH_Comment(StdMeshers_ViscousLayers::GetHypType()) << " hypothesis not found",0);

  return true;
}

//================================================================================
/*!
 * \brief 
 */
//================================================================================

bool _ViscousBuilder::findFacesWithLayers(const bool onlyWith)
{
  SMESH_MesherHelper helper( *_mesh );
  TopExp_Explorer exp;
  TopTools_IndexedMapOfShape solids;

  // collect all faces-to-ignore defined by hyp
  for ( size_t i = 0; i < _sdVec.size(); ++i )
  {
    solids.Add( _sdVec[i]._solid );

    // get faces-to-ignore defined by each hyp
    typedef const StdMeshers_ViscousLayers* THyp;
    typedef std::pair< set<TGeomID>, THyp > TFacesOfHyp;
    list< TFacesOfHyp > ignoreFacesOfHyps;
    list< THyp >::iterator              hyp = _sdVec[i]._hyps.begin();
    list< TopoDS_Shape >::iterator hypShape = _sdVec[i]._hypShapes.begin();
    for ( ; hyp != _sdVec[i]._hyps.end(); ++hyp, ++hypShape )
    {
      ignoreFacesOfHyps.push_back( TFacesOfHyp( set<TGeomID>(), *hyp ));
      getIgnoreFaces( _sdVec[i]._solid, *hyp, *hypShape, ignoreFacesOfHyps.back().first );
    }

    // fill _SolidData::_face2hyp and check compatibility of hypotheses
    const int nbHyps = _sdVec[i]._hyps.size();
    if ( nbHyps > 1 )
    {
      // check if two hypotheses define different parameters for the same FACE
      list< TFacesOfHyp >::iterator igFacesOfHyp;
      for ( exp.Init( _sdVec[i]._solid, TopAbs_FACE ); exp.More(); exp.Next() )
      {
        const TGeomID faceID = getMeshDS()->ShapeToIndex( exp.Current() );
        THyp hyp = 0;
        igFacesOfHyp = ignoreFacesOfHyps.begin();
        for ( ; igFacesOfHyp != ignoreFacesOfHyps.end(); ++igFacesOfHyp )
          if ( ! igFacesOfHyp->first.count( faceID ))
          {
            if ( hyp )
              return error(SMESH_Comment("Several hypotheses define "
                                         "Viscous Layers on the face #") << faceID );
            hyp = igFacesOfHyp->second;
          }
        if ( hyp )
          _sdVec[i]._face2hyp.insert( make_pair( faceID, hyp ));
        else
          _sdVec[i]._ignoreFaceIds.insert( faceID );
      }

      // check if two hypotheses define different number of viscous layers for
      // adjacent faces of a solid
      set< int > nbLayersSet;
      igFacesOfHyp = ignoreFacesOfHyps.begin();
      for ( ; igFacesOfHyp != ignoreFacesOfHyps.end(); ++igFacesOfHyp )
      {
        nbLayersSet.insert( igFacesOfHyp->second->GetNumberLayers() );
      }
      if ( nbLayersSet.size() > 1 )
      {
        for ( exp.Init( _sdVec[i]._solid, TopAbs_EDGE ); exp.More(); exp.Next() )
        {
          PShapeIteratorPtr fIt = helper.GetAncestors( exp.Current(), *_mesh, TopAbs_FACE );
          THyp hyp1 = 0, hyp2 = 0;
          while( const TopoDS_Shape* face = fIt->next() )
          {
            const TGeomID faceID = getMeshDS()->ShapeToIndex( *face );
            map< TGeomID, THyp >::iterator f2h = _sdVec[i]._face2hyp.find( faceID );
            if ( f2h != _sdVec[i]._face2hyp.end() )
            {
              ( hyp1 ? hyp2 : hyp1 ) = f2h->second;
            }
          }
          if ( hyp1 && hyp2 &&
               hyp1->GetNumberLayers() != hyp2->GetNumberLayers() )
          {
            return error("Two hypotheses define different number of "
                         "viscous layers on adjacent faces");
          }
        }
      }
    } // if ( nbHyps > 1 )
    else
    {
      _sdVec[i]._ignoreFaceIds.swap( ignoreFacesOfHyps.back().first );
    }
  } // loop on _sdVec

  if ( onlyWith ) // is called to check hypotheses compatibility only
    return true;

  // fill _SolidData::_reversedFaceIds
  for ( size_t i = 0; i < _sdVec.size(); ++i )
  {
    exp.Init( _sdVec[i]._solid.Oriented( TopAbs_FORWARD ), TopAbs_FACE );
    for ( ; exp.More(); exp.Next() )
    {
      const TopoDS_Face& face = TopoDS::Face( exp.Current() );
      const TGeomID faceID = getMeshDS()->ShapeToIndex( face );
      if ( //!sdVec[i]._ignoreFaceIds.count( faceID ) &&
          helper.NbAncestors( face, *_mesh, TopAbs_SOLID ) > 1 &&
          helper.IsReversedSubMesh( face ))
      {
        _sdVec[i]._reversedFaceIds.insert( faceID );
      }
    }
  }

  // Find faces to shrink mesh on (solution 2 in issue 0020832);
  TopTools_IndexedMapOfShape shapes;
  for ( size_t i = 0; i < _sdVec.size(); ++i )
  {
    shapes.Clear();
    TopExp::MapShapes(_sdVec[i]._solid, TopAbs_EDGE, shapes);
    for ( int iE = 1; iE <= shapes.Extent(); ++iE )
    {
      const TopoDS_Shape& edge = shapes(iE);
      // find 2 faces sharing an edge
      TopoDS_Shape FF[2];
      PShapeIteratorPtr fIt = helper.GetAncestors(edge, *_mesh, TopAbs_FACE);
      while ( fIt->more())
      {
        const TopoDS_Shape* f = fIt->next();
        if ( helper.IsSubShape( *f, _sdVec[i]._solid))
          FF[ int( !FF[0].IsNull()) ] = *f;
      }
      if( FF[1].IsNull() ) continue; // seam edge can be shared by 1 FACE only
      // check presence of layers on them
      int ignore[2];
      for ( int j = 0; j < 2; ++j )
        ignore[j] = _sdVec[i]._ignoreFaceIds.count ( getMeshDS()->ShapeToIndex( FF[j] ));
      if ( ignore[0] == ignore[1] )
        continue; // nothing interesting
      TopoDS_Shape fWOL = FF[ ignore[0] ? 0 : 1 ];
      // check presence of layers on fWOL within an adjacent SOLID
      bool collision = false;
      PShapeIteratorPtr sIt = helper.GetAncestors( fWOL, *_mesh, TopAbs_SOLID );
      while ( const TopoDS_Shape* solid = sIt->next() )
        if ( !solid->IsSame( _sdVec[i]._solid ))
        {
          int iSolid = solids.FindIndex( *solid );
          int  iFace = getMeshDS()->ShapeToIndex( fWOL );
          if ( iSolid > 0 && !_sdVec[ iSolid-1 ]._ignoreFaceIds.count( iFace ))
          {
            //_sdVec[i]._noShrinkShapes.insert( iFace );
            //fWOL.Nullify();
            collision = true;
          }
        }
      // add edge to maps
      if ( !fWOL.IsNull())
      {
        TGeomID edgeInd = getMeshDS()->ShapeToIndex( edge );
        _sdVec[i]._shrinkShape2Shape.insert( make_pair( edgeInd, fWOL ));
        if ( collision )
        {
          // _shrinkShape2Shape will be used to temporary inflate _LayerEdge's based
          // on the edge but shrink won't be performed
          _sdVec[i]._noShrinkShapes.insert( edgeInd );
        }
      }
    }
  }
  // Exclude from _shrinkShape2Shape FACE's that can't be shrinked since
  // the algo of the SOLID sharing the FACE does not support it
  set< string > notSupportAlgos; notSupportAlgos.insert("Hexa_3D");
  for ( size_t i = 0; i < _sdVec.size(); ++i )
  {
    map< TGeomID, TopoDS_Shape >::iterator e2f = _sdVec[i]._shrinkShape2Shape.begin();
    for ( ; e2f != _sdVec[i]._shrinkShape2Shape.end(); ++e2f )
    {
      const TopoDS_Shape& fWOL = e2f->second;
      const TGeomID     edgeID = e2f->first;
      bool notShrinkFace = false;
      PShapeIteratorPtr soIt = helper.GetAncestors(fWOL, *_mesh, TopAbs_SOLID);
      while ( soIt->more() )
      {
        const TopoDS_Shape* solid = soIt->next();
        if ( _sdVec[i]._solid.IsSame( *solid )) continue;
        SMESH_Algo* algo = _mesh->GetGen()->GetAlgo( *_mesh, *solid );
        if ( !algo || !notSupportAlgos.count( algo->GetName() )) continue;
        notShrinkFace = true;
        size_t iSolid = 0;
        for ( ; iSolid < _sdVec.size(); ++iSolid )
        {
          if ( _sdVec[iSolid]._solid.IsSame( *solid ) ) {
            if ( _sdVec[iSolid]._shrinkShape2Shape.count( edgeID ))
              notShrinkFace = false;
            break;
          }
        }
        if ( notShrinkFace )
        {
          _sdVec[i]._noShrinkShapes.insert( edgeID );

          // add VERTEXes of the edge in _noShrinkShapes
          TopoDS_Shape edge = getMeshDS()->IndexToShape( edgeID );
          for ( TopoDS_Iterator vIt( edge ); vIt.More(); vIt.Next() )
            _sdVec[i]._noShrinkShapes.insert( getMeshDS()->ShapeToIndex( vIt.Value() ));

          // check if there is a collision with to-shrink-from EDGEs in iSolid
          if ( iSolid == _sdVec.size() )
            continue; // no VL in the solid
          shapes.Clear();
          TopExp::MapShapes( fWOL, TopAbs_EDGE, shapes);
          for ( int iE = 1; iE <= shapes.Extent(); ++iE )
          {
            const TopoDS_Edge& E = TopoDS::Edge( shapes( iE ));
            const TGeomID    eID = getMeshDS()->ShapeToIndex( E );
            if ( eID == edgeID ||
                 !_sdVec[iSolid]._shrinkShape2Shape.count( eID ) ||
                 _sdVec[i]._noShrinkShapes.count( eID ))
              continue;
            for ( int is1st = 0; is1st < 2; ++is1st )
            {
              TopoDS_Vertex V = helper.IthVertex( is1st, E );
              if ( _sdVec[i]._noShrinkShapes.count( getMeshDS()->ShapeToIndex( V ) ))
              {
                // _sdVec[i]._noShrinkShapes.insert( eID );
                // V = helper.IthVertex( !is1st, E );
                // _sdVec[i]._noShrinkShapes.insert( getMeshDS()->ShapeToIndex( V ));
                //iE = 0; // re-start the loop on EDGEs of fWOL
                return error("No way to make a conformal mesh with "
                             "the given set of faces with layers", _sdVec[i]._index);
              }
            }
          }
        }

      } // while ( soIt->more() )
    } // loop on _sdVec[i]._shrinkShape2Shape
  } // loop on _sdVec to fill in _SolidData::_noShrinkShapes

  // Find the SHAPE along which to inflate _LayerEdge based on VERTEX

  for ( size_t i = 0; i < _sdVec.size(); ++i )
  {
    shapes.Clear();
    TopExp::MapShapes(_sdVec[i]._solid, TopAbs_VERTEX, shapes);
    for ( int iV = 1; iV <= shapes.Extent(); ++iV )
    {
      const TopoDS_Shape& vertex = shapes(iV);
      // find faces WOL sharing the vertex
      vector< TopoDS_Shape > facesWOL;
      int totalNbFaces = 0;
      PShapeIteratorPtr fIt = helper.GetAncestors(vertex, *_mesh, TopAbs_FACE);
      while ( fIt->more())
      {
        const TopoDS_Shape* f = fIt->next();
        if ( helper.IsSubShape( *f, _sdVec[i]._solid ) )
        {
          totalNbFaces++;
          const int fID = getMeshDS()->ShapeToIndex( *f );
          if ( _sdVec[i]._ignoreFaceIds.count ( fID ) /*&&
               !_sdVec[i]._noShrinkShapes.count( fID )*/)
            facesWOL.push_back( *f );
        }
      }
      if ( facesWOL.size() == totalNbFaces || facesWOL.empty() )
        continue; // no layers at this vertex or no WOL
      TGeomID vInd = getMeshDS()->ShapeToIndex( vertex );
      switch ( facesWOL.size() )
      {
      case 1:
      {
        helper.SetSubShape( facesWOL[0] );
        if ( helper.IsRealSeam( vInd )) // inflate along a seam edge?
        {
          TopoDS_Shape seamEdge;
          PShapeIteratorPtr eIt = helper.GetAncestors(vertex, *_mesh, TopAbs_EDGE);
          while ( eIt->more() && seamEdge.IsNull() )
          {
            const TopoDS_Shape* e = eIt->next();
            if ( helper.IsRealSeam( *e ) )
              seamEdge = *e;
          }
          if ( !seamEdge.IsNull() )
          {
            _sdVec[i]._shrinkShape2Shape.insert( make_pair( vInd, seamEdge ));
            break;
          }
        }
        _sdVec[i]._shrinkShape2Shape.insert( make_pair( vInd, facesWOL[0] ));
        break;
      }
      case 2:
      {
        // find an edge shared by 2 faces
        PShapeIteratorPtr eIt = helper.GetAncestors(vertex, *_mesh, TopAbs_EDGE);
        while ( eIt->more())
        {
          const TopoDS_Shape* e = eIt->next();
          if ( helper.IsSubShape( *e, facesWOL[0]) &&
               helper.IsSubShape( *e, facesWOL[1]))
          {
            _sdVec[i]._shrinkShape2Shape.insert( make_pair( vInd, *e )); break;
          }
        }
        break;
      }
      default:
        return error("Not yet supported case", _sdVec[i]._index);
      }
    }
  }

  // add FACEs of other SOLIDs to _ignoreFaceIds
  for ( size_t i = 0; i < _sdVec.size(); ++i )
  {
    shapes.Clear();
    TopExp::MapShapes(_sdVec[i]._solid, TopAbs_FACE, shapes);

    for ( exp.Init( _mesh->GetShapeToMesh(), TopAbs_FACE ); exp.More(); exp.Next() )
    {
      if ( !shapes.Contains( exp.Current() ))
        _sdVec[i]._ignoreFaceIds.insert( getMeshDS()->ShapeToIndex( exp.Current() ));
    }
  }

  return true;
}

//================================================================================
/*!
 * \brief Finds FACEs w/o layers for a given SOLID by an hypothesis
 */
//================================================================================

void _ViscousBuilder::getIgnoreFaces(const TopoDS_Shape&             solid,
                                     const StdMeshers_ViscousLayers* hyp,
                                     const TopoDS_Shape&             hypShape,
                                     set<TGeomID>&                   ignoreFaceIds)
{
  TopExp_Explorer exp;

  vector<TGeomID> ids = hyp->GetBndShapes();
  if ( hyp->IsToIgnoreShapes() ) // FACEs to ignore are given
  {
    for ( size_t ii = 0; ii < ids.size(); ++ii )
    {
      const TopoDS_Shape& s = getMeshDS()->IndexToShape( ids[ii] );
      if ( !s.IsNull() && s.ShapeType() == TopAbs_FACE )
        ignoreFaceIds.insert( ids[ii] );
    }
  }
  else // FACEs with layers are given
  {
    exp.Init( solid, TopAbs_FACE );
    for ( ; exp.More(); exp.Next() )
    {
      TGeomID faceInd = getMeshDS()->ShapeToIndex( exp.Current() );
      if ( find( ids.begin(), ids.end(), faceInd ) == ids.end() )
        ignoreFaceIds.insert( faceInd );
    }
  }

  // ignore internal FACEs if inlets and outlets are specified
  if ( hyp->IsToIgnoreShapes() )
  {
    TopTools_IndexedDataMapOfShapeListOfShape solidsOfFace;
    TopExp::MapShapesAndAncestors( hypShape,
                                   TopAbs_FACE, TopAbs_SOLID, solidsOfFace);

    for ( exp.Init( solid, TopAbs_FACE ); exp.More(); exp.Next() )
    {
      const TopoDS_Face& face = TopoDS::Face( exp.Current() );
      if ( SMESH_MesherHelper::NbAncestors( face, *_mesh, TopAbs_SOLID ) < 2 )
        continue;

      int nbSolids = solidsOfFace.FindFromKey( face ).Extent();
      if ( nbSolids > 1 )
        ignoreFaceIds.insert( getMeshDS()->ShapeToIndex( face ));
    }
  }
}

//================================================================================
/*!
 * \brief Create the inner surface of the viscous layer and prepare data for infation
 */
//================================================================================

bool _ViscousBuilder::makeLayer(_SolidData& data)
{
  // get all sub-shapes to make layers on
  set<TGeomID> subIds, faceIds;
  subIds = data._noShrinkShapes;
  TopExp_Explorer exp( data._solid, TopAbs_FACE );
  for ( ; exp.More(); exp.Next() )
  {
    SMESH_subMesh* fSubM = _mesh->GetSubMesh( exp.Current() );
    if ( ! data._ignoreFaceIds.count( fSubM->GetId() ))
    {
      faceIds.insert( fSubM->GetId() );
      SMESH_subMeshIteratorPtr subIt = fSubM->getDependsOnIterator(/*includeSelf=*/true);
      while ( subIt->more() )
        subIds.insert( subIt->next()->GetId() );
    }
  }

  // make a map to find new nodes on sub-shapes shared with other SOLID
  map< TGeomID, TNode2Edge* >::iterator s2ne;
  map< TGeomID, TopoDS_Shape >::iterator s2s = data._shrinkShape2Shape.begin();
  for (; s2s != data._shrinkShape2Shape.end(); ++s2s )
  {
    TGeomID shapeInd = s2s->first;
    for ( size_t i = 0; i < _sdVec.size(); ++i )
    {
      if ( _sdVec[i]._index == data._index ) continue;
      map< TGeomID, TopoDS_Shape >::iterator s2s2 = _sdVec[i]._shrinkShape2Shape.find( shapeInd );
      if ( s2s2 != _sdVec[i]._shrinkShape2Shape.end() &&
           *s2s == *s2s2 && !_sdVec[i]._n2eMap.empty() )
      {
        data._s2neMap.insert( make_pair( shapeInd, &_sdVec[i]._n2eMap ));
        break;
      }
    }
  }

  // Create temporary faces and _LayerEdge's

  dumpFunction(SMESH_Comment("makeLayers_")<<data._index);

  data._stepSize = Precision::Infinite();
  data._stepSizeNodes[0] = 0;

  SMESH_MesherHelper helper( *_mesh );
  helper.SetSubShape( data._solid );
  helper.SetElementsOnShape( true );

  vector< const SMDS_MeshNode*> newNodes; // of a mesh face
  TNode2Edge::iterator n2e2;

  // collect _LayerEdge's of shapes they are based on
  vector< _EdgesOnShape >& edgesByGeom = data._edgesOnShape;
  const int nbShapes = getMeshDS()->MaxShapeIndex();
  edgesByGeom.resize( nbShapes+1 );

  // set data of _EdgesOnShape's
  if ( SMESH_subMesh* sm = _mesh->GetSubMesh( data._solid ))
  {
    SMESH_subMeshIteratorPtr smIt = sm->getDependsOnIterator(/*includeSelf=*/false);
    while ( smIt->more() )
    {
      sm = smIt->next();
      if ( sm->GetSubShape().ShapeType() == TopAbs_FACE &&
           !faceIds.count( sm->GetId() ))
        continue;
      setShapeData( edgesByGeom[ sm->GetId() ], sm, data );
    }
  }
  // make _LayerEdge's
  for ( set<TGeomID>::iterator id = faceIds.begin(); id != faceIds.end(); ++id )
  {
    const TopoDS_Face& F = TopoDS::Face( getMeshDS()->IndexToShape( *id ));
    SMESH_subMesh* sm = _mesh->GetSubMesh( F );
    SMESH_ProxyMesh::SubMesh* proxySub =
      data._proxyMesh->getFaceSubM( F, /*create=*/true);

    SMESHDS_SubMesh* smDS = sm->GetSubMeshDS();
    if ( !smDS ) return error(SMESH_Comment("Not meshed face ") << *id, data._index );

    SMDS_ElemIteratorPtr eIt = smDS->GetElements();
    while ( eIt->more() )
    {
      const SMDS_MeshElement* face = eIt->next();
      double          faceMaxCosin = -1;
      _LayerEdge*     maxCosinEdge = 0;
      int             nbDegenNodes = 0;

      newNodes.resize( face->NbCornerNodes() );
      for ( size_t i = 0 ; i < newNodes.size(); ++i )
      {
        const SMDS_MeshNode* n = face->GetNode( i );
        const int      shapeID = n->getshapeId();
        const bool onDegenShap = helper.IsDegenShape( shapeID );
        const bool onDegenEdge = ( onDegenShap && n->GetPosition()->GetDim() == 1 );
        if ( onDegenShap )
        {
          if ( onDegenEdge )
          {
            // substitute n on a degenerated EDGE with a node on a corresponding VERTEX
            const TopoDS_Shape& E = getMeshDS()->IndexToShape( shapeID );
            TopoDS_Vertex       V = helper.IthVertex( 0, TopoDS::Edge( E ));
            if ( const SMDS_MeshNode* vN = SMESH_Algo::VertexNode( V, getMeshDS() )) {
              n = vN;
              nbDegenNodes++;
            }
          }
          else
          {
            nbDegenNodes++;
          }
        }
        TNode2Edge::iterator n2e = data._n2eMap.insert( make_pair( n, (_LayerEdge*)0 )).first;
        if ( !(*n2e).second )
        {
          // add a _LayerEdge
          _LayerEdge* edge = new _LayerEdge();
          edge->_nodes.push_back( n );
          n2e->second = edge;
          edgesByGeom[ shapeID ]._edges.push_back( edge );
          const bool noShrink = data._noShrinkShapes.count( shapeID );

          SMESH_TNodeXYZ xyz( n );

          // set edge data or find already refined _LayerEdge and get data from it
          if (( !noShrink                                                     ) &&
              ( n->GetPosition()->GetTypeOfPosition() != SMDS_TOP_FACE        ) &&
              (( s2ne = data._s2neMap.find( shapeID )) != data._s2neMap.end() ) &&
              (( n2e2 = (*s2ne).second->find( n )) != s2ne->second->end()     ))
          {
            _LayerEdge* foundEdge = (*n2e2).second;
            gp_XYZ        lastPos = edge->Copy( *foundEdge, edgesByGeom[ shapeID ], helper );
            foundEdge->_pos.push_back( lastPos );
            // location of the last node is modified and we restore it by foundEdge->_pos.back()
            const_cast< SMDS_MeshNode* >
              ( edge->_nodes.back() )->setXYZ( xyz.X(), xyz.Y(), xyz.Z() );
          }
          else
          {
            if ( !noShrink )
            {
              edge->_nodes.push_back( helper.AddNode( xyz.X(), xyz.Y(), xyz.Z() ));
            }
            if ( !setEdgeData( *edge, edgesByGeom[ shapeID ], subIds, helper, data ))
              return false;
          }
          dumpMove(edge->_nodes.back());

          if ( edge->_cosin > faceMaxCosin )
          {
            faceMaxCosin = edge->_cosin;
            maxCosinEdge = edge;
          }
        }
        newNodes[ i ] = n2e->second->_nodes.back();

        if ( onDegenEdge )
          data._n2eMap.insert( make_pair( face->GetNode( i ), n2e->second ));
      }
      if ( newNodes.size() - nbDegenNodes < 2 )
        continue;

      // create a temporary face
      const SMDS_MeshElement* newFace =
        new _TmpMeshFace( newNodes, --_tmpFaceID, face->getshapeId() );
      proxySub->AddElement( newFace );

      // compute inflation step size by min size of element on a convex surface
      if ( faceMaxCosin > theMinSmoothCosin )
        limitStepSize( data, face, maxCosinEdge );

    } // loop on 2D elements on a FACE
  } // loop on FACEs of a SOLID

  data._epsilon = 1e-7;
  if ( data._stepSize < 1. )
    data._epsilon *= data._stepSize;

  if ( !findShapesToSmooth( data ))
    return false;

  // limit data._stepSize depending on surface curvature and fill data._convexFaces
  limitStepSizeByCurvature( data ); // !!! it must be before node substitution in _Simplex

  // Set target nodes into _Simplex and _LayerEdge's to _2NearEdges
  TNode2Edge::iterator n2e;
  const SMDS_MeshNode* nn[2];
  for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
  {
    _EdgesOnShape& eos = data._edgesOnShape[iS];
    vector< _LayerEdge* >& localEdges = eos._edges;
    for ( size_t i = 0; i < localEdges.size(); ++i )
    {
      _LayerEdge* edge = localEdges[i];
      if ( edge->IsOnEdge() )
      {
        // get neighbor nodes
        bool hasData = ( edge->_2neibors->_edges[0] );
        if ( hasData ) // _LayerEdge is a copy of another one
        {
          nn[0] = edge->_2neibors->srcNode(0);
          nn[1] = edge->_2neibors->srcNode(1);
        }
        else if ( !findNeiborsOnEdge( edge, nn[0],nn[1], eos, data ))
        {
          return false;
        }
        // set neighbor _LayerEdge's
        for ( int j = 0; j < 2; ++j )
        {
          if (( n2e = data._n2eMap.find( nn[j] )) == data._n2eMap.end() )
            return error("_LayerEdge not found by src node", data._index);
          edge->_2neibors->_edges[j] = n2e->second;
        }
        if ( !hasData )
          edge->SetDataByNeighbors( nn[0], nn[1], eos, helper );
      }

      for ( size_t j = 0; j < edge->_simplices.size(); ++j )
      {
        _Simplex& s = edge->_simplices[j];
        s._nNext = data._n2eMap[ s._nNext ]->_nodes.back();
        s._nPrev = data._n2eMap[ s._nPrev ]->_nodes.back();
      }

      // For an _LayerEdge on a degenerated EDGE, copy some data from
      // a corresponding _LayerEdge on a VERTEX
      // (issue 52453, pb on a downloaded SampleCase2-Tet-netgen-mephisto.hdf)
      if ( helper.IsDegenShape( edge->_nodes[0]->getshapeId() ))
      {
        // Generally we should not get here
        if ( eos.ShapeType() != TopAbs_EDGE )
          continue;
        TopoDS_Vertex V = helper.IthVertex( 0, TopoDS::Edge( eos._shape ));
        const SMDS_MeshNode* vN = SMESH_Algo::VertexNode( V, getMeshDS() );
        if (( n2e = data._n2eMap.find( vN )) == data._n2eMap.end() )
          continue;
        const _LayerEdge* vEdge = n2e->second;
        edge->_normal    = vEdge->_normal;
        edge->_lenFactor = vEdge->_lenFactor;
        edge->_cosin     = vEdge->_cosin;
      }
    }
  }

  // fix _LayerEdge::_2neibors on EDGEs to smooth
  map< TGeomID,Handle(Geom_Curve)>::iterator e2c = data._edge2curve.begin();
  for ( ; e2c != data._edge2curve.end(); ++e2c )
    if ( !e2c->second.IsNull() )
    {
      if ( _EdgesOnShape* eos = data.GetShapeEdges( e2c->first ))
        data.Sort2NeiborsOnEdge( eos->_edges );
    }

  dumpFunctionEnd();
  return true;
}

//================================================================================
/*!
 * \brief Compute inflation step size by min size of element on a convex surface
 */
//================================================================================

void _ViscousBuilder::limitStepSize( _SolidData&             data,
                                     const SMDS_MeshElement* face,
                                     const _LayerEdge*       maxCosinEdge )
{
  int iN = 0;
  double minSize = 10 * data._stepSize;
  const int nbNodes = face->NbCornerNodes();
  for ( int i = 0; i < nbNodes; ++i )
  {
    const SMDS_MeshNode* nextN = face->GetNode( SMESH_MesherHelper::WrapIndex( i+1, nbNodes ));
    const SMDS_MeshNode*  curN = face->GetNode( i );
    if ( nextN->GetPosition()->GetTypeOfPosition() == SMDS_TOP_FACE ||
         curN-> GetPosition()->GetTypeOfPosition() == SMDS_TOP_FACE )
    {
      double dist = SMESH_TNodeXYZ( curN ).Distance( nextN );
      if ( dist < minSize )
        minSize = dist, iN = i;
    }
  }
  double newStep = 0.8 * minSize / maxCosinEdge->_lenFactor;
  if ( newStep < data._stepSize )
  {
    data._stepSize = newStep;
    data._stepSizeCoeff = 0.8 / maxCosinEdge->_lenFactor;
    data._stepSizeNodes[0] = face->GetNode( iN );
    data._stepSizeNodes[1] = face->GetNode( SMESH_MesherHelper::WrapIndex( iN+1, nbNodes ));
  }
}

//================================================================================
/*!
 * \brief Compute inflation step size by min size of element on a convex surface
 */
//================================================================================

void _ViscousBuilder::limitStepSize( _SolidData& data, const double minSize )
{
  if ( minSize < data._stepSize )
  {
    data._stepSize = minSize;
    if ( data._stepSizeNodes[0] )
    {
      double dist =
        SMESH_TNodeXYZ(data._stepSizeNodes[0]).Distance(data._stepSizeNodes[1]);
      data._stepSizeCoeff = data._stepSize / dist;
    }
  }
}

//================================================================================
/*!
 * \brief Limit data._stepSize by evaluating curvature of shapes and fill data._convexFaces
 */
//================================================================================

void _ViscousBuilder::limitStepSizeByCurvature( _SolidData& data )
{
  const int nbTestPnt = 5; // on a FACE sub-shape

  BRepLProp_SLProps surfProp( 2, 1e-6 );
  SMESH_MesherHelper helper( *_mesh );

  data._convexFaces.clear();

  for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
  {
    _EdgesOnShape& eos = data._edgesOnShape[iS];
    if ( eos.ShapeType() != TopAbs_FACE ||
         data._ignoreFaceIds.count( eos._shapeID ))
      continue;

    TopoDS_Face        F = TopoDS::Face( eos._shape );
    SMESH_subMesh *   sm = eos._subMesh;
    const TGeomID faceID = eos._shapeID;

    BRepAdaptor_Surface surface( F, false );
    surfProp.SetSurface( surface );

    bool isTooCurved = false;

    _ConvexFace cnvFace;
    const double        oriFactor = ( F.Orientation() == TopAbs_REVERSED ? +1. : -1. );
    SMESH_subMeshIteratorPtr smIt = sm->getDependsOnIterator(/*includeSelf=*/true);
    while ( smIt->more() )
    {
      sm = smIt->next();
      const TGeomID subID = sm->GetId();
      // find _LayerEdge's of a sub-shape
      size_t edgesEnd;
      if ( _EdgesOnShape* eos = data.GetShapeEdges( subID ))
        cnvFace._subIdToEOS.insert( make_pair( subID, eos ));
      else
        continue;
      // check concavity and curvature and limit data._stepSize
      const double minCurvature =
        1. / ( eos._hyp.GetTotalThickness() * ( 1+theThickToIntersection ));
      size_t iStep = Max( 1, eos._edges.size() / nbTestPnt );
      for ( size_t i = 0; i < eos._edges.size(); i += iStep )
      {
        gp_XY uv = helper.GetNodeUV( F, eos._edges[ i ]->_nodes[0] );
        surfProp.SetParameters( uv.X(), uv.Y() );
        if ( !surfProp.IsCurvatureDefined() )
          continue;
        if ( surfProp.MaxCurvature() * oriFactor > minCurvature )
        {
          limitStepSize( data, 0.9 / surfProp.MaxCurvature() * oriFactor );
          isTooCurved = true;
        }
        if ( surfProp.MinCurvature() * oriFactor > minCurvature )
        {
          limitStepSize( data, 0.9 / surfProp.MinCurvature() * oriFactor );
          isTooCurved = true;
        }
      }
    } // loop on sub-shapes of the FACE

    if ( !isTooCurved ) continue;

    _ConvexFace & convFace =
      data._convexFaces.insert( make_pair( faceID, cnvFace )).first->second;

    convFace._face = F;
    convFace._normalsFixed = false;

    // Fill _ConvexFace::_simplexTestEdges. These _LayerEdge's are used to detect
    // prism distortion.
    map< TGeomID, _EdgesOnShape* >::iterator id2eos = convFace._subIdToEOS.find( faceID );
    if ( id2eos != convFace._subIdToEOS.end() && !id2eos->second->_edges.empty() )
    {
      // there are _LayerEdge's on the FACE it-self;
      // select _LayerEdge's near EDGEs
      _EdgesOnShape& eos = * id2eos->second;
      for ( size_t i = 0; i < eos._edges.size(); ++i )
      {
        _LayerEdge* ledge = eos._edges[ i ];
        for ( size_t j = 0; j < ledge->_simplices.size(); ++j )
          if ( ledge->_simplices[j]._nNext->GetPosition()->GetDim() < 2 )
          {
            convFace._simplexTestEdges.push_back( ledge );
            break;
          }
      }
    }
    else
    {
      // where there are no _LayerEdge's on a _ConvexFace,
      // as e.g. on a fillet surface with no internal nodes - issue 22580,
      // so that collision of viscous internal faces is not detected by check of
      // intersection of _LayerEdge's with the viscous internal faces.

      set< const SMDS_MeshNode* > usedNodes;

      // look for _LayerEdge's with null _sWOL
      map< TGeomID, _EdgesOnShape* >::iterator id2oes = convFace._subIdToEOS.begin();
      for ( ; id2oes != convFace._subIdToEOS.end(); ++id2oes )
      {
        _EdgesOnShape& eos = * id2eos->second;
        if ( !eos._sWOL.IsNull() )
          continue;
        for ( size_t i = 0; i < eos._edges.size(); ++i )
        {
          _LayerEdge* ledge = eos._edges[ i ];
          const SMDS_MeshNode* srcNode = ledge->_nodes[0];
          if ( !usedNodes.insert( srcNode ).second ) continue;

          _Simplex::GetSimplices( srcNode, ledge->_simplices, data._ignoreFaceIds, &data );
          for ( size_t i = 0; i < ledge->_simplices.size(); ++i )
          {
            usedNodes.insert( ledge->_simplices[i]._nPrev );
            usedNodes.insert( ledge->_simplices[i]._nNext );
          }
          convFace._simplexTestEdges.push_back( ledge );
        }
      }
    }
  } // loop on FACEs of data._solid
}

//================================================================================
/*!
 * \brief Detect shapes (and _LayerEdge's on them) to smooth
 */
//================================================================================

bool _ViscousBuilder::findShapesToSmooth( _SolidData& data )
{
  // define allowed thickness
  computeGeomSize( data ); // compute data._geomSize

  data._maxThickness = 0;
  data._minThickness = 1e100;
  list< const StdMeshers_ViscousLayers* >::iterator hyp = data._hyps.begin();
  for ( ; hyp != data._hyps.end(); ++hyp )
  {
    data._maxThickness = Max( data._maxThickness, (*hyp)->GetTotalThickness() );
    data._minThickness = Min( data._minThickness, (*hyp)->GetTotalThickness() );
  }
  const double tgtThick = /*Min( 0.5 * data._geomSize, */data._maxThickness;

  // Find shapes needing smoothing; such a shape has _LayerEdge._normal on it's
  // boundry inclined to the shape at a sharp angle

  //list< TGeomID > shapesToSmooth;
  TopTools_MapOfShape edgesOfSmooFaces;

  SMESH_MesherHelper helper( *_mesh );
  bool ok = true;

  vector< _EdgesOnShape >& edgesByGeom = data._edgesOnShape;
  data._nbShapesToSmooth = 0;

  for ( size_t iS = 0; iS < edgesByGeom.size(); ++iS ) // check FACEs
  {
    _EdgesOnShape& eos = edgesByGeom[iS];
    eos._toSmooth = false;
    if ( eos._edges.empty() || eos.ShapeType() != TopAbs_FACE )
      continue;

    TopExp_Explorer eExp( edgesByGeom[iS]._shape, TopAbs_EDGE );
    for ( ; eExp.More() && !eos._toSmooth; eExp.Next() )
    {
      TGeomID iE = getMeshDS()->ShapeToIndex( eExp.Current() );
      vector<_LayerEdge*>& eE = edgesByGeom[ iE ]._edges;
      if ( eE.empty() ) continue;
      // TopLoc_Location loc;
      // Handle(Geom_Surface) surface = BRep_Tool::Surface( TopoDS::Face( S ), loc );
      // bool isPlane = GeomLib_IsPlanarSurface( surface ).IsPlanar();
      //if ( eE[0]->_sWOL.IsNull() )
      {
        double faceSize;
        for ( size_t i = 0; i < eE.size() && !eos._toSmooth; ++i )
          if ( eE[i]->_cosin > theMinSmoothCosin )
          {
            SMDS_ElemIteratorPtr fIt = eE[i]->_nodes[0]->GetInverseElementIterator(SMDSAbs_Face);
            while ( fIt->more() && !eos._toSmooth )
            {
              const SMDS_MeshElement* face = fIt->next();
              if ( getDistFromEdge( face, eE[i]->_nodes[0], faceSize ))
                eos._toSmooth = needSmoothing( eE[i]->_cosin, tgtThick, faceSize );
            }
          }
      }
      // else
      // {
      //   const TopoDS_Face& F1 = TopoDS::Face( S );
      //   const TopoDS_Face& F2 = TopoDS::Face( eE[0]->_sWOL );
      //   const TopoDS_Edge& E  = TopoDS::Edge( eExp.Current() );
      //   for ( size_t i = 0; i < eE.size() && !eos._toSmooth; ++i )
      //   {
      //     gp_Vec dir1 = getFaceDir( F1, E, eE[i]->_nodes[0], helper, ok );
      //     gp_Vec dir2 = getFaceDir( F2, E, eE[i]->_nodes[0], helper, ok );
      //     double angle = dir1.Angle(  );
      //     double cosin = cos( angle );
      //     eos._toSmooth = ( cosin > theMinSmoothCosin );
      //   }
      // }
    }
    if ( eos._toSmooth )
    {
      for ( eExp.ReInit(); eExp.More(); eExp.Next() )
        edgesOfSmooFaces.Add( eExp.Current() );

      data.PrepareEdgesToSmoothOnFace( &edgesByGeom[iS], /*substituteSrcNodes=*/false );
    }
    data._nbShapesToSmooth += eos._toSmooth;

  }  // check FACEs

  for ( size_t iS = 0; iS < edgesByGeom.size(); ++iS ) // check EDGEs
  {
    _EdgesOnShape& eos = edgesByGeom[iS];
    if ( eos._edges.empty() || eos.ShapeType() != TopAbs_EDGE ) continue;
    if ( !eos._hyp.ToSmooth() ) continue;

    const TopoDS_Edge& E = TopoDS::Edge( edgesByGeom[iS]._shape );
    if ( SMESH_Algo::isDegenerated( E ) || !edgesOfSmooFaces.Contains( E ))
      continue;

    for ( TopoDS_Iterator vIt( E ); vIt.More() && !eos._toSmooth; vIt.Next() )
    {
      TGeomID iV = getMeshDS()->ShapeToIndex( vIt.Value() );
      vector<_LayerEdge*>& eV = edgesByGeom[ iV ]._edges;
      if ( eV.empty() ) continue;
      gp_Vec  eDir = getEdgeDir( E, TopoDS::Vertex( vIt.Value() ));
      double angle = eDir.Angle( eV[0]->_normal );
      double cosin = Cos( angle );
      double cosinAbs = Abs( cosin );
      if ( cosinAbs > theMinSmoothCosin )
      {
        // always smooth analytic EDGEs
        eos._toSmooth = ! data.CurveForSmooth( E, eos, helper ).IsNull();

        // compare tgtThick with the length of an end segment
        SMDS_ElemIteratorPtr eIt = eV[0]->_nodes[0]->GetInverseElementIterator(SMDSAbs_Edge);
        while ( eIt->more() && !eos._toSmooth )
        {
          const SMDS_MeshElement* endSeg = eIt->next();
          if ( endSeg->getshapeId() == iS )
          {
            double segLen =
              SMESH_TNodeXYZ( endSeg->GetNode(0) ).Distance( endSeg->GetNode(1 ));
            eos._toSmooth = needSmoothing( cosinAbs, tgtThick, segLen );
          }
        }
      }
    }
    data._nbShapesToSmooth += eos._toSmooth;

  } // check EDGEs

  // Reset _cosin if no smooth is allowed by the user
  for ( size_t iS = 0; iS < edgesByGeom.size(); ++iS )
  {
    _EdgesOnShape& eos = edgesByGeom[iS];
    if ( eos._edges.empty() ) continue;

    if ( !eos._hyp.ToSmooth() )
      for ( size_t i = 0; i < eos._edges.size(); ++i )
        eos._edges[i]->SetCosin( 0 );
  }


  // int nbShapes = 0;
  // for ( size_t iS = 0; iS < edgesByGeom.size(); ++iS )
  // {
  //   nbShapes += ( edgesByGeom[iS]._edges.size() > 0 );
  // }
  // data._edgesOnShape.reserve( nbShapes );

  // // first we put _LayerEdge's on shapes to smooth (EGDEs go first)
  // vector< _LayerEdge* > edges;
  // list< TGeomID >::iterator gIt = shapesToSmooth.begin();
  // for ( ; gIt != shapesToSmooth.end(); ++gIt )
  // {
  //   _EdgesOnShape& eos = edgesByGeom[ *gIt ];
  //   if ( eos._edges.empty() ) continue;
  //   eos._edges.swap( edges ); // avoid copying array
  //   eos._toSmooth = true;
  //   data._edgesOnShape.push_back( eos );
  //   data._edgesOnShape.back()._edges.swap( edges );
  // }

  // // then the rest _LayerEdge's
  // for ( size_t iS = 0; iS < edgesByGeom.size(); ++iS )
  // {
  //   _EdgesOnShape& eos = edgesByGeom[ *gIt ];
  //   if ( eos._edges.empty() ) continue;
  //   eos._edges.swap( edges ); // avoid copying array
  //   eos._toSmooth = false;
  //   data._edgesOnShape.push_back( eos );
  //   data._edgesOnShape.back()._edges.swap( edges );
  // }

  return ok;
}

//================================================================================
/*!
 * \brief initialize data of _EdgesOnShape
 */
//================================================================================

void _ViscousBuilder::setShapeData( _EdgesOnShape& eos,
                                    SMESH_subMesh* sm,
                                    _SolidData&    data )
{
  if ( !eos._shape.IsNull() ||
       sm->GetSubShape().ShapeType() == TopAbs_WIRE )
    return;

  SMESH_MesherHelper helper( *_mesh );

  eos._subMesh = sm;
  eos._shapeID = sm->GetId();
  eos._shape   = sm->GetSubShape();
  if ( eos.ShapeType() == TopAbs_FACE )
    eos._shape.Orientation( helper.GetSubShapeOri( data._solid, eos._shape ));
  eos._toSmooth = false;

  // set _SWOL
  map< TGeomID, TopoDS_Shape >::const_iterator s2s =
    data._shrinkShape2Shape.find( eos._shapeID );
  if ( s2s != data._shrinkShape2Shape.end() )
    eos._sWOL = s2s->second;

  // set _hyp
  if ( data._hyps.size() == 1 )
  {
    eos._hyp = data._hyps.back();
  }
  else
  {
    // compute average StdMeshers_ViscousLayers parameters
    map< TGeomID, const StdMeshers_ViscousLayers* >::iterator f2hyp;
    if ( eos.ShapeType() == TopAbs_FACE )
    {
      if (( f2hyp = data._face2hyp.find( eos._shapeID )) != data._face2hyp.end() )
        eos._hyp = f2hyp->second;
    }
    else
    {
      PShapeIteratorPtr fIt = helper.GetAncestors( eos._shape, *_mesh, TopAbs_FACE );
      while ( const TopoDS_Shape* face = fIt->next() )
      {
        TGeomID faceID = getMeshDS()->ShapeToIndex( *face );
        if (( f2hyp = data._face2hyp.find( faceID )) != data._face2hyp.end() )
          eos._hyp.Add( f2hyp->second );
      }
    }
  }

  // set _faceNormals
  if ( ! eos._hyp.UseSurfaceNormal() )
  {
    if ( eos.ShapeType() == TopAbs_FACE ) // get normals to elements on a FACE
    {
      SMESHDS_SubMesh* smDS = sm->GetSubMeshDS();
      eos._faceNormals.resize( smDS->NbElements() );

      SMDS_ElemIteratorPtr eIt = smDS->GetElements();
      for ( int iF = 0; eIt->more(); ++iF )
      {
        const SMDS_MeshElement* face = eIt->next();
        if ( !SMESH_MeshAlgos::FaceNormal( face, eos._faceNormals[iF], /*normalized=*/true ))
          eos._faceNormals[iF].SetCoord( 0,0,0 );
      }

      if ( !helper.IsReversedSubMesh( TopoDS::Face( eos._shape )))
        for ( size_t iF = 0; iF < eos._faceNormals.size(); ++iF )
          eos._faceNormals[iF].Reverse();
    }
    else // find EOS of adjacent FACEs
    {
      PShapeIteratorPtr fIt = helper.GetAncestors( eos._shape, *_mesh, TopAbs_FACE );
      while ( const TopoDS_Shape* face = fIt->next() )
      {
        TGeomID faceID = getMeshDS()->ShapeToIndex( *face );
        eos._faceEOS.push_back( & data._edgesOnShape[ faceID ]);
        if ( eos._faceEOS.back()->_shape.IsNull() )
          // avoid using uninitialised _shapeID in GetNormal()
          eos._faceEOS.back()->_shapeID = faceID;
      }
    }
  }
}

//================================================================================
/*!
 * \brief Returns normal of a face
 */
//================================================================================

bool _EdgesOnShape::GetNormal( const SMDS_MeshElement* face, gp_Vec& norm )
{
  bool ok = false;
  const _EdgesOnShape* eos = 0;

  if ( face->getshapeId() == _shapeID )
  {
    eos = this;
  }
  else
  {
    for ( size_t iF = 0; iF < _faceEOS.size() && !eos; ++iF )
      if ( face->getshapeId() == _faceEOS[ iF ]->_shapeID )
        eos = _faceEOS[ iF ];
  }

  if (( eos ) &&
      ( ok = ( face->getIdInShape() < eos->_faceNormals.size() )))
  {
    norm = eos->_faceNormals[ face->getIdInShape() ];
  }
  else if ( !eos )
  {
    debugMsg( "_EdgesOnShape::Normal() failed for face "<<face->GetID()
              << " on _shape #" << _shapeID );
  }
  return ok;
}


//================================================================================
/*!
 * \brief Set data of _LayerEdge needed for smoothing
 *  \param subIds - ids of sub-shapes of a SOLID to take into account faces from
 */
//================================================================================

bool _ViscousBuilder::setEdgeData(_LayerEdge&         edge,
                                  _EdgesOnShape&      eos,
                                  const set<TGeomID>& subIds,
                                  SMESH_MesherHelper& helper,
                                  _SolidData&         data)
{
  const SMDS_MeshNode* node = edge._nodes[0]; // source node

  edge._len       = 0;
  edge._2neibors  = 0;
  edge._curvature = 0;

  // --------------------------
  // Compute _normal and _cosin
  // --------------------------

  edge._cosin = 0;
  edge._normal.SetCoord(0,0,0);

  int totalNbFaces = 0;
  TopoDS_Face F;
  std::pair< TopoDS_Face, gp_XYZ > face2Norm[20];
  gp_Vec geomNorm;
  bool normOK = true;

  const bool onShrinkShape = !eos._sWOL.IsNull();
  const bool useGeometry   = (( eos._hyp.UseSurfaceNormal() ) ||
                              ( eos.ShapeType() != TopAbs_FACE && !onShrinkShape ));

  // get geom FACEs the node lies on
  //if ( useGeometry )
  {
    set<TGeomID> faceIds;
    if  ( eos.ShapeType() == TopAbs_FACE )
    {
      faceIds.insert( eos._shapeID );
    }
    else
    {
      SMDS_ElemIteratorPtr fIt = node->GetInverseElementIterator(SMDSAbs_Face);
      while ( fIt->more() )
        faceIds.insert( fIt->next()->getshapeId() );
    }
    set<TGeomID>::iterator id = faceIds.begin();
    for ( ; id != faceIds.end(); ++id )
    {
      const TopoDS_Shape& s = getMeshDS()->IndexToShape( *id );
      if ( s.IsNull() || s.ShapeType() != TopAbs_FACE || !subIds.count( *id ))
        continue;
      F = TopoDS::Face( s );
      face2Norm[ totalNbFaces ].first = F;
      totalNbFaces++;
    }
  }

  // find _normal
  if ( useGeometry )
  {
    if ( onShrinkShape ) // one of faces the node is on has no layers
    {
      if ( eos.SWOLType() == TopAbs_EDGE )
      {
        // inflate from VERTEX along EDGE
        edge._normal = getEdgeDir( TopoDS::Edge( eos._sWOL ), TopoDS::Vertex( eos._shape ));
      }
      else if ( eos.ShapeType() == TopAbs_VERTEX )
      {
        // inflate from VERTEX along FACE
        edge._normal = getFaceDir( TopoDS::Face( eos._sWOL ), TopoDS::Vertex( eos._shape ),
                                   node, helper, normOK, &edge._cosin);
      }
      else
      {
        // inflate from EDGE along FACE
        edge._normal = getFaceDir( TopoDS::Face( eos._sWOL ), TopoDS::Edge( eos._shape ),
                                   node, helper, normOK);
      }
    }

    // layers are on all faces of SOLID the node is on
    else
    {
      int nbOkNorms = 0;
      for ( int iF = 0; iF < totalNbFaces; ++iF )
      {
        F = TopoDS::Face( face2Norm[ iF ].first );
        geomNorm = getFaceNormal( node, F, helper, normOK );
        if ( !normOK ) continue;
        nbOkNorms++;

        if ( helper.GetSubShapeOri( data._solid, F ) != TopAbs_REVERSED )
          geomNorm.Reverse();
        face2Norm[ iF ].second = geomNorm.XYZ();
        edge._normal += geomNorm.XYZ();
      }
      if ( nbOkNorms == 0 )
        return error(SMESH_Comment("Can't get normal to node ") << node->GetID(), data._index);

      if ( edge._normal.Modulus() < 1e-3 && nbOkNorms > 1 )
      {
        // opposite normals, re-get normals at shifted positions (IPAL 52426)
        edge._normal.SetCoord( 0,0,0 );
        for ( int iF = 0; iF < totalNbFaces; ++iF )
        {
          const TopoDS_Face& F = face2Norm[iF].first;
          geomNorm = getFaceNormal( node, F, helper, normOK, /*shiftInside=*/true );
          if ( helper.GetSubShapeOri( data._solid, F ) != TopAbs_REVERSED )
            geomNorm.Reverse();
          if ( normOK )
            face2Norm[ iF ].second = geomNorm.XYZ();
          edge._normal += face2Norm[ iF ].second;
        }
      }

      if ( totalNbFaces < 3 )
      {
        //edge._normal /= totalNbFaces;
      }
      else
      {
        edge._normal = getWeigthedNormal( node, face2Norm, totalNbFaces );
      }
    }
  }
  else // !useGeometry - get _normal using surrounding mesh faces
  {

    SMDS_ElemIteratorPtr fIt = node->GetInverseElementIterator(SMDSAbs_Face);
    while ( fIt->more() )
    {
      const SMDS_MeshElement* face = fIt->next();
      if ( eos.GetNormal( face, geomNorm ))
      {
        edge._normal += geomNorm.XYZ();
        totalNbFaces++;
      }
    }
  }

  // compute _cosin
  //if ( eos._hyp.UseSurfaceNormal() )
  {
    switch ( eos.ShapeType() )
    {
    case TopAbs_FACE: {
      edge._cosin = 0;
      break;
    }
    case TopAbs_EDGE: {
      TopoDS_Edge E    = TopoDS::Edge( eos._shape );
      gp_Vec inFaceDir = getFaceDir( F, E, node, helper, normOK );
      double angle     = inFaceDir.Angle( edge._normal ); // [0,PI]
      edge._cosin      = Cos( angle );
      //cout << "Cosin on EDGE " << edge._cosin << " node " << node->GetID() << endl;
      break;
    }
    case TopAbs_VERTEX: {
      if ( eos.SWOLType() != TopAbs_FACE ) { // else _cosin is set by getFaceDir()
        TopoDS_Vertex V  = TopoDS::Vertex( eos._shape );
        gp_Vec inFaceDir = getFaceDir( F, V, node, helper, normOK );
        double angle     = inFaceDir.Angle( edge._normal ); // [0,PI]
        edge._cosin      = Cos( angle );
        if ( totalNbFaces > 2 || helper.IsSeamShape( node->getshapeId() ))
          for ( int iF = totalNbFaces-2; iF >=0; --iF )
          {
            F = face2Norm[ iF ].first;
            inFaceDir = getFaceDir( F, V, node, helper, normOK=true );
            if ( normOK ) {
              double angle = inFaceDir.Angle( edge._normal );
              edge._cosin = Max( edge._cosin, Cos( angle ));
            }
          }
      }
      //cout << "Cosin on VERTEX " << edge._cosin << " node " << node->GetID() << endl;
      break;
    }
    default:
      return error(SMESH_Comment("Invalid shape position of node ")<<node, data._index);
    }
  }

  double normSize = edge._normal.SquareModulus();
  if ( normSize < numeric_limits<double>::min() )
    return error(SMESH_Comment("Bad normal at node ")<< node->GetID(), data._index );

  edge._normal /= sqrt( normSize );

  // TODO: if ( !normOK ) then get normal by mesh faces

  // Set the rest data
  // --------------------
  if ( onShrinkShape )
  {
    SMDS_MeshNode* tgtNode = const_cast<SMDS_MeshNode*>( edge._nodes.back() );
    if ( SMESHDS_SubMesh* sm = getMeshDS()->MeshElements( data._solid ))
      sm->RemoveNode( tgtNode , /*isNodeDeleted=*/false );

    // set initial position which is parameters on _sWOL in this case
    if ( eos.SWOLType() == TopAbs_EDGE )
    {
      double u = helper.GetNodeU( TopoDS::Edge( eos._sWOL ), node, 0, &normOK );
      edge._pos.push_back( gp_XYZ( u, 0, 0 ));
      if ( edge._nodes.size() > 1 )
        getMeshDS()->SetNodeOnEdge( tgtNode, TopoDS::Edge( eos._sWOL ), u );
    }
    else // TopAbs_FACE
    {
      gp_XY uv = helper.GetNodeUV( TopoDS::Face( eos._sWOL ), node, 0, &normOK );
      edge._pos.push_back( gp_XYZ( uv.X(), uv.Y(), 0));
      if ( edge._nodes.size() > 1 )
        getMeshDS()->SetNodeOnFace( tgtNode, TopoDS::Face( eos._sWOL ), uv.X(), uv.Y() );
    }
  }
  else
  {
    edge._pos.push_back( SMESH_TNodeXYZ( node ));

    if ( eos.ShapeType() == TopAbs_FACE )
    {
      _Simplex::GetSimplices( node, edge._simplices, data._ignoreFaceIds, &data );
    }
  }

  // Set neighbour nodes for a _LayerEdge based on EDGE

  if ( eos.ShapeType() == TopAbs_EDGE /*||
       ( onShrinkShape && posType == SMDS_TOP_VERTEX && fabs( edge._cosin ) < 1e-10 )*/)
  {
    edge._2neibors = new _2NearEdges;
    // target node instead of source ones will be set later
    // if ( ! findNeiborsOnEdge( &edge,
    //                           edge._2neibors->_nodes[0],
    //                           edge._2neibors->_nodes[1], eos,
    //                           data))
    //   return false;
    // edge.SetDataByNeighbors( edge._2neibors->_nodes[0],
    //                          edge._2neibors->_nodes[1],
    //                          helper);
  }

  edge.SetCosin( edge._cosin ); // to update edge._lenFactor

  return true;
}

//================================================================================
/*!
 * \brief Return normal to a FACE at a node
 *  \param [in] n - node
 *  \param [in] face - FACE
 *  \param [in] helper - helper
 *  \param [out] isOK - true or false
 *  \param [in] shiftInside - to find normal at a position shifted inside the face
 *  \return gp_XYZ - normal
 */
//================================================================================

gp_XYZ _ViscousBuilder::getFaceNormal(const SMDS_MeshNode* node,
                                      const TopoDS_Face&   face,
                                      SMESH_MesherHelper&  helper,
                                      bool&                isOK,
                                      bool                 shiftInside)
{
  gp_XY uv;
  if ( shiftInside )
  {
    // get a shifted position
    gp_Pnt p = SMESH_TNodeXYZ( node );
    gp_XYZ shift( 0,0,0 );
    TopoDS_Shape S = helper.GetSubShapeByNode( node, helper.GetMeshDS() );
    switch ( S.ShapeType() ) {
    case TopAbs_VERTEX:
    {
      shift = getFaceDir( face, TopoDS::Vertex( S ), node, helper, isOK );
      break;
    }
    case TopAbs_EDGE:
    {
      shift = getFaceDir( face, TopoDS::Edge( S ), node, helper, isOK );
      break;
    }
    default:
      isOK = false;
    }
    if ( isOK )
      shift.Normalize();
    p.Translate( shift * 1e-5 );

    TopLoc_Location loc;
    GeomAPI_ProjectPointOnSurf& projector = helper.GetProjector( face, loc, 1e-7 );

    if ( !loc.IsIdentity() ) p.Transform( loc.Transformation().Inverted() );
    
    projector.Perform( p );
    if ( !projector.IsDone() || projector.NbPoints() < 1 )
    {
      isOK = false;
      return p.XYZ();
    }
    Quantity_Parameter U,V;
    projector.LowerDistanceParameters(U,V);
    uv.SetCoord( U,V );
  }
  else
  {
    uv = helper.GetNodeUV( face, node, 0, &isOK );
  }

  gp_Dir normal;
  isOK = false;

  Handle(Geom_Surface) surface = BRep_Tool::Surface( face );

  if ( !shiftInside &&
       helper.IsDegenShape( node->getshapeId() ) &&
       getFaceNormalAtSingularity( uv, face, helper, normal ))
  {
    isOK = true;
    return normal.XYZ();
  }

  int pointKind = GeomLib::NormEstim( surface, uv, 1e-5, normal );
  enum { REGULAR = 0, QUASYSINGULAR, CONICAL, IMPOSSIBLE };

  if ( pointKind == IMPOSSIBLE &&
       node->GetPosition()->GetDim() == 2 ) // node inside the FACE
  {
    // probably NormEstim() failed due to a too high tolerance
    pointKind = GeomLib::NormEstim( surface, uv, 1e-20, normal );
    isOK = ( pointKind < IMPOSSIBLE );
  }
  if ( pointKind < IMPOSSIBLE )
  {
    if ( pointKind != REGULAR &&
         !shiftInside &&
         node->GetPosition()->GetDim() < 2 ) // FACE boundary
    {
      gp_XYZ normShift = getFaceNormal( node, face, helper, isOK, /*shiftInside=*/true );
      if ( normShift * normal.XYZ() < 0. )
        normal = normShift;
    }
    isOK = true;
  }

  if ( !isOK ) // hard singularity, to call with shiftInside=true ?
  {
    const TGeomID faceID = helper.GetMeshDS()->ShapeToIndex( face );

    SMDS_ElemIteratorPtr fIt = node->GetInverseElementIterator(SMDSAbs_Face);
    while ( fIt->more() )
    {
      const SMDS_MeshElement* f = fIt->next();
      if ( f->getshapeId() == faceID )
      {
        isOK = SMESH_MeshAlgos::FaceNormal( f, (gp_XYZ&) normal.XYZ(), /*normalized=*/true );
        if ( isOK )
        {
          TopoDS_Face ff = face;
          ff.Orientation( TopAbs_FORWARD );
          if ( helper.IsReversedSubMesh( ff ))
            normal.Reverse();
          break;
        }
      }
    }
  }
  return normal.XYZ();
}

//================================================================================
/*!
 * \brief Try to get normal at a singularity of a surface basing on it's nature
 */
//================================================================================

bool _ViscousBuilder::getFaceNormalAtSingularity( const gp_XY&        uv,
                                                  const TopoDS_Face&  face,
                                                  SMESH_MesherHelper& helper,
                                                  gp_Dir&             normal )
{
  BRepAdaptor_Surface surface( face );
  gp_Dir axis;
  if ( !getRovolutionAxis( surface, axis ))
    return false;

  double f,l, d, du, dv;
  f = surface.FirstUParameter();
  l = surface.LastUParameter();
  d = ( uv.X() - f ) / ( l - f );
  du = ( d < 0.5 ? +1. : -1 ) * 1e-5 * ( l - f );
  f = surface.FirstVParameter();
  l = surface.LastVParameter();
  d = ( uv.Y() - f ) / ( l - f );
  dv = ( d < 0.5 ? +1. : -1 ) * 1e-5 * ( l - f );

  gp_Dir refDir;
  gp_Pnt2d testUV = uv;
  enum { REGULAR = 0, QUASYSINGULAR, CONICAL, IMPOSSIBLE };
  double tol = 1e-5;
  Handle(Geom_Surface) geomsurf = surface.Surface().Surface();
  for ( int iLoop = 0; true ; ++iLoop )
  {
    testUV.SetCoord( testUV.X() + du, testUV.Y() + dv );
    if ( GeomLib::NormEstim( geomsurf, testUV, tol, refDir ) == REGULAR )
      break;
    if ( iLoop > 20 )
      return false;
    tol /= 10.;
  }

  if ( axis * refDir < 0. )
    axis.Reverse();

  normal = axis;

  return true;
}

//================================================================================
/*!
 * \brief Return a normal at a node weighted with angles taken by FACEs
 *  \param [in] n - the node
 *  \param [in] fId2Normal - FACE ids and normals
 *  \param [in] nbFaces - nb of FACEs meeting at the node
 *  \return gp_XYZ - computed normal
 */
//================================================================================

gp_XYZ _ViscousBuilder::getWeigthedNormal( const SMDS_MeshNode*             n,
                                           std::pair< TopoDS_Face, gp_XYZ > fId2Normal[],
                                           int                              nbFaces )
{
  gp_XYZ resNorm(0,0,0);
  TopoDS_Shape V = SMESH_MesherHelper::GetSubShapeByNode( n, getMeshDS() );
  if ( V.ShapeType() != TopAbs_VERTEX )
  {
    for ( int i = 0; i < nbFaces; ++i )
      resNorm += fId2Normal[i].second;
    return resNorm;
  }

  // exclude equal normals
  //int nbUniqNorms = nbFaces;
  for ( int i = 0; i < nbFaces; ++i )
    for ( int j = i+1; j < nbFaces; ++j )
      if ( fId2Normal[i].second.IsEqual( fId2Normal[j].second, 0.1 ))
      {
        fId2Normal[i].second.SetCoord( 0,0,0 );
        //--nbUniqNorms;
        break;
      }
  //if ( nbUniqNorms < 3 )
  {
    for ( int i = 0; i < nbFaces; ++i )
      resNorm += fId2Normal[i].second;
    return resNorm;
  }

  double angles[30];
  for ( int i = 0; i < nbFaces; ++i )
  {
    const TopoDS_Face& F = fId2Normal[i].first;

    // look for two EDGEs shared by F and other FACEs within fId2Normal
    TopoDS_Edge ee[2];
    int nbE = 0;
    PShapeIteratorPtr eIt = SMESH_MesherHelper::GetAncestors( V, *_mesh, TopAbs_EDGE );
    while ( const TopoDS_Shape* E = eIt->next() )
    {
      if ( !SMESH_MesherHelper::IsSubShape( *E, F ))
        continue;
      bool isSharedEdge = false;
      for ( int j = 0; j < nbFaces && !isSharedEdge; ++j )
      {
        if ( i == j ) continue;
        const TopoDS_Shape& otherF = fId2Normal[j].first;
        isSharedEdge = SMESH_MesherHelper::IsSubShape( *E, otherF );
      }
      if ( !isSharedEdge )
        continue;
      ee[ nbE ] = TopoDS::Edge( *E );
      ee[ nbE ].Orientation( SMESH_MesherHelper::GetSubShapeOri( F, *E ));
      if ( ++nbE == 2 )
        break;
    }

    // get an angle between the two EDGEs
    angles[i] = 0;
    if ( nbE < 1 ) continue;
    if ( nbE == 1 )
    {
      ee[ 1 ] == ee[ 0 ];
    }
    else
    {
      if ( !V.IsSame( SMESH_MesherHelper::IthVertex( 0, ee[ 1 ] )))
        std::swap( ee[0], ee[1] );
    }
    angles[i] = SMESH_MesherHelper::GetAngle( ee[0], ee[1], F, TopoDS::Vertex( V ));
  }

  // compute a weighted normal
  double sumAngle = 0;
  for ( int i = 0; i < nbFaces; ++i )
  {
    angles[i] = ( angles[i] > 2*M_PI )  ?  0  :  M_PI - angles[i];
    sumAngle += angles[i];
  }
  for ( int i = 0; i < nbFaces; ++i )
    resNorm += angles[i] / sumAngle * fId2Normal[i].second;

  return resNorm;
}

//================================================================================
/*!
 * \brief Find 2 neigbor nodes of a node on EDGE
 */
//================================================================================

bool _ViscousBuilder::findNeiborsOnEdge(const _LayerEdge*     edge,
                                        const SMDS_MeshNode*& n1,
                                        const SMDS_MeshNode*& n2,
                                        _EdgesOnShape&        eos,
                                        _SolidData&           data)
{
  const SMDS_MeshNode* node = edge->_nodes[0];
  const int        shapeInd = eos._shapeID;
  SMESHDS_SubMesh*   edgeSM = 0;
  if ( eos.ShapeType() == TopAbs_EDGE )
  {
    edgeSM = eos._subMesh->GetSubMeshDS();
    if ( !edgeSM || edgeSM->NbElements() == 0 )
      return error(SMESH_Comment("Not meshed EDGE ") << shapeInd, data._index);
  }
  int iN = 0;
  n2 = 0;
  SMDS_ElemIteratorPtr eIt = node->GetInverseElementIterator(SMDSAbs_Edge);
  while ( eIt->more() && !n2 )
  {
    const SMDS_MeshElement* e = eIt->next();
    const SMDS_MeshNode*   nNeibor = e->GetNode( 0 );
    if ( nNeibor == node ) nNeibor = e->GetNode( 1 );
    if ( edgeSM )
    {
      if (!edgeSM->Contains(e)) continue;
    }
    else
    {
      TopoDS_Shape s = SMESH_MesherHelper::GetSubShapeByNode( nNeibor, getMeshDS() );
      if ( !SMESH_MesherHelper::IsSubShape( s, eos._sWOL )) continue;
    }
    ( iN++ ? n2 : n1 ) = nNeibor;
  }
  if ( !n2 )
    return error(SMESH_Comment("Wrongly meshed EDGE ") << shapeInd, data._index);
  return true;
}

//================================================================================
/*!
 * \brief Set _curvature and _2neibors->_plnNorm by 2 neigbor nodes residing the same EDGE
 */
//================================================================================

void _LayerEdge::SetDataByNeighbors( const SMDS_MeshNode* n1,
                                     const SMDS_MeshNode* n2,
                                     const _EdgesOnShape& eos,
                                     SMESH_MesherHelper&  helper)
{
  if ( eos.ShapeType() != TopAbs_EDGE )
    return;

  gp_XYZ pos = SMESH_TNodeXYZ( _nodes[0] );
  gp_XYZ vec1 = pos - SMESH_TNodeXYZ( n1 );
  gp_XYZ vec2 = pos - SMESH_TNodeXYZ( n2 );

  // Set _curvature

  double      sumLen = vec1.Modulus() + vec2.Modulus();
  _2neibors->_wgt[0] = 1 - vec1.Modulus() / sumLen;
  _2neibors->_wgt[1] = 1 - vec2.Modulus() / sumLen;
  double avgNormProj = 0.5 * ( _normal * vec1 + _normal * vec2 );
  double      avgLen = 0.5 * ( vec1.Modulus() + vec2.Modulus() );
  if ( _curvature ) delete _curvature;
  _curvature = _Curvature::New( avgNormProj, avgLen );
  // if ( _curvature )
  //   debugMsg( _nodes[0]->GetID()
  //             << " CURV r,k: " << _curvature->_r<<","<<_curvature->_k
  //             << " proj = "<<avgNormProj<< " len = " << avgLen << "| lenDelta(0) = "
  //             << _curvature->lenDelta(0) );

  // Set _plnNorm

  if ( eos._sWOL.IsNull() )
  {
    TopoDS_Edge  E = TopoDS::Edge( eos._shape );
    // if ( SMESH_Algo::isDegenerated( E ))
    //   return;
    gp_XYZ dirE    = getEdgeDir( E, _nodes[0], helper );
    gp_XYZ plnNorm = dirE ^ _normal;
    double proj0   = plnNorm * vec1;
    double proj1   = plnNorm * vec2;
    if ( fabs( proj0 ) > 1e-10 || fabs( proj1 ) > 1e-10 )
    {
      if ( _2neibors->_plnNorm ) delete _2neibors->_plnNorm;
      _2neibors->_plnNorm = new gp_XYZ( plnNorm.Normalized() );
    }
  }
}

//================================================================================
/*!
 * \brief Copy data from a _LayerEdge of other SOLID and based on the same node;
 * this and other _LayerEdge's are inflated along a FACE or an EDGE
 */
//================================================================================

gp_XYZ _LayerEdge::Copy( _LayerEdge&         other,
                         _EdgesOnShape&      eos,
                         SMESH_MesherHelper& helper )
{
  _nodes     = other._nodes;
  _normal    = other._normal;
  _len       = 0;
  _lenFactor = other._lenFactor;
  _cosin     = other._cosin;
  _2neibors  = other._2neibors;
  _curvature = 0; std::swap( _curvature, other._curvature );
  _2neibors  = 0; std::swap( _2neibors,  other._2neibors );

  gp_XYZ lastPos( 0,0,0 );
  if ( eos.SWOLType() == TopAbs_EDGE )
  {
    double u = helper.GetNodeU( TopoDS::Edge( eos._sWOL ), _nodes[0] );
    _pos.push_back( gp_XYZ( u, 0, 0));

    u = helper.GetNodeU( TopoDS::Edge( eos._sWOL ), _nodes.back() );
    lastPos.SetX( u );
  }
  else // TopAbs_FACE
  {
    gp_XY uv = helper.GetNodeUV( TopoDS::Face( eos._sWOL ), _nodes[0]);
    _pos.push_back( gp_XYZ( uv.X(), uv.Y(), 0));

    uv = helper.GetNodeUV( TopoDS::Face( eos._sWOL ), _nodes.back() );
    lastPos.SetX( uv.X() );
    lastPos.SetY( uv.Y() );
  }
  return lastPos;
}

//================================================================================
/*!
 * \brief Set _cosin and _lenFactor
 */
//================================================================================

void _LayerEdge::SetCosin( double cosin )
{
  _cosin = cosin;
  cosin = Abs( _cosin );
  _lenFactor = ( /*0.1 < cosin &&*/ cosin < 1-1e-12 ) ?  1./sqrt(1-cosin*cosin) : 1.0;
}

//================================================================================
/*!
 * \brief Fills a vector<_Simplex > 
 */
//================================================================================

void _Simplex::GetSimplices( const SMDS_MeshNode* node,
                             vector<_Simplex>&    simplices,
                             const set<TGeomID>&  ingnoreShapes,
                             const _SolidData*    dataToCheckOri,
                             const bool           toSort)
{
  simplices.clear();
  SMDS_ElemIteratorPtr fIt = node->GetInverseElementIterator(SMDSAbs_Face);
  while ( fIt->more() )
  {
    const SMDS_MeshElement* f = fIt->next();
    const TGeomID    shapeInd = f->getshapeId();
    if ( ingnoreShapes.count( shapeInd )) continue;
    const int nbNodes = f->NbCornerNodes();
    const int  srcInd = f->GetNodeIndex( node );
    const SMDS_MeshNode* nPrev = f->GetNode( SMESH_MesherHelper::WrapIndex( srcInd-1, nbNodes ));
    const SMDS_MeshNode* nNext = f->GetNode( SMESH_MesherHelper::WrapIndex( srcInd+1, nbNodes ));
    const SMDS_MeshNode* nOpp  = f->GetNode( SMESH_MesherHelper::WrapIndex( srcInd+2, nbNodes ));
    if ( dataToCheckOri && dataToCheckOri->_reversedFaceIds.count( shapeInd ))
      std::swap( nPrev, nNext );
    simplices.push_back( _Simplex( nPrev, nNext, nOpp ));
  }

  if ( toSort )
    SortSimplices( simplices );
}

//================================================================================
/*!
 * \brief Set neighbor simplices side by side
 */
//================================================================================

void _Simplex::SortSimplices(vector<_Simplex>& simplices)
{
  vector<_Simplex> sortedSimplices( simplices.size() );
  sortedSimplices[0] = simplices[0];
  int nbFound = 0;
  for ( size_t i = 1; i < simplices.size(); ++i )
  {
    for ( size_t j = 1; j < simplices.size(); ++j )
      if ( sortedSimplices[i-1]._nNext == simplices[j]._nPrev )
      {
        sortedSimplices[i] = simplices[j];
        nbFound++;
        break;
      }
  }
  if ( nbFound == simplices.size() - 1 )
    simplices.swap( sortedSimplices );
}

//================================================================================
/*!
 * \brief DEBUG. Create groups contating temorary data of _LayerEdge's
 */
//================================================================================

void _ViscousBuilder::makeGroupOfLE()
{
#ifdef _DEBUG_
  for ( size_t i = 0 ; i < _sdVec.size(); ++i )
  {
    if ( _sdVec[i]._n2eMap.empty() ) continue;

    dumpFunction( SMESH_Comment("make_LayerEdge_") << i );
    TNode2Edge::iterator n2e;
    for ( n2e = _sdVec[i]._n2eMap.begin(); n2e != _sdVec[i]._n2eMap.end(); ++n2e )
    {
      _LayerEdge* le = n2e->second;
      for ( size_t iN = 1; iN < le->_nodes.size(); ++iN )
        dumpCmd(SMESH_Comment("mesh.AddEdge([ ") <<le->_nodes[iN-1]->GetID()
                << ", " << le->_nodes[iN]->GetID() <<"])");
    }
    dumpFunctionEnd();

    dumpFunction( SMESH_Comment("makeNormals") << i );
    for ( n2e = _sdVec[i]._n2eMap.begin(); n2e != _sdVec[i]._n2eMap.end(); ++n2e )
    {
      _LayerEdge* edge = n2e->second;
      SMESH_TNodeXYZ nXYZ( edge->_nodes[0] );
      nXYZ += edge->_normal * _sdVec[i]._stepSize;
      dumpCmd(SMESH_Comment("mesh.AddEdge([ ") << edge->_nodes[0]->GetID()
              << ", mesh.AddNode( " << nXYZ.X()<<","<< nXYZ.Y()<<","<< nXYZ.Z()<<")])");
    }
    dumpFunctionEnd();

    dumpFunction( SMESH_Comment("makeTmpFaces_") << i );
    dumpCmd( "faceId1 = mesh.NbElements()" );
    TopExp_Explorer fExp( _sdVec[i]._solid, TopAbs_FACE );
    for ( ; fExp.More(); fExp.Next() )
    {
      if (const SMESHDS_SubMesh* sm = _sdVec[i]._proxyMesh->GetProxySubMesh( fExp.Current()))
      {
        if ( sm->NbElements() == 0 ) continue;
        SMDS_ElemIteratorPtr fIt = sm->GetElements();
        while ( fIt->more())
        {
          const SMDS_MeshElement* e = fIt->next();
          SMESH_Comment cmd("mesh.AddFace([");
          for ( int j=0; j < e->NbCornerNodes(); ++j )
            cmd << e->GetNode(j)->GetID() << (j+1<e->NbCornerNodes() ? ",": "])");
          dumpCmd( cmd );
        }
      }
    }
    dumpCmd( "faceId2 = mesh.NbElements()" );
    dumpCmd( SMESH_Comment( "mesh.MakeGroup( 'tmpFaces_" ) << i << "',"
             << "SMESH.FACE, SMESH.FT_RangeOfIds,'=',"
             << "'%s-%s' % (faceId1+1, faceId2))");
    dumpFunctionEnd();
  }
#endif
}

//================================================================================
/*!
 * \brief Find maximal _LayerEdge length (layer thickness) limited by geometry
 */
//================================================================================

void _ViscousBuilder::computeGeomSize( _SolidData& data )
{
  data._geomSize = Precision::Infinite();
  double intersecDist;
  auto_ptr<SMESH_ElementSearcher> searcher
    ( SMESH_MeshAlgos::GetElementSearcher( *getMeshDS(),
                                           data._proxyMesh->GetFaces( data._solid )) );

  for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
  {
    _EdgesOnShape& eos = data._edgesOnShape[ iS ];
    if ( eos._edges.empty() || eos.ShapeType() == TopAbs_EDGE )
      continue;
    for ( size_t i = 0; i < eos._edges.size(); ++i )
    {
      eos._edges[i]->FindIntersection( *searcher, intersecDist, data._epsilon, eos );
      if ( data._geomSize > intersecDist && intersecDist > 0 )
        data._geomSize = intersecDist;
    }
  }
}

//================================================================================
/*!
 * \brief Increase length of _LayerEdge's to reach the required thickness of layers
 */
//================================================================================

bool _ViscousBuilder::inflate(_SolidData& data)
{
  SMESH_MesherHelper helper( *_mesh );

  // Limit inflation step size by geometry size found by itersecting
  // normals of _LayerEdge's with mesh faces
  if ( data._stepSize > 0.3 * data._geomSize )
    limitStepSize( data, 0.3 * data._geomSize );

  const double tgtThick = data._maxThickness;
  if ( data._stepSize > data._minThickness )
    limitStepSize( data, data._minThickness );

  if ( data._stepSize < 1. )
    data._epsilon = data._stepSize * 1e-7;

  debugMsg( "-- geomSize = " << data._geomSize << ", stepSize = " << data._stepSize );

  const double safeFactor = ( 2*data._maxThickness < data._geomSize ) ? 1 : theThickToIntersection;

  double avgThick = 0, curThick = 0, distToIntersection = Precision::Infinite();
  int nbSteps = 0, nbRepeats = 0;
  while ( avgThick < 0.99 )
  {
    // new target length
    curThick += data._stepSize;
    if ( curThick > tgtThick )
    {
      curThick = tgtThick + tgtThick*( 1.-avgThick ) * nbRepeats;
      nbRepeats++;
    }

    // Elongate _LayerEdge's
    dumpFunction(SMESH_Comment("inflate")<<data._index<<"_step"<<nbSteps); // debug
    for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
    {
      _EdgesOnShape& eos = data._edgesOnShape[iS];
      if ( eos._edges.empty() ) continue;

      const double shapeCurThick = Min( curThick, eos._hyp.GetTotalThickness() );
      for ( size_t i = 0; i < eos._edges.size(); ++i )
      {
        eos._edges[i]->SetNewLength( shapeCurThick, eos, helper );
      }
    }
    dumpFunctionEnd();

    if ( !updateNormals( data, helper, nbSteps ))
      return false;

    // Improve and check quality
    if ( !smoothAndCheck( data, nbSteps, distToIntersection ))
    {
      if ( nbSteps > 0 )
      {
#ifdef __NOT_INVALIDATE_BAD_SMOOTH
        debugMsg("NOT INVALIDATED STEP!");
        return error("Smoothing failed", data._index);
#endif
        dumpFunction(SMESH_Comment("invalidate")<<data._index<<"_step"<<nbSteps); // debug
        for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
        {
          _EdgesOnShape& eos = data._edgesOnShape[iS];
          for ( size_t i = 0; i < eos._edges.size(); ++i )
            eos._edges[i]->InvalidateStep( nbSteps+1, eos );
        }
        dumpFunctionEnd();
      }
      break; // no more inflating possible
    }
    nbSteps++;

    // Evaluate achieved thickness
    avgThick = 0;
    for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
    {
      _EdgesOnShape& eos = data._edgesOnShape[iS];
      if ( eos._edges.empty() ) continue;

      const double shapeTgtThick = eos._hyp.GetTotalThickness();
      for ( size_t i = 0; i < eos._edges.size(); ++i )
      {
        avgThick += Min( 1., eos._edges[i]->_len / shapeTgtThick );
      }
    }
    avgThick /= data._n2eMap.size();
    debugMsg( "-- Thickness " << curThick << " ("<< avgThick*100 << "%) reached" );

    if ( distToIntersection < tgtThick * avgThick * safeFactor && avgThick < 0.9 )
    {
      debugMsg( "-- Stop inflation since "
                << " distToIntersection( "<<distToIntersection<<" ) < avgThick( "
                << tgtThick * avgThick << " ) * " << safeFactor );
      break;
    }
    // new step size
    limitStepSize( data, 0.25 * distToIntersection );
    if ( data._stepSizeNodes[0] )
      data._stepSize = data._stepSizeCoeff *
        SMESH_TNodeXYZ(data._stepSizeNodes[0]).Distance(data._stepSizeNodes[1]);

  } // while ( avgThick < 0.99 )

  if (nbSteps == 0 )
    return error("failed at the very first inflation step", data._index);

  if ( avgThick < 0.99 )
  {
    if ( !data._proxyMesh->_warning || data._proxyMesh->_warning->IsOK() )
    {
      data._proxyMesh->_warning.reset
        ( new SMESH_ComputeError (COMPERR_WARNING,
                                  SMESH_Comment("Thickness ") << tgtThick <<
                                  " of viscous layers not reached,"
                                  " average reached thickness is " << avgThick*tgtThick));
    }
  }

  // Restore position of src nodes moved by infaltion on _noShrinkShapes
  dumpFunction(SMESH_Comment("restoNoShrink_So")<<data._index); // debug
  for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
  {
    _EdgesOnShape& eos = data._edgesOnShape[iS];
    if ( !eos._edges.empty() && eos._edges[0]->_nodes.size() == 1 )
      for ( size_t i = 0; i < eos._edges.size(); ++i )
      {
        restoreNoShrink( *eos._edges[ i ] );
      }
  }
  dumpFunctionEnd();

  return true;
}

//================================================================================
/*!
 * \brief Improve quality of layer inner surface and check intersection
 */
//================================================================================

bool _ViscousBuilder::smoothAndCheck(_SolidData& data,
                                     const int   nbSteps,
                                     double &    distToIntersection)
{
  if ( data._nbShapesToSmooth == 0 )
    return true; // no shapes needing smoothing

  bool moved, improved;
  vector< _LayerEdge* > badSmooEdges;

  SMESH_MesherHelper helper(*_mesh);
  Handle(Geom_Surface) surface;
  TopoDS_Face F;

  for ( int isFace = 0; isFace < 2; ++isFace ) // smooth on [ EDGEs, FACEs ]
  {
    const TopAbs_ShapeEnum shapeType = isFace ? TopAbs_FACE : TopAbs_EDGE;

    for ( int iS = 0; iS < data._edgesOnShape.size(); ++iS )
    {
      _EdgesOnShape& eos = data._edgesOnShape[ iS ];
      if ( !eos._toSmooth || eos.ShapeType() != shapeType )
        continue;

      // already smoothed?
      bool toSmooth = ( eos._edges[ 0 ]->NbSteps() >= nbSteps+1 );
      if ( !toSmooth ) continue;

      if ( !eos._hyp.ToSmooth() )
      {
        // smooth disabled by the user; check validy only
        if ( !isFace ) continue;
        double vol;
        for ( size_t i = 0; i < eos._edges.size(); ++i )
        {
          _LayerEdge* edge = eos._edges[i];
          const gp_XYZ& curPos (  );
          for ( size_t iF = 0; iF < edge->_simplices.size(); ++iF )
            if ( !edge->_simplices[iF].IsForward( edge->_nodes[0],
                                                 &edge->_pos.back(), vol ))
              return false;
        }
        continue; // goto to the next EDGE or FACE
      }

      // prepare data
      if ( eos.SWOLType() == TopAbs_FACE )
      {
        if ( !F.IsSame( eos._sWOL )) {
          F = TopoDS::Face( eos._sWOL );
          helper.SetSubShape( F );
          surface = BRep_Tool::Surface( F );
        }
      }
      else
      {
        F.Nullify(); surface.Nullify();
      }
      const TGeomID sInd = eos._shapeID;

      // perform smoothing

      if ( eos.ShapeType() == TopAbs_EDGE )
      {
        dumpFunction(SMESH_Comment("smooth")<<data._index << "_Ed"<<sInd <<"_InfStep"<<nbSteps);

        // try a simple solution on an analytic EDGE
        if ( !smoothAnalyticEdge( data, eos, surface, F, helper ))
        {
          // smooth on EDGE's
          int step = 0;
          do {
            moved = false;
            for ( size_t i = 0; i < eos._edges.size(); ++i )
            {
              moved |= eos._edges[i]->SmoothOnEdge( surface, F, helper );
            }
            dumpCmd( SMESH_Comment("# end step ")<<step);
          }
          while ( moved && step++ < 5 );
        }
        dumpFunctionEnd();
      }
      else
      {
        // smooth on FACE's

        const bool isConcaveFace = data._concaveFaces.count( sInd );

        int step = 0, stepLimit = 5, badNb = 0;
        while (( ++step <= stepLimit ) || improved )
        {
          dumpFunction(SMESH_Comment("smooth")<<data._index<<"_Fa"<<sInd
                       <<"_InfStep"<<nbSteps<<"_"<<step); // debug
          int oldBadNb = badNb;
          badSmooEdges.clear();

          if ( step % 2 ) {
            for ( size_t i = 0; i < eos._edges.size(); ++i )  // iterate forward
              if ( eos._edges[i]->Smooth( step, isConcaveFace, false ))
                badSmooEdges.push_back( eos._edges[i] );
          }

          else {
            for ( int i = eos._edges.size()-1; i >= 0; --i ) // iterate backward
              if ( eos._edges[i]->Smooth( step, isConcaveFace, false ))
                badSmooEdges.push_back( eos._edges[i] );
          }
          badNb = badSmooEdges.size();
          improved = ( badNb < oldBadNb );

          if ( !badSmooEdges.empty() && step >= stepLimit / 2 )
          {
            // look for the best smooth of _LayerEdge's neighboring badSmooEdges
            vector<_Simplex> simplices;
            for ( size_t i = 0; i < badSmooEdges.size(); ++i )
            {
              _LayerEdge* ledge = badSmooEdges[i];
              _Simplex::GetSimplices( ledge->_nodes[0], simplices, data._ignoreFaceIds );
              for ( size_t iS = 0; iS < simplices.size(); ++iS )
              {
                TNode2Edge::iterator n2e = data._n2eMap.find( simplices[iS]._nNext );
                if ( n2e != data._n2eMap.end()) {
                  _LayerEdge* ledge2 = n2e->second;
                  if ( ledge2->_nodes[0]->getshapeId() == sInd )
                    ledge2->Smooth( step, isConcaveFace, /*findBest=*/true );
                }
              }
            }
          }
          // issue 22576 -- no bad faces but still there are intersections to fix
          // if ( improved && badNb == 0 )
          //   stepLimit = step + 3;

          dumpFunctionEnd();
        }
        if ( badNb > 0 )
        {
#ifdef __myDEBUG
          double vol = 0;
          for ( int i = 0; i < eos._edges.size(); ++i )
          {
            _LayerEdge* edge = eos._edges[i];
            SMESH_TNodeXYZ tgtXYZ( edge->_nodes.back() );
            for ( size_t j = 0; j < edge->_simplices.size(); ++j )
              if ( !edge->_simplices[j].IsForward( edge->_nodes[0], &tgtXYZ, vol ))
              {
                cout << "Bad simplex ( " << edge->_nodes[0]->GetID()<< " "<< tgtXYZ._node->GetID()
                     << " "<< edge->_simplices[j]._nPrev->GetID()
                     << " "<< edge->_simplices[j]._nNext->GetID() << " )" << endl;
                return false;
              }
          }
#endif
          return false;
        }
      } // // smooth on FACE's
    } // loop on shapes
  } // smooth on [ EDGEs, FACEs ]

  // Check orientation of simplices of _ConvexFace::_simplexTestEdges
  map< TGeomID, _ConvexFace >::iterator id2face = data._convexFaces.begin();
  for ( ; id2face != data._convexFaces.end(); ++id2face )
  {
    _ConvexFace & convFace = (*id2face).second;
    if ( !convFace._simplexTestEdges.empty() &&
         convFace._simplexTestEdges[0]->_nodes[0]->GetPosition()->GetDim() == 2 )
      continue; // _simplexTestEdges are based on FACE -- already checked while smoothing

    if ( !convFace.CheckPrisms() )
      return false;
  }

  // Check if the last segments of _LayerEdge intersects 2D elements;
  // checked elements are either temporary faces or faces on surfaces w/o the layers

  auto_ptr<SMESH_ElementSearcher> searcher
    ( SMESH_MeshAlgos::GetElementSearcher( *getMeshDS(),
                                           data._proxyMesh->GetFaces( data._solid )) );

  distToIntersection = Precision::Infinite();
  double dist;
  const SMDS_MeshElement* intFace = 0;
  const SMDS_MeshElement* closestFace = 0;
  _LayerEdge* le = 0;
  for ( int iS = 0; iS < data._edgesOnShape.size(); ++iS )
  {
    _EdgesOnShape& eos = data._edgesOnShape[ iS ];
    if ( eos._edges.empty() || !eos._sWOL.IsNull() )
      continue;
    for ( size_t i = 0; i < eos._edges.size(); ++i )
    {
      if ( eos._edges[i]->FindIntersection( *searcher, dist, data._epsilon, eos, &intFace ))
        return false;
      if ( distToIntersection > dist )
      {
        // ignore intersection of a _LayerEdge based on a _ConvexFace with a face
        // lying on this _ConvexFace
        if ( _ConvexFace* convFace = data.GetConvexFace( intFace->getshapeId() ))
          if ( convFace->_subIdToEOS.count ( eos._shapeID ))
            continue;

        // ignore intersection of a _LayerEdge based on a FACE with an element on this FACE
        // ( avoid limiting the thickness on the case of issue 22576)
        if ( intFace->getshapeId() == eos._shapeID  )
          continue;

        distToIntersection = dist;
        le = eos._edges[i];
        closestFace = intFace;
      }
    }
  }
#ifdef __myDEBUG
  if ( closestFace )
  {
    SMDS_MeshElement::iterator nIt = closestFace->begin_nodes();
    cout << "Shortest distance: _LayerEdge nodes: tgt " << le->_nodes.back()->GetID()
         << " src " << le->_nodes[0]->GetID()<< ", intersection with face ("
         << (*nIt++)->GetID()<<" "<< (*nIt++)->GetID()<<" "<< (*nIt++)->GetID()
         << ") distance = " << distToIntersection<< endl;
  }
#endif

  return true;
}

//================================================================================
/*!
 * \brief Return a curve of the EDGE to be used for smoothing and arrange
 *        _LayerEdge's to be in a consequent order
 */
//================================================================================

Handle(Geom_Curve) _SolidData::CurveForSmooth( const TopoDS_Edge&    E,
                                               _EdgesOnShape&        eos,
                                               SMESH_MesherHelper&   helper)
{
  const TGeomID eIndex = eos._shapeID;

  map< TGeomID, Handle(Geom_Curve)>::iterator i2curve = _edge2curve.find( eIndex );

  if ( i2curve == _edge2curve.end() )
  {
    // sort _LayerEdge's by position on the EDGE
    SortOnEdge( E, eos._edges, helper );

    SMESHDS_SubMesh* smDS = eos._subMesh->GetSubMeshDS();

    TopLoc_Location loc; double f,l;

    Handle(Geom_Line)   line;
    Handle(Geom_Circle) circle;
    bool isLine, isCirc;
    if ( eos._sWOL.IsNull() ) /////////////////////////////////////////// 3D case
    {
      // check if the EDGE is a line
      Handle(Geom_Curve) curve = BRep_Tool::Curve( E, loc, f, l);
      if ( curve->IsKind( STANDARD_TYPE( Geom_TrimmedCurve )))
        curve = Handle(Geom_TrimmedCurve)::DownCast( curve )->BasisCurve();

      line   = Handle(Geom_Line)::DownCast( curve );
      circle = Handle(Geom_Circle)::DownCast( curve );
      isLine = (!line.IsNull());
      isCirc = (!circle.IsNull());

      if ( !isLine && !isCirc ) // Check if the EDGE is close to a line
      {
        // Bnd_B3d bndBox;
        // SMDS_NodeIteratorPtr nIt = smDS->GetNodes();
        // while ( nIt->more() )
        //   bndBox.Add( SMESH_TNodeXYZ( nIt->next() ));
        // gp_XYZ size = bndBox.CornerMax() - bndBox.CornerMin();

        // gp_Pnt p0, p1;
        // if ( eos._edges.size() > 1 ) {
        //   p0 = SMESH_TNodeXYZ( eos._edges[0]->_nodes[0] );
        //   p1 = SMESH_TNodeXYZ( eos._edges[1]->_nodes[0] );
        // }
        // else {
        //   p0 = curve->Value( f );
        //   p1 = curve->Value( l );
        // }
        // const double lineTol = 1e-2 * p0.Distance( p1 );
        // for ( int i = 0; i < 3 && !isLine; ++i )
        //   isLine = ( size.Coord( i+1 ) <= lineTol ); ////////// <--- WRONG

        isLine = SMESH_Algo::IsStraight( E );

        if ( isLine )
          line = new Geom_Line( gp::OX() ); // only type does matter
      }
      if ( !isLine && !isCirc && eos._edges.size() > 2) // Check if the EDGE is close to a circle
      {
        // TODO
      }
    }
    else //////////////////////////////////////////////////////////////////////// 2D case
    {
      const TopoDS_Face& F = TopoDS::Face( eos._sWOL );

      // check if the EDGE is a line
      Handle(Geom2d_Curve) curve = BRep_Tool::CurveOnSurface( E, F, f, l);
      if ( curve->IsKind( STANDARD_TYPE( Geom2d_TrimmedCurve )))
        curve = Handle(Geom2d_TrimmedCurve)::DownCast( curve )->BasisCurve();

      Handle(Geom2d_Line)   line2d   = Handle(Geom2d_Line)::DownCast( curve );
      Handle(Geom2d_Circle) circle2d = Handle(Geom2d_Circle)::DownCast( curve );
      isLine = (!line2d.IsNull());
      isCirc = (!circle2d.IsNull());

      if ( !isLine && !isCirc) // Check if the EDGE is close to a line
      {
        Bnd_B2d bndBox;
        SMDS_NodeIteratorPtr nIt = smDS->GetNodes();
        while ( nIt->more() )
          bndBox.Add( helper.GetNodeUV( F, nIt->next() ));
        gp_XY size = bndBox.CornerMax() - bndBox.CornerMin();

        const double lineTol = 1e-2 * sqrt( bndBox.SquareExtent() );
        for ( int i = 0; i < 2 && !isLine; ++i )
          isLine = ( size.Coord( i+1 ) <= lineTol );
      }
      if ( !isLine && !isCirc && eos._edges.size() > 2) // Check if the EDGE is close to a circle
      {
        // TODO
      }
      if ( isLine )
      {
        line = new Geom_Line( gp::OX() ); // only type does matter
      }
      else if ( isCirc )
      {
        gp_Pnt2d p = circle2d->Location();
        gp_Ax2 ax( gp_Pnt( p.X(), p.Y(), 0), gp::DX());
        circle = new Geom_Circle( ax, 1.); // only center position does matter
      }
    }

    Handle(Geom_Curve)& res = _edge2curve[ eIndex ];
    if ( isLine )
      res = line;
    else if ( isCirc )
      res = circle;

    return res;
  }
  return i2curve->second;
}

//================================================================================
/*!
 * \brief Sort _LayerEdge's by a parameter on a given EDGE
 */
//================================================================================

void _SolidData::SortOnEdge( const TopoDS_Edge&     E,
                             vector< _LayerEdge* >& edges,
                             SMESH_MesherHelper&    helper)
{
  map< double, _LayerEdge* > u2edge;
  for ( size_t i = 0; i < edges.size(); ++i )
    u2edge.insert( make_pair( helper.GetNodeU( E, edges[i]->_nodes[0] ), edges[i] ));

  ASSERT( u2edge.size() == edges.size() );
  map< double, _LayerEdge* >::iterator u2e = u2edge.begin();
  for ( int i = 0; i < edges.size(); ++i, ++u2e )
    edges[i] = u2e->second;

  Sort2NeiborsOnEdge( edges );
}

//================================================================================
/*!
 * \brief Set _2neibors according to the order of _LayerEdge on EDGE
 */
//================================================================================

void _SolidData::Sort2NeiborsOnEdge( vector< _LayerEdge* >& edges )
{
  for ( size_t i = 0; i < edges.size()-1; ++i )
    if ( edges[i]->_2neibors->tgtNode(1) != edges[i+1]->_nodes.back() )
      edges[i]->_2neibors->reverse();

  const size_t iLast = edges.size() - 1;
  if ( edges.size() > 1 &&
       edges[iLast]->_2neibors->tgtNode(0) != edges[iLast-1]->_nodes.back() )
    edges[iLast]->_2neibors->reverse();
}

//================================================================================
/*!
 * \brief Return _EdgesOnShape* corresponding to the shape
 */
//================================================================================

_EdgesOnShape* _SolidData::GetShapeEdges(const TGeomID shapeID )
{
  if ( shapeID < _edgesOnShape.size() &&
       _edgesOnShape[ shapeID ]._shapeID == shapeID )
    return & _edgesOnShape[ shapeID ];

  for ( size_t i = 0; i < _edgesOnShape.size(); ++i )
    if ( _edgesOnShape[i]._shapeID == shapeID )
      return & _edgesOnShape[i];

  return 0;
}

//================================================================================
/*!
 * \brief Return _EdgesOnShape* corresponding to the shape
 */
//================================================================================

_EdgesOnShape* _SolidData::GetShapeEdges(const TopoDS_Shape& shape )
{
  SMESHDS_Mesh* meshDS = _proxyMesh->GetMesh()->GetMeshDS();
  return GetShapeEdges( meshDS->ShapeToIndex( shape ));
}

//================================================================================
/*!
 * \brief Prepare data of the _LayerEdge for smoothing on FACE
 */
//================================================================================

void _SolidData::PrepareEdgesToSmoothOnFace( _EdgesOnShape* eof, bool substituteSrcNodes )
{
  set< TGeomID > vertices;
  SMESH_MesherHelper helper( *_proxyMesh->GetMesh() );
  if ( isConcave( TopoDS::Face( eof->_shape ), helper, &vertices ))
    _concaveFaces.insert( eof->_shapeID );

  for ( size_t i = 0; i < eof->_edges.size(); ++i )
    eof->_edges[i]->_smooFunction = 0;

  for ( size_t i = 0; i < eof->_edges.size(); ++i )
  {
    _LayerEdge* edge = eof->_edges[i];
    _Simplex::GetSimplices
      ( edge->_nodes[0], edge->_simplices, _ignoreFaceIds, this, /*sort=*/true );

    edge->ChooseSmooFunction( vertices, _n2eMap );

    double avgNormProj = 0, avgLen = 0;
    for ( size_t i = 0; i < edge->_simplices.size(); ++i )
    {
      _Simplex& s = edge->_simplices[i];

      gp_XYZ  vec = edge->_pos.back() - SMESH_TNodeXYZ( s._nPrev );
      avgNormProj += edge->_normal * vec;
      avgLen      += vec.Modulus();
      if ( substituteSrcNodes )
      {
        s._nNext = _n2eMap[ s._nNext ]->_nodes.back();
        s._nPrev = _n2eMap[ s._nPrev ]->_nodes.back();
      }
    }
    avgNormProj /= edge->_simplices.size();
    avgLen      /= edge->_simplices.size();
    edge->_curvature = _Curvature::New( avgNormProj, avgLen );
  }
}

//================================================================================
/*!
 * \brief Add faces for smoothing
 */
//================================================================================

void _SolidData::AddShapesToSmooth( const set< _EdgesOnShape* >& eosSet )
{
  set< _EdgesOnShape * >::const_iterator eos = eosSet.begin();
  for ( ; eos != eosSet.end(); ++eos )
  {
    if ( !*eos || (*eos)->_toSmooth ) continue;

    (*eos)->_toSmooth = true;

    if ( (*eos)->ShapeType() == TopAbs_FACE )
    {
      PrepareEdgesToSmoothOnFace( *eos, /*substituteSrcNodes=*/true );
    }
  }
}

//================================================================================
/*!
 * \brief smooth _LayerEdge's on a staight EDGE or circular EDGE
 */
//================================================================================

bool _ViscousBuilder::smoothAnalyticEdge( _SolidData&           data,
                                          _EdgesOnShape&        eos,
                                          Handle(Geom_Surface)& surface,
                                          const TopoDS_Face&    F,
                                          SMESH_MesherHelper&   helper)
{
  const TopoDS_Edge& E = TopoDS::Edge( eos._shape );

  Handle(Geom_Curve) curve = data.CurveForSmooth( E, eos, helper );
  if ( curve.IsNull() ) return false;

  const size_t iFrom = 0, iTo = eos._edges.size();

  // compute a relative length of segments
  vector< double > len( iTo-iFrom+1 );
  {
    double curLen, prevLen = len[0] = 1.0;
    for ( int i = iFrom; i < iTo; ++i )
    {
      curLen = prevLen * eos._edges[i]->_2neibors->_wgt[0] / eos._edges[i]->_2neibors->_wgt[1];
      len[i-iFrom+1] = len[i-iFrom] + curLen;
      prevLen = curLen;
    }
  }

  if ( curve->IsKind( STANDARD_TYPE( Geom_Line )))
  {
    if ( F.IsNull() ) // 3D
    {
      SMESH_TNodeXYZ p0( eos._edges[iFrom]->_2neibors->tgtNode(0));
      SMESH_TNodeXYZ p1( eos._edges[iTo-1]->_2neibors->tgtNode(1));
      for ( int i = iFrom; i < iTo; ++i )
      {
        double r = len[i-iFrom] / len.back();
        gp_XYZ newPos = p0 * ( 1. - r ) + p1 * r;
        eos._edges[i]->_pos.back() = newPos;
        SMDS_MeshNode* tgtNode = const_cast<SMDS_MeshNode*>( eos._edges[i]->_nodes.back() );
        tgtNode->setXYZ( newPos.X(), newPos.Y(), newPos.Z() );
        dumpMove( tgtNode );
      }
    }
    else
    {
      // gp_XY uv0 = helper.GetNodeUV( F, eos._edges[iFrom]->_2neibors->tgtNode(0));
      // gp_XY uv1 = helper.GetNodeUV( F, eos._edges[iTo-1]->_2neibors->tgtNode(1));
      _LayerEdge* e0 = eos._edges[iFrom]->_2neibors->_edges[0];
      _LayerEdge* e1 = eos._edges[iTo-1]->_2neibors->_edges[1];
      gp_XY uv0 = e0->LastUV( F, *data.GetShapeEdges( e0 ));
      gp_XY uv1 = e1->LastUV( F, *data.GetShapeEdges( e1 ));
      if ( eos._edges[iFrom]->_2neibors->tgtNode(0) ==
           eos._edges[iTo-1]->_2neibors->tgtNode(1) ) // closed edge
      {
        int iPeriodic = helper.GetPeriodicIndex();
        if ( iPeriodic == 1 || iPeriodic == 2 )
        {
          uv1.SetCoord( iPeriodic, helper.GetOtherParam( uv1.Coord( iPeriodic )));
          if ( uv0.Coord( iPeriodic ) > uv1.Coord( iPeriodic ))
            std::swap( uv0, uv1 );
        }
      }
      const gp_XY rangeUV = uv1 - uv0;
      for ( int i = iFrom; i < iTo; ++i )
      {
        double r = len[i-iFrom] / len.back();
        gp_XY newUV = uv0 + r * rangeUV;
        eos._edges[i]->_pos.back().SetCoord( newUV.X(), newUV.Y(), 0 );

        gp_Pnt newPos = surface->Value( newUV.X(), newUV.Y() );
        SMDS_MeshNode* tgtNode = const_cast<SMDS_MeshNode*>( eos._edges[i]->_nodes.back() );
        tgtNode->setXYZ( newPos.X(), newPos.Y(), newPos.Z() );
        dumpMove( tgtNode );

        SMDS_FacePosition* pos = static_cast<SMDS_FacePosition*>( tgtNode->GetPosition() );
        pos->SetUParameter( newUV.X() );
        pos->SetVParameter( newUV.Y() );
      }
    }
    return true;
  }

  if ( curve->IsKind( STANDARD_TYPE( Geom_Circle )))
  {
    Handle(Geom_Circle) circle = Handle(Geom_Circle)::DownCast( curve );
    gp_Pnt center3D = circle->Location();

    if ( F.IsNull() ) // 3D
    {
      if ( eos._edges[iFrom]->_2neibors->tgtNode(0) ==
           eos._edges[iTo-1]->_2neibors->tgtNode(1) )
        return true; // closed EDGE - nothing to do

      return false; // TODO ???
    }
    else // 2D
    {
      const gp_XY center( center3D.X(), center3D.Y() );

      _LayerEdge* e0 = eos._edges[iFrom]->_2neibors->_edges[0];
      _LayerEdge* eM = eos._edges[iFrom];
      _LayerEdge* e1 = eos._edges[iTo-1]->_2neibors->_edges[1];
      gp_XY uv0 = e0->LastUV( F, *data.GetShapeEdges( e0 ) );
      gp_XY uvM = eM->LastUV( F, *data.GetShapeEdges( eM ) );
      gp_XY uv1 = e1->LastUV( F, *data.GetShapeEdges( e1 ) );
      gp_Vec2d vec0( center, uv0 );
      gp_Vec2d vecM( center, uvM );
      gp_Vec2d vec1( center, uv1 );
      double uLast = vec0.Angle( vec1 ); // -PI - +PI
      double uMidl = vec0.Angle( vecM );
      if ( uLast * uMidl <= 0. )
        uLast += ( uMidl > 0 ? +2. : -2. ) * M_PI;
      const double radius = 0.5 * ( vec0.Magnitude() + vec1.Magnitude() );

      gp_Ax2d   axis( center, vec0 );
      gp_Circ2d circ( axis, radius );
      for ( int i = iFrom; i < iTo; ++i )
      {
        double    newU = uLast * len[i-iFrom] / len.back();
        gp_Pnt2d newUV = ElCLib::Value( newU, circ );
        eos._edges[i]->_pos.back().SetCoord( newUV.X(), newUV.Y(), 0 );

        gp_Pnt newPos = surface->Value( newUV.X(), newUV.Y() );
        SMDS_MeshNode* tgtNode = const_cast<SMDS_MeshNode*>( eos._edges[i]->_nodes.back() );
        tgtNode->setXYZ( newPos.X(), newPos.Y(), newPos.Z() );
        dumpMove( tgtNode );

        SMDS_FacePosition* pos = static_cast<SMDS_FacePosition*>( tgtNode->GetPosition() );
        pos->SetUParameter( newUV.X() );
        pos->SetVParameter( newUV.Y() );
      }
    }
    return true;
  }

  return false;
}

//================================================================================
/*!
 * \brief Modify normals of _LayerEdge's on EDGE's to avoid intersection with
 * _LayerEdge's on neighbor EDGE's
 */
//================================================================================

bool _ViscousBuilder::updateNormals( _SolidData&         data,
                                     SMESH_MesherHelper& helper,
                                     int                 stepNb )
{
  if ( stepNb > 0 )
    return updateNormalsOfConvexFaces( data, helper, stepNb );

  // make temporary quadrangles got by extrusion of
  // mesh edges along _LayerEdge._normal's

  vector< const SMDS_MeshElement* > tmpFaces;
  {
    set< SMESH_TLink > extrudedLinks; // contains target nodes
    vector< const SMDS_MeshNode*> nodes(4); // of a tmp mesh face

    dumpFunction(SMESH_Comment("makeTmpFacesOnEdges")<<data._index);
    for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
    {
      _EdgesOnShape& eos = data._edgesOnShape[ iS ];
      if ( eos.ShapeType() != TopAbs_EDGE || !eos._sWOL.IsNull() )
        continue;
      for ( size_t i = 0; i < eos._edges.size(); ++i )
      {
        _LayerEdge* edge = eos._edges[i];
        const SMDS_MeshNode* tgt1 = edge->_nodes.back();
        for ( int j = 0; j < 2; ++j ) // loop on _2NearEdges
        {
          const SMDS_MeshNode* tgt2 = edge->_2neibors->tgtNode(j);
          pair< set< SMESH_TLink >::iterator, bool > link_isnew =
            extrudedLinks.insert( SMESH_TLink( tgt1, tgt2 ));
          if ( !link_isnew.second )
          {
            extrudedLinks.erase( link_isnew.first );
            continue; // already extruded and will no more encounter
          }
          // a _LayerEdge containg tgt2
          _LayerEdge* neiborEdge = edge->_2neibors->_edges[j];

          _TmpMeshFaceOnEdge* f = new _TmpMeshFaceOnEdge( edge, neiborEdge, --_tmpFaceID );
          tmpFaces.push_back( f );

          dumpCmd(SMESH_Comment("mesh.AddFace([ ")
                  <<f->_nn[0]->GetID()<<", "<<f->_nn[1]->GetID()<<", "
                  <<f->_nn[2]->GetID()<<", "<<f->_nn[3]->GetID()<<" ])");
        }
      }
    }
    dumpFunctionEnd();
  }
  // Check if _LayerEdge's based on EDGE's intersects tmpFaces.
  // Perform two loops on _LayerEdge on EDGE's:
  // 1) to find and fix intersection
  // 2) to check that no new intersection appears as result of 1)

  SMDS_ElemIteratorPtr fIt( new SMDS_ElementVectorIterator( tmpFaces.begin(),
                                                            tmpFaces.end()));
  auto_ptr<SMESH_ElementSearcher> searcher
    ( SMESH_MeshAlgos::GetElementSearcher( *getMeshDS(), fIt ));

  // 1) Find intersections
  double dist;
  const SMDS_MeshElement* face;
  typedef map< _LayerEdge*, set< _LayerEdge*, _LayerEdgeCmp >, _LayerEdgeCmp > TLEdge2LEdgeSet;
  TLEdge2LEdgeSet edge2CloseEdge;

  const double eps = data._epsilon * data._epsilon;
  for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
  {
    _EdgesOnShape& eos = data._edgesOnShape[ iS ];
    if (( eos.ShapeType() != TopAbs_EDGE ) && 
        ( eos._sWOL.IsNull() || eos.SWOLType() != TopAbs_FACE ))
      continue;
    for ( size_t i = 0; i < eos._edges.size(); ++i )
    {
      _LayerEdge* edge = eos._edges[i];
      if ( edge->FindIntersection( *searcher, dist, eps, eos, &face ))
      {
        const _TmpMeshFaceOnEdge* f = (const _TmpMeshFaceOnEdge*) face;
        set< _LayerEdge*, _LayerEdgeCmp > & ee = edge2CloseEdge[ edge ];
        ee.insert( f->_le1 );
        ee.insert( f->_le2 );
        if ( f->_le1->IsOnEdge() && data.GetShapeEdges( f->_le1 )->_sWOL.IsNull() )
          edge2CloseEdge[ f->_le1 ].insert( edge );
        if ( f->_le2->IsOnEdge() && data.GetShapeEdges( f->_le2 )->_sWOL.IsNull() )
          edge2CloseEdge[ f->_le2 ].insert( edge );
      }
    }
  }

  // Set _LayerEdge._normal

  if ( !edge2CloseEdge.empty() )
  {
    dumpFunction(SMESH_Comment("updateNormals")<<data._index);

    set< _EdgesOnShape* > shapesToSmooth;

    // vector to store new _normal and _cosin for each edge in edge2CloseEdge
    vector< pair< _LayerEdge*, _LayerEdge > > edge2newEdge( edge2CloseEdge.size() );

    TLEdge2LEdgeSet::iterator e2ee = edge2CloseEdge.begin();
    for ( size_t iE = 0; e2ee != edge2CloseEdge.end(); ++e2ee, ++iE )
    {
      _LayerEdge* edge1 = e2ee->first;
      _LayerEdge* edge2 = 0;
      set< _LayerEdge*, _LayerEdgeCmp >& ee = e2ee->second;

      edge2newEdge[ iE ].first = NULL;

      _EdgesOnShape* eos1 = data.GetShapeEdges( edge1 );
      if ( !eos1 ) continue;

      // find EDGEs the edges reside
      // TopoDS_Edge E1, E2;
      // TopoDS_Shape S = helper.GetSubShapeByNode( edge1->_nodes[0], getMeshDS() );
      // if ( S.ShapeType() != TopAbs_EDGE )
      //   continue; // TODO: find EDGE by VERTEX
      // E1 = TopoDS::Edge( S );
      set< _LayerEdge*, _LayerEdgeCmp >::iterator eIt = ee.begin();
      for ( ; !edge2 && eIt != ee.end(); ++eIt )
      {
        if ( eos1->_sWOL == data.GetShapeEdges( *eIt  )->_sWOL )
          edge2 = *eIt;
      }
      if ( !edge2 ) continue;

      edge2newEdge[ iE ].first = edge1;
      _LayerEdge& newEdge = edge2newEdge[ iE ].second;
      // while ( E2.IsNull() && eIt != ee.end())
      // {
      //   _LayerEdge* e2 = *eIt++;
      //   TopoDS_Shape S = helper.GetSubShapeByNode( e2->_nodes[0], getMeshDS() );
      //   if ( S.ShapeType() == TopAbs_EDGE )
      //     E2 = TopoDS::Edge( S ), edge2 = e2;
      // }
      // if ( E2.IsNull() ) continue; // TODO: find EDGE by VERTEX

      // find 3 FACEs sharing 2 EDGEs

      // TopoDS_Face FF1[2], FF2[2];
      // PShapeIteratorPtr fIt = helper.GetAncestors(E1, *_mesh, TopAbs_FACE);
      // while ( fIt->more() && FF1[1].IsNull() )
      // {
      //   const TopoDS_Face *F = (const TopoDS_Face*) fIt->next();
      //   if ( helper.IsSubShape( *F, data._solid))
      //     FF1[ FF1[0].IsNull() ? 0 : 1 ] = *F;
      // }
      // fIt = helper.GetAncestors(E2, *_mesh, TopAbs_FACE);
      // while ( fIt->more() && FF2[1].IsNull())
      // {
      //   const TopoDS_Face *F = (const TopoDS_Face*) fIt->next();
      //   if ( helper.IsSubShape( *F, data._solid))
      //     FF2[ FF2[0].IsNull() ? 0 : 1 ] = *F;
      // }
      // // exclude a FACE common to E1 and E2 (put it to FFn[1] )
      // if ( FF1[0].IsSame( FF2[0]) || FF1[0].IsSame( FF2[1]))
      //   std::swap( FF1[0], FF1[1] );
      // if ( FF2[0].IsSame( FF1[0]) )
      //   std::swap( FF2[0], FF2[1] );
      // if ( FF1[0].IsNull() || FF2[0].IsNull() )
      //   continue;

      // get a new normal for edge1
      //bool ok;
      gp_Vec dir1 = edge1->_normal, dir2 = edge2->_normal;
      // if ( edge1->_cosin < 0 )
      //   dir1 = getFaceDir( FF1[0], E1, edge1->_nodes[0], helper, ok ).Normalized();
      // if ( edge2->_cosin < 0 )
      //   dir2 = getFaceDir( FF2[0], E2, edge2->_nodes[0], helper, ok ).Normalized();

      double cos1 = Abs( edge1->_cosin ), cos2 = Abs( edge2->_cosin );
      double wgt1 = ( cos1 + 0.001 ) / ( cos1 + cos2 + 0.002 );
      double wgt2 = ( cos2 + 0.001 ) / ( cos1 + cos2 + 0.002 );
      newEdge._normal = ( wgt1 * dir1 + wgt2 * dir2 ).XYZ();
      newEdge._normal.Normalize();

      // cout << edge1->_nodes[0]->GetID() << " "
      //      << edge2->_nodes[0]->GetID() << " NORM: "
      //      << newEdge._normal.X() << ", " << newEdge._normal.Y() << ", " << newEdge._normal.Z() << endl;

      // get new cosin
      if ( cos1 < theMinSmoothCosin )
      {
        newEdge._cosin = edge2->_cosin;
      }
      else if ( cos2 > theMinSmoothCosin ) // both cos1 and cos2 > theMinSmoothCosin
      {
        // gp_Vec dirInFace;
        // if ( edge1->_cosin < 0 )
        //   dirInFace = dir1;
        // else
        //   dirInFace = getFaceDir( FF1[0], E1, edge1->_nodes[0], helper, ok );
        // double angle = dirInFace.Angle( edge1->_normal ); // [0,PI]
        // edge1->SetCosin( Cos( angle ));
        //newEdge._cosin = 0; // ???????????
        newEdge._cosin = ( wgt1 * cos1 + wgt2 * cos2 ) * edge1->_cosin / cos1;
      }
      else
      {
        newEdge._cosin = edge1->_cosin;
      }

      // find shapes that need smoothing due to change of _normal
      if ( edge1->_cosin  < theMinSmoothCosin &&
           newEdge._cosin > theMinSmoothCosin )
      {
        if ( eos1->_sWOL.IsNull() )
        {
          SMDS_ElemIteratorPtr fIt = edge1->_nodes[0]->GetInverseElementIterator(SMDSAbs_Face);
          while ( fIt->more() )
            shapesToSmooth.insert( data.GetShapeEdges( fIt->next()->getshapeId() ));
          //limitStepSize( data, fIt->next(), edge1->_cosin ); // too late
        }
        else // edge1 inflates along a FACE
        {
          TopoDS_Shape V = helper.GetSubShapeByNode( edge1->_nodes[0], getMeshDS() );
          PShapeIteratorPtr eIt = helper.GetAncestors( V, *_mesh, TopAbs_EDGE );
          while ( const TopoDS_Shape* E = eIt->next() )
          {
            if ( !helper.IsSubShape( *E, /*FACE=*/eos1->_sWOL ))
              continue;
            gp_Vec edgeDir = getEdgeDir( TopoDS::Edge( *E ), TopoDS::Vertex( V ));
            double   angle = edgeDir.Angle( newEdge._normal ); // [0,PI]
            if ( angle < M_PI / 2 )
              shapesToSmooth.insert( data.GetShapeEdges( *E ));
          }
        }
      }
    }

    data.AddShapesToSmooth( shapesToSmooth );

    // Update data of edges depending on a new _normal

    for ( size_t iE = 0; iE < edge2newEdge.size(); ++iE )
    {
      _LayerEdge*   edge1 = edge2newEdge[ iE ].first;
      _LayerEdge& newEdge = edge2newEdge[ iE ].second;
      if ( !edge1 ) continue;
      _EdgesOnShape* eos1 = data.GetShapeEdges( edge1 );
      if ( !eos1 ) continue;

      edge1->_normal = newEdge._normal;
      edge1->SetCosin( newEdge._cosin );
      edge1->InvalidateStep( 1, *eos1 );
      edge1->_len = 0;
      edge1->SetNewLength( data._stepSize, *eos1, helper );
      if ( edge1->IsOnEdge() )
      {
        const SMDS_MeshNode * n1 = edge1->_2neibors->srcNode(0);
        const SMDS_MeshNode * n2 = edge1->_2neibors->srcNode(1);
        edge1->SetDataByNeighbors( n1, n2, *eos1, helper );
      }

      // Update normals and other dependent data of not intersecting _LayerEdge's
      // neighboring the intersecting ones

      if ( !edge1->_2neibors )
        continue;
      for ( int j = 0; j < 2; ++j ) // loop on 2 neighbors
      {
        _LayerEdge* neighbor = edge1->_2neibors->_edges[j];
        if ( edge2CloseEdge.count ( neighbor ))
          continue; // j-th neighbor is also intersected
        _EdgesOnShape* eos = data.GetShapeEdges( neighbor );
        if ( !eos ) continue;
        _LayerEdge* prevEdge = edge1;
        const int nbSteps = 10;
        for ( int step = nbSteps; step; --step ) // step from edge1 in j-th direction
        {
          if ( !neighbor->_2neibors )
            break; // neighbor is on VERTEX
          int iNext = 0;
          _LayerEdge* nextEdge = neighbor->_2neibors->_edges[iNext];
          if ( nextEdge == prevEdge )
            nextEdge = neighbor->_2neibors->_edges[ ++iNext ];
          double r = double(step-1)/nbSteps;
          if ( !nextEdge->_2neibors )
            r = 0.5;

          gp_XYZ newNorm = prevEdge->_normal * r + nextEdge->_normal * (1-r);
          newNorm.Normalize();

          neighbor->_normal = newNorm;
          neighbor->SetCosin( prevEdge->_cosin * r + nextEdge->_cosin * (1-r) );
          neighbor->SetDataByNeighbors( prevEdge->_nodes[0], nextEdge->_nodes[0], *eos, helper );

          neighbor->InvalidateStep( 1, *eos );
          neighbor->_len = 0;
          neighbor->SetNewLength( data._stepSize, *eos, helper );

          // goto the next neighbor
          prevEdge = neighbor;
          neighbor = nextEdge;
        }
      }
    }
    dumpFunctionEnd();
  }
  // 2) Check absence of intersections
  // TODO?

  for ( size_t i = 0 ; i < tmpFaces.size(); ++i )
    delete tmpFaces[i];

  return true;
}

//================================================================================
/*!
 * \brief Modify normals of _LayerEdge's on _ConvexFace's
 */
//================================================================================

bool _ViscousBuilder::updateNormalsOfConvexFaces( _SolidData&         data,
                                                  SMESH_MesherHelper& helper,
                                                  int                 stepNb )
{
  SMESHDS_Mesh* meshDS = helper.GetMeshDS();
  bool isOK;

  map< TGeomID, _ConvexFace >::iterator id2face = data._convexFaces.begin();
  for ( ; id2face != data._convexFaces.end(); ++id2face )
  {
    _ConvexFace & convFace = (*id2face).second;
    if ( convFace._normalsFixed )
      continue; // already fixed
    if ( convFace.CheckPrisms() )
      continue; // nothing to fix

    convFace._normalsFixed = true;

    BRepAdaptor_Surface surface ( convFace._face, false );
    BRepLProp_SLProps   surfProp( surface, 2, 1e-6 );

    // check if the convex FACE is of spherical shape

    Bnd_B3d centersBox; // bbox of centers of curvature of _LayerEdge's on VERTEXes
    Bnd_B3d nodesBox;
    gp_Pnt  center;

    map< TGeomID, _EdgesOnShape* >::iterator id2oes = convFace._subIdToEOS.begin();
    for ( ; id2oes != convFace._subIdToEOS.end(); ++id2oes )
    {
      _EdgesOnShape& eos = *(id2oes->second);
      if ( eos.ShapeType() == TopAbs_VERTEX )
      {
        _LayerEdge* ledge = eos._edges[ 0 ];
        if ( convFace.GetCenterOfCurvature( ledge, surfProp, helper, center ))
          centersBox.Add( center );
      }
      for ( size_t i = 0; i < eos._edges.size(); ++i )
        nodesBox.Add( SMESH_TNodeXYZ( eos._edges[ i ]->_nodes[0] ));
    }
    if ( centersBox.IsVoid() )
    {
      debugMsg( "Error: centersBox.IsVoid()" );
      return false;
    }
    const bool isSpherical =
      ( centersBox.SquareExtent() < 1e-6 * nodesBox.SquareExtent() );

    int nbEdges = helper.Count( convFace._face, TopAbs_EDGE, /*ignoreSame=*/false );
    vector < _CentralCurveOnEdge > centerCurves( nbEdges );

    if ( isSpherical )
    {
      // set _LayerEdge::_normal as average of all normals

      // WARNING: different density of nodes on EDGEs is not taken into account that
      // can lead to an improper new normal

      gp_XYZ avgNormal( 0,0,0 );
      nbEdges = 0;
      id2oes = convFace._subIdToEOS.begin();
      for ( ; id2oes != convFace._subIdToEOS.end(); ++id2oes )
      {
        _EdgesOnShape& eos = *(id2oes->second);
        // set data of _CentralCurveOnEdge
        if ( eos.ShapeType() == TopAbs_EDGE )
        {
          _CentralCurveOnEdge& ceCurve = centerCurves[ nbEdges++ ];
          ceCurve.SetShapes( TopoDS::Edge( eos._shape ), convFace, data, helper );
          if ( !eos._sWOL.IsNull() )
            ceCurve._adjFace.Nullify();
          else
            ceCurve._ledges.insert( ceCurve._ledges.end(),
                                    eos._edges.begin(), eos._edges.end());
        }
        // summarize normals
        for ( size_t i = 0; i < eos._edges.size(); ++i )
          avgNormal += eos._edges[ i ]->_normal;
      }
      double normSize = avgNormal.SquareModulus();
      if ( normSize < 1e-200 )
      {
        debugMsg( "updateNormalsOfConvexFaces(): zero avgNormal" );
        return false;
      }
      avgNormal /= Sqrt( normSize );

      // compute new _LayerEdge::_cosin on EDGEs
      double avgCosin = 0;
      int     nbCosin = 0;
      gp_Vec inFaceDir;
      for ( size_t iE = 0; iE < centerCurves.size(); ++iE )
      {
        _CentralCurveOnEdge& ceCurve = centerCurves[ iE ];
        if ( ceCurve._adjFace.IsNull() )
          continue;
        for ( size_t iLE = 0; iLE < ceCurve._ledges.size(); ++iLE )
        {
          const SMDS_MeshNode* node = ceCurve._ledges[ iLE ]->_nodes[0];
          inFaceDir = getFaceDir( ceCurve._adjFace, ceCurve._edge, node, helper, isOK );
          if ( isOK )
          {
            double angle = inFaceDir.Angle( avgNormal ); // [0,PI]
            ceCurve._ledges[ iLE ]->_cosin = Cos( angle );
            avgCosin += ceCurve._ledges[ iLE ]->_cosin;
            nbCosin++;
          }
        }
      }
      if ( nbCosin > 0 )
        avgCosin /= nbCosin;

      // set _LayerEdge::_normal = avgNormal
      id2oes = convFace._subIdToEOS.begin();
      for ( ; id2oes != convFace._subIdToEOS.end(); ++id2oes )
      {
        _EdgesOnShape& eos = *(id2oes->second);
        if ( eos.ShapeType() != TopAbs_EDGE )
          for ( size_t i = 0; i < eos._edges.size(); ++i )
            eos._edges[ i ]->_cosin = avgCosin;

        for ( size_t i = 0; i < eos._edges.size(); ++i )
          eos._edges[ i ]->_normal = avgNormal;
      }
    }
    else // if ( isSpherical )
    {
      // We suppose that centers of curvature at all points of the FACE
      // lie on some curve, let's call it "central curve". For all _LayerEdge's
      // having a common center of curvature we define the same new normal
      // as a sum of normals of _LayerEdge's on EDGEs among them.

      // get all centers of curvature for each EDGE

      helper.SetSubShape( convFace._face );
      _LayerEdge* vertexLEdges[2], **edgeLEdge, **edgeLEdgeEnd;

      TopExp_Explorer edgeExp( convFace._face, TopAbs_EDGE );
      for ( int iE = 0; edgeExp.More(); edgeExp.Next(), ++iE )
      {
        const TopoDS_Edge& edge = TopoDS::Edge( edgeExp.Current() );

        // set adjacent FACE
        centerCurves[ iE ].SetShapes( edge, convFace, data, helper );

        // get _LayerEdge's of the EDGE
        TGeomID edgeID = meshDS->ShapeToIndex( edge );
        _EdgesOnShape* eos = data.GetShapeEdges( edgeID );
        if ( !eos || eos->_edges.empty() )
        {
          // no _LayerEdge's on EDGE, use _LayerEdge's on VERTEXes
          for ( int iV = 0; iV < 2; ++iV )
          {
            TopoDS_Vertex v = helper.IthVertex( iV, edge );
            TGeomID     vID = meshDS->ShapeToIndex( v );
            eos = data.GetShapeEdges( vID );
            vertexLEdges[ iV ] = eos->_edges[ 0 ];
          }
          edgeLEdge    = &vertexLEdges[0];
          edgeLEdgeEnd = edgeLEdge + 2;

          centerCurves[ iE ]._adjFace.Nullify();
        }
        else
        {
          if ( ! eos->_toSmooth )
            data.SortOnEdge( edge, eos->_edges, helper );
          edgeLEdge    = &eos->_edges[ 0 ];
          edgeLEdgeEnd = edgeLEdge + eos->_edges.size();
          vertexLEdges[0] = eos->_edges.front()->_2neibors->_edges[0];
          vertexLEdges[1] = eos->_edges.back() ->_2neibors->_edges[1];

          if ( ! eos->_sWOL.IsNull() )
            centerCurves[ iE ]._adjFace.Nullify();
        }

        // Get curvature centers

        centersBox.Clear();

        if ( edgeLEdge[0]->IsOnEdge() &&
             convFace.GetCenterOfCurvature( vertexLEdges[0], surfProp, helper, center ))
        { // 1st VERTEX
          centerCurves[ iE ].Append( center, vertexLEdges[0] );
          centersBox.Add( center );
        }
        for ( ; edgeLEdge < edgeLEdgeEnd; ++edgeLEdge )
          if ( convFace.GetCenterOfCurvature( *edgeLEdge, surfProp, helper, center ))
          { // EDGE or VERTEXes
            centerCurves[ iE ].Append( center, *edgeLEdge );
            centersBox.Add( center );
          }
        if ( edgeLEdge[-1]->IsOnEdge() &&
             convFace.GetCenterOfCurvature( vertexLEdges[1], surfProp, helper, center ))
        { // 2nd VERTEX
          centerCurves[ iE ].Append( center, vertexLEdges[1] );
          centersBox.Add( center );
        }
        centerCurves[ iE ]._isDegenerated =
          ( centersBox.IsVoid() || centersBox.SquareExtent() < 1e-6 * nodesBox.SquareExtent() );

      } // loop on EDGES of convFace._face to set up data of centerCurves

      // Compute new normals for _LayerEdge's on EDGEs

      double avgCosin = 0;
      int     nbCosin = 0;
      gp_Vec inFaceDir;
      for ( size_t iE1 = 0; iE1 < centerCurves.size(); ++iE1 )
      {
        _CentralCurveOnEdge& ceCurve = centerCurves[ iE1 ];
        if ( ceCurve._isDegenerated )
          continue;
        const vector< gp_Pnt >& centers = ceCurve._curvaCenters;
        vector< gp_XYZ > &   newNormals = ceCurve._normals;
        for ( size_t iC1 = 0; iC1 < centers.size(); ++iC1 )
        {
          isOK = false;
          for ( size_t iE2 = 0; iE2 < centerCurves.size() && !isOK; ++iE2 )
          {
            if ( iE1 != iE2 )
              isOK = centerCurves[ iE2 ].FindNewNormal( centers[ iC1 ], newNormals[ iC1 ]);
          }
          if ( isOK && !ceCurve._adjFace.IsNull() )
          {
            // compute new _LayerEdge::_cosin
            const SMDS_MeshNode* node = ceCurve._ledges[ iC1 ]->_nodes[0];
            inFaceDir = getFaceDir( ceCurve._adjFace, ceCurve._edge, node, helper, isOK );
            if ( isOK )
            {
              double angle = inFaceDir.Angle( newNormals[ iC1 ] ); // [0,PI]
              ceCurve._ledges[ iC1 ]->_cosin = Cos( angle );
              avgCosin += ceCurve._ledges[ iC1 ]->_cosin;
              nbCosin++;
            }
          }
        }
      }
      // set new normals to _LayerEdge's of NOT degenerated central curves
      for ( size_t iE = 0; iE < centerCurves.size(); ++iE )
      {
        if ( centerCurves[ iE ]._isDegenerated )
          continue;
        for ( size_t iLE = 0; iLE < centerCurves[ iE ]._ledges.size(); ++iLE )
          centerCurves[ iE ]._ledges[ iLE ]->_normal = centerCurves[ iE ]._normals[ iLE ];
      }
      // set new normals to _LayerEdge's of     degenerated central curves
      for ( size_t iE = 0; iE < centerCurves.size(); ++iE )
      {
        if ( !centerCurves[ iE ]._isDegenerated ||
             centerCurves[ iE ]._ledges.size() < 3 )
          continue;
        // new normal is an average of new normals at VERTEXes that
        // was computed on non-degenerated _CentralCurveOnEdge's
        gp_XYZ newNorm = ( centerCurves[ iE ]._ledges.front()->_normal +
                           centerCurves[ iE ]._ledges.back ()->_normal );
        double sz = newNorm.Modulus();
        if ( sz < 1e-200 )
          continue;
        newNorm /= sz;
        double newCosin = ( 0.5 * centerCurves[ iE ]._ledges.front()->_cosin +
                            0.5 * centerCurves[ iE ]._ledges.back ()->_cosin );
        for ( size_t iLE = 1, nb = centerCurves[ iE ]._ledges.size() - 1; iLE < nb; ++iLE )
        {
          centerCurves[ iE ]._ledges[ iLE ]->_normal = newNorm;
          centerCurves[ iE ]._ledges[ iLE ]->_cosin  = newCosin;
        }
      }

      // Find new normals for _LayerEdge's based on FACE

      if ( nbCosin > 0 )
        avgCosin /= nbCosin;
      const TGeomID faceID = meshDS->ShapeToIndex( convFace._face );
      map< TGeomID, _EdgesOnShape* >::iterator id2oes = convFace._subIdToEOS.find( faceID );
      if ( id2oes != convFace._subIdToEOS.end() )
      {
        int iE = 0;
        gp_XYZ newNorm;
        _EdgesOnShape& eos = * ( id2oes->second );
        for ( size_t i = 0; i < eos._edges.size(); ++i )
        {
          _LayerEdge* ledge = eos._edges[ i ];
          if ( !convFace.GetCenterOfCurvature( ledge, surfProp, helper, center ))
            continue;
          for ( size_t i = 0; i < centerCurves.size(); ++i, ++iE )
          {
            iE = iE % centerCurves.size();
            if ( centerCurves[ iE ]._isDegenerated )
              continue;
            newNorm.SetCoord( 0,0,0 );
            if ( centerCurves[ iE ].FindNewNormal( center, newNorm ))
            {
              ledge->_normal = newNorm;
              ledge->_cosin  = avgCosin;
              break;
            }
          }
        }
      }

    } // not a quasi-spherical FACE

    // Update _LayerEdge's data according to a new normal

    dumpFunction(SMESH_Comment("updateNormalsOfConvexFaces")<<data._index
                 <<"_F"<<meshDS->ShapeToIndex( convFace._face ));

    id2oes = convFace._subIdToEOS.begin();
    for ( ; id2oes != convFace._subIdToEOS.end(); ++id2oes )
    {
      _EdgesOnShape& eos = * ( id2oes->second );
      for ( size_t i = 0; i < eos._edges.size(); ++i )
      {
        _LayerEdge* & ledge = eos._edges[ i ];
        double len = ledge->_len;
        ledge->InvalidateStep( stepNb + 1, eos, /*restoreLength=*/true );
        ledge->SetCosin( ledge->_cosin );
        ledge->SetNewLength( len, eos, helper );
      }

    } // loop on sub-shapes of convFace._face

    // Find FACEs adjacent to convFace._face that got necessity to smooth
    // as a result of normals modification

    set< _EdgesOnShape* > adjFacesToSmooth;
    for ( size_t iE = 0; iE < centerCurves.size(); ++iE )
    {
      if ( centerCurves[ iE ]._adjFace.IsNull() ||
           centerCurves[ iE ]._adjFaceToSmooth )
        continue;
      for ( size_t iLE = 0; iLE < centerCurves[ iE ]._ledges.size(); ++iLE )
      {
        if ( centerCurves[ iE ]._ledges[ iLE ]->_cosin > theMinSmoothCosin )
        {
          adjFacesToSmooth.insert( data.GetShapeEdges( centerCurves[ iE ]._adjFace ));
          break;
        }
      }
    }
    data.AddShapesToSmooth( adjFacesToSmooth );

    dumpFunctionEnd();


  } // loop on data._convexFaces

  return true;
}

//================================================================================
/*!
 * \brief Finds a center of curvature of a surface at a _LayerEdge
 */
//================================================================================

bool _ConvexFace::GetCenterOfCurvature( _LayerEdge*         ledge,
                                        BRepLProp_SLProps&  surfProp,
                                        SMESH_MesherHelper& helper,
                                        gp_Pnt &            center ) const
{
  gp_XY uv = helper.GetNodeUV( _face, ledge->_nodes[0] );
  surfProp.SetParameters( uv.X(), uv.Y() );
  if ( !surfProp.IsCurvatureDefined() )
    return false;

  const double oriFactor = ( _face.Orientation() == TopAbs_REVERSED ? +1. : -1. );
  double surfCurvatureMax = surfProp.MaxCurvature() * oriFactor;
  double surfCurvatureMin = surfProp.MinCurvature() * oriFactor;
  if ( surfCurvatureMin > surfCurvatureMax )
    center = surfProp.Value().Translated( surfProp.Normal().XYZ() / surfCurvatureMin * oriFactor );
  else
    center = surfProp.Value().Translated( surfProp.Normal().XYZ() / surfCurvatureMax * oriFactor );

  return true;
}

//================================================================================
/*!
 * \brief Check that prisms are not distorted
 */
//================================================================================

bool _ConvexFace::CheckPrisms() const
{
  double vol = 0;
  for ( size_t i = 0; i < _simplexTestEdges.size(); ++i )
  {
    const _LayerEdge* edge = _simplexTestEdges[i];
    SMESH_TNodeXYZ tgtXYZ( edge->_nodes.back() );
    for ( size_t j = 0; j < edge->_simplices.size(); ++j )
      if ( !edge->_simplices[j].IsForward( edge->_nodes[0], &tgtXYZ, vol ))
      {
        debugMsg( "Bad simplex of _simplexTestEdges ("
                  << " "<< edge->_nodes[0]->GetID()<< " "<< tgtXYZ._node->GetID()
                  << " "<< edge->_simplices[j]._nPrev->GetID()
                  << " "<< edge->_simplices[j]._nNext->GetID() << " )" );
        return false;
      }
  }
  return true;
}

//================================================================================
/*!
 * \brief Try to compute a new normal by interpolating normals of _LayerEdge's
 *        stored in this _CentralCurveOnEdge.
 *  \param [in] center - curvature center of a point of another _CentralCurveOnEdge.
 *  \param [in,out] newNormal - current normal at this point, to be redefined
 *  \return bool - true if succeeded.
 */
//================================================================================

bool _CentralCurveOnEdge::FindNewNormal( const gp_Pnt& center, gp_XYZ& newNormal )
{
  if ( this->_isDegenerated )
    return false;

  // find two centers the given one lies between

  for ( size_t i = 0, nb = _curvaCenters.size()-1;  i < nb;  ++i )
  {
    double sl2 = 1.001 * _segLength2[ i ];

    double d1 = center.SquareDistance( _curvaCenters[ i ]);
    if ( d1 > sl2 )
      continue;
    
    double d2 = center.SquareDistance( _curvaCenters[ i+1 ]);
    if ( d2 > sl2 || d2 + d1 < 1e-100 )
      continue;

    d1 = Sqrt( d1 );
    d2 = Sqrt( d2 );
    double r = d1 / ( d1 + d2 );
    gp_XYZ norm = (( 1. - r ) * _ledges[ i   ]->_normal +
                   (      r ) * _ledges[ i+1 ]->_normal );
    norm.Normalize();

    newNormal += norm;
    double sz = newNormal.Modulus();
    if ( sz < 1e-200 )
      break;
    newNormal /= sz;
    return true;
  }
  return false;
}

//================================================================================
/*!
 * \brief Set shape members
 */
//================================================================================

void _CentralCurveOnEdge::SetShapes( const TopoDS_Edge&  edge,
                                     const _ConvexFace&  convFace,
                                     _SolidData&         data,
                                     SMESH_MesherHelper& helper)
{
  _edge = edge;

  PShapeIteratorPtr fIt = helper.GetAncestors( edge, *helper.GetMesh(), TopAbs_FACE );
  while ( const TopoDS_Shape* F = fIt->next())
    if ( !convFace._face.IsSame( *F ))
    {
      _adjFace = TopoDS::Face( *F );
      _adjFaceToSmooth = false;
      // _adjFace already in a smoothing queue ?
      if ( _EdgesOnShape* eos = data.GetShapeEdges( _adjFace ))
        _adjFaceToSmooth = eos->_toSmooth;
      break;
    }
}

//================================================================================
/*!
 * \brief Looks for intersection of it's last segment with faces
 *  \param distance - returns shortest distance from the last node to intersection
 */
//================================================================================

bool _LayerEdge::FindIntersection( SMESH_ElementSearcher&   searcher,
                                   double &                 distance,
                                   const double&            epsilon,
                                   _EdgesOnShape&           eos,
                                   const SMDS_MeshElement** face)
{
  vector< const SMDS_MeshElement* > suspectFaces;
  double segLen;
  gp_Ax1 lastSegment = LastSegment( segLen, eos );
  searcher.GetElementsNearLine( lastSegment, SMDSAbs_Face, suspectFaces );

  bool segmentIntersected = false;
  distance = Precision::Infinite();
  int iFace = -1; // intersected face
  for ( size_t j = 0 ; j < suspectFaces.size() /*&& !segmentIntersected*/; ++j )
  {
    const SMDS_MeshElement* face = suspectFaces[j];
    if ( face->GetNodeIndex( _nodes.back() ) >= 0 ||
         face->GetNodeIndex( _nodes[0]     ) >= 0 )
      continue; // face sharing _LayerEdge node
    const int nbNodes = face->NbCornerNodes();
    bool intFound = false;
    double dist;
    SMDS_MeshElement::iterator nIt = face->begin_nodes();
    if ( nbNodes == 3 )
    {
      intFound = SegTriaInter( lastSegment, *nIt++, *nIt++, *nIt++, dist, epsilon );
    }
    else
    {
      const SMDS_MeshNode* tria[3];
      tria[0] = *nIt++;
      tria[1] = *nIt++;
      for ( int n2 = 2; n2 < nbNodes && !intFound; ++n2 )
      {
        tria[2] = *nIt++;
        intFound = SegTriaInter(lastSegment, tria[0], tria[1], tria[2], dist, epsilon );
        tria[1] = tria[2];
      }
    }
    if ( intFound )
    {
      if ( dist < segLen*(1.01) && dist > -(_len*_lenFactor-segLen) )
        segmentIntersected = true;
      if ( distance > dist )
        distance = dist, iFace = j;
    }
  }
  if ( iFace != -1 && face ) *face = suspectFaces[iFace];

  if ( segmentIntersected )
  {
#ifdef __myDEBUG
    SMDS_MeshElement::iterator nIt = suspectFaces[iFace]->begin_nodes();
    gp_XYZ intP( lastSegment.Location().XYZ() + lastSegment.Direction().XYZ() * distance );
    cout << "nodes: tgt " << _nodes.back()->GetID() << " src " << _nodes[0]->GetID()
         << ", intersection with face ("
         << (*nIt++)->GetID()<<" "<< (*nIt++)->GetID()<<" "<< (*nIt++)->GetID()
         << ") at point (" << intP.X() << ", " << intP.Y() << ", " << intP.Z()
         << ") distance = " << distance - segLen<< endl;
#endif
  }

  distance -= segLen;

  return segmentIntersected;
}

//================================================================================
/*!
 * \brief Returns size and direction of the last segment
 */
//================================================================================

gp_Ax1 _LayerEdge::LastSegment(double& segLen, _EdgesOnShape& eos) const
{
  // find two non-coincident positions
  gp_XYZ orig = _pos.back();
  gp_XYZ dir;
  int iPrev = _pos.size() - 2;
  const double tol = ( _len > 0 ) ? 0.3*_len : 1e-100; // adjusted for IPAL52478 + PAL22576
  while ( iPrev >= 0 )
  {
    dir = orig - _pos[iPrev];
    if ( dir.SquareModulus() > tol*tol )
      break;
    else
      iPrev--;
  }

  // make gp_Ax1
  gp_Ax1 segDir;
  if ( iPrev < 0 )
  {
    segDir.SetLocation( SMESH_TNodeXYZ( _nodes[0] ));
    segDir.SetDirection( _normal );
    segLen = 0;
  }
  else
  {
    gp_Pnt pPrev = _pos[ iPrev ];
    if ( !eos._sWOL.IsNull() )
    {
      TopLoc_Location loc;
      if ( eos.SWOLType() == TopAbs_EDGE )
      {
        double f,l;
        Handle(Geom_Curve) curve = BRep_Tool::Curve( TopoDS::Edge( eos._sWOL ), loc, f,l);
        pPrev = curve->Value( pPrev.X() ).Transformed( loc );
      }
      else
      {
        Handle(Geom_Surface) surface = BRep_Tool::Surface( TopoDS::Face( eos._sWOL ), loc );
        pPrev = surface->Value( pPrev.X(), pPrev.Y() ).Transformed( loc );
      }
      dir = SMESH_TNodeXYZ( _nodes.back() ) - pPrev.XYZ();
    }
    segDir.SetLocation( pPrev );
    segDir.SetDirection( dir );
    segLen = dir.Modulus();
  }

  return segDir;
}

//================================================================================
/*!
 * \brief Return the last position of the target node on a FACE. 
 *  \param [in] F - the FACE this _LayerEdge is inflated along
 *  \return gp_XY - result UV
 */
//================================================================================

gp_XY _LayerEdge::LastUV( const TopoDS_Face& F, _EdgesOnShape& eos ) const
{
  if ( F.IsSame( eos._sWOL )) // F is my FACE
    return gp_XY( _pos.back().X(), _pos.back().Y() );

  if ( eos.SWOLType() != TopAbs_EDGE ) // wrong call
    return gp_XY( 1e100, 1e100 );

  // _sWOL is EDGE of F; _pos.back().X() is the last U on the EDGE
  double f, l, u = _pos.back().X();
  Handle(Geom2d_Curve) C2d = BRep_Tool::CurveOnSurface( TopoDS::Edge(eos._sWOL), F, f,l);
  if ( !C2d.IsNull() && f <= u && u <= l )
    return C2d->Value( u ).XY();

  return gp_XY( 1e100, 1e100 );
}

//================================================================================
/*!
 * \brief Test intersection of the last segment with a given triangle
 *   using Moller-Trumbore algorithm
 * Intersection is detected if distance to intersection is less than _LayerEdge._len
 */
//================================================================================

bool _LayerEdge::SegTriaInter( const gp_Ax1&        lastSegment,
                               const SMDS_MeshNode* n0,
                               const SMDS_MeshNode* n1,
                               const SMDS_MeshNode* n2,
                               double&              t,
                               const double&        EPSILON) const
{
  //const double EPSILON = 1e-6;

  const gp_Pnt& orig = lastSegment.Location();
  const gp_Dir& dir  = lastSegment.Direction();

  SMESH_TNodeXYZ vert0( n0 );
  SMESH_TNodeXYZ vert1( n1 );
  SMESH_TNodeXYZ vert2( n2 );

  /* calculate distance from vert0 to ray origin */
  gp_XYZ tvec = orig.XYZ() - vert0;

  //if ( tvec * dir > EPSILON )
    // intersected face is at back side of the temporary face this _LayerEdge belongs to
    //return false;

  gp_XYZ edge1 = vert1 - vert0;
  gp_XYZ edge2 = vert2 - vert0;

  /* begin calculating determinant - also used to calculate U parameter */
  gp_XYZ pvec = dir.XYZ() ^ edge2;

  /* if determinant is near zero, ray lies in plane of triangle */
  double det = edge1 * pvec;

  if (det > -EPSILON && det < EPSILON)
    return false;

  /* calculate U parameter and test bounds */
  double u = ( tvec * pvec ) / det;
  //if (u < 0.0 || u > 1.0)
  if (u < -EPSILON || u > 1.0 + EPSILON)
    return false;

  /* prepare to test V parameter */
  gp_XYZ qvec = tvec ^ edge1;

  /* calculate V parameter and test bounds */
  double v = (dir.XYZ() * qvec) / det;
  //if ( v < 0.0 || u + v > 1.0 )
  if ( v < -EPSILON || u + v > 1.0 + EPSILON)
    return false;

  /* calculate t, ray intersects triangle */
  t = (edge2 * qvec) / det;

  //return true;
  return t > 0.;
}

//================================================================================
/*!
 * \brief Perform smooth of _LayerEdge's based on EDGE's
 *  \retval bool - true if node has been moved
 */
//================================================================================

bool _LayerEdge::SmoothOnEdge(Handle(Geom_Surface)& surface,
                              const TopoDS_Face&    F,
                              SMESH_MesherHelper&   helper)
{
  ASSERT( IsOnEdge() );

  SMDS_MeshNode* tgtNode = const_cast<SMDS_MeshNode*>( _nodes.back() );
  SMESH_TNodeXYZ oldPos( tgtNode );
  double dist01, distNewOld;
  
  SMESH_TNodeXYZ p0( _2neibors->tgtNode(0));
  SMESH_TNodeXYZ p1( _2neibors->tgtNode(1));
  dist01 = p0.Distance( _2neibors->tgtNode(1) );

  gp_Pnt newPos = p0 * _2neibors->_wgt[0] + p1 * _2neibors->_wgt[1];
  double lenDelta = 0;
  if ( _curvature )
  {
    //lenDelta = _curvature->lenDelta( _len );
    lenDelta = _curvature->lenDeltaByDist( dist01 );
    newPos.ChangeCoord() += _normal * lenDelta;
  }

  distNewOld = newPos.Distance( oldPos );

  if ( F.IsNull() )
  {
    if ( _2neibors->_plnNorm )
    {
      // put newPos on the plane defined by source node and _plnNorm
      gp_XYZ new2src = SMESH_TNodeXYZ( _nodes[0] ) - newPos.XYZ();
      double new2srcProj = (*_2neibors->_plnNorm) * new2src;
      newPos.ChangeCoord() += (*_2neibors->_plnNorm) * new2srcProj;
    }
    tgtNode->setXYZ( newPos.X(), newPos.Y(), newPos.Z() );
    _pos.back() = newPos.XYZ();
  }
  else
  {
    tgtNode->setXYZ( newPos.X(), newPos.Y(), newPos.Z() );
    gp_XY uv( Precision::Infinite(), 0 );
    helper.CheckNodeUV( F, tgtNode, uv, 1e-10, /*force=*/true );
    _pos.back().SetCoord( uv.X(), uv.Y(), 0 );

    newPos = surface->Value( uv.X(), uv.Y() );
    tgtNode->setXYZ( newPos.X(), newPos.Y(), newPos.Z() );
  }

  // commented for IPAL0052478
  // if ( _curvature && lenDelta < 0 )
  // {
  //   gp_Pnt prevPos( _pos[ _pos.size()-2 ]);
  //   _len -= prevPos.Distance( oldPos );
  //   _len += prevPos.Distance( newPos );
  // }
  bool moved = distNewOld > dist01/50;
  //if ( moved )
  dumpMove( tgtNode ); // debug

  return moved;
}

//================================================================================
/*!
 * \brief Perform laplacian smooth in 3D of nodes inflated from FACE
 *  \retval bool - true if _tgtNode has been moved
 */
//================================================================================

int _LayerEdge::Smooth(const int step, const bool isConcaveFace, const bool findBest )
{
  if ( _simplices.size() < 2 )
    return 0; // _LayerEdge inflated along EDGE or FACE

  const gp_XYZ& curPos ( _pos.back() );
  const gp_XYZ& prevPos( _pos[ _pos.size()-2 ]);

  // quality metrics (orientation) of tetras around _tgtNode
  int nbOkBefore = 0;
  double vol, minVolBefore = 1e100;
  for ( size_t i = 0; i < _simplices.size(); ++i )
  {
    nbOkBefore += _simplices[i].IsForward( _nodes[0], &curPos, vol );
    minVolBefore = Min( minVolBefore, vol );
  }
  int nbBad = _simplices.size() - nbOkBefore;

  // compute new position for the last _pos using different _funs
  gp_XYZ newPos;
  for ( int iFun = -1; iFun < theNbSmooFuns; ++iFun )
  {
    if ( iFun < 0 )
      newPos = (this->*_smooFunction)(); // fun chosen by ChooseSmooFunction()
    else if ( _funs[ iFun ] == _smooFunction )
      continue; // _smooFunction again
    else if ( step > 0 )
      newPos = (this->*_funs[ iFun ])(); // try other smoothing fun
    else
      break; // let "easy" functions improve elements around distorted ones

    if ( _curvature )
    {
      double delta  = _curvature->lenDelta( _len );
      if ( delta > 0 )
        newPos += _normal * delta;
      else
      {
        double segLen = _normal * ( newPos - prevPos );
        if ( segLen + delta > 0 )
          newPos += _normal * delta;
      }
      // double segLenChange = _normal * ( curPos - newPos );
      // newPos += 0.5 * _normal * segLenChange;
    }

    int nbOkAfter = 0;
    double minVolAfter = 1e100;
    for ( size_t i = 0; i < _simplices.size(); ++i )
    {
      nbOkAfter += _simplices[i].IsForward( _nodes[0], &newPos, vol );
      minVolAfter = Min( minVolAfter, vol );
    }
    // get worse?
    if ( nbOkAfter < nbOkBefore )
      continue;
    if (( isConcaveFace || findBest ) &&
        ( nbOkAfter == nbOkBefore ) &&
        //( iFun > -1 || nbOkAfter < _simplices.size() ) &&
        ( minVolAfter <= minVolBefore ))
      continue;

    SMDS_MeshNode* n = const_cast< SMDS_MeshNode* >( _nodes.back() );

    // commented for IPAL0052478
    // _len -= prevPos.Distance(SMESH_TNodeXYZ( n ));
    // _len += prevPos.Distance(newPos);

    n->setXYZ( newPos.X(), newPos.Y(), newPos.Z());
    _pos.back() = newPos;
    dumpMoveComm( n, _funNames[ iFun < 0 ? smooFunID() : iFun ]);

    nbBad = _simplices.size() - nbOkAfter;

    if ( iFun > -1 )
    {
      //_smooFunction = _funs[ iFun ];
      // cout << "# " << _funNames[ iFun ] << "\t N:" << _nodes.back()->GetID()
      // << "\t nbBad: " << _simplices.size() - nbOkAfter
      // << " minVol: " << minVolAfter
      // << " " << newPos.X() << " " << newPos.Y() << " " << newPos.Z()
      // << endl;
      minVolBefore = minVolAfter;
      nbOkBefore = nbOkAfter;
      continue; // look for a better function
    }

    if ( !findBest )
      break;

  } // loop on smoothing functions

  return nbBad;
}

//================================================================================
/*!
 * \brief Chooses a smoothing technic giving a position most close to an initial one.
 *        For a correct result, _simplices must contain nodes lying on geometry.
 */
//================================================================================

void _LayerEdge::ChooseSmooFunction( const set< TGeomID >& concaveVertices,
                                     const TNode2Edge&     n2eMap)
{
  if ( _smooFunction ) return;

  // use smoothNefPolygon() near concaveVertices
  if ( !concaveVertices.empty() )
  {
    for ( size_t i = 0; i < _simplices.size(); ++i )
    {
      if ( concaveVertices.count( _simplices[i]._nPrev->getshapeId() ))
      {
        _smooFunction = _funs[ FUN_NEFPOLY ];

        // set FUN_CENTROIDAL to neighbor edges
        TNode2Edge::const_iterator n2e;
        for ( i = 0; i < _simplices.size(); ++i )
        {
          if (( _simplices[i]._nPrev->GetPosition()->GetDim() == 2 ) &&
              (( n2e = n2eMap.find( _simplices[i]._nPrev )) != n2eMap.end() ))
          {
            n2e->second->_smooFunction = _funs[ FUN_CENTROIDAL ];
          }
        }
        return;
      }
    }
    //}

    // this coice is done only if ( !concaveVertices.empty() ) for Grids/smesh/bugs_19/X1
    // where the nodes are smoothed too far along a sphere thus creating
    // inverted _simplices
    double dist[theNbSmooFuns];
    //double coef[theNbSmooFuns] = { 1., 1.2, 1.4, 1.4 };
    double coef[theNbSmooFuns] = { 1., 1., 1., 1. };

    double minDist = Precision::Infinite();
    gp_Pnt p = SMESH_TNodeXYZ( _nodes[0] );
    for ( int i = 0; i < FUN_NEFPOLY; ++i )
    {
      gp_Pnt newP = (this->*_funs[i])();
      dist[i] = p.SquareDistance( newP );
      if ( dist[i]*coef[i] < minDist )
      {
        _smooFunction = _funs[i];
        minDist = dist[i]*coef[i];
      }
    }
  }
  else
  {
    _smooFunction = _funs[ FUN_LAPLACIAN ];
  }
  // int minDim = 3;
  // for ( size_t i = 0; i < _simplices.size(); ++i )
  //   minDim = Min( minDim, _simplices[i]._nPrev->GetPosition()->GetDim() );
  // if ( minDim == 0 )
  //   _smooFunction = _funs[ FUN_CENTROIDAL ];
  // else if ( minDim == 1 )
  //   _smooFunction = _funs[ FUN_CENTROIDAL ];


  // int iMin;
  // for ( int i = 0; i < FUN_NB; ++i )
  // {
  //   //cout << dist[i] << " ";
  //   if ( _smooFunction == _funs[i] ) {
  //     iMin = i;
  //     //debugMsg( fNames[i] );
  //     break;
  //   }
  // }
  // cout << _funNames[ iMin ] << "\t N:" << _nodes.back()->GetID() << endl;
}

//================================================================================
/*!
 * \brief Returns a name of _SmooFunction
 */
//================================================================================

int _LayerEdge::smooFunID( _LayerEdge::PSmooFun fun) const
{
  if ( !fun )
    fun = _smooFunction;
  for ( int i = 0; i < theNbSmooFuns; ++i )
    if ( fun == _funs[i] )
      return i;

  return theNbSmooFuns;
}

//================================================================================
/*!
 * \brief Computes a new node position using Laplacian smoothing
 */
//================================================================================

gp_XYZ _LayerEdge::smoothLaplacian()
{
  gp_XYZ newPos (0,0,0);
  for ( size_t i = 0; i < _simplices.size(); ++i )
    newPos += SMESH_TNodeXYZ( _simplices[i]._nPrev );
  newPos /= _simplices.size();

  return newPos;
}

//================================================================================
/*!
 * \brief Computes a new node position using angular-based smoothing
 */
//================================================================================

gp_XYZ _LayerEdge::smoothAngular()
{
  vector< gp_Vec > edgeDir;  edgeDir. reserve( _simplices.size() + 1);
  vector< double > edgeSize; edgeSize.reserve( _simplices.size() );
  vector< gp_XYZ > points;   points.  reserve( _simplices.size() );

  gp_XYZ pPrev = SMESH_TNodeXYZ( _simplices.back()._nPrev );
  gp_XYZ pN( 0,0,0 );
  for ( size_t i = 0; i < _simplices.size(); ++i )
  {
    gp_XYZ p = SMESH_TNodeXYZ( _simplices[i]._nPrev );
    edgeDir.push_back( p - pPrev );
    edgeSize.push_back( edgeDir.back().Magnitude() );
    //double edgeSize = edgeDir.back().Magnitude();
    if ( edgeSize.back() < numeric_limits<double>::min() )
    {
      edgeDir.pop_back();
      edgeSize.pop_back();
    }
    else
    {
      edgeDir.back() /= edgeSize.back();
      points.push_back( p );
      pN += p;
    }
    pPrev = p;
  }
  edgeDir.push_back ( edgeDir[0] );
  edgeSize.push_back( edgeSize[0] );
  pN /= points.size();

  gp_XYZ newPos(0,0,0);
  //gp_XYZ pN = SMESH_TNodeXYZ( _nodes.back() );
  double sumSize = 0;
  for ( size_t i = 0; i < points.size(); ++i )
  {
    gp_Vec toN( pN - points[i]);
    double toNLen = toN.Magnitude();
    if ( toNLen < numeric_limits<double>::min() )
    {
      newPos += pN;
      continue;
    }
    gp_Vec bisec = edgeDir[i] + edgeDir[i+1];
    double bisecLen = bisec.SquareMagnitude();
    if ( bisecLen < numeric_limits<double>::min() )
    {
      gp_Vec norm = edgeDir[i] ^ toN;
      bisec = norm ^ edgeDir[i];
      bisecLen = bisec.SquareMagnitude();
    }
    bisecLen = Sqrt( bisecLen );
    bisec /= bisecLen;

#if 1
    //bisecLen = 1.;
    gp_XYZ pNew = ( points[i] + bisec.XYZ() * toNLen ) * bisecLen;
    sumSize += bisecLen;
#else
    gp_XYZ pNew = ( points[i] + bisec.XYZ() * toNLen ) * ( edgeSize[i] + edgeSize[i+1] );
    sumSize += ( edgeSize[i] + edgeSize[i+1] );
#endif
    newPos += pNew;
  }
  newPos /= sumSize;

  return newPos;
}

//================================================================================
/*!
 * \brief Computes a new node position using weigthed node positions
 */
//================================================================================

gp_XYZ _LayerEdge::smoothLengthWeighted()
{
  vector< double > edgeSize; edgeSize.reserve( _simplices.size() + 1);
  vector< gp_XYZ > points;   points.  reserve( _simplices.size() );

  gp_XYZ pPrev = SMESH_TNodeXYZ( _simplices.back()._nPrev );
  for ( size_t i = 0; i < _simplices.size(); ++i )
  {
    gp_XYZ p = SMESH_TNodeXYZ( _simplices[i]._nPrev );
    edgeSize.push_back( ( p - pPrev ).Modulus() );
    if ( edgeSize.back() < numeric_limits<double>::min() )
    {
      edgeSize.pop_back();
    }
    else
    {
      points.push_back( p );
    }
    pPrev = p;
  }
  edgeSize.push_back( edgeSize[0] );

  gp_XYZ newPos(0,0,0);
  double sumSize = 0;
  for ( size_t i = 0; i < points.size(); ++i )
  {
    newPos += points[i] * ( edgeSize[i] + edgeSize[i+1] );
    sumSize += edgeSize[i] + edgeSize[i+1];
  }
  newPos /= sumSize;
  return newPos;
}

//================================================================================
/*!
 * \brief Computes a new node position using angular-based smoothing
 */
//================================================================================

gp_XYZ _LayerEdge::smoothCentroidal()
{
  gp_XYZ newPos(0,0,0);
  gp_XYZ pN = SMESH_TNodeXYZ( _nodes.back() );
  double sumSize = 0;
  for ( size_t i = 0; i < _simplices.size(); ++i )
  {
    gp_XYZ p1 = SMESH_TNodeXYZ( _simplices[i]._nPrev );
    gp_XYZ p2 = SMESH_TNodeXYZ( _simplices[i]._nNext );
    gp_XYZ gc = ( pN + p1 + p2 ) / 3.;
    double size = (( p1 - pN ) ^ ( p2 - pN )).Modulus();

    sumSize += size;
    newPos += gc * size;
  }
  newPos /= sumSize;

  return newPos;
}

//================================================================================
/*!
 * \brief Computes a new node position located inside a Nef polygon
 */
//================================================================================

gp_XYZ _LayerEdge::smoothNefPolygon()
{
  gp_XYZ newPos(0,0,0);

  // get a plane to seach a solution on

  vector< gp_XYZ > vecs( _simplices.size() + 1 );
  size_t i;
  const double tol = numeric_limits<double>::min();
  gp_XYZ center(0,0,0);
  for ( i = 0; i < _simplices.size(); ++i )
  {
    vecs[i] = ( SMESH_TNodeXYZ( _simplices[i]._nNext ) -
                SMESH_TNodeXYZ( _simplices[i]._nPrev ));
    center += SMESH_TNodeXYZ( _simplices[i]._nPrev );
  }
  vecs.back() = vecs[0];
  center /= _simplices.size();

  gp_XYZ zAxis(0,0,0);
  for ( i = 0; i < _simplices.size(); ++i )
    zAxis += vecs[i] ^ vecs[i+1];

  gp_XYZ yAxis;
  for ( i = 0; i < _simplices.size(); ++i )
  {
    yAxis = vecs[i];
    if ( yAxis.SquareModulus() > tol )
      break;
  }
  gp_XYZ xAxis = yAxis ^ zAxis;
  // SMESH_TNodeXYZ p0( _simplices[0]._nPrev );
  // const double tol = 1e-6 * ( p0.Distance( _simplices[1]._nPrev ) +
  //                             p0.Distance( _simplices[2]._nPrev ));
  // gp_XYZ center = smoothLaplacian();
  // gp_XYZ xAxis, yAxis, zAxis;
  // for ( i = 0; i < _simplices.size(); ++i )
  // {
  //   xAxis = SMESH_TNodeXYZ( _simplices[i]._nPrev ) - center;
  //   if ( xAxis.SquareModulus() > tol*tol )
  //     break;
  // }
  // for ( i = 1; i < _simplices.size(); ++i )
  // {
  //   yAxis = SMESH_TNodeXYZ( _simplices[i]._nPrev ) - center;
  //   zAxis = xAxis ^ yAxis;
  //   if ( zAxis.SquareModulus() > tol*tol )
  //     break;
  // }
  // if ( i == _simplices.size() ) return newPos;

  yAxis = zAxis ^ xAxis;
  xAxis /= xAxis.Modulus();
  yAxis /= yAxis.Modulus();

  // get half-planes of _simplices

  vector< _halfPlane > halfPlns( _simplices.size() );
  int nbHP = 0;
  for ( size_t i = 0; i < _simplices.size(); ++i )
  {
    gp_XYZ OP1 = SMESH_TNodeXYZ( _simplices[i]._nPrev ) - center;
    gp_XYZ OP2 = SMESH_TNodeXYZ( _simplices[i]._nNext ) - center;
    gp_XY  p1( OP1 * xAxis, OP1 * yAxis );
    gp_XY  p2( OP2 * xAxis, OP2 * yAxis );
    gp_XY  vec12 = p2 - p1;
    double dist12 = vec12.Modulus();
    if ( dist12 < tol )
      continue;
    vec12 /= dist12;
    halfPlns[ nbHP ]._pos = p1;
    halfPlns[ nbHP ]._dir = vec12;
    halfPlns[ nbHP ]._inNorm.SetCoord( -vec12.Y(), vec12.X() );
    ++nbHP;
  }

  // intersect boundaries of half-planes, define state of intersection points
  // in relation to all half-planes and calculate internal point of a 2D polygon

  double sumLen = 0;
  gp_XY newPos2D (0,0);

  enum { UNDEF = -1, NOT_OUT, IS_OUT, NO_INT };
  typedef std::pair< gp_XY, int > TIntPntState; // coord and isOut state
  TIntPntState undefIPS( gp_XY(1e100,1e100), UNDEF );

  vector< vector< TIntPntState > > allIntPnts( nbHP );
  for ( int iHP1 = 0; iHP1 < nbHP; ++iHP1 )
  {
    vector< TIntPntState > & intPnts1 = allIntPnts[ iHP1 ];
    if ( intPnts1.empty() ) intPnts1.resize( nbHP, undefIPS );

    int iPrev = SMESH_MesherHelper::WrapIndex( iHP1 - 1, nbHP );
    int iNext = SMESH_MesherHelper::WrapIndex( iHP1 + 1, nbHP );

    int nbNotOut = 0;
    const gp_XY* segEnds[2] = { 0, 0 }; // NOT_OUT points

    for ( int iHP2 = 0; iHP2 < nbHP; ++iHP2 )
    {
      if ( iHP1 == iHP2 ) continue;

      TIntPntState & ips1 = intPnts1[ iHP2 ];
      if ( ips1.second == UNDEF )
      {
        // find an intersection point of boundaries of iHP1 and iHP2

        if ( iHP2 == iPrev ) // intersection with neighbors is known
          ips1.first = halfPlns[ iHP1 ]._pos;
        else if ( iHP2 == iNext )
          ips1.first = halfPlns[ iHP2 ]._pos;
        else if ( !halfPlns[ iHP1 ].FindInterestion( halfPlns[ iHP2 ], ips1.first ))
          ips1.second = NO_INT;

        // classify the found intersection point
        if ( ips1.second != NO_INT )
        {
          ips1.second = NOT_OUT;
          for ( int i = 0; i < nbHP && ips1.second == NOT_OUT; ++i )
            if ( i != iHP1 && i != iHP2 &&
                 halfPlns[ i ].IsOut( ips1.first, tol ))
              ips1.second = IS_OUT;
        }
        vector< TIntPntState > & intPnts2 = allIntPnts[ iHP2 ];
        if ( intPnts2.empty() ) intPnts2.resize( nbHP, undefIPS );
        TIntPntState & ips2 = intPnts2[ iHP1 ];
        ips2 = ips1;
      }
      if ( ips1.second == NOT_OUT )
      {
        ++nbNotOut;
        segEnds[ bool(segEnds[0]) ] = & ips1.first;
      }
    }

    // find a NOT_OUT segment of boundary which is located between
    // two NOT_OUT int points

    if ( nbNotOut < 2 )
      continue; // no such a segment

    if ( nbNotOut > 2 )
    {
      // sort points along the boundary
      map< double, TIntPntState* > ipsByParam;
      for ( int iHP2 = 0; iHP2 < nbHP; ++iHP2 )
      {
        TIntPntState & ips1 = intPnts1[ iHP2 ];
        if ( ips1.second != NO_INT )
        {
          gp_XY     op = ips1.first - halfPlns[ iHP1 ]._pos;
          double param = op * halfPlns[ iHP1 ]._dir;
          ipsByParam.insert( make_pair( param, & ips1 ));
        }
      }
      // look for two neighboring NOT_OUT points
      nbNotOut = 0;
      map< double, TIntPntState* >::iterator u2ips = ipsByParam.begin();
      for ( ; u2ips != ipsByParam.end(); ++u2ips )
      {
        TIntPntState & ips1 = *(u2ips->second);
        if ( ips1.second == NOT_OUT )
          segEnds[ bool( nbNotOut++ ) ] = & ips1.first;
        else if ( nbNotOut >= 2 )
          break;
        else
          nbNotOut = 0;
      }
    }

    if ( nbNotOut >= 2 )
    {
      double len = ( *segEnds[0] - *segEnds[1] ).Modulus();
      sumLen += len;

      newPos2D += 0.5 * len * ( *segEnds[0] + *segEnds[1] );
    }
  }

  if ( sumLen > 0 )
  {
    newPos2D /= sumLen;
    newPos = center + xAxis * newPos2D.X() + yAxis * newPos2D.Y();
  }
  else
  {
    newPos = center;
  }

  return newPos;
}

//================================================================================
/*!
 * \brief Add a new segment to _LayerEdge during inflation
 */
//================================================================================

void _LayerEdge::SetNewLength( double len, _EdgesOnShape& eos, SMESH_MesherHelper& helper )
{
  if ( _len - len > -1e-6 )
  {
    //_pos.push_back( _pos.back() );
    return;
  }

  SMDS_MeshNode* n = const_cast< SMDS_MeshNode*>( _nodes.back() );
  gp_XYZ oldXYZ = SMESH_TNodeXYZ( n );
  gp_XYZ newXYZ;
  if ( eos._hyp.IsOffsetMethod() )
  {
    newXYZ = oldXYZ;
    gp_Vec faceNorm;
    SMDS_ElemIteratorPtr faceIt = _nodes[0]->GetInverseElementIterator( SMDSAbs_Face );
    while ( faceIt->more() )
    {
      const SMDS_MeshElement* face = faceIt->next();
      if ( !eos.GetNormal( face, faceNorm ))
        continue;

      // translate plane of a face
      gp_XYZ baryCenter = oldXYZ + faceNorm.XYZ() * ( len - _len );

      // find point of intersection of the face plane located at baryCenter
      // and _normal located at newXYZ
      double d    = -( faceNorm.XYZ() * baryCenter ); // d of plane equation ax+by+cz+d=0
      double dot  = ( faceNorm.XYZ() * _normal );
      if ( dot < std::numeric_limits<double>::min() )
        dot = ( len - _len ) * 1e-3;
      double step = -( faceNorm.XYZ() * newXYZ + d ) / dot;
      newXYZ += step * _normal;
    }
  }
  else
  {
    newXYZ = oldXYZ + _normal * ( len - _len ) * _lenFactor;
  }
  n->setXYZ( newXYZ.X(), newXYZ.Y(), newXYZ.Z() );

  _pos.push_back( newXYZ );
  _len = len;

  if ( !eos._sWOL.IsNull() )
  {
    double distXYZ[4];
    if ( eos.SWOLType() == TopAbs_EDGE )
    {
      double u = Precision::Infinite(); // to force projection w/o distance check
      helper.CheckNodeU( TopoDS::Edge( eos._sWOL ), n, u, 1e-10, /*force=*/true, distXYZ );
      _pos.back().SetCoord( u, 0, 0 );
      if ( _nodes.size() > 1 )
      {
        SMDS_EdgePosition* pos = static_cast<SMDS_EdgePosition*>( n->GetPosition() );
        pos->SetUParameter( u );
      }
    }
    else //  TopAbs_FACE
    {
      gp_XY uv( Precision::Infinite(), 0 );
      helper.CheckNodeUV( TopoDS::Face( eos._sWOL ), n, uv, 1e-10, /*force=*/true, distXYZ );
      _pos.back().SetCoord( uv.X(), uv.Y(), 0 );
      if ( _nodes.size() > 1 )
      {
        SMDS_FacePosition* pos = static_cast<SMDS_FacePosition*>( n->GetPosition() );
        pos->SetUParameter( uv.X() );
        pos->SetVParameter( uv.Y() );
      }
    }
    n->setXYZ( distXYZ[1], distXYZ[2], distXYZ[3]);
  }
  dumpMove( n ); //debug
}

//================================================================================
/*!
 * \brief Remove last inflation step
 */
//================================================================================

void _LayerEdge::InvalidateStep( int curStep, const _EdgesOnShape& eos, bool restoreLength )
{
  if ( _pos.size() > curStep )
  {
    if ( restoreLength )
      _len -= ( _pos[ curStep-1 ] - _pos.back() ).Modulus();

    _pos.resize( curStep );
    gp_Pnt nXYZ = _pos.back();
    SMDS_MeshNode* n = const_cast< SMDS_MeshNode*>( _nodes.back() );
    if ( !eos._sWOL.IsNull() )
    {
      TopLoc_Location loc;
      if ( eos.SWOLType() == TopAbs_EDGE )
      {
        SMDS_EdgePosition* pos = static_cast<SMDS_EdgePosition*>( n->GetPosition() );
        pos->SetUParameter( nXYZ.X() );
        double f,l;
        Handle(Geom_Curve) curve = BRep_Tool::Curve( TopoDS::Edge( eos._sWOL ), loc, f,l);
        nXYZ = curve->Value( nXYZ.X() ).Transformed( loc );
      }
      else
      {
        SMDS_FacePosition* pos = static_cast<SMDS_FacePosition*>( n->GetPosition() );
        pos->SetUParameter( nXYZ.X() );
        pos->SetVParameter( nXYZ.Y() );
        Handle(Geom_Surface) surface = BRep_Tool::Surface( TopoDS::Face(eos._sWOL), loc );
        nXYZ = surface->Value( nXYZ.X(), nXYZ.Y() ).Transformed( loc );
      }
    }
    n->setXYZ( nXYZ.X(), nXYZ.Y(), nXYZ.Z() );
    dumpMove( n );
  }
}

//================================================================================
/*!
 * \brief Create layers of prisms
 */
//================================================================================

bool _ViscousBuilder::refine(_SolidData& data)
{
  SMESH_MesherHelper helper( *_mesh );
  helper.SetSubShape( data._solid );
  helper.SetElementsOnShape(false);

  Handle(Geom_Curve) curve;
  Handle(Geom_Surface) surface;
  TopoDS_Edge geomEdge;
  TopoDS_Face geomFace;
  TopoDS_Shape prevSWOL;
  TopLoc_Location loc;
  double f,l, u;
  gp_XY uv;
  bool isOnEdge;
  TGeomID prevBaseId = -1;
  TNode2Edge* n2eMap = 0;
  TNode2Edge::iterator n2e;

  // Create intermediate nodes on each _LayerEdge

  for ( size_t iS = 0; iS < data._edgesOnShape.size(); ++iS )
  {
    _EdgesOnShape& eos = data._edgesOnShape[iS];
    if ( eos._edges.empty() ) continue;

    if ( eos._edges[0]->_nodes.size() < 2 )
      continue; // on _noShrinkShapes

    for ( size_t i = 0; i < eos._edges.size(); ++i )
    {
      _LayerEdge& edge = *eos._edges[i];

      // get accumulated length of segments
      vector< double > segLen( edge._pos.size() );
      segLen[0] = 0.0;
      for ( size_t j = 1; j < edge._pos.size(); ++j )
        segLen[j] = segLen[j-1] + (edge._pos[j-1] - edge._pos[j] ).Modulus();

      // allocate memory for new nodes if it is not yet refined
      const SMDS_MeshNode* tgtNode = edge._nodes.back();
      if ( edge._nodes.size() == 2 )
      {
        edge._nodes.resize( eos._hyp.GetNumberLayers() + 1, 0 );
        edge._nodes[1] = 0;
        edge._nodes.back() = tgtNode;
      }
      // get data of a shrink shape
      if ( !eos._sWOL.IsNull() && eos._sWOL != prevSWOL )
      {
        isOnEdge = ( eos.SWOLType() == TopAbs_EDGE );
        if ( isOnEdge )
        {
          geomEdge = TopoDS::Edge( eos._sWOL );
          curve    = BRep_Tool::Curve( geomEdge, loc, f,l);
        }
        else
        {
          geomFace = TopoDS::Face( eos._sWOL );
          surface  = BRep_Tool::Surface( geomFace, loc );
        }
        prevSWOL = eos._sWOL;
      }
      // restore shapePos of the last node by already treated _LayerEdge of another _SolidData
      const TGeomID baseShapeId = edge._nodes[0]->getshapeId();
      if ( baseShapeId != prevBaseId )
      {
        map< TGeomID, TNode2Edge* >::iterator s2ne = data._s2neMap.find( baseShapeId );
        n2eMap = ( s2ne == data._s2neMap.end() ) ? 0 : n2eMap = s2ne->second;
        prevBaseId = baseShapeId;
      }
      _LayerEdge* edgeOnSameNode = 0;
      if ( n2eMap && (( n2e = n2eMap->find( edge._nodes[0] )) != n2eMap->end() ))
      {
        edgeOnSameNode = n2e->second;
        const gp_XYZ& otherTgtPos = edgeOnSameNode->_pos.back();
        SMDS_PositionPtr  lastPos = tgtNode->GetPosition();
        if ( isOnEdge )
        {
          SMDS_EdgePosition* epos = static_cast<SMDS_EdgePosition*>( lastPos );
          epos->SetUParameter( otherTgtPos.X() );
        }
        else
        {
          SMDS_FacePosition* fpos = static_cast<SMDS_FacePosition*>( lastPos );
          fpos->SetUParameter( otherTgtPos.X() );
          fpos->SetVParameter( otherTgtPos.Y() );
        }
      }
      // calculate height of the first layer
      double h0;
      const double T = segLen.back(); //data._hyp.GetTotalThickness();
      const double f = eos._hyp.GetStretchFactor();
      const int    N = eos._hyp.GetNumberLayers();
      const double fPowN = pow( f, N );
      if ( fPowN - 1 <= numeric_limits<double>::min() )
        h0 = T / N;
      else
        h0 = T * ( f - 1 )/( fPowN - 1 );

      const double zeroLen = std::numeric_limits<double>::min();

      // create intermediate nodes
      double hSum = 0, hi = h0/f;
      size_t iSeg = 1;
      for ( size_t iStep = 1; iStep < edge._nodes.size(); ++iStep )
      {
        // compute an intermediate position
        hi *= f;
        hSum += hi;
        while ( hSum > segLen[iSeg] && iSeg < segLen.size()-1)
          ++iSeg;
        int iPrevSeg = iSeg-1;
        while ( fabs( segLen[iPrevSeg] - segLen[iSeg]) <= zeroLen && iPrevSeg > 0 )
          --iPrevSeg;
        double r = ( segLen[iSeg] - hSum ) / ( segLen[iSeg] - segLen[iPrevSeg] );
        gp_Pnt pos = r * edge._pos[iPrevSeg] + (1-r) * edge._pos[iSeg];

        SMDS_MeshNode*& node = const_cast< SMDS_MeshNode*& >( edge._nodes[ iStep ]);
        if ( !eos._sWOL.IsNull() )
        {
          // compute XYZ by parameters <pos>
          if ( isOnEdge )
          {
            u = pos.X();
            if ( !node )
              pos = curve->Value( u ).Transformed(loc);
          }
          else
          {
            uv.SetCoord( pos.X(), pos.Y() );
            if ( !node )
              pos = surface->Value( pos.X(), pos.Y() ).Transformed(loc);
          }
        }
        // create or update the node
        if ( !node )
        {
          node = helper.AddNode( pos.X(), pos.Y(), pos.Z());
          if ( !eos._sWOL.IsNull() )
          {
            if ( isOnEdge )
              getMeshDS()->SetNodeOnEdge( node, geomEdge, u );
            else
              getMeshDS()->SetNodeOnFace( node, geomFace, uv.X(), uv.Y() );
          }
          else
          {
            getMeshDS()->SetNodeInVolume( node, helper.GetSubShapeID() );
          }
        }
        else
        {
          if ( !eos._sWOL.IsNull() )
          {
            // make average pos from new and current parameters
            if ( isOnEdge )
            {
              u = 0.5 * ( u + helper.GetNodeU( geomEdge, node ));
              pos = curve->Value( u ).Transformed(loc);

              SMDS_EdgePosition* epos = static_cast<SMDS_EdgePosition*>( node->GetPosition() );
              epos->SetUParameter( u );
            }
            else
            {
              uv = 0.5 * ( uv + helper.GetNodeUV( geomFace, node ));
              pos = surface->Value( uv.X(), uv.Y()).Transformed(loc);

              SMDS_FacePosition* fpos = static_cast<SMDS_FacePosition*>( node->GetPosition() );
              fpos->SetUParameter( uv.X() );
              fpos->SetVParameter( uv.Y() );
            }
          }
          node->setXYZ( pos.X(), pos.Y(), pos.Z() );
        }
      } // loop on edge._nodes

      if ( !eos._sWOL.IsNull() ) // prepare for shrink()
      {
        if ( isOnEdge )
          edge._pos.back().SetCoord( u, 0,0);
        else
          edge._pos.back().SetCoord( uv.X(), uv.Y() ,0);

        if ( edgeOnSameNode )
          edgeOnSameNode->_pos.back() = edge._pos.back();
      }

    } // loop on eos._edges to create nodes


    if ( !getMeshDS()->IsEmbeddedMode() )
      // Log node movement
      for ( size_t i = 0; i < eos._edges.size(); ++i )
      {
        SMESH_TNodeXYZ p ( eos._edges[i]->_nodes.back() );
        getMeshDS()->MoveNode( p._node, p.X(), p.Y(), p.Z() );
      }
  }


  // Create volumes

  helper.SetElementsOnShape(true);

  vector< vector<const SMDS_MeshNode*>* > nnVec;
  set< vector<const SMDS_MeshNode*>* >    nnSet;
  set< int > degenEdgeInd;
  vector<const SMDS_MeshElement*> degenVols;

  TopExp_Explorer exp( data._solid, TopAbs_FACE );
  for ( ; exp.More(); exp.Next() )
  {
    const TGeomID faceID = getMeshDS()->ShapeToIndex( exp.Current() );
    if ( data._ignoreFaceIds.count( faceID ))
      continue;
    const bool isReversedFace = data._reversedFaceIds.count( faceID );
    SMESHDS_SubMesh*    fSubM = getMeshDS()->MeshElements( exp.Current() );
    SMDS_ElemIteratorPtr  fIt = fSubM->GetElements();
    while ( fIt->more() )
    {
      const SMDS_MeshElement* face = fIt->next();
      const int            nbNodes = face->NbCornerNodes();
      nnVec.resize( nbNodes );
      nnSet.clear();
      degenEdgeInd.clear();
      int nbZ = 0;
      SMDS_NodeIteratorPtr nIt = face->nodeIterator();
      for ( int iN = 0; iN < nbNodes; ++iN )
      {
        const SMDS_MeshNode* n = nIt->next();
        const int i = isReversedFace ? nbNodes-1-iN : iN;
        nnVec[ i ] = & data._n2eMap[ n ]->_nodes;
        if ( nnVec[ i ]->size() < 2 )
          degenEdgeInd.insert( iN );
        else
          nbZ = nnVec[ i ]->size();

        if ( helper.HasDegeneratedEdges() )
          nnSet.insert( nnVec[ i ]);
      }
      if ( nbZ == 0 )
        continue;
      if ( 0 < nnSet.size() && nnSet.size() < 3 )
        continue;

      switch ( nbNodes )
      {
      case 3:
        switch ( degenEdgeInd.size() )
        {
        case 0: // PENTA
        {
          for ( int iZ = 1; iZ < nbZ; ++iZ )
            helper.AddVolume( (*nnVec[0])[iZ-1], (*nnVec[1])[iZ-1], (*nnVec[2])[iZ-1],
                              (*nnVec[0])[iZ],   (*nnVec[1])[iZ],   (*nnVec[2])[iZ]);
          break;
        }
        case 1: // PYRAM
        {
          int i2 = *degenEdgeInd.begin();
          int i0 = helper.WrapIndex( i2 - 1, nbNodes );
          int i1 = helper.WrapIndex( i2 + 1, nbNodes );
          for ( int iZ = 1; iZ < nbZ; ++iZ )
            helper.AddVolume( (*nnVec[i0])[iZ-1], (*nnVec[i1])[iZ-1],
                              (*nnVec[i1])[iZ],   (*nnVec[i0])[iZ],   (*nnVec[i2])[0]);
          break;
        }
        case 2: // TETRA
        {
          int i3 = !degenEdgeInd.count(0) ? 0 : !degenEdgeInd.count(1) ? 1 : 2;
          for ( int iZ = 1; iZ < nbZ; ++iZ )
            helper.AddVolume( (*nnVec[0])[iZ-1], (*nnVec[1])[iZ-1], (*nnVec[2])[iZ-1],
                              (*nnVec[i3])[iZ]);
          break;
        }
        }
        break;

      case 4:
        switch ( degenEdgeInd.size() )
        {
        case 0: // HEX
        {
          for ( int iZ = 1; iZ < nbZ; ++iZ )
            helper.AddVolume( (*nnVec[0])[iZ-1], (*nnVec[1])[iZ-1],
                              (*nnVec[2])[iZ-1], (*nnVec[3])[iZ-1],
                              (*nnVec[0])[iZ],   (*nnVec[1])[iZ],
                              (*nnVec[2])[iZ],   (*nnVec[3])[iZ]);
          break;
        }
        case 2: // PENTA?
        {
          int i2 = *degenEdgeInd.begin();
          int i3 = *degenEdgeInd.rbegin();
          bool ok = ( i3 - i2 == 1 );
          if ( i2 == 0 && i3 == 3 ) { i2 = 3; i3 = 0; ok = true; }
          int i0 = helper.WrapIndex( i3 + 1, nbNodes );
          int i1 = helper.WrapIndex( i0 + 1, nbNodes );
          for ( int iZ = 1; iZ < nbZ; ++iZ )
          {
            const SMDS_MeshElement* vol =
              helper.AddVolume( (*nnVec[i3])[0], (*nnVec[i0])[iZ], (*nnVec[i0])[iZ-1],
                                (*nnVec[i2])[0], (*nnVec[i1])[iZ], (*nnVec[i1])[iZ-1]);
            if ( !ok && vol )
              degenVols.push_back( vol );
          }
          break;
        }
        case 3: // degen HEX
        {
          const SMDS_MeshNode* nn[8];
          for ( int iZ = 1; iZ < nbZ; ++iZ )
          {
            const SMDS_MeshElement* vol =
              helper.AddVolume( nnVec[0]->size() > 1 ? (*nnVec[0])[iZ-1] : (*nnVec[0])[0],
                                nnVec[1]->size() > 1 ? (*nnVec[1])[iZ-1] : (*nnVec[1])[0],
                                nnVec[2]->size() > 1 ? (*nnVec[2])[iZ-1] : (*nnVec[2])[0],
                                nnVec[3]->size() > 1 ? (*nnVec[3])[iZ-1] : (*nnVec[3])[0],
                                nnVec[0]->size() > 1 ? (*nnVec[0])[iZ]   : (*nnVec[0])[0],
                                nnVec[1]->size() > 1 ? (*nnVec[1])[iZ]   : (*nnVec[1])[0],
                                nnVec[2]->size() > 1 ? (*nnVec[2])[iZ]   : (*nnVec[2])[0],
                                nnVec[3]->size() > 1 ? (*nnVec[3])[iZ]   : (*nnVec[3])[0]);
            degenVols.push_back( vol );
          }
        }
        break;
        }
        break;

      default:
        return error("Not supported type of element", data._index);

      } // switch ( nbNodes )
    } // while ( fIt->more() )
  } // loop on FACEs

  if ( !degenVols.empty() )
  {
    SMESH_ComputeErrorPtr& err = _mesh->GetSubMesh( data._solid )->GetComputeError();
    if ( !err || err->IsOK() )
    {
      err.reset( new SMESH_ComputeError( COMPERR_WARNING,
                                         "Degenerated volumes created" ));
      err->myBadElements.insert( err->myBadElements.end(),
                                 degenVols.begin(),degenVols.end() );
    }
  }

  return true;
}

//================================================================================
/*!
 * \brief Shrink 2D mesh on faces to let space for inflated layers
 */
//================================================================================

bool _ViscousBuilder::shrink()
{
  // make map of (ids of FACEs to shrink mesh on) to (_SolidData containing _LayerEdge's
  // inflated along FACE or EDGE)
  map< TGeomID, _SolidData* > f2sdMap;
  for ( size_t i = 0 ; i < _sdVec.size(); ++i )
  {
    _SolidData& data = _sdVec[i];
    TopTools_MapOfShape FFMap;
    map< TGeomID, TopoDS_Shape >::iterator s2s = data._shrinkShape2Shape.begin();
    for (; s2s != data._shrinkShape2Shape.end(); ++s2s )
      if ( s2s->second.ShapeType() == TopAbs_FACE )
      {
        f2sdMap.insert( make_pair( getMeshDS()->ShapeToIndex( s2s->second ), &data ));

        if ( FFMap.Add( (*s2s).second ))
          // Put mesh faces on the shrinked FACE to the proxy sub-mesh to avoid
          // usage of mesh faces made in addBoundaryElements() by the 3D algo or
          // by StdMeshers_QuadToTriaAdaptor
          if ( SMESHDS_SubMesh* smDS = getMeshDS()->MeshElements( s2s->second ))
          {
            SMESH_ProxyMesh::SubMesh* proxySub =
              data._proxyMesh->getFaceSubM( TopoDS::Face( s2s->second ), /*create=*/true);
            SMDS_ElemIteratorPtr fIt = smDS->GetElements();
            while ( fIt->more() )
              proxySub->AddElement( fIt->next() );
            // as a result 3D algo will use elements from proxySub and not from smDS
          }
      }
  }

  SMESH_MesherHelper helper( *_mesh );
  helper.ToFixNodeParameters( true );

  // EDGE's to shrink
  map< TGeomID, _Shrinker1D > e2shrMap;
  vector< _EdgesOnShape* > subEOS;
  vector< _LayerEdge* > lEdges;

  // loop on FACES to srink mesh on
  map< TGeomID, _SolidData* >::iterator f2sd = f2sdMap.begin();
  for ( ; f2sd != f2sdMap.end(); ++f2sd )
  {
    _SolidData&      data = *f2sd->second;
    const TopoDS_Face&  F = TopoDS::Face( getMeshDS()->IndexToShape( f2sd->first ));
    SMESH_subMesh*     sm = _mesh->GetSubMesh( F );
    SMESHDS_SubMesh* smDS = sm->GetSubMeshDS();

    Handle(Geom_Surface) surface = BRep_Tool::Surface(F);

    helper.SetSubShape(F);

    // ===========================
    // Prepare data for shrinking
    // ===========================

    // Collect nodes to smooth, as src nodes are not yet replaced by tgt ones
    // and thus all nodes on a FACE connected to 2d elements are to be smoothed
    vector < const SMDS_MeshNode* > smoothNodes;
    {
      SMDS_NodeIteratorPtr nIt = smDS->GetNodes();
      while ( nIt->more() )
      {
        const SMDS_MeshNode* n = nIt->next();
        if ( n->NbInverseElements( SMDSAbs_Face ) > 0 )
          smoothNodes.push_back( n );
      }
    }
    // Find out face orientation
    double refSign = 1;
    const set<TGeomID> ignoreShapes;
    bool isOkUV;
    if ( !smoothNodes.empty() )
    {
      vector<_Simplex> simplices;
      _Simplex::GetSimplices( smoothNodes[0], simplices, ignoreShapes );
      helper.GetNodeUV( F, simplices[0]._nPrev, 0, &isOkUV ); // fix UV of silpmex nodes
      helper.GetNodeUV( F, simplices[0]._nNext, 0, &isOkUV );
      gp_XY uv = helper.GetNodeUV( F, smoothNodes[0], 0, &isOkUV );
      if ( !simplices[0].IsForward(uv, smoothNodes[0], F, helper,refSign) )
        refSign = -1;
    }

    // Find _LayerEdge's inflated along F
    subEOS.clear();
    lEdges.clear();
    {
      SMESH_subMeshIteratorPtr subIt = sm->getDependsOnIterator(/*includeSelf=*/false);
      while ( subIt->more() )
      {
        const TGeomID subID = subIt->next()->GetId();
        if ( data._noShrinkShapes.count( subID ))
          continue;
        _EdgesOnShape* eos = data.GetShapeEdges( subID );
        if ( !eos || eos->_sWOL.IsNull() ) continue;

        subEOS.push_back( eos );

        for ( size_t i = 0; i < eos->_edges.size(); ++i )
        {
          lEdges.push_back( eos->_edges[ i ] );
          prepareEdgeToShrink( *eos->_edges[ i ], *eos, helper, smDS );
        }
      }
    }

    dumpFunction(SMESH_Comment("beforeShrinkFace")<<f2sd->first); // debug
    SMDS_ElemIteratorPtr fIt = smDS->GetElements();
    while ( fIt->more() )
      if ( const SMDS_MeshElement* f = fIt->next() )
        dumpChangeNodes( f );
    dumpFunctionEnd();

    // Replace source nodes by target nodes in mesh faces to shrink
    dumpFunction(SMESH_Comment("replNodesOnFace")<<f2sd->first); // debug
    const SMDS_MeshNode* nodes[20];
    for ( size_t iS = 0; iS < subEOS.size(); ++iS )
    {
      _EdgesOnShape& eos = * subEOS[ iS ];
      for ( size_t i = 0; i < eos._edges.size(); ++i )
      {
        _LayerEdge& edge = *eos._edges[i];
        const SMDS_MeshNode* srcNode = edge._nodes[0];
        const SMDS_MeshNode* tgtNode = edge._nodes.back();
        SMDS_ElemIteratorPtr fIt = srcNode->GetInverseElementIterator(SMDSAbs_Face);
        while ( fIt->more() )
        {
          const SMDS_MeshElement* f = fIt->next();
          if ( !smDS->Contains( f ))
            continue;
          SMDS_NodeIteratorPtr nIt = f->nodeIterator();
          for ( int iN = 0; nIt->more(); ++iN )
          {
            const SMDS_MeshNode* n = nIt->next();
            nodes[iN] = ( n == srcNode ? tgtNode : n );
          }
          helper.GetMeshDS()->ChangeElementNodes( f, nodes, f->NbNodes() );
          dumpChangeNodes( f );
        }
      }
    }
    dumpFunctionEnd();

    // find out if a FACE is concave
    const bool isConcaveFace = isConcave( F, helper );

    // Create _SmoothNode's on face F
    vector< _SmoothNode > nodesToSmooth( smoothNodes.size() );
    {
      dumpFunction(SMESH_Comment("fixUVOnFace")<<f2sd->first); // debug
      const bool sortSimplices = isConcaveFace;
      for ( size_t i = 0; i < smoothNodes.size(); ++i )
      {
        const SMDS_MeshNode* n = smoothNodes[i];
        nodesToSmooth[ i ]._node = n;
        // src nodes must be replaced by tgt nodes to have tgt nodes in _simplices
        _Simplex::GetSimplices( n, nodesToSmooth[ i ]._simplices, ignoreShapes, 0, sortSimplices);
        // fix up incorrect uv of nodes on the FACE
        helper.GetNodeUV( F, n, 0, &isOkUV);
        dumpMove( n );
      }
      dumpFunctionEnd();
    }
    //if ( nodesToSmooth.empty() ) continue;

    // Find EDGE's to shrink and set simpices to LayerEdge's
    set< _Shrinker1D* > eShri1D;
    {
      for ( size_t iS = 0; iS < subEOS.size(); ++iS )
      {
        _EdgesOnShape& eos = * subEOS[ iS ];
        if ( eos.SWOLType() == TopAbs_EDGE )
        {
          SMESH_subMesh* edgeSM = _mesh->GetSubMesh( eos._sWOL );
          _Shrinker1D& srinker  = e2shrMap[ edgeSM->GetId() ];
          eShri1D.insert( & srinker );
          srinker.AddEdge( eos._edges[0], eos, helper );
          VISCOUS_3D::ToClearSubWithMain( edgeSM, data._solid );
          // restore params of nodes on EGDE if the EDGE has been already
          // srinked while srinking other FACE
          srinker.RestoreParams();
        }
        for ( size_t i = 0; i < eos._edges.size(); ++i )
        {
          _LayerEdge& edge = * eos._edges[i];
          _Simplex::GetSimplices( /*tgtNode=*/edge._nodes.back(), edge._simplices, ignoreShapes );
        }
      }
    }

    bool toFixTria = false; // to improve quality of trias by diagonal swap
    if ( isConcaveFace )
    {
      const bool hasTria = _mesh->NbTriangles(), hasQuad = _mesh->NbQuadrangles();
      if ( hasTria != hasQuad ) {
        toFixTria = hasTria;
      }
      else {
        set<int> nbNodesSet;
        SMDS_ElemIteratorPtr fIt = smDS->GetElements();
        while ( fIt->more() && nbNodesSet.size() < 2 )
          nbNodesSet.insert( fIt->next()->NbCornerNodes() );
        toFixTria = ( *nbNodesSet.begin() == 3 );
      }
    }

    // ==================
    // Perform shrinking
    // ==================

    bool shrinked = true;
    int badNb, shriStep=0, smooStep=0;
    _SmoothNode::SmoothType smoothType
      = isConcaveFace ? _SmoothNode::ANGULAR : _SmoothNode::LAPLACIAN;
    while ( shrinked )
    {
      shriStep++;
      // Move boundary nodes (actually just set new UV)
      // -----------------------------------------------
      dumpFunction(SMESH_Comment("moveBoundaryOnF")<<f2sd->first<<"_st"<<shriStep ); // debug
      shrinked = false;
      for ( size_t iS = 0; iS < subEOS.size(); ++iS )
      {
        _EdgesOnShape& eos = * subEOS[ iS ];
        for ( size_t i = 0; i < eos._edges.size(); ++i )
        {
          shrinked |= eos._edges[i]->SetNewLength2d( surface, F, eos, helper );
        }
      }
      dumpFunctionEnd();

      // Move nodes on EDGE's
      // (XYZ is set as soon as a needed length reached in SetNewLength2d())
      set< _Shrinker1D* >::iterator shr = eShri1D.begin();
      for ( ; shr != eShri1D.end(); ++shr )
        (*shr)->Compute( /*set3D=*/false, helper );

      // Smoothing in 2D
      // -----------------
      int nbNoImpSteps = 0;
      bool       moved = true;
      badNb = 1;
      while (( nbNoImpSteps < 5 && badNb > 0) && moved)
      {
        dumpFunction(SMESH_Comment("shrinkFace")<<f2sd->first<<"_st"<<++smooStep); // debug

        int oldBadNb = badNb;
        badNb = 0;
        moved = false;
        for ( size_t i = 0; i < nodesToSmooth.size(); ++i )
        {
          moved |= nodesToSmooth[i].Smooth( badNb, surface, helper, refSign,
                                            smoothType, /*set3D=*/isConcaveFace);
        }
        if ( badNb < oldBadNb )
          nbNoImpSteps = 0;
        else
          nbNoImpSteps++;

        dumpFunctionEnd();
      }
      if ( badNb > 0 )
        return error(SMESH_Comment("Can't shrink 2D mesh on face ") << f2sd->first );
      if ( shriStep > 200 )
        return error(SMESH_Comment("Infinite loop at shrinking 2D mesh on face ") << f2sd->first );

      // Fix narrow triangles by swapping diagonals
      // ---------------------------------------
      if ( toFixTria )
      {
        set<const SMDS_MeshNode*> usedNodes;
        fixBadFaces( F, helper, /*is2D=*/true, shriStep, & usedNodes); // swap diagonals

        // update working data
        set<const SMDS_MeshNode*>::iterator n;
        for ( size_t i = 0; i < nodesToSmooth.size() && !usedNodes.empty(); ++i )
        {
          n = usedNodes.find( nodesToSmooth[ i ]._node );
          if ( n != usedNodes.end())
          {
            _Simplex::GetSimplices( nodesToSmooth[ i ]._node,
                                    nodesToSmooth[ i ]._simplices,
                                    ignoreShapes, NULL,
                                    /*sortSimplices=*/ smoothType == _SmoothNode::ANGULAR );
            usedNodes.erase( n );
          }
        }
        for ( size_t i = 0; i < lEdges.size() && !usedNodes.empty(); ++i )
        {
          n = usedNodes.find( /*tgtNode=*/ lEdges[i]->_nodes.back() );
          if ( n != usedNodes.end())
          {
            _Simplex::GetSimplices( lEdges[i]->_nodes.back(),
                                    lEdges[i]->_simplices,
                                    ignoreShapes );
            usedNodes.erase( n );
          }
        }
      }
      // TODO: check effect of this additional smooth
      // additional laplacian smooth to increase allowed shrink step
      // for ( int st = 1; st; --st )
      // {
      //   dumpFunction(SMESH_Comment("shrinkFace")<<f2sd->first<<"_st"<<++smooStep); // debug
      //   for ( size_t i = 0; i < nodesToSmooth.size(); ++i )
      //   {
      //     nodesToSmooth[i].Smooth( badNb,surface,helper,refSign,
      //                              _SmoothNode::LAPLACIAN,/*set3D=*/false);
      //   }
      // }
    } // while ( shrinked )

    // No wrongly shaped faces remain; final smooth. Set node XYZ.
    bool isStructuredFixed = false;
    if ( SMESH_2D_Algo* algo = dynamic_cast<SMESH_2D_Algo*>( sm->GetAlgo() ))
      isStructuredFixed = algo->FixInternalNodes( *data._proxyMesh, F );
    if ( !isStructuredFixed )
    {
      if ( isConcaveFace ) // fix narrow faces by swapping diagonals
        fixBadFaces( F, helper, /*is2D=*/false, ++shriStep );

      for ( int st = 3; st; --st )
      {
        switch( st ) {
        case 1: smoothType = _SmoothNode::LAPLACIAN; break;
        case 2: smoothType = _SmoothNode::LAPLACIAN; break;
        case 3: smoothType = _SmoothNode::ANGULAR; break;
        }
        dumpFunction(SMESH_Comment("shrinkFace")<<f2sd->first<<"_st"<<++smooStep); // debug
        for ( size_t i = 0; i < nodesToSmooth.size(); ++i )
        {
          nodesToSmooth[i].Smooth( badNb,surface,helper,refSign,
                                   smoothType,/*set3D=*/st==1 );
        }
        dumpFunctionEnd();
      }
    }
    // Set an event listener to clear FACE sub-mesh together with SOLID sub-mesh
    VISCOUS_3D::ToClearSubWithMain( sm, data._solid );

    if ( !getMeshDS()->IsEmbeddedMode() )
      // Log node movement
      for ( size_t i = 0; i < nodesToSmooth.size(); ++i )
      {
        SMESH_TNodeXYZ p ( nodesToSmooth[i]._node );
        getMeshDS()->MoveNode( nodesToSmooth[i]._node, p.X(), p.Y(), p.Z() );
      }

  } // loop on FACES to srink mesh on


  // Replace source nodes by target nodes in shrinked mesh edges

  map< int, _Shrinker1D >::iterator e2shr = e2shrMap.begin();
  for ( ; e2shr != e2shrMap.end(); ++e2shr )
    e2shr->second.SwapSrcTgtNodes( getMeshDS() );

  return true;
}

//================================================================================
/*!
 * \brief Computes 2d shrink direction and finds nodes limiting shrinking
 */
//================================================================================

bool _ViscousBuilder::prepareEdgeToShrink( _LayerEdge&            edge,
                                           _EdgesOnShape&         eos,
                                           SMESH_MesherHelper&    helper,
                                           const SMESHDS_SubMesh* faceSubMesh)
{
  const SMDS_MeshNode* srcNode = edge._nodes[0];
  const SMDS_MeshNode* tgtNode = edge._nodes.back();

  if ( eos.SWOLType() == TopAbs_FACE )
  {
    gp_XY srcUV ( edge._pos[0].X(), edge._pos[0].Y() );          //helper.GetNodeUV( F, srcNode );
    gp_XY tgtUV = edge.LastUV( TopoDS::Face( eos._sWOL ), eos ); //helper.GetNodeUV( F, tgtNode );
    gp_Vec2d uvDir( srcUV, tgtUV );
    double uvLen = uvDir.Magnitude();
    uvDir /= uvLen;
    edge._normal.SetCoord( uvDir.X(),uvDir.Y(), 0 );
    edge._len = uvLen;

    edge._pos.resize(1);
    edge._pos[0].SetCoord( tgtUV.X(), tgtUV.Y(), 0 );

    // set UV of source node to target node
    SMDS_FacePosition* pos = static_cast<SMDS_FacePosition*>( tgtNode->GetPosition() );
    pos->SetUParameter( srcUV.X() );
    pos->SetVParameter( srcUV.Y() );
  }
  else // _sWOL is TopAbs_EDGE
  {
    const TopoDS_Edge&    E = TopoDS::Edge( eos._sWOL );
    SMESHDS_SubMesh* edgeSM = getMeshDS()->MeshElements( E );
    if ( !edgeSM || edgeSM->NbElements() == 0 )
      return error(SMESH_Comment("Not meshed EDGE ") << getMeshDS()->ShapeToIndex( E ));

    const SMDS_MeshNode* n2 = 0;
    SMDS_ElemIteratorPtr eIt = srcNode->GetInverseElementIterator(SMDSAbs_Edge);
    while ( eIt->more() && !n2 )
    {
      const SMDS_MeshElement* e = eIt->next();
      if ( !edgeSM->Contains(e)) continue;
      n2 = e->GetNode( 0 );
      if ( n2 == srcNode ) n2 = e->GetNode( 1 );
    }
    if ( !n2 )
      return error(SMESH_Comment("Wrongly meshed EDGE ") << getMeshDS()->ShapeToIndex( E ));

    double uSrc = helper.GetNodeU( E, srcNode, n2 );
    double uTgt = helper.GetNodeU( E, tgtNode, srcNode );
    double u2   = helper.GetNodeU( E, n2, srcNode );

    edge._pos.clear();

    if ( fabs( uSrc-uTgt ) < 0.99 * fabs( uSrc-u2 ))
    {
      // tgtNode is located so that it does not make faces with wrong orientation
      return true;
    }
    edge._pos.resize(1);
    edge._pos[0].SetCoord( U_TGT, uTgt );
    edge._pos[0].SetCoord( U_SRC, uSrc );
    edge._pos[0].SetCoord( LEN_TGT, fabs( uSrc-uTgt ));

    edge._simplices.resize( 1 );
    edge._simplices[0]._nPrev = n2;

    // set U of source node to the target node
    SMDS_EdgePosition* pos = static_cast<SMDS_EdgePosition*>( tgtNode->GetPosition() );
    pos->SetUParameter( uSrc );
  }
  return true;
}

//================================================================================
/*!
 * \brief Restore position of a sole node of a _LayerEdge based on _noShrinkShapes
 */
//================================================================================

void _ViscousBuilder::restoreNoShrink( _LayerEdge& edge ) const
{
  if ( edge._nodes.size() == 1 )
  {
    edge._pos.clear();
    edge._len = 0;

    const SMDS_MeshNode* srcNode = edge._nodes[0];
    TopoDS_Shape S = SMESH_MesherHelper::GetSubShapeByNode( srcNode, getMeshDS() );
    if ( S.IsNull() ) return;

    gp_Pnt p;

    switch ( S.ShapeType() )
    {
    case TopAbs_EDGE:
    {
      double f,l;
      TopLoc_Location loc;
      Handle(Geom_Curve) curve = BRep_Tool::Curve( TopoDS::Edge( S ), loc, f, l );
      if ( curve.IsNull() ) return;
      SMDS_EdgePosition* ePos = static_cast<SMDS_EdgePosition*>( srcNode->GetPosition() );
      p = curve->Value( ePos->GetUParameter() );
      break;
    }
    case TopAbs_VERTEX:
    {
      p = BRep_Tool::Pnt( TopoDS::Vertex( S ));
      break;
    }
    default: return;
    }
    getMeshDS()->MoveNode( srcNode, p.X(), p.Y(), p.Z() );
    dumpMove( srcNode );
  }
}

//================================================================================
/*!
 * \brief Try to fix triangles with high aspect ratio by swaping diagonals
 */
//================================================================================

void _ViscousBuilder::fixBadFaces(const TopoDS_Face&          F,
                                  SMESH_MesherHelper&         helper,
                                  const bool                  is2D,
                                  const int                   step,
                                  set<const SMDS_MeshNode*> * involvedNodes)
{
  SMESH::Controls::AspectRatio qualifier;
  SMESH::Controls::TSequenceOfXYZ points(3), points1(3), points2(3);
  const double maxAspectRatio = is2D ? 4. : 2;
  _NodeCoordHelper xyz( F, helper, is2D );

  // find bad triangles

  vector< const SMDS_MeshElement* > badTrias;
  vector< double >                  badAspects;
  SMESHDS_SubMesh*      sm = helper.GetMeshDS()->MeshElements( F );
  SMDS_ElemIteratorPtr fIt = sm->GetElements();
  while ( fIt->more() )
  {
    const SMDS_MeshElement * f = fIt->next();
    if ( f->NbCornerNodes() != 3 ) continue;
    for ( int iP = 0; iP < 3; ++iP ) points(iP+1) = xyz( f->GetNode(iP));
    double aspect = qualifier.GetValue( points );
    if ( aspect > maxAspectRatio )
    {
      badTrias.push_back( f );
      badAspects.push_back( aspect );
    }
  }
  if ( step == 1 )
  {
    dumpFunction(SMESH_Comment("beforeSwapDiagonals_F")<<helper.GetSubShapeID());
    SMDS_ElemIteratorPtr fIt = sm->GetElements();
    while ( fIt->more() )
    {
      const SMDS_MeshElement * f = fIt->next();
      if ( f->NbCornerNodes() == 3 )
        dumpChangeNodes( f );
    }
    dumpFunctionEnd();
  }
  if ( badTrias.empty() )
    return;

  // find couples of faces to swap diagonal

  typedef pair < const SMDS_MeshElement* , const SMDS_MeshElement* > T2Trias;
  vector< T2Trias > triaCouples; 

  TIDSortedElemSet involvedFaces, emptySet;
  for ( size_t iTia = 0; iTia < badTrias.size(); ++iTia )
  {
    T2Trias trias    [3];
    double  aspRatio [3];
    int i1, i2, i3;

    if ( !involvedFaces.insert( badTrias[iTia] ).second )
      continue;
    for ( int iP = 0; iP < 3; ++iP )
      points(iP+1) = xyz( badTrias[iTia]->GetNode(iP));

    // find triangles adjacent to badTrias[iTia] with better aspect ratio after diag-swaping
    int bestCouple = -1;
    for ( int iSide = 0; iSide < 3; ++iSide )
    {
      const SMDS_MeshNode* n1 = badTrias[iTia]->GetNode( iSide );
      const SMDS_MeshNode* n2 = badTrias[iTia]->GetNode(( iSide+1 ) % 3 );
      trias [iSide].first  = badTrias[iTia];
      trias [iSide].second = SMESH_MeshAlgos::FindFaceInSet( n1, n2, emptySet, involvedFaces,
                                                             & i1, & i2 );
      if (( ! trias[iSide].second ) ||
          ( trias[iSide].second->NbCornerNodes() != 3 ) ||
          ( ! sm->Contains( trias[iSide].second )))
        continue;

      // aspect ratio of an adjacent tria
      for ( int iP = 0; iP < 3; ++iP )
        points2(iP+1) = xyz( trias[iSide].second->GetNode(iP));
      double aspectInit = qualifier.GetValue( points2 );

      // arrange nodes as after diag-swaping
      if ( helper.WrapIndex( i1+1, 3 ) == i2 )
        i3 = helper.WrapIndex( i1-1, 3 );
      else
        i3 = helper.WrapIndex( i1+1, 3 );
      points1 = points;
      points1( 1+ iSide ) = points2( 1+ i3 );
      points2( 1+ i2    ) = points1( 1+ ( iSide+2 ) % 3 );

      // aspect ratio after diag-swaping
      aspRatio[ iSide ] = qualifier.GetValue( points1 ) + qualifier.GetValue( points2 );
      if ( aspRatio[ iSide ] > aspectInit + badAspects[ iTia ] )
        continue;

      // prevent inversion of a triangle
      gp_Vec norm1 = gp_Vec( points1(1), points1(3) ) ^ gp_Vec( points1(1), points1(2) );
      gp_Vec norm2 = gp_Vec( points2(1), points2(3) ) ^ gp_Vec( points2(1), points2(2) );
      if ( norm1 * norm2 < 0. && norm1.Angle( norm2 ) > 70./180.*M_PI )
        continue;

      if ( bestCouple < 0 || aspRatio[ bestCouple ] > aspRatio[ iSide ] )
        bestCouple = iSide;
    }

    if ( bestCouple >= 0 )
    {
      triaCouples.push_back( trias[bestCouple] );
      involvedFaces.insert ( trias[bestCouple].second );
    }
    else
    {
      involvedFaces.erase( badTrias[iTia] );
    }
  }
  if ( triaCouples.empty() )
    return;

  // swap diagonals

  SMESH_MeshEditor editor( helper.GetMesh() );
  dumpFunction(SMESH_Comment("beforeSwapDiagonals_F")<<helper.GetSubShapeID()<<"_"<<step);
  for ( size_t i = 0; i < triaCouples.size(); ++i )
  {
    dumpChangeNodes( triaCouples[i].first );
    dumpChangeNodes( triaCouples[i].second );
    editor.InverseDiag( triaCouples[i].first, triaCouples[i].second );
  }

  if ( involvedNodes )
    for ( size_t i = 0; i < triaCouples.size(); ++i )
    {
      involvedNodes->insert( triaCouples[i].first->begin_nodes(),
                             triaCouples[i].first->end_nodes() );
      involvedNodes->insert( triaCouples[i].second->begin_nodes(),
                             triaCouples[i].second->end_nodes() );
    }

  // just for debug dump resulting triangles
  dumpFunction(SMESH_Comment("swapDiagonals_F")<<helper.GetSubShapeID()<<"_"<<step);
  for ( size_t i = 0; i < triaCouples.size(); ++i )
  {
    dumpChangeNodes( triaCouples[i].first );
    dumpChangeNodes( triaCouples[i].second );
  }
}

//================================================================================
/*!
 * \brief Move target node to it's final position on the FACE during shrinking
 */
//================================================================================

bool _LayerEdge::SetNewLength2d( Handle(Geom_Surface)& surface,
                                 const TopoDS_Face&    F,
                                 _EdgesOnShape&        eos,
                                 SMESH_MesherHelper&   helper )
{
  if ( _pos.empty() )
    return false; // already at the target position

  SMDS_MeshNode* tgtNode = const_cast< SMDS_MeshNode*& >( _nodes.back() );

  if ( eos.SWOLType() == TopAbs_FACE )
  {
    gp_XY    curUV = helper.GetNodeUV( F, tgtNode );
    gp_Pnt2d tgtUV( _pos[0].X(), _pos[0].Y() );
    gp_Vec2d uvDir( _normal.X(), _normal.Y() );
    const double uvLen = tgtUV.Distance( curUV );
    const double kSafe = Max( 0.5, 1. - 0.1 * _simplices.size() );

    // Select shrinking step such that not to make faces with wrong orientation.
    double stepSize = 1e100;
    for ( size_t i = 0; i < _simplices.size(); ++i )
    {
      // find intersection of 2 lines: curUV-tgtUV and that connecting simplex nodes
      gp_XY uvN1 = helper.GetNodeUV( F, _simplices[i]._nPrev );
      gp_XY uvN2 = helper.GetNodeUV( F, _simplices[i]._nNext );
      gp_XY dirN = uvN2 - uvN1;
      double det = uvDir.Crossed( dirN );
      if ( Abs( det )  < std::numeric_limits<double>::min() ) continue;
      gp_XY dirN2Cur = curUV - uvN1;
      double step = dirN.Crossed( dirN2Cur ) / det;
      if ( step > 0 )
        stepSize = Min( step, stepSize );
    }
    gp_Pnt2d newUV;
    if ( uvLen <= stepSize )
    {
      newUV = tgtUV;
      _pos.clear();
    }
    else if ( stepSize > 0 )
    {
      newUV = curUV + uvDir.XY() * stepSize * kSafe;
    }
    else
    {
      return true;
    }
    SMDS_FacePosition* pos = static_cast<SMDS_FacePosition*>( tgtNode->GetPosition() );
    pos->SetUParameter( newUV.X() );
    pos->SetVParameter( newUV.Y() );

#ifdef __myDEBUG
    gp_Pnt p = surface->Value( newUV.X(), newUV.Y() );
    tgtNode->setXYZ( p.X(), p.Y(), p.Z() );
    dumpMove( tgtNode );
#endif
  }
  else // _sWOL is TopAbs_EDGE
  {
    const TopoDS_Edge&      E = TopoDS::Edge( eos._sWOL );
    const SMDS_MeshNode*   n2 = _simplices[0]._nPrev;
    SMDS_EdgePosition* tgtPos = static_cast<SMDS_EdgePosition*>( tgtNode->GetPosition() );

    const double u2     = helper.GetNodeU( E, n2, tgtNode );
    const double uSrc   = _pos[0].Coord( U_SRC );
    const double lenTgt = _pos[0].Coord( LEN_TGT );

    double newU = _pos[0].Coord( U_TGT );
    if ( lenTgt < 0.99 * fabs( uSrc-u2 )) // n2 got out of src-tgt range
    {
      _pos.clear();
    }
    else
    {
      newU = 0.1 * tgtPos->GetUParameter() + 0.9 * u2;
    }
    tgtPos->SetUParameter( newU );
#ifdef __myDEBUG
    gp_XY newUV = helper.GetNodeUV( F, tgtNode, _nodes[0]);
    gp_Pnt p = surface->Value( newUV.X(), newUV.Y() );
    tgtNode->setXYZ( p.X(), p.Y(), p.Z() );
    dumpMove( tgtNode );
#endif
  }
  return true;
}

//================================================================================
/*!
 * \brief Perform smooth on the FACE
 *  \retval bool - true if the node has been moved
 */
//================================================================================

bool _SmoothNode::Smooth(int&                  badNb,
                         Handle(Geom_Surface)& surface,
                         SMESH_MesherHelper&   helper,
                         const double          refSign,
                         SmoothType            how,
                         bool                  set3D)
{
  const TopoDS_Face& face = TopoDS::Face( helper.GetSubShape() );

  // get uv of surrounding nodes
  vector<gp_XY> uv( _simplices.size() );
  for ( size_t i = 0; i < _simplices.size(); ++i )
    uv[i] = helper.GetNodeUV( face, _simplices[i]._nPrev, _node );

  // compute new UV for the node
  gp_XY newPos (0,0);
  if ( how == TFI && _simplices.size() == 4 )
  {
    gp_XY corners[4];
    for ( size_t i = 0; i < _simplices.size(); ++i )
      if ( _simplices[i]._nOpp )
        corners[i] = helper.GetNodeUV( face, _simplices[i]._nOpp, _node );
      else
        throw SALOME_Exception(LOCALIZED("TFI smoothing: _Simplex::_nOpp not set!"));

    newPos = helper.calcTFI ( 0.5, 0.5,
                              corners[0], corners[1], corners[2], corners[3],
                              uv[1], uv[2], uv[3], uv[0] );
  }
  else if ( how == ANGULAR )
  {
    newPos = computeAngularPos( uv, helper.GetNodeUV( face, _node ), refSign );
  }
  else if ( how == CENTROIDAL && _simplices.size() > 3 )
  {
    // average centers of diagonals wieghted with their reciprocal lengths
    if ( _simplices.size() == 4 )
    {
      double w1 = 1. / ( uv[2]-uv[0] ).SquareModulus();
      double w2 = 1. / ( uv[3]-uv[1] ).SquareModulus();
      newPos = ( w1 * ( uv[2]+uv[0] ) + w2 * ( uv[3]+uv[1] )) / ( w1+w2 ) / 2;
    }
    else
    {
      double sumWeight = 0;
      int nb = _simplices.size() == 4 ? 2 : _simplices.size();
      for ( int i = 0; i < nb; ++i )
      {
        int iFrom = i + 2;
        int iTo   = i + _simplices.size() - 1;
        for ( int j = iFrom; j < iTo; ++j )
        {
          int i2 = SMESH_MesherHelper::WrapIndex( j, _simplices.size() );
          double w = 1. / ( uv[i]-uv[i2] ).SquareModulus();
          sumWeight += w;
          newPos += w * ( uv[i]+uv[i2] );
        }
      }
      newPos /= 2 * sumWeight; // 2 is to get a middle between uv's
    }
  }
  else
  {
    // Laplacian smooth
    for ( size_t i = 0; i < _simplices.size(); ++i )
      newPos += uv[i];
    newPos /= _simplices.size();
  }

  // count quality metrics (orientation) of triangles around the node
  int nbOkBefore = 0;
  gp_XY tgtUV = helper.GetNodeUV( face, _node );
  for ( size_t i = 0; i < _simplices.size(); ++i )
    nbOkBefore += _simplices[i].IsForward( tgtUV, _node, face, helper, refSign );

  int nbOkAfter = 0;
  for ( size_t i = 0; i < _simplices.size(); ++i )
    nbOkAfter += _simplices[i].IsForward( newPos, _node, face, helper, refSign );

  if ( nbOkAfter < nbOkBefore )
  {
    badNb += _simplices.size() - nbOkBefore;
    return false;
  }

  SMDS_FacePosition* pos = static_cast<SMDS_FacePosition*>( _node->GetPosition() );
  pos->SetUParameter( newPos.X() );
  pos->SetVParameter( newPos.Y() );

#ifdef __myDEBUG
  set3D = true;
#endif
  if ( set3D )
  {
    gp_Pnt p = surface->Value( newPos.X(), newPos.Y() );
    const_cast< SMDS_MeshNode* >( _node )->setXYZ( p.X(), p.Y(), p.Z() );
    dumpMove( _node );
  }

  badNb += _simplices.size() - nbOkAfter;
  return ( (tgtUV-newPos).SquareModulus() > 1e-10 );
}

//================================================================================
/*!
 * \brief Computes new UV using angle based smoothing technic
 */
//================================================================================

gp_XY _SmoothNode::computeAngularPos(vector<gp_XY>& uv,
                                     const gp_XY&   uvToFix,
                                     const double   refSign)
{
  uv.push_back( uv.front() );

  vector< gp_XY >  edgeDir ( uv.size() );
  vector< double > edgeSize( uv.size() );
  for ( size_t i = 1; i < edgeDir.size(); ++i )
  {
    edgeDir [i-1] = uv[i] - uv[i-1];
    edgeSize[i-1] = edgeDir[i-1].Modulus();
    if ( edgeSize[i-1] < numeric_limits<double>::min() )
      edgeDir[i-1].SetX( 100 );
    else
      edgeDir[i-1] /= edgeSize[i-1] * refSign;
  }
  edgeDir.back()  = edgeDir.front();
  edgeSize.back() = edgeSize.front();

  gp_XY  newPos(0,0);
  //int    nbEdges = 0;
  double sumSize = 0;
  for ( size_t i = 1; i < edgeDir.size(); ++i )
  {
    if ( edgeDir[i-1].X() > 1. ) continue;
    int i1 = i-1;
    while ( edgeDir[i].X() > 1. && ++i < edgeDir.size() );
    if ( i == edgeDir.size() ) break;
    gp_XY p = uv[i];
    gp_XY norm1( -edgeDir[i1].Y(), edgeDir[i1].X() );
    gp_XY norm2( -edgeDir[i].Y(),  edgeDir[i].X() );
    gp_XY bisec = norm1 + norm2;
    double bisecSize = bisec.Modulus();
    if ( bisecSize < numeric_limits<double>::min() )
    {
      bisec = -edgeDir[i1] + edgeDir[i];
      bisecSize = bisec.Modulus();
    }
    bisec /= bisecSize;

    gp_XY  dirToN  = uvToFix - p;
    double distToN = dirToN.Modulus();
    if ( bisec * dirToN < 0 )
      distToN = -distToN;

    newPos += ( p + bisec * distToN ) * ( edgeSize[i1] + edgeSize[i] );
    //++nbEdges;
    sumSize += edgeSize[i1] + edgeSize[i];
  }
  newPos /= /*nbEdges * */sumSize;
  return newPos;
}

//================================================================================
/*!
 * \brief Delete _SolidData
 */
//================================================================================

_SolidData::~_SolidData()
{
  TNode2Edge::iterator n2e = _n2eMap.begin();
  for ( ; n2e != _n2eMap.end(); ++n2e )
  {
    _LayerEdge* & e = n2e->second;
    if ( e && e->_2neibors )
      delete e->_2neibors;
    delete e;
    e = NULL;
  }
  _n2eMap.clear();
}
//================================================================================
/*!
 * \brief Keep a _LayerEdge inflated along the EDGE
 */
//================================================================================

void _Shrinker1D::AddEdge( const _LayerEdge*   e,
                           _EdgesOnShape&      eos,
                           SMESH_MesherHelper& helper )
{
  // init
  if ( _nodes.empty() )
  {
    _edges[0] = _edges[1] = 0;
    _done = false;
  }
  // check _LayerEdge
  if ( e == _edges[0] || e == _edges[1] )
    return;
  if ( eos.SWOLType() != TopAbs_EDGE )
    throw SALOME_Exception(LOCALIZED("Wrong _LayerEdge is added"));
  if ( _edges[0] && !_geomEdge.IsSame( eos._sWOL ))
    throw SALOME_Exception(LOCALIZED("Wrong _LayerEdge is added"));

  // store _LayerEdge
  _geomEdge = TopoDS::Edge( eos._sWOL );
  double f,l;
  BRep_Tool::Range( _geomEdge, f,l );
  double u = helper.GetNodeU( _geomEdge, e->_nodes[0], e->_nodes.back());
  _edges[ u < 0.5*(f+l) ? 0 : 1 ] = e;

  // Update _nodes

  const SMDS_MeshNode* tgtNode0 = _edges[0] ? _edges[0]->_nodes.back() : 0;
  const SMDS_MeshNode* tgtNode1 = _edges[1] ? _edges[1]->_nodes.back() : 0;

  if ( _nodes.empty() )
  {
    SMESHDS_SubMesh * eSubMesh = helper.GetMeshDS()->MeshElements( _geomEdge );
    if ( !eSubMesh || eSubMesh->NbNodes() < 1 )
      return;
    TopLoc_Location loc;
    Handle(Geom_Curve) C = BRep_Tool::Curve( _geomEdge, loc, f,l );
    GeomAdaptor_Curve aCurve(C, f,l);
    const double totLen = GCPnts_AbscissaPoint::Length(aCurve, f, l);

    int nbExpectNodes = eSubMesh->NbNodes();
    _initU  .reserve( nbExpectNodes );
    _normPar.reserve( nbExpectNodes );
    _nodes  .reserve( nbExpectNodes );
    SMDS_NodeIteratorPtr nIt = eSubMesh->GetNodes();
    while ( nIt->more() )
    {
      const SMDS_MeshNode* node = nIt->next();
      if ( node->NbInverseElements(SMDSAbs_Edge) == 0 ||
           node == tgtNode0 || node == tgtNode1 )
        continue; // refinement nodes
      _nodes.push_back( node );
      _initU.push_back( helper.GetNodeU( _geomEdge, node ));
      double len = GCPnts_AbscissaPoint::Length(aCurve, f, _initU.back());
      _normPar.push_back(  len / totLen );
    }
  }
  else
  {
    // remove target node of the _LayerEdge from _nodes
    int nbFound = 0;
    for ( size_t i = 0; i < _nodes.size(); ++i )
      if ( !_nodes[i] || _nodes[i] == tgtNode0 || _nodes[i] == tgtNode1 )
        _nodes[i] = 0, nbFound++;
    if ( nbFound == _nodes.size() )
      _nodes.clear();
  }
}

//================================================================================
/*!
 * \brief Move nodes on EDGE from ends where _LayerEdge's are inflated
 */
//================================================================================

void _Shrinker1D::Compute(bool set3D, SMESH_MesherHelper& helper)
{
  if ( _done || _nodes.empty())
    return;
  const _LayerEdge* e = _edges[0];
  if ( !e ) e = _edges[1];
  if ( !e ) return;

  _done =  (( !_edges[0] || _edges[0]->_pos.empty() ) &&
            ( !_edges[1] || _edges[1]->_pos.empty() ));

  double f,l;
  if ( set3D || _done )
  {
    Handle(Geom_Curve) C = BRep_Tool::Curve(_geomEdge, f,l);
    GeomAdaptor_Curve aCurve(C, f,l);

    if ( _edges[0] )
      f = helper.GetNodeU( _geomEdge, _edges[0]->_nodes.back(), _nodes[0] );
    if ( _edges[1] )
      l = helper.GetNodeU( _geomEdge, _edges[1]->_nodes.back(), _nodes.back() );
    double totLen = GCPnts_AbscissaPoint::Length( aCurve, f, l );

    for ( size_t i = 0; i < _nodes.size(); ++i )
    {
      if ( !_nodes[i] ) continue;
      double len = totLen * _normPar[i];
      GCPnts_AbscissaPoint discret( aCurve, len, f );
      if ( !discret.IsDone() )
        return throw SALOME_Exception(LOCALIZED("GCPnts_AbscissaPoint failed"));
      double u = discret.Parameter();
      SMDS_EdgePosition* pos = static_cast<SMDS_EdgePosition*>( _nodes[i]->GetPosition() );
      pos->SetUParameter( u );
      gp_Pnt p = C->Value( u );
      const_cast< SMDS_MeshNode*>( _nodes[i] )->setXYZ( p.X(), p.Y(), p.Z() );
    }
  }
  else
  {
    BRep_Tool::Range( _geomEdge, f,l );
    if ( _edges[0] )
      f = helper.GetNodeU( _geomEdge, _edges[0]->_nodes.back(), _nodes[0] );
    if ( _edges[1] )
      l = helper.GetNodeU( _geomEdge, _edges[1]->_nodes.back(), _nodes.back() );
    
    for ( size_t i = 0; i < _nodes.size(); ++i )
    {
      if ( !_nodes[i] ) continue;
      double u = f * ( 1-_normPar[i] ) + l * _normPar[i];
      SMDS_EdgePosition* pos = static_cast<SMDS_EdgePosition*>( _nodes[i]->GetPosition() );
      pos->SetUParameter( u );
    }
  }
}

//================================================================================
/*!
 * \brief Restore initial parameters of nodes on EDGE
 */
//================================================================================

void _Shrinker1D::RestoreParams()
{
  if ( _done )
    for ( size_t i = 0; i < _nodes.size(); ++i )
    {
      if ( !_nodes[i] ) continue;
      SMDS_EdgePosition* pos = static_cast<SMDS_EdgePosition*>( _nodes[i]->GetPosition() );
      pos->SetUParameter( _initU[i] );
    }
  _done = false;
}

//================================================================================
/*!
 * \brief Replace source nodes by target nodes in shrinked mesh edges
 */
//================================================================================

void _Shrinker1D::SwapSrcTgtNodes( SMESHDS_Mesh* mesh )
{
  const SMDS_MeshNode* nodes[3];
  for ( int i = 0; i < 2; ++i )
  {
    if ( !_edges[i] ) continue;

    SMESHDS_SubMesh * eSubMesh = mesh->MeshElements( _geomEdge );
    if ( !eSubMesh ) return;
    const SMDS_MeshNode* srcNode = _edges[i]->_nodes[0];
    const SMDS_MeshNode* tgtNode = _edges[i]->_nodes.back();
    SMDS_ElemIteratorPtr eIt = srcNode->GetInverseElementIterator(SMDSAbs_Edge);
    while ( eIt->more() )
    {
      const SMDS_MeshElement* e = eIt->next();
      if ( !eSubMesh->Contains( e ))
          continue;
      SMDS_ElemIteratorPtr nIt = e->nodesIterator();
      for ( int iN = 0; iN < e->NbNodes(); ++iN )
      {
        const SMDS_MeshNode* n = static_cast<const SMDS_MeshNode*>( nIt->next() );
        nodes[iN] = ( n == srcNode ? tgtNode : n );
      }
      mesh->ChangeElementNodes( e, nodes, e->NbNodes() );
    }
  }
}

//================================================================================
/*!
 * \brief Creates 2D and 1D elements on boundaries of new prisms
 */
//================================================================================

bool _ViscousBuilder::addBoundaryElements()
{
  SMESH_MesherHelper helper( *_mesh );

  vector< const SMDS_MeshNode* > faceNodes;

  for ( size_t i = 0; i < _sdVec.size(); ++i )
  {
    _SolidData& data = _sdVec[i];
    TopTools_IndexedMapOfShape geomEdges;
    TopExp::MapShapes( data._solid, TopAbs_EDGE, geomEdges );
    for ( int iE = 1; iE <= geomEdges.Extent(); ++iE )
    {
      const TopoDS_Edge& E = TopoDS::Edge( geomEdges(iE));
      if ( data._noShrinkShapes.count( getMeshDS()->ShapeToIndex( E )))
        continue;

      // Get _LayerEdge's based on E

      map< double, const SMDS_MeshNode* > u2nodes;
      if ( !SMESH_Algo::GetSortedNodesOnEdge( getMeshDS(), E, /*ignoreMedium=*/false, u2nodes))
        continue;

      vector< _LayerEdge* > ledges; ledges.reserve( u2nodes.size() );
      TNode2Edge & n2eMap = data._n2eMap;
      map< double, const SMDS_MeshNode* >::iterator u2n = u2nodes.begin();
      {
        //check if 2D elements are needed on E
        TNode2Edge::iterator n2e = n2eMap.find( u2n->second );
        if ( n2e == n2eMap.end() ) continue; // no layers on vertex
        ledges.push_back( n2e->second );
        u2n++;
        if (( n2e = n2eMap.find( u2n->second )) == n2eMap.end() )
          continue; // no layers on E
        ledges.push_back( n2eMap[ u2n->second ]);

        const SMDS_MeshNode* tgtN0 = ledges[0]->_nodes.back();
        const SMDS_MeshNode* tgtN1 = ledges[1]->_nodes.back();
        int nbSharedPyram = 0;
        SMDS_ElemIteratorPtr vIt = tgtN0->GetInverseElementIterator(SMDSAbs_Volume);
        while ( vIt->more() )
        {
          const SMDS_MeshElement* v = vIt->next();
          nbSharedPyram += int( v->GetNodeIndex( tgtN1 ) >= 0 );
        }
        if ( nbSharedPyram > 1 )
          continue; // not free border of the pyramid

        faceNodes.clear();
        faceNodes.push_back( ledges[0]->_nodes[0] );
        faceNodes.push_back( ledges[1]->_nodes[0] );
        if ( ledges[0]->_nodes.size() > 1 ) faceNodes.push_back( ledges[0]->_nodes[1] );
        if ( ledges[1]->_nodes.size() > 1 ) faceNodes.push_back( ledges[1]->_nodes[1] );

        if ( getMeshDS()->FindElement( faceNodes, SMDSAbs_Face, /*noMedium=*/true))
          continue; // faces already created
      }
      for ( ++u2n; u2n != u2nodes.end(); ++u2n )
        ledges.push_back( n2eMap[ u2n->second ]);

      // Find out orientation and type of face to create

      bool reverse = false, isOnFace;
      
      map< TGeomID, TopoDS_Shape >::iterator e2f =
        data._shrinkShape2Shape.find( getMeshDS()->ShapeToIndex( E ));
      TopoDS_Shape F;
      if (( isOnFace = ( e2f != data._shrinkShape2Shape.end() )))
      {
        F = e2f->second.Oriented( TopAbs_FORWARD );
        reverse = ( helper.GetSubShapeOri( F, E ) == TopAbs_REVERSED );
        if ( helper.GetSubShapeOri( data._solid, F ) == TopAbs_REVERSED )
          reverse = !reverse, F.Reverse();
        if ( helper.IsReversedSubMesh( TopoDS::Face(F) ))
          reverse = !reverse;
      }
      else
      {
        // find FACE with layers sharing E
        PShapeIteratorPtr fIt = helper.GetAncestors( E, *_mesh, TopAbs_FACE );
        while ( fIt->more() && F.IsNull() )
        {
          const TopoDS_Shape* pF = fIt->next();
          if ( helper.IsSubShape( *pF, data._solid) &&
               !data._ignoreFaceIds.count( e2f->first ))
            F = *pF;
        }
      }
      // Find the sub-mesh to add new faces
      SMESHDS_SubMesh* sm = 0;
      if ( isOnFace )
        sm = getMeshDS()->MeshElements( F );
      else
        sm = data._proxyMesh->getFaceSubM( TopoDS::Face(F), /*create=*/true );
      if ( !sm )
        return error("error in addBoundaryElements()", data._index);

      // Make faces
      const int dj1 = reverse ? 0 : 1;
      const int dj2 = reverse ? 1 : 0;
      for ( size_t j = 1; j < ledges.size(); ++j )
      {
        vector< const SMDS_MeshNode*>&  nn1 = ledges[j-dj1]->_nodes;
        vector< const SMDS_MeshNode*>&  nn2 = ledges[j-dj2]->_nodes;
        if ( nn1.size() == nn2.size() )
        {
          if ( isOnFace )
            for ( size_t z = 1; z < nn1.size(); ++z )
              sm->AddElement( getMeshDS()->AddFace( nn1[z-1], nn2[z-1], nn2[z], nn1[z] ));
          else
            for ( size_t z = 1; z < nn1.size(); ++z )
              sm->AddElement( new SMDS_FaceOfNodes( nn1[z-1], nn2[z-1], nn2[z], nn1[z] ));
        }
        else if ( nn1.size() == 1 )
        {
          if ( isOnFace )
            for ( size_t z = 1; z < nn2.size(); ++z )
              sm->AddElement( getMeshDS()->AddFace( nn1[0], nn2[z-1], nn2[z] ));
          else
            for ( size_t z = 1; z < nn2.size(); ++z )
              sm->AddElement( new SMDS_FaceOfNodes( nn1[0], nn2[z-1], nn2[z] ));
        }
        else
        {
          if ( isOnFace )
            for ( size_t z = 1; z < nn1.size(); ++z )
              sm->AddElement( getMeshDS()->AddFace( nn1[z-1], nn2[0], nn1[z] ));
          else
            for ( size_t z = 1; z < nn1.size(); ++z )
              sm->AddElement( new SMDS_FaceOfNodes( nn1[z-1], nn2[0], nn2[z] ));
        }
      }

      // Make edges
      for ( int isFirst = 0; isFirst < 2; ++isFirst )
      {
        _LayerEdge* edge = isFirst ? ledges.front() : ledges.back();
        _EdgesOnShape* eos = data.GetShapeEdges( edge );
        if ( eos && eos->SWOLType() == TopAbs_EDGE )
        {
          vector< const SMDS_MeshNode*>&  nn = edge->_nodes;
          if ( nn.size() < 2 || nn[1]->GetInverseElementIterator( SMDSAbs_Edge )->more() )
            continue;
          helper.SetSubShape( eos->_sWOL );
          helper.SetElementsOnShape( true );
          for ( size_t z = 1; z < nn.size(); ++z )
            helper.AddEdge( nn[z-1], nn[z] );
        }
      }

    } // loop on EDGE's
  } // loop on _SolidData's

  return true;
}