netgen/libsrc/occ/Partition_Loop2d.cxx

#ifdef OCCGEOMETRY

//  GEOM PARTITION : partition algorithm
//
//  Copyright (C) 2003  CEA/DEN, EDF R& D
//
//
//
//  File   : Partition_Loop2d.cxx
//  Author : Benedicte MARTIN
//  Module : GEOM
//  $Header: /cvs/netgen/netgen/libsrc/occ/Partition_Loop2d.cxx,v 1.6 2008/03/31 14:20:28 wabro Exp $

//using namespace std;
#include <climits>
#include "Partition_Loop2d.ixx"

#include "utilities.h"
#include <stdio.h>

#include <BRepAdaptor_Curve2d.hxx>
#include <BRepAdaptor_Surface.hxx>
#include <BRepAlgo_AsDes.hxx>
#include <BRepAlgo_FaceRestrictor.hxx>
// #include <BRepOffset_DataMapOfShapeReal.hxx>   // V6.3
#include <BRepTopAdaptor_FClass2d.hxx>
#include <BRep_Builder.hxx>
#include <BRep_Tool.hxx>
#include <Geom2dInt_GInter.hxx>
#include <Geom2d_Curve.hxx>
#include <IntRes2d_IntersectionPoint.hxx>
#include <Precision.hxx>
#include <TColStd_MapOfInteger.hxx>
#include <TColStd_SequenceOfReal.hxx>
#include <TopExp.hxx>
#include <TopExp_Explorer.hxx>
#include <TopTools_DataMapIteratorOfDataMapOfShapeListOfShape.hxx>
#include <TopTools_DataMapIteratorOfDataMapOfShapeShape.hxx>
#include <TopTools_DataMapOfShapeInteger.hxx>
#include <TopTools_DataMapOfShapeReal.hxx>    // V6.5
#include <TopTools_DataMapOfShapeShape.hxx>
#include <TopTools_IndexedMapOfShape.hxx>
#include <TopTools_ListIteratorOfListOfShape.hxx>
#include <TopTools_MapIteratorOfMapOfShape.hxx>
#include <TopTools_MapOfOrientedShape.hxx>
#include <TopTools_MapOfShape.hxx>
#include <TopTools_SequenceOfShape.hxx>
#include <TopoDS.hxx>
#include <TopoDS_Iterator.hxx>
#include <TopoDS_Vertex.hxx>
#include <TopoDS_Wire.hxx>
#include <gp_Pnt.hxx>
#include <gp_Pnt2d.hxx>

#define PI 3.14159265358979323846

//=======================================================================
//function : Partition_Loop2d
//purpose  :
//=======================================================================

Partition_Loop2d::Partition_Loop2d()
{
}

//=======================================================================
//function : Init
//purpose  : Init with <F> the set of edges must have
//           pcurves on <F>.
//=======================================================================

void Partition_Loop2d::Init(const TopoDS_Face& F)
{
  myConstEdges.Clear();
  myNewWires  .Clear();
  myNewFaces  .Clear();
  myFace = F;
  myFaceOri = myFace.Orientation();
  myFace.Orientation( TopAbs_FORWARD );
}

//=======================================================================
//function : AddConstEdge
//purpose  : Add <E> as unique edge in the result.
//=======================================================================

void Partition_Loop2d::AddConstEdge (const TopoDS_Edge& E)
{
#ifdef DEB
  Standard_Real f,l;
  Handle(Geom2d_Curve) pc = BRep_Tool::CurveOnSurface( E, myFace, f,l);
  if (pc.IsNull()) {
    INFOS( "AddConstEdge(): EDGE W/O PCURVE on FACE");
  } else
#endif
  {
    myConstEdges.Append(E);
  }
}

void Partition_Loop2d::AddSectionEdge (const TopoDS_Edge& E)
{
#ifdef DEB
  Standard_Real f,l;
  Handle(Geom2d_Curve) pc = BRep_Tool::CurveOnSurface( E, myFace, f,l);
  if (pc.IsNull())
    pc = BRep_Tool::CurveOnSurface( E, myFace, f,l);
  gp_Vec2d Tg1;
  gp_Pnt2d PC;
  pc->D1(0.5*(f+l), PC, Tg1);
  if (Tg1.Magnitude()  <= gp::Resolution()) {
    MESSAGE ("");
  }
  if (pc.IsNull()) {
    INFOS( "AddConstEdge(): EDGE W/O PCURVE on FACE");
  } else
#endif
  {
    myConstEdges.Append(E);
    myConstEdges.Append(E.Reversed());
    mySectionEdges.Add( E );
  }
}

//=======================================================================
//function : preciseU
//purpose  : find u such that the 3D point on theE is just out of tolerance
//           of theV
//=======================================================================

static Standard_Real preciseU (const BRepAdaptor_Surface&  theSurf,
                               const TopoDS_Edge&          theE,
                               const TopoDS_Vertex&        theV,
                               const Handle(Geom2d_Curve)& theC,
                               const Standard_Boolean      theFirstEnd)
{
  Standard_Boolean isForward = ( theE.Orientation () == TopAbs_FORWARD );
  if (theFirstEnd) isForward = !isForward;

  // find the first point in 2d and 3d
  Standard_Real f,l;
  BRep_Tool::Range( theE, f, l );
  Standard_Real u0 = isForward ? l : f;
  gp_Pnt2d aP2d0 = theC->Value( u0 );
  gp_Pnt aPnt0 = theSurf.Value( aP2d0.X(), aP2d0.Y() );

  // shift in 2d and 3d
  Standard_Real du = ( l - f ) / 100, du3d = 0;
  if (isForward)
    du = -du;

  // target parameter
  Standard_Real u;

  while (du3d < ::RealSmall())
  {
    // u for test
    u = u0 + du;
    du *= 10; // for the next iteration: increase du untill du3d is large enough

    // find out how u is far from u0 in 3D
    gp_Pnt2d aP2d  = theC->Value( u );
    gp_Pnt aPnt  = theSurf.Value( aP2d.X(), aP2d.Y() );
    du3d = aPnt0.Distance( aPnt );
  }

  // find u such that the 3D point is just out of tolerance of theV
  Standard_Real tolV = BRep_Tool::Tolerance( theV ) + Precision::Confusion();
  u = u0 + du * tolV / du3d;

  // check that u is within the range
  if ( isForward ? (u < f) : (u > l) )
    u = u0 + du;

  return u;
}

//=======================================================================
//function : SelectEdge
//purpose  : Find in the list <LE> the edge <NE> connected with <CE> by
//           the vertex <CV>.
//           <NE> is removed from the list. If <CE> is in <LE>
//           with the same orientation, it's removed from the list
//=======================================================================

static Standard_Boolean  SelectEdge(const BRepAdaptor_Surface& Surf,
                                    const TopoDS_Edge&    CE,
                                    const TopoDS_Vertex&  CV,
                                    TopoDS_Edge&          NE,
                                    const TopTools_ListOfShape& LE)
{
  NE.Nullify();

  if (LE.Extent() > 1) {
    //--------------------------------------------------------------
    // Several possible edges.
    // - Test the edges differents of CE
    //--------------------------------------------------------------
    TopoDS_Face FForward = Surf.Face();
    TopoDS_Edge aPrevNE;

    gp_Vec2d CTg1, Tg1, CTg2, Tg2;
    gp_Pnt2d PC, P;

    Standard_Real f, l;
    Handle(Geom2d_Curve) Cc, C;
    Cc = BRep_Tool::CurveOnSurface(CE,FForward,f,l);

    Standard_Boolean isForward = ( CE.Orientation () == TopAbs_FORWARD );
    Standard_Real uc, u, du = Precision::PConfusion();
    uc = isForward ? ( l - du ) : ( f + du );
    Cc->D1(uc, PC, CTg1);
    if (!isForward) CTg1.Reverse();

    Standard_Real anglemin = 3 * M_PI, tolAng = 1.e-8;

    // select an edge whose first derivative is most left of CTg1
    // ie an angle between Tg1 and CTg1 is least
    TopTools_ListIteratorOfListOfShape itl;
    for ( itl.Initialize(LE); itl.More(); itl.Next()) {
      const TopoDS_Edge& E = TopoDS::Edge(itl.Value());
      if (E.IsSame(CE))
        continue;
      if (! CV.IsSame( TopExp::FirstVertex( E, Standard_True )))
        continue;

      isForward = ( E.Orientation () == TopAbs_FORWARD );

      // get E curve
      C = BRep_Tool::CurveOnSurface(E,FForward,f,l);
      // get the first derivative Tg1
      u = isForward ? ( f + du ) : ( l - du );
      C->D1(u, P, Tg1);
      if (!isForward) Tg1.Reverse();

      // -PI < angle < PI
      Standard_Real angle = Tg1.Angle(CTg1);

      if (M_PI - Abs(angle) <= tolAng)
      {
        // an angle is too close to PI; assure that an angle sign really
        // reflects an edge position: +PI - an edge is worst,
        // -PI - an edge is best.
        u = preciseU( Surf, CE, CV, Cc, Standard_False);
        gp_Vec2d CTg;
        Cc->D1(u, PC, CTg);
        if (CE.Orientation() == TopAbs_REVERSED) CTg.Reverse();

        u = preciseU( Surf, E, CV, C, Standard_True);
        C->D1(u, P, Tg1);
        if (!isForward) Tg1.Reverse();

        angle = Tg1.Angle(CTg);
      }

      Standard_Boolean isClose = ( Abs( angle - anglemin ) <= tolAng );
      if (angle <= anglemin) {
        if (isClose)
          aPrevNE = NE;
        else
          aPrevNE.Nullify();
        anglemin = angle ;
        NE = E;
      }
      else
        if (isClose)
          aPrevNE = E;

    }
    if (!aPrevNE.IsNull()) {
      // select one of close edges, the most left one.
      Cc = BRep_Tool::CurveOnSurface( NE, FForward, f, l );
      uc = preciseU( Surf, NE, CV, Cc, Standard_True);
      Cc->D1(uc, PC, CTg1);
      if (NE.Orientation() != TopAbs_FORWARD) CTg1.Reverse();
      
      u = preciseU( Surf, aPrevNE, CV, C, Standard_True);
      C->D1(u, P, Tg1);
      if (aPrevNE.Orientation() != TopAbs_FORWARD) Tg1.Reverse();

      if ( Tg1.Angle(CTg1) < 0)
        NE = aPrevNE;
    }
  }
  else if (LE.Extent() == 1) {
    NE = TopoDS::Edge(LE.First());
  }
  else {
    return Standard_False;
  }
  return !NE.IsNull();
}

//=======================================================================
//function : SamePnt2d
//purpose  :
//=======================================================================

static Standard_Boolean  SamePnt2d(const TopoDS_Vertex& V1,
                                   const TopoDS_Edge&   E1,
                                   const TopoDS_Vertex& V2,
                                   const TopoDS_Edge&   E2,
                                   const TopoDS_Face&   F)
{
  Standard_Real   f1,f2,l1,l2;
  Handle(Geom2d_Curve) C1 = BRep_Tool::CurveOnSurface(E1,F,f1,l1);
  Handle(Geom2d_Curve) C2 = BRep_Tool::CurveOnSurface(E2,F,f2,l2);

  gp_Pnt2d P1 = C1->Value( BRep_Tool::Parameter(V1,E1));
  gp_Pnt2d P2 = C2->Value( BRep_Tool::Parameter(V2,E2));

  Standard_Real Tol  = 100 * BRep_Tool::Tolerance(V1);
  Standard_Real Dist = P1.Distance(P2);
  return Dist < Tol;
}


//=======================================================================
//function : StoreInMVE
//purpose  :
//=======================================================================

static void StoreInMVE (const TopoDS_Face& /*F*/,
                        TopoDS_Edge& E,
                        TopTools_DataMapOfShapeListOfShape& MVE )

{
  TopoDS_Vertex V1, V2;
  TopTools_ListOfShape Empty;

  TopExp::Vertices(E,V1,V2);
  if (!MVE.IsBound(V1)) {
    MVE.Bind(V1,Empty);
  }
  MVE(V1).Append(E);

  if (!MVE.IsBound(V2)) {
    MVE.Bind(V2,Empty);
  }
  MVE(V2).Append(E);
}

//=======================================================================
//function : RemoveFromMVE
//purpose  :
//=======================================================================

static void RemoveFromMVE(const TopoDS_Edge& E,
                          TopTools_DataMapOfShapeListOfShape& MVE)
{
  TopTools_ListIteratorOfListOfShape itl;
  TopoDS_Vertex  V1,V2;
  TopExp::Vertices (E,V1,V2);
  if (MVE.IsBound(V1))
    for ( itl.Initialize(MVE(V1)); itl.More(); itl.Next()) {
      if (itl.Value().IsEqual(E)) {
        MVE(V1).Remove(itl);
        break;
      }
    }
  if (MVE.IsBound(V2))
    for ( itl.Initialize(MVE(V2)); itl.More(); itl.Next()) {
      if (itl.Value().IsEqual(E)) {
        MVE(V2).Remove(itl);
        break;
      }
    }
}
//=======================================================================
//function : addConnected
//purpose  : add to <EM> all edges reachable from <E>
//=======================================================================

static void addConnected(const TopoDS_Shape& E,
                         TopTools_MapOfShape& EM,
                         TopTools_MapOfShape& VM,
                         const TopTools_DataMapOfShapeListOfShape& MVE)
{
  // Loop on vertices of E
  TopoDS_Iterator itV ( E );
  for ( ; itV.More(); itV.Next()) {

    if ( ! VM.Add ( itV.Value() )) continue;

    // Loop on edges sharing V
    TopTools_ListIteratorOfListOfShape itE( MVE( itV.Value() ) );
    for (; itE.More(); itE.Next()) {
      if ( EM.Add( itE.Value() ))
        addConnected ( itE.Value(), EM, VM, MVE );
    }
  }
}
//=======================================================================
//function : canPassToOld
//purpose  :
//=======================================================================

// static Standard_Boolean canPassToOld (const TopoDS_Shape& V,
//                                    TopTools_MapOfShape& UsedShapesMap,
//                                    const TopTools_DataMapOfShapeListOfShape& MVE,
//                                    const TopTools_MapOfShape& SectionEdgesMap)
// {
//   TopTools_ListIteratorOfListOfShape itE( MVE(V) );
//   // Loop on edges sharing V
//   for (; itE.More(); itE.Next()) {
//     if ( !UsedShapesMap.Add( itE.Value() ))
//       continue; // already checked

//     if ( !SectionEdgesMap.Contains( itE.Value() ))
//       return Standard_True; // WE PASSED

//     TopoDS_Iterator itV( itE.Value() );
//     // Loop on vertices of an edge
//     for (; itV.More(); itV.Next()) {
//       if ( !UsedShapesMap.Add( itV.Value() ))
//      continue; // already checked
//       else
//      return canPassToOld( itV.Value(), UsedShapesMap, MVE, SectionEdgesMap);
//     }
//   }
//   return Standard_False;
// }

//=======================================================================
//function : MakeDegenAndSelect
//purpose  : Find parameter of intersection of <CE> with <DE> and
//           select an edge with its parameter closest to found one.
//           Return new degenerated edge trimming <DE> by found parameters
//=======================================================================

static TopoDS_Edge MakeDegenAndSelect(const TopoDS_Edge& CE,
                                      const TopoDS_Vertex& CV,
                                      TopoDS_Edge& NE,
                                      TopTools_SequenceOfShape& EdgesSeq,
                                      TColStd_SequenceOfReal& USeq,
                                      const TopoDS_Edge& DE)
{
  if (EdgesSeq.Length() < 3) {
    if (CE == EdgesSeq.First())
      NE = TopoDS::Edge( EdgesSeq.Last() );
    else
      NE = TopoDS::Edge( EdgesSeq.First() );
    return DE;
  }

  // find parameter on DE where it intersects CE

  Standard_Real U1;
  Standard_Integer i, nb = EdgesSeq.Length();
  for (i=1; i<= nb; ++i) {
    if (CE == EdgesSeq(i)) {
      U1 = USeq(i);
      break;
    }
  }

  // select NE with param closest to U1 thus finding U2 for a new degen edge

  Standard_Real U2, dU, dUmin = 1.e100;
  Standard_Boolean isReversed = ( DE.Orientation() == TopAbs_REVERSED );
  for (i=1; i<= nb; ++i) {
    dU = USeq(i) - U1;
    if (isReversed ? (dU > 0) : (dU < 0))
        continue;
    dU = Abs( dU );
    if ( dU  > dUmin || IsEqual( dU, 0.))
      continue;
    const TopoDS_Edge& E = TopoDS::Edge ( EdgesSeq(i) );
    if ( ! CV.IsSame( TopExp::FirstVertex( E , Standard_True )))
      continue;
    NE = E;
    dUmin = dU + Epsilon(dU);
    U2 = USeq(i);
  }

  // make a new degenerated edge
  TopoDS_Edge NewDegen = TopoDS::Edge ( DE.EmptyCopied() );

  Standard_Real Tol = BRep_Tool::Tolerance( CV );
  TopoDS_Vertex V = CV;

  BRep_Builder B;
  V.Orientation( NewDegen.Orientation() );
  B.UpdateVertex( V, U1, NewDegen, Tol);
  B.Add ( NewDegen , V );

  V.Reverse();
  B.UpdateVertex( V, U2, NewDegen, Tol);
  B.Add ( NewDegen , V );

  return NewDegen;
}

//=======================================================================
//function : prepareDegen
//purpose  : Intersect <DegEdge> with edges bound to its vertex in <MVE>
//           and store intersection parameter on <DegEdge> in
//           <USeq> as well as the edges them-self in <EdgesSeq>.
//           Bind <DegEdgeIndex> to vertex of <DegEdge> in <MVDEI>
//=======================================================================

static void prepareDegen (const TopoDS_Edge&                        DegEdge,
                          const TopoDS_Face&                        F,
                          const TopTools_DataMapOfShapeListOfShape& MVE,
                          TopTools_SequenceOfShape&                 EdgesSeq,
                          TColStd_SequenceOfReal&                   USeq,
                          TopTools_DataMapOfShapeInteger&           MVDEI,
                          const Standard_Integer                    DegEdgeIndex)
{
  const TopoDS_Vertex& V = TopExp::FirstVertex ( DegEdge );
  MVDEI.Bind ( V, DegEdgeIndex );

  const TopTools_ListOfShape& EdgesList = MVE ( V );
  // if only 2 edges come to degenerated one, no pb in selection and
  // no need to intersect them, just simulate asked data
  Standard_Boolean doIntersect =  ( EdgesList.Extent() > 2 );

  BRepAdaptor_Curve2d DC, C;
  Geom2dInt_GInter InterCC;
  Standard_Real Tol = Precision::PConfusion();
  if ( doIntersect )
    DC.Initialize( DegEdge, F );

  // avoid intersecting twice the same edge
  // BRepOffset_DataMapOfShapeReal EUMap ( EdgesList.Extent() );  // V6.3
  TopTools_DataMapOfShapeReal EUMap ( EdgesList.Extent() );   // V6.5

  Standard_Real U, f, l;
  BRep_Tool::Range (DegEdge, f, l);

  TopTools_ListIteratorOfListOfShape itE (EdgesList);
  for (; itE.More(); itE.Next()) {

    const TopoDS_Edge& E = TopoDS::Edge ( itE.Value() );

    if ( !doIntersect) {
      U = 0.; // it won't be used
    }
    else if ( BRep_Tool::IsClosed( E, F )) {
      // seam edge: select U among f and l
      Standard_Boolean first = Standard_True;
      if ( V.IsSame ( TopExp::FirstVertex( E, Standard_True ) ))
        first = Standard_False;
      if ( DegEdge.Orientation() == TopAbs_REVERSED )
        first = !first;
      U = first ? f : l;
    }
    else if ( EUMap.IsBound( E ) ) {
      // same edge already bound
      U = EUMap( E );
    }
    else {
      // intersect 2d curves
      C.Initialize( E, F );
      InterCC.Perform ( DC, C , Tol, Tol );
      if (! InterCC.IsDone() || InterCC.NbPoints() == 0) {
        MESSAGE ( "NO 2d INTERSECTION ON DEGENERATED EDGE" );
        continue;
      }
      // hope there is only one point of intersection
      U = InterCC.Point( 1 ).ParamOnFirst();
    }
    USeq.Append ( U );
    EdgesSeq.Append ( E );
  }
}
//=======================================================================
//function : Perform
//purpose  : Make loops.
//=======================================================================

void Partition_Loop2d::Perform()
{

  Standard_Integer NbConstEdges = myConstEdges.Extent();
  TopTools_DataMapOfShapeListOfShape MVE(NbConstEdges) , MVE2(NbConstEdges);
  TopTools_DataMapIteratorOfDataMapOfShapeListOfShape Mapit;
  TopTools_ListIteratorOfListOfShape itl;
  TopoDS_Vertex V1,V2;
  BRepAdaptor_Surface Surface ( myFace, Standard_False );

  // degenerated edges and parameters of their 2d intersection with other edges
  TopoDS_Edge                    DE [2];
  TopTools_SequenceOfShape       SEID [2]; // seq of edges intersecting degenerated
  TColStd_SequenceOfReal         SeqU [2]; // n-th U corresponds to n-th edge in SEID
  TopTools_DataMapOfShapeInteger MVDEI(2); // map vertex - degenerated edge index
  Standard_Integer               iDeg = 0; // index of degenerated edge [0,1]

  //---------------------------------------------------------
  // Construction map vertex => edges, find degenerated edges
  //---------------------------------------------------------
  for (itl.Initialize(myConstEdges); itl.More(); itl.Next()) {
    TopoDS_Edge& E = TopoDS::Edge(itl.Value());
    if ( BRep_Tool::Degenerated( E )) {
      if (DE[0].IsNull()) DE[0] = E;
      else                DE[1] = E;
    }
    else
      StoreInMVE(myFace,E,MVE);
  }

  // fill data for degenerated edges
  if ( ! DE[0].IsNull() )
    prepareDegen ( DE[0], myFace, MVE, SEID[0], SeqU[0], MVDEI, 0);
  if ( ! DE[1].IsNull() )
    prepareDegen ( DE[1], myFace, MVE, SEID[1], SeqU[1], MVDEI, 1);


  // to detect internal wires
  Standard_Boolean isInternCW = 0;
  MVE2 = MVE;


  //------------------------------
  // Construction of all the wires
  //------------------------------
  // first, we collect wire edges in WEL list looking for same edges that
  // will be then removed possibly exploding a wire into parts;
  // second, build wire(s)

  while (!MVE.IsEmpty()) {

    TopoDS_Vertex    VF,CV;
    TopoDS_Edge      CE,NE,EF;
    TopoDS_Wire      NW;
    BRep_Builder     B;
    Standard_Boolean End = Standard_False;
    TopTools_ListOfShape WEL;

    Mapit.Initialize(MVE);
    if (Mapit.Value().IsEmpty()) {
      MVE.UnBind(Mapit.Key());
      continue;
    }

    // EF first edge.
    EF = CE = TopoDS::Edge(Mapit.Value().First());
    // VF first vertex
    VF = TopExp::FirstVertex( CE, Standard_True);

    isInternCW = Standard_True;

    TopTools_MapOfShape addedEM  (NbConstEdges); // map of edges added to WEL
    TopTools_MapOfShape doubleEM (NbConstEdges); // edges encountered twice in WEL

    //-------------------------------
    // Construction of a wire.
    //-------------------------------
    while (!End) {

      // only a seam is allowed twice in a wire, the others should be removed
      if (addedEM.Add ( CE ) || BRep_Tool::IsClosed( CE, myFace ) )
        WEL.Append( CE );
      else {
        doubleEM.Add( CE );
        RemoveFromMVE (CE,MVE2);
        TopoDS_Edge CERev = CE;
        CERev.Reverse();
        RemoveFromMVE (CERev,MVE2);
      }

      RemoveFromMVE (CE,MVE);

      CV = TopExp::LastVertex( CE, Standard_True);

      if (isInternCW && !mySectionEdges.Contains(CE))
        // wire is internal if all edges are section ones
        isInternCW = Standard_False;

      if (MVDEI.IsBound( CV )) { // CE comes to the degeneration
        iDeg = MVDEI( CV );
        TopoDS_Edge NewDegen;
        NewDegen = MakeDegenAndSelect( CE, CV, NE, SEID[iDeg], SeqU[iDeg], DE[iDeg]);
        WEL.Append( NewDegen );
        CE = NE;
        End = CV.IsSame( VF );
        continue;
      }

      //--------------
      // stop test
      //--------------
      if (MVE(CV).IsEmpty()) {
        End=Standard_True;
        MVE.UnBind(CV);
      }
      else if (CV.IsSame(VF) && SamePnt2d(CV,CE, VF,EF, myFace) ) {
        End = Standard_True;
      }
      else {
        //----------------------------
        // select new current edge
        //----------------------------
        if (! SelectEdge (Surface,CE,CV,NE,MVE(CV))) {
          MESSAGE ( " NOT CLOSED WIRE " );
          End=Standard_True;
        }
        else
          CE = NE;
      }
    } // while ( !End )


    // WEL is built, built wire(s)


    itl.Initialize( WEL );
    if ( doubleEM.IsEmpty()) { // no double edges
      B.MakeWire( NW );
      for (; itl.More(); itl.Next())
        B.Add ( NW, itl.Value());
      if (isInternCW) myInternalWL.Append(NW);
      else            myNewWires.Append  (NW);
    }

    else {
      // remove double and degenerated edges from WEL
      while (itl.More()) {
        const TopoDS_Edge& E = TopoDS::Edge ( itl.Value() );
        if ( doubleEM.Contains( E ) || BRep_Tool::Degenerated( E ))
          WEL.Remove( itl );
        else
           itl.Next();
      }
      if ( WEL.IsEmpty())
        continue;
      // remove double edges from SEID and SeqU
      Standard_Integer i,j;
      for (j=0; j<2; ++j) {
        for (i=1; i<=SEID[j].Length(); ++i) {
          if (doubleEM.Contains( SEID[j].Value(i))) {
            SEID[j].Remove( i );
            SeqU[j].Remove( i-- );
          }
        }
      }
      // removal of doulbe edges can explode a wire into parts,
      // make new wires of them.
      // A Loop like previous one but without 2d check
      while ( !WEL.IsEmpty() ) {
        CE = TopoDS::Edge( WEL.First() );
        WEL.RemoveFirst();
        B.MakeWire( NW );
        VF = TopExp::FirstVertex ( CE, Standard_True);

        End = Standard_False;
        while ( !End) {
          B.Add( NW, CE );
          CV = TopExp::LastVertex  ( CE, Standard_True);

          if (MVDEI.IsBound( CV )) {   // CE comes to the degeneration
            iDeg = MVDEI( CV );
            TopoDS_Edge NewDegen;
            NewDegen = MakeDegenAndSelect( CE, CV, NE, SEID[iDeg], SeqU[iDeg], DE[iDeg]);
            B.Add( NW, NewDegen );
            End = CV.IsSame( VF );
            CE = NE;
            if (!NE.IsNull()) { // remove NE from WEL
              for (itl.Initialize( WEL ); itl.More(); itl.Next())
                if ( NE == itl.Value()) {
                  WEL.Remove( itl );
                  break;
                }
            }
          }  // end degeneration

          else {
            if (CV.IsSame( VF )) {
              End = Standard_True;
              continue;
            }
            // edges in WEL most often are well ordered
            // so try to iterate until the End
            Standard_Boolean add = Standard_False;
            itl.Initialize(WEL);
            while ( itl.More() && !End) {
              NE = TopoDS::Edge( itl.Value() );
              if ( CV.IsSame( TopExp::FirstVertex( NE, Standard_True ))) {
                WEL.Remove( itl );
                if (add)
                  B.Add( NW, CE );
                CE = NE;
                add = Standard_True;
                CV = TopExp::LastVertex( CE, Standard_True);
                if (MVDEI.IsBound( CV ) || CV.IsSame( VF ))
                  break;
              }
              else
                itl.Next();
            }
            if (!add)
              End = Standard_True;
          }
        } // !End

        myInternalWL.Append( NW );
      }
    } // end building new wire(s) from WEL

  } // end Loop on MVE

  // all wires are built


  // ============================================================
  // select really internal wires i.e. those from which we can`t
  // pass to an old (not section) edge
  // ============================================================

  Standard_Integer nbIW = myInternalWL.Extent();
  if (nbIW == 0)
    return;

  if ( myNewWires.Extent() != 1 && nbIW > 1) {
    TopTools_MapOfShape outerEM (NbConstEdges); // edges connected to non-section ones
    TopTools_MapOfShape visitedVM (NbConstEdges);
    for ( itl.Initialize( myConstEdges ); itl.More(); itl.Next()) {
      if ( ! mySectionEdges.Contains( itl.Value() ))
        addConnected (itl.Value(), outerEM, visitedVM, MVE2);
    }
    // if an edge of a wire is in <outerEM>, the wire is not internal
    TopExp_Explorer expIWE;
    TopTools_ListIteratorOfListOfShape itIW ( myInternalWL );
    while (itIW.More()) {
      expIWE.Init ( itIW.Value() , TopAbs_EDGE );
      if ( outerEM.Contains( expIWE.Current() )) {
        myNewWires.Append ( itIW.Value() );
        myInternalWL.Remove( itIW ); // == itIW.Next()
      }
      else
        itIW.Next();
    }
  }
}
//=======================================================================
//function : isHole
//purpose  :
//=======================================================================

static Standard_Boolean isHole (const TopoDS_Wire& W,
                                const TopoDS_Face& F)
{
  BRep_Builder B;
  TopoDS_Shape newFace = F.EmptyCopied();
  B.Add(newFace,W.Oriented(TopAbs_FORWARD));
  BRepTopAdaptor_FClass2d classif (TopoDS::Face(newFace),
                                   Precision::PConfusion());
  return (classif.PerformInfinitePoint() == TopAbs_IN);
}

//=======================================================================
//function : IsInside
//purpose  : check if W1 is inside W2. Suppose W2 is not a hole !!!!
//=======================================================================

static Standard_Boolean isInside(const TopoDS_Face& F,
                                 const TopoDS_Wire& W1,
                                 const TopoDS_Wire& W2)
{
  // make a face with wire W2
  BRep_Builder B;
  TopoDS_Shape aLocalShape = F.EmptyCopied();
  TopoDS_Face newFace = TopoDS::Face(aLocalShape);
  B.Add(newFace,W2);

  // get any 2d point of W1
  TopExp_Explorer exp(W1,TopAbs_EDGE);
  if (BRep_Tool::Degenerated( TopoDS::Edge( exp.Current() )))
    exp.Next();
  const TopoDS_Edge& e = TopoDS::Edge(exp.Current());
  Standard_Real f,l;
  Handle(Geom2d_Curve) C2d = BRep_Tool::CurveOnSurface(e,F,f,l);
  gp_Pnt2d pt2d(C2d->Value( 0.5 * ( f + l )));

  BRepTopAdaptor_FClass2d classif(newFace,Precision::PConfusion());
  return (classif.Perform(pt2d) == TopAbs_IN);
}

//=======================================================================
//function : NewWires
//purpose  : Returns the list of wires performed.
//           can be an empty list.
//=======================================================================

const TopTools_ListOfShape&  Partition_Loop2d::NewWires() const
{
  return myNewWires;
}

//=======================================================================
//function : NewFaces
//purpose  : Returns the list of faces.
//Warning  : The method <WiresToFaces> as to be called before.
//           can be an empty list.
//=======================================================================

const TopTools_ListOfShape&  Partition_Loop2d::NewFaces() const
{
  return myNewFaces;
}

//=======================================================================
//function : findEqual
//purpose  : move wires form <WL> to <EqWL> pairs of wires build of the same edges
//=======================================================================

static void findEqual (TopTools_ListOfShape& WL,
                       TopTools_DataMapOfShapeShape& EqWM,
                       const TopoDS_Face& F)
{
  TopTools_ListIteratorOfListOfShape it1, it2;
  Standard_Integer i,j;
  TColStd_MapOfInteger IndMap;
  for (it1.Initialize(WL), i=1;  it1.More();  it1.Next(), i++) {

    if (IndMap.Contains(i)) continue;
    const TopoDS_Wire& Wire1 = TopoDS::Wire( it1.Value());

    for (it2.Initialize(WL), j=1;  it2.More();  it2.Next(), j++) {

      if (j <= i || IndMap.Contains(j)) continue;

      TopTools_IndexedMapOfShape EdgesMap;
      TopExp::MapShapes (Wire1, TopAbs_EDGE, EdgesMap);

      const TopoDS_Shape& Wire2 = it2.Value();
      TopoDS_Iterator itE ( Wire2);
      for (; itE.More(); itE.Next()) {
        if ( !EdgesMap.Contains( itE.Value()) )
          break;
      }
      if (!itE.More()) { // all edges are same
        if (isHole( Wire1, F)) {
          EqWM.Bind ( Wire1, Wire2 );
        }
        else {
          EqWM.Bind ( Wire2, Wire1 );
        }
        IndMap.Add(i);
        IndMap.Add(j);
        break;
      }
    }
  }
  // clear WL
  it1.Initialize(WL);
  i=1;
  while (it1.More()) {
    if (IndMap.Contains(i))
      WL.Remove(it1); // next node becomes current and with Next() we would miss it
    else
      it1.Next();
    i++;
  }
}

//=======================================================================
//function : classify
//purpose  : bind to a wire a list of internal wires
//=======================================================================

static void classify(const TopTools_DataMapOfShapeShape& EqWM,
                     BRepAlgo_AsDes& OuterInner,
                     const TopoDS_Face& F)
{
  TopTools_DataMapIteratorOfDataMapOfShapeShape it1, it2;

  for (it1.Initialize(EqWM);  it1.More();  it1.Next()) {
    // find next after it1.Value()
    for (it2.Initialize(EqWM);  it2.More();  it2.Next())
      if (it1.Value().IsSame( it2.Value() ))
      {
        it2.Next();
        break;
      }
    for ( ;  it2.More();  it2.Next()) {
      const TopoDS_Wire& Wire1 = TopoDS::Wire( it1.Value() );
      const TopoDS_Wire& Wire2 = TopoDS::Wire( it2.Value() );
      if (isInside(F, Wire1, Wire2))
        OuterInner.Add (Wire2, Wire1);
      else if (isInside(F, Wire2, Wire1))
        OuterInner.Add (Wire1, Wire2);
    }
  }
}
//=======================================================================
//function : WiresToFaces
//purpose  : Build faces from the wires result.
//           <EdgeImage> serves to  find  original edge by new
//           one. <Section> contains edges resulting from face
//           intersections
//=======================================================================

void  Partition_Loop2d::WiresToFaces(const BRepAlgo_Image& )
{
  Standard_Integer nbW = myNewWires.Extent() + myInternalWL.Extent();
  if (nbW==0)
    return;

  BRepAlgo_FaceRestrictor FR;
  FR.Init (myFace,Standard_False);

  // FaceRestrictor is instable in rather simple cases
  // (ex. a single face of bellecoque.brep splited by 10 planes:
  // sometimes 1-2 faces are missing ).
  // So we use it as less as possible: no holes -> make faces by hands


  // are there holes in myFace ?
  Standard_Boolean hasOldHoles = Standard_False;
  TopoDS_Iterator itOldW (myFace);
  if ( itOldW.More()) {
    const TopoDS_Wire& FirstOldWire = TopoDS::Wire( itOldW.Value() );
    itOldW.Next();
    hasOldHoles = itOldW.More() || isHole( FirstOldWire, myFace);
  }
  if (myInternalWL.IsEmpty() && !hasOldHoles) {
    // each wire bounds one face
    BRep_Builder B;
    TopTools_ListIteratorOfListOfShape itNW (myNewWires);
    for (; itNW.More(); itNW.Next()) {
      TopoDS_Face NF = TopoDS::Face ( myFace.EmptyCopied() );
      B.Add ( NF, itNW.Value() );
      NF.Orientation( myFaceOri);
      myNewFaces.Append ( NF );
    }
    return;
  }

  // FaceRestrictor can't classify wires build on all the same edges
  // and gives incorrect result in such cases (ex. a plane cut into 2 parts by cylinder)
  // We must make faces of equal wires separately. One of equal wires makes a
  // hole in a face and should come together with outer wires of face.
  // The other of a wires pair bounds a face that may have holes in turn.

  // Find equal wires among internal wires
  TopTools_DataMapOfShapeShape EqWM; // key is a hole part of a pair of equal wires
  findEqual (myInternalWL, EqWM, myFace);

  if (!EqWM.IsEmpty()) { // there are equal wires

    if (hasOldHoles)
      myInternalWL.Append( myNewWires ); // an old wire can be inside an equal wire

    // classify equal wire pairs
    BRepAlgo_AsDes OuterInner;
    classify (EqWM,OuterInner,myFace);

    // make face of most internal of equal wires and its inner wires
    while ( !EqWM.IsEmpty()) {

      TopTools_ListOfShape prevHolesL; // list of hole-part of previous most internal equal wires

      // find most internal wires among pairs (key - hole, value - outer part)
      TopTools_DataMapIteratorOfDataMapOfShapeShape it(EqWM);
      Standard_Integer nbEqW = EqWM.Extent(); // protection against infinite loop
      for ( ; it.More(); it.Next()) {

        TopoDS_Wire outerW = TopoDS::Wire ( it.Value() );
        if (  OuterInner.HasDescendant( outerW ) && // has internal
             ! OuterInner.Descendant( outerW ).IsEmpty() )
          continue;

        FR.Add( outerW );

        // add internal wires that are inside of outerW
        TopTools_ListIteratorOfListOfShape itIW (myInternalWL);
        while ( itIW.More()) {
          TopoDS_Wire IW = TopoDS::Wire ( itIW.Value() );
          if ( isInside (myFace, IW, outerW)) {
            FR.Add (IW);
            myInternalWL.Remove( itIW ); // == itIW.Next() !!!
          }
          else
            itIW.Next();
        }

        // the hole-part of current pair of equal wires will be in the next new face
        prevHolesL.Append ( it.Key() );

      } // Loop on map of equal pairs searching for innermost wires

      // make faces
      FR.Perform();
      if (FR.IsDone()) {
        for (; FR.More(); FR.Next())
          myNewFaces.Append(FR.Current());
      }

      FR.Clear();

      // add hole-parts to FaceRestrictor,
      // remove them from the EqWM,
      // remove found wires as internal of resting classified wires
      Standard_Boolean clearOuterInner =  ( prevHolesL.Extent() < EqWM.Extent() );
      TopTools_ListIteratorOfListOfShape itPrev (prevHolesL);
      for (; itPrev.More(); itPrev.Next()) {
        TopoDS_Wire& Hole = TopoDS::Wire ( itPrev.Value() );
        FR.Add ( Hole );
        if (clearOuterInner) {
          const TopoDS_Wire& outerW = TopoDS::Wire ( EqWM.Find( Hole ) );
          // Loop on wires including outerW
          TopTools_ListIteratorOfListOfShape itO( OuterInner.Ascendant( outerW ));
          for (; itO.More(); itO.Next()) {
            TopTools_ListOfShape& innerL = OuterInner.ChangeDescendant( itO.Value() );
            TopTools_ListIteratorOfListOfShape itI (innerL);
            // Loop on internal wires of current including wire
            for (; itI.More(); itI.Next())
              if ( outerW.IsSame( itI.Value() )) {
                innerL.Remove( itI );   break;
              }
          }
        }
        EqWM.UnBind ( Hole );
      }

      if (nbEqW == EqWM.Extent())
      {
        // error: pb with wires classification
#ifdef DEB
        MESSAGE("Partition_Loop2d::WiresToFaces(), pb with wires classification");
#endif
        break;
      }

    } // while (!EqWM.IsEmpty)

  } //  if !EqWM.IsEmpty()

  myNewWires.Append ( myInternalWL );

  TopTools_ListIteratorOfListOfShape itW (myNewWires);
  for (; itW.More(); itW.Next()) {
    TopoDS_Wire& W = TopoDS::Wire ( itW.Value() );
    FR.Add(W);
  }
  FR.Perform();
  for (; FR.IsDone() && FR.More(); FR.Next())
    myNewFaces.Append(FR.Current());


  TopTools_ListIteratorOfListOfShape itNF (myNewFaces);
  for (; itNF.More(); itNF.Next())
    itNF.Value().Orientation( myFaceOri );
}

#endif