// Created on: 2003-10-21
// Created by: Mikhail KLOKOV
// Copyright (c) 2003-2014 OPEN CASCADE SAS
//
// This file is part of Open CASCADE Technology software library.
//
// This library is free software; you can redistribute it and/or modify it under
// the terms of the GNU Lesser General Public License version 2.1 as published
// by the Free Software Foundation, with special exception defined in the file
// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
// distribution for complete text of the license and disclaimer of any warranty.
//
// Alternatively, this file may be used under the terms of Open CASCADE
// commercial license or contractual agreement.


#include <BOPAlgo_BOP.hxx>
#include <BOPAlgo_PaveFiller.hxx>
#include <BOPDS_DS.hxx>
#include <BRep_Builder.hxx>
#include <BRep_Tool.hxx>
#include <BRepAlgoAPI_Section.hxx>
#include <BRepFill_TrimShellCorner.hxx>
#include <BRepLib_MakeEdge.hxx>
#include <BRepLib_MakeWire.hxx>
#include <BRepLib_MakeVertex.hxx>
#include <BRepTools_ReShape.hxx>
#include <gce_MakeLin.hxx>
#include <GCPnts_UniformAbscissa.hxx>
#include <Geom2d_Curve.hxx>
#include <Geom_Curve.hxx>
#include <GeomLib.hxx>
#include <gp_Ax2.hxx>
#include <gp_Pln.hxx>
#include <gp_Pnt2d.hxx>
#include <IntTools_BeanFaceIntersector.hxx>
#include <IntTools_Context.hxx>
#include <IntTools_Range.hxx>
#include <IntTools_Tools.hxx>
#include <TColgp_Array1OfDir.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <TColgp_Array2OfPnt.hxx>
#include <TColgp_SequenceOfPnt.hxx>
#include <TColStd_Array1OfBoolean.hxx>
#include <TColStd_ListIteratorOfListOfInteger.hxx>
#include <TColStd_ListOfInteger.hxx>
#include <TopExp.hxx>
#include <TopExp_Explorer.hxx>
#include <TopLoc_Location.hxx>
#include <TopoDS.hxx>
#include <TopoDS_Compound.hxx>
#include <TopoDS_Face.hxx>
#include <TopoDS_Iterator.hxx>
#include <TopoDS_Shape.hxx>
#include <TopoDS_Shell.hxx>
#include <TopoDS_Wire.hxx>
#include <TopTools_Array1OfListOfShape.hxx>
#include <TopTools_DataMapIteratorOfDataMapOfShapeListOfShape.hxx>
#include <TopTools_DataMapOfShapeListOfShape.hxx>
#include <TopTools_IndexedDataMapOfShapeListOfShape.hxx>
#include <TopTools_ListIteratorOfListOfShape.hxx>
#include <TopTools_ListOfShape.hxx>
#include <TopTools_MapOfShape.hxx>
#include <TopTools_SequenceOfShape.hxx>
#include <BRepExtrema_ExtCC.hxx>

static TopoDS_Edge FindEdgeCloseToBisectorPlane(const TopoDS_Vertex& theVertex,
                                                TopoDS_Compound&     theComp,
                                                const gp_Ax1&        theAxis);

static Standard_Boolean FindMiddleEdges(const TopoDS_Vertex&  theVertex1,
                                        const TopoDS_Vertex&  theVertex2,
                                        const gp_Ax1&         theAxis,
                                        TopoDS_Compound&      theComp,
                                        TopTools_ListOfShape& theElist);

static Standard_Boolean FindCommonVertex(const TopoDS_Edge&   theFirstEdge,
                                         const TopoDS_Edge&   theLastEdge,
                                         const TopoDS_Vertex& theFirstVertex,
                                         const TopoDS_Vertex& theLastVertex,
                                         TopoDS_Vertex&       theCommonVertex);

static Standard_Boolean FindCommonVertex(const BOPDS_PDS&         theDS,
                                         const Standard_Integer   theEIndex1,
                                         const Standard_Integer   theEIndex2,
                                         TopoDS_Vertex&           theCommonVertex,
                                         Standard_Real&           theParamOnE1,
                                         Standard_Real&           theParamOnE2);

static Standard_Boolean SplitUEdges(const Handle(TopTools_HArray2OfShape)&     theUEdges, 
                                    const BOPDS_PDS&                           theDS,
                                    TopTools_DataMapOfShapeListOfShape&        theHistMap);

static void StoreVedgeInHistMap(const Handle(TopTools_HArray1OfShape)&     theVEdges,
                                const Standard_Integer                     theIndex,
                                const TopoDS_Shape&                        theNewVedge,
                                TopTools_DataMapOfShapeListOfShape&        theHistMap);

static void FindFreeVertices(const TopoDS_Shape&         theShape,
                             const TopTools_MapOfShape&  theVerticesToAvoid,
                             TopTools_ListOfShape&       theListOfVertex);

static Standard_Boolean CheckAndOrientEdges(const TopTools_ListOfShape&  theOrderedList,
                                            const gp_Pnt2d&              theFirstPoint,
                                            const gp_Pnt2d&              theLastPoint,
                                            const TopoDS_Face&           theFace,
                                            TopTools_ListOfShape&        theOrientedList);

static Standard_Boolean FillGap(const TopoDS_Vertex&   theFirstVertex,
                                const TopoDS_Vertex&   theLastVertex,
                                const gp_Pnt2d&        theFirstPoint,
                                const gp_Pnt2d&        theLastPoint,
                                const TopoDS_Face&     theFace,
                                const TopoDS_Compound& theSectionEdges,
                                TopTools_ListOfShape&  theOrderedList);

static Standard_Boolean FindNextEdge(const TopoDS_Vertex&   theFirstVertex,
                                     const TopoDS_Vertex&   theLastVertex,
                                     const TopTools_IndexedDataMapOfShapeListOfShape& theMapVE,
                                     const TopTools_MapOfShape& theMapToAvoid,
                                     TopTools_ListOfShape&  theOrderedList);

static Standard_Boolean FindVertex(const TopoDS_Edge&                        theEdge,
                                   const Standard_Integer                    theRank, 
                                   const BOPDS_PDS&                          theDS,
                                   const TopTools_DataMapOfShapeListOfShape& theHistMap, 
                                   TopoDS_Vertex&                            theVertex,
                                   BOPDS_Pave&                               thePave);

static Standard_Boolean FindNextVertex(const Standard_Integer                    theEdgeIndex,
                                       const BOPDS_Pave&                         thePrevPave,
                                       const BOPDS_PDS&                          theDS,
                                       TopoDS_Vertex&                            theNextVertex,
                                       BOPDS_Pave&                               thePave);

static Standard_Boolean GetPave(const Standard_Integer    theEdgeIndex,
                                const Standard_Boolean    isFirst,
                                const BOPDS_PDS&          theDS,
                                BOPDS_Pave&               thePave);

static Standard_Boolean FindFromUEdge(const TopoDS_Edge&                        theUE1Old, 
                                      const TopoDS_Edge&                        theUE2Old, 
                                      const TopoDS_Edge&                        theUE1New, 
                                      const TopoDS_Edge&                        theUE2New, 
                                      const TopoDS_Face&                        theFace, 
                                      const TopoDS_Compound&                    theSecEdges, 
                                      const Standard_Integer                    theRank, 
                                      const TopoDS_Edge&                        theBoundEdge, 
                                      const Standard_Integer                    theBoundEdgeIndex, 
                                      const BOPDS_PDS&                          theDS,
                                      const TopTools_DataMapOfShapeListOfShape& theHistMap,
                                      TopoDS_Compound&                          theSecEdgesNew, 
                                      TopTools_ListOfShape&                     theListOfWireEdges, 
                                      BOPDS_Pave&                               theFoundPave,
                                      Standard_Boolean&                         isOnUEdge);

static Standard_Boolean FindFromVEdge(const BOPDS_Pave&                         thePrevPave,
                                      const Standard_Boolean&                   isOnUEdge,
                                      const TopoDS_Edge&                        theUE1Old, 
                                      const TopoDS_Edge&                        theUE2Old, 
                                      const TopoDS_Face&                        theFace, 
                                      const TopoDS_Compound&                    theSecEdges, 
                                      const Standard_Integer                    theRank, 
                                      const TopoDS_Edge&                        theBoundEdge, 
                                      const Standard_Integer                    theBoundEdgeIndex, 
                                      const BOPDS_PDS&                          theDS,
                                      const TopTools_DataMapOfShapeListOfShape& theHistMap,
                                      TopTools_ListOfShape&                     theListOfWireEdges, 
                                      Standard_Boolean&                         isSectionFound);

static void RemoveEdges(const TopoDS_Compound&      theSourceComp,
                        const TopTools_ListOfShape& theListToRemove,
                        TopoDS_Compound&            theResultComp);

static Standard_Boolean FilterSectionEdges(const BOPDS_VectorOfCurve&       theBCurves,
                                           const TopoDS_Face&               theSecPlane,
                                           const BOPDS_PDS&                 theDS,
                                           TopoDS_Compound&                 theResult);

static Standard_Boolean GetUEdges(const Standard_Integer                     theIndex,
                                  const Standard_Integer                     theRank,
                                  const Handle(TopTools_HArray2OfShape)&     theUEdges,
                                  const TopoDS_Edge&                         theBoundEdge,
                                  const TopoDS_Face&                         theFace,
                                  TopoDS_Edge&                               theFirstUEdge,
                                  TopoDS_Edge&                               theSecondUEdge);

static Standard_Real ComputeAveragePlaneAndMaxDeviation(const TopoDS_Shape& aWire,
                                                        gp_Pln& thePlane,
                                                        Standard_Boolean& IsSingular);

static void UpdateSectionEdge(TopoDS_Edge&         theEdge,
                              const TopoDS_Vertex& theConstVertex,
                              TopoDS_Vertex&       theVertex,
                              const Standard_Real  theParam);

  
// ===========================================================================================
// function: Constructor
// purpose:
// ===========================================================================================
BRepFill_TrimShellCorner::BRepFill_TrimShellCorner(const Handle(TopTools_HArray2OfShape)& theFaces,
                                                   const BRepFill_TransitionStyle         theTransition,
                                                   const gp_Ax2&                          theAxeOfBisPlane) :
  myTransition(theTransition),
  myAxeOfBisPlane(theAxeOfBisPlane),
  myDone(Standard_False),
  myHasSection(Standard_False)
{
  myFaces = new TopTools_HArray2OfShape(theFaces->LowerRow(), theFaces->UpperRow(), 
                                        theFaces->LowerCol(), theFaces->UpperCol());
  myFaces->ChangeArray2() = theFaces->Array2();
}

// ===========================================================================================
// function: AddBounds
// purpose:
// ===========================================================================================
void BRepFill_TrimShellCorner::AddBounds(const Handle(TopTools_HArray2OfShape)& theBounds) 
{
  myBounds = new TopTools_HArray2OfShape(theBounds->LowerRow(), theBounds->UpperRow(), 
                                         theBounds->LowerCol(), theBounds->UpperCol());
  myBounds->ChangeArray2() = theBounds->Array2();
}

// ===========================================================================================
// function: AddUEdges
// purpose:
// ===========================================================================================
void BRepFill_TrimShellCorner::AddUEdges(const Handle(TopTools_HArray2OfShape)& theUEdges) 
{
  myUEdges = new TopTools_HArray2OfShape(theUEdges->LowerRow(), theUEdges->UpperRow(), 
                                         theUEdges->LowerCol(), theUEdges->UpperCol());
  myUEdges->ChangeArray2() = theUEdges->Array2();
}

// ===========================================================================================
// function: AddVEdges
// purpose:
// ===========================================================================================
void BRepFill_TrimShellCorner::AddVEdges(const Handle(TopTools_HArray2OfShape)& theVEdges,
                                         const Standard_Integer theIndex)
{
  myVEdges = new TopTools_HArray1OfShape(theVEdges->LowerRow(), theVEdges->UpperRow());

  for (Standard_Integer i = theVEdges->LowerRow(); i <= theVEdges->UpperRow(); i++)
    myVEdges->SetValue(i, theVEdges->Value(i, theIndex));
}

// ===========================================================================================
// function: Perform
// purpose:
// ===========================================================================================
void BRepFill_TrimShellCorner::Perform() 
{
  Standard_Integer anIndex1, anIndex2, nF1, nF2, i, j, aNbP, aNbC;
  Standard_Boolean bhassec;

  myDone = Standard_False;
  myHistMap.Clear();

  if(myFaces->RowLength() != 2)
    return;
  Standard_Integer ii = 0, jj = 0;
  BRep_Builder aBB;

  for(jj = myFaces->LowerCol(); jj <= myFaces->UpperCol(); jj++) {
    TopoDS_Shell aShell;
    aBB.MakeShell(aShell);

    for(ii = myFaces->LowerRow(); ii <= myFaces->UpperRow(); ii++) {
      aBB.Add(aShell, myFaces->Value(ii, jj));
    }
    aShell.Closed (BRep_Tool::IsClosed (aShell));

    if(jj == myFaces->LowerCol()) {
      myShape1 = aShell;
    }
    else {
      myShape2 = aShell;
    }
  }
  
  BOPAlgo_PaveFiller aPF;
  TopTools_ListOfShape aLS;
  aLS.Append(myShape1);
  aLS.Append(myShape2);
  aPF.SetArguments(aLS);
  //
  aPF.Perform();
  if (aPF.HasErrors()) {
    return;
  }
  //
  const BOPDS_PDS& theDS = aPF.PDS();
  //
  BOPDS_VectorOfInterfFF& aFFs = theDS->InterfFF();
  Standard_Integer aNbFFs = aFFs.Length();

  if(!SplitUEdges(myUEdges, theDS, myHistMap)) {
    return;
  }

  for(ii = myFaces->LowerRow(); ii <= myFaces->UpperRow(); ii++) {
    TopoDS_Shape aF1 = myFaces->Value(ii, myFaces->LowerCol());
    TopoDS_Shape aF2 = myFaces->Value(ii, myFaces->UpperCol());
    //
    anIndex1 = theDS->Index(aF1);
    anIndex2 = theDS->Index(aF2);
    
    if((anIndex1 == -1) || (anIndex2 == -1))
      continue;
    
    for (i=0; i < aNbFFs; ++i) {
      BOPDS_InterfFF& aFFi = aFFs(i);
      aFFi.Indices(nF1, nF2);
      //
      BOPDS_VectorOfPoint& aVP=aFFi.ChangePoints();
      aNbP=aVP.Length();
      const BOPDS_VectorOfCurve& aVC=aFFi.Curves();
      aNbC=aVC.Length();
      if (!aNbP && !aNbC) {
	if (!theDS->HasInterfSubShapes(nF1, nF2)) {
          continue;
        }
      }
      //
      if((nF1 == anIndex1) && (nF2 == anIndex2)) {
        bhassec = Standard_False;
        //
        for (j = 0; j < aNbC; ++j) {
          const BOPDS_Curve& aBCurve = aVC(j);
          const BOPDS_ListOfPaveBlock& aSectEdges = aBCurve.PaveBlocks();
          //
          if (aSectEdges.Extent()) {
            bhassec = Standard_True;
            break;
          }
        }

        if(!bhassec) {
          if(!MakeFacesNonSec(ii, theDS, anIndex1, anIndex2)) {
            myHistMap.Clear();
            return;
          }
        }
        else {
          if(!MakeFacesSec(ii, theDS, anIndex1, anIndex2, i)) {
            myHistMap.Clear();
            return;
          }
        }
        break;
      }
    }
  }
  myDone = Standard_True;
}

// ===========================================================================================
// function: IsDone
// purpose:
// ===========================================================================================
Standard_Boolean BRepFill_TrimShellCorner::IsDone() const
{
  return myDone;
}

// ===========================================================================================
// function: HasSection
// purpose:
// ===========================================================================================
Standard_Boolean BRepFill_TrimShellCorner::HasSection() const
{
  return myHasSection;
}

// ===========================================================================================
// function: Modified
// purpose:
// ===========================================================================================
void BRepFill_TrimShellCorner::Modified(const TopoDS_Shape&   theShape,
                                        TopTools_ListOfShape& theModified) 
{
  theModified.Clear();

  if(myHistMap.IsBound(theShape)) {
    theModified = myHistMap.Find(theShape);
  }
}

// ----------------------------------------------------------------------------------------------------
// function: MakeFacesNonSec
// purpose:         Updates <myHistMap> by new faces in the case when old faces do not intersect
// ----------------------------------------------------------------------------------------------------
Standard_Boolean
BRepFill_TrimShellCorner::MakeFacesNonSec(const Standard_Integer                     theIndex,
                                          const BOPDS_PDS&                           theDS,
                                          const Standard_Integer                     theFaceIndex1, 
                                          const Standard_Integer                     theFaceIndex2)
{
  Standard_Boolean bHasNewEdge = Standard_False;
  TopoDS_Edge aNewEdge;

  BRep_Builder aBB;
  const TopoDS_Shape& aE1 = myBounds->Value(theIndex, 1);
  const TopoDS_Shape& aE2 = myBounds->Value(theIndex, 2);

  // search common vertex between bounds. begin
  TopoDS_Vertex aCommonVertex;
  Standard_Integer anIndex1 = theDS->Index(aE1);
  Standard_Integer anIndex2 = theDS->Index(aE2);
  Standard_Real apar1 = 0., apar2 = 0.;

  Standard_Boolean bvertexfound = 
    FindCommonVertex(theDS, anIndex1, anIndex2, aCommonVertex, apar1, apar2);
  // search common vertex between bounds. end

  Handle(BRepTools_ReShape) aSubstitutor = new BRepTools_ReShape();

  // search common vertices between uedges. begin
  TopTools_ListOfShape aCommonVertices;
  Standard_Integer acommonflag = 0; // 0 - no, 1 - first pair, 2 - second pair, 3 - both
  Standard_Integer ueit = 0, eindex = 0;

  for(ueit = 1, eindex = theIndex; ueit <= 2; ueit++, eindex++) {
    const TopoDS_Shape& aShape1 = myUEdges->Value(eindex, myUEdges->LowerCol());
    const TopoDS_Shape& aShape2 = myUEdges->Value(eindex, myUEdges->UpperCol());
    TopoDS_Edge aUE1 = TopoDS::Edge(aShape1);
    TopoDS_Edge aUE2 = TopoDS::Edge(aShape2);

    if (myHistMap.IsBound(aShape1)) {
      const TopTools_ListOfShape& lst = myHistMap.Find(aShape1);

      if(!lst.IsEmpty())
        aUE1 = TopoDS::Edge(lst.First());
    }

    if (myHistMap.IsBound(aShape2)) {
      const TopTools_ListOfShape& lst = myHistMap.Find(aShape2);

      if(!lst.IsEmpty())
        aUE2 = TopoDS::Edge(lst.First());
    }

    if(!aShape1.IsSame(aUE1))
      aSubstitutor->Replace(aShape1.Oriented(TopAbs_FORWARD), aUE1.Oriented(TopAbs_FORWARD));

    if(!aShape2.IsSame(aUE2))
      aSubstitutor->Replace(aShape2.Oriented(TopAbs_FORWARD), aUE2.Oriented(TopAbs_FORWARD));

    TopoDS_Vertex V1 = TopExp::LastVertex(aUE1);
    TopoDS_Vertex V2 = TopExp::FirstVertex(aUE2);

    if(V1.IsSame(V2)) {
      acommonflag = (acommonflag == 0) ? ueit : 3;
      aCommonVertices.Append(V1);
    }
  }
  // search common vertices between uedges. end

  if(bvertexfound) {
    if(aCommonVertices.Extent() != 1)
      return Standard_False;

    if(acommonflag == 1)
      aNewEdge = BRepLib_MakeEdge(TopoDS::Vertex(aCommonVertices.First()), aCommonVertex);
    else
      aNewEdge = BRepLib_MakeEdge(aCommonVertex, TopoDS::Vertex(aCommonVertices.First()));

    bHasNewEdge = Standard_True;
  }

  if(aCommonVertices.Extent() == 2) {
    aNewEdge = BRepLib_MakeEdge(TopoDS::Vertex(aCommonVertices.First()),
                                TopoDS::Vertex(aCommonVertices.Last()));
    bHasNewEdge = Standard_True;
  }
  Standard_Integer fit = 0;

  for(fit = 1; fit <= 2; fit++) {
    TopoDS_Compound aComp;
    TopTools_MapOfShape aMapV;
    aBB.MakeCompound(aComp);

    for(ueit = 1, eindex = theIndex; ueit <= 2; ueit++, eindex++) {
      const TopoDS_Shape& aShape = myUEdges->Value(eindex, myUEdges->LowerCol() + fit - 1);
      TopoDS_Shape aUE = aShape;

      if(myHistMap.IsBound(aShape)) {
        const TopTools_ListOfShape& lst = myHistMap.Find(aShape);

        if(!lst.IsEmpty())
          aUE = TopoDS::Edge(lst.First());
      }
      const TopoDS_Shape& aV = (fit == 1) ? TopExp::FirstVertex(TopoDS::Edge(aUE)) : TopExp::LastVertex(TopoDS::Edge(aUE));
      aMapV.Add(aV);
      aBB.Add(aComp, aUE);
    }
    
    if(bHasNewEdge) {
      aBB.Add(aComp, aNewEdge);
      StoreVedgeInHistMap(myVEdges, theIndex, aNewEdge, myHistMap);
    }
    
    TopTools_ListOfShape alonevertices;
    FindFreeVertices(aComp, aMapV, alonevertices);

    if(!alonevertices.IsEmpty() && (alonevertices.Extent() != 2))
      return Standard_False;

    Standard_Integer aFaceIndex = (fit == 1) ? theFaceIndex1 : theFaceIndex2;
    TopoDS_Shape aFace          = theDS->Shape(aFaceIndex);
    TopAbs_Orientation aFaceOri = aFace.Orientation();
    aFace.Orientation(TopAbs_FORWARD);

    TopExp_Explorer anExpE(aFace, TopAbs_EDGE);

    if(bHasNewEdge) {
      aNewEdge.Orientation(TopAbs_FORWARD);
    }

    TopTools_ListOfShape aOrderedList;

    if(!alonevertices.IsEmpty()) {
      Standard_Integer anEIndex = (fit == 1) ? anIndex1 : anIndex2;
      Standard_Boolean bfound1 = Standard_False;
      Standard_Boolean bfound2 = Standard_False;
      Standard_Real aparam1 = 0., aparam2 = 0.;

      BOPDS_ListOfPave aLP;
      theDS->Paves(anEIndex, aLP);
      BOPDS_ListIteratorOfListOfPave aIt;
      aIt.Initialize(aLP);
      for ( ; aIt.More(); aIt.Next()) {
        const BOPDS_Pave& aPave = aIt.Value();
        TopoDS_Shape aV = theDS->Shape(aPave.Index());
        
        if(aV.IsSame(alonevertices.First())) {
          if(!bfound1) {
            aparam1 = aPave.Parameter();
            bfound1 = Standard_True;
          }
        }
        
        if(aV.IsSame(alonevertices.Last())) {
          if(!bfound2) {
            aparam2 = aPave.Parameter();
            bfound2 = Standard_True;
          }
        }
      }

      if(bfound1 && bfound2) {
        TopoDS_Edge aNewBoundE;

        if(fit == 1) {
          aNewBoundE = TopoDS::Edge(aE1.EmptyCopied());
        }
        else {
          aNewBoundE = TopoDS::Edge(aE2.EmptyCopied());
        }
        TopoDS_Vertex aV1, aV2;

        if(aparam1 < aparam2) {
          aV1 = TopoDS::Vertex(alonevertices.First());
          aV2 = TopoDS::Vertex(alonevertices.Last());
        }
        else {
          aV1 = TopoDS::Vertex(alonevertices.Last());
          aV2 = TopoDS::Vertex(alonevertices.First());
          Standard_Real tmp = aparam1;
          aparam1 = aparam2;
          aparam2 = tmp;
        }
        aV1.Orientation(TopAbs_FORWARD);
        aV2.Orientation(TopAbs_REVERSED);
        aBB.Add(aNewBoundE, aV1);
        aBB.Add(aNewBoundE, aV2);
        aBB.Range(aNewBoundE, aparam1, aparam2);
        aNewBoundE.Orientation(TopAbs_FORWARD);

        aOrderedList.Append(aNewBoundE);

        if(bHasNewEdge) {
          TopExp_Explorer anExpV(aNewEdge, TopAbs_VERTEX);
          Standard_Boolean bfoundv = Standard_False;

          for(; !bfoundv && anExpV.More(); anExpV.Next()) {
            if(aV2.IsSame(anExpV.Current()))
              bfoundv = Standard_True;
          }

          if(bfoundv)
            aOrderedList.Append(aNewEdge);
          else
            aOrderedList.Prepend(aNewEdge);
        }
      }
      else {
        return Standard_False;
      }
    }
    else {
      if(bHasNewEdge) {
        aOrderedList.Append(aNewEdge);
      }
    }

    if(!aOrderedList.IsEmpty()) {
      TopoDS_Wire aW;
      aBB.MakeWire(aW);
      TopTools_ListIteratorOfListOfShape anItE(aOrderedList);

      for(; anItE.More(); anItE.Next()) {
        aBB.Add(aW, anItE.Value());
      }
      if(fit == 1)
        aSubstitutor->Replace(aE1.Oriented(TopAbs_FORWARD), aW);
      else
        aSubstitutor->Replace(aE2.Oriented(TopAbs_FORWARD), aW);
    }

    aSubstitutor->Apply(aFace);
    TopoDS_Shape aNewFace = aSubstitutor->Value(aFace);
    aNewFace.Orientation(aFaceOri);
    TopTools_ListOfShape atmpList;
    atmpList.Append(aNewFace);
    myHistMap.Bind(aFace, atmpList);

    anExpE.Init(aFace, TopAbs_EDGE);

    for(; anExpE.More(); anExpE.Next()) {
      TopoDS_Shape aNewValue = aSubstitutor->Value(anExpE.Current());

      if(aNewValue.IsNull() || aNewValue.IsSame(anExpE.Current()))
        continue;

      if (myHistMap.IsBound(anExpE.Current()))
        continue;
      TopTools_ListOfShape aListOfNewEdge;
      TopExp_Explorer anExpE2(aNewValue, TopAbs_EDGE);

      for(; anExpE2.More(); anExpE2.Next()) {
        aListOfNewEdge.Append(anExpE2.Current());
      }
      myHistMap.Bind(anExpE.Current(), aListOfNewEdge);
    }
  }

  return Standard_True;
}

// ----------------------------------------------------------------------------------------------------
// function: MakeFacesSec
// purpose:  Updates <myHistMap> by new faces in the case when old faces intersect each other
// ----------------------------------------------------------------------------------------------------
Standard_Boolean
BRepFill_TrimShellCorner::MakeFacesSec(const Standard_Integer                     theIndex,
                                       const BOPDS_PDS&                           theDS,
                                       const Standard_Integer                     theFaceIndex1, 
                                       const Standard_Integer                     theFaceIndex2, 
                                       const Standard_Integer                     theSSInterfIndex)
{
  const BOPDS_VectorOfInterfFF& aFFs = theDS->InterfFF();
  const BOPDS_InterfFF& aFFi = aFFs(theSSInterfIndex);
  const BOPDS_VectorOfCurve& aBCurves = aFFi.Curves();
  
  TopoDS_Compound aSecEdges;
  TopoDS_Face aSecPlane;

  if(!FilterSectionEdges(aBCurves, aSecPlane, theDS, aSecEdges))
    return Standard_False;

  //Extract vertices on the intersection of correspondent U-edges
  const TopoDS_Shape& LeftE1  = myUEdges->Value(theIndex, 1);
  const TopoDS_Shape& LeftE2  = myUEdges->Value(theIndex, 2);
  const TopoDS_Shape& RightE1 = myUEdges->Value(theIndex+1, 1);
  const TopoDS_Shape& RightE2 = myUEdges->Value(theIndex+1, 2);

  Standard_Integer IndexOfLeftE1  = theDS->Index(LeftE1);
  Standard_Integer IndexOfLeftE2  = theDS->Index(LeftE2);
  Standard_Integer IndexOfRightE1 = theDS->Index(RightE1);
  Standard_Integer IndexOfRightE2 = theDS->Index(RightE2);

  TopoDS_Vertex FirstVertex, LastVertex;
  Standard_Real ParamOnLeftE1, ParamOnLeftE2, ParamOnRightE1, ParamOnRightE2;
  FindCommonVertex(theDS, IndexOfLeftE1, IndexOfLeftE2,
                   FirstVertex, ParamOnLeftE1, ParamOnLeftE2);
  FindCommonVertex(theDS, IndexOfRightE1, IndexOfRightE2,
                   LastVertex, ParamOnRightE1, ParamOnRightE2);

  TopoDS_Shape SecWire;
  gp_Pln SecPlane;
  Standard_Boolean IsSingular;
  Standard_Boolean WireFound = ChooseSection(aSecEdges,
                                             FirstVertex, LastVertex,
                                             SecWire, SecPlane, IsSingular );

  if(WireFound) {
    //aSecEdges = SecWire;
    TopoDS_Compound aComp;
    BRep_Builder BB;
    BB.MakeCompound(aComp);
    TopExp_Explorer explo( SecWire, TopAbs_EDGE );

    for (; explo.More(); explo.Next())
      BB.Add( aComp, explo.Current() );
    aSecEdges = aComp;

    StoreVedgeInHistMap(myVEdges, theIndex, SecWire, myHistMap);
  }

  TopTools_ListOfShape aCommonVertices;
//  Standard_Integer acommonflag = 0; // 0 - no, 1 - first pair, 2 - second pair, 3 - both
  Standard_Integer fit = 0; //, ueit = 0, eindex = 0, i = 0;
  Handle(BRepTools_ReShape) aSubstitutor = new BRepTools_ReShape();

  for(fit = 0; fit < 2; fit++) {
    Standard_Integer aFaceIndex = (fit == 0) ? theFaceIndex1 : theFaceIndex2;
    TopoDS_Face aFace = TopoDS::Face(theDS->Shape(aFaceIndex));
    TopAbs_Orientation aFaceOri = aFace.Orientation();
    TopoDS_Face aFaceF = aFace;
    aFaceF.Orientation(TopAbs_FORWARD);
    TopoDS_Edge aBoundEdge = TopoDS::Edge(myBounds->Value(theIndex, myBounds->LowerCol() +fit));
    Standard_Integer aBoundEdgeIndex = theDS->Index(aBoundEdge);
    TopoDS_Edge aUE1;
    TopoDS_Edge aUE2;

    if(!GetUEdges(theIndex, fit, myUEdges, aBoundEdge, aFaceF, aUE1, aUE2))
      return Standard_False;

    TopoDS_Edge aUE1old = aUE1;
    TopoDS_Edge aUE2old = aUE2;

    if (myHistMap.IsBound(aUE1)) {
      const TopTools_ListOfShape& lst = myHistMap.Find(aUE1);

      if(!lst.IsEmpty()) {
        const TopoDS_Shape& anEdge = lst.First().Oriented(aUE1.Orientation());

        if(!aUE1.IsSame(anEdge))
          aSubstitutor->Replace(aUE1.Oriented(TopAbs_FORWARD), anEdge.Oriented(TopAbs_FORWARD));
        aUE1 = TopoDS::Edge(anEdge);
      }
    }

    if (myHistMap.IsBound(aUE2)) {
      const TopTools_ListOfShape& lst = myHistMap.Find(aUE2);

      if(!lst.IsEmpty()) {
        const TopoDS_Shape& anEdge = lst.First().Oriented(aUE2.Orientation());

        if(!aUE2.IsSame(anEdge))
          aSubstitutor->Replace(aUE2.Oriented(TopAbs_FORWARD), anEdge.Oriented(TopAbs_FORWARD));
        aUE2 = TopoDS::Edge(anEdge);
      }
    }
    TopoDS_Vertex aPrevVertex, aNextVertex;
    TopoDS_Compound aCompOfSecEdges = aSecEdges;
    TopTools_ListOfShape aListOfWireEdges;
    BRep_Builder aBB;
    BOPDS_Pave aPave1;
    Standard_Boolean isPave1OnUEdge = Standard_True;

    if(FindFromUEdge(aUE1old, aUE2old, aUE1, aUE2, aFace, aSecEdges, fit, aBoundEdge, aBoundEdgeIndex, 
                     theDS, myHistMap, aCompOfSecEdges, aListOfWireEdges, aPave1, isPave1OnUEdge)) {
      TopTools_ListOfShape aSecondListOfEdges;
      Standard_Boolean bisSectionFound = Standard_False;

      if(!FindFromVEdge(aPave1, isPave1OnUEdge, aUE1old, aUE2old, aFace, aCompOfSecEdges, fit, aBoundEdge, 
                        aBoundEdgeIndex, theDS, myHistMap, aSecondListOfEdges, bisSectionFound)) {
        return Standard_False;
      }

      if(!bisSectionFound && aListOfWireEdges.IsEmpty()) {
        return Standard_False;
      }
      aListOfWireEdges.Append(aSecondListOfEdges);
    }
    else {
      return Standard_False;
    }

    if(!aListOfWireEdges.IsEmpty()) {
      TopoDS_Wire aW;
      aBB.MakeWire(aW);
      TopTools_ListIteratorOfListOfShape aEIt(aListOfWireEdges);

      for(; aEIt.More(); aEIt.Next()) {
        if(!aBoundEdge.IsSame(aEIt.Value()))
          aBB.Add(aW, aEIt.Value());
      }
      aSubstitutor->Replace(aBoundEdge.Oriented(TopAbs_FORWARD), aW);
    }

    aSubstitutor->Apply(aFace);
    TopoDS_Shape aNewFace = aSubstitutor->Value(aFace);
    aNewFace.Orientation(aFaceOri);
    TopTools_ListOfShape atmpList;
    atmpList.Append(aNewFace);
    myHistMap.Bind(aFace, atmpList);

    TopExp_Explorer anExpE(aFace, TopAbs_EDGE);

    for(; anExpE.More(); anExpE.Next()) {
      TopoDS_Shape aNewValue = aSubstitutor->Value(anExpE.Current());

      if(aNewValue.IsNull() || aNewValue.IsSame(anExpE.Current()))
        continue;

      if (myHistMap.IsBound(anExpE.Current()))
        continue;
      TopTools_ListOfShape aListOfNewEdge;
      TopExp_Explorer anExpE2(aNewValue, TopAbs_EDGE);
      
      for(; anExpE2.More(); anExpE2.Next()) {
        aListOfNewEdge.Append(anExpE2.Current());
      }
      myHistMap.Bind(anExpE.Current(), aListOfNewEdge);
    }
  }
  return Standard_True;
}

//=======================================================================
//function : ChooseSection
//purpose  : 
//=======================================================================
Standard_Boolean BRepFill_TrimShellCorner::ChooseSection(const TopoDS_Shape& Comp,
                                                         const TopoDS_Vertex& theFirstVertex,
                                                         const TopoDS_Vertex& theLastVertex,
                                                         TopoDS_Shape& resWire,
                                                         gp_Pln& resPlane,
                                                         Standard_Boolean& IsSingular)
{
  IsSingular = Standard_False;

  Standard_Integer ind, i, j;
  BRep_Builder BB;

  if (myTransition == BRepFill_Right &&
      !theFirstVertex.IsNull() &&
      !theLastVertex.IsNull()) //the case where section wire goes from
    //its known first vertex to its known last vertex
  {
    TopoDS_Wire NewWire;
    BB.MakeWire(NewWire);
    
    TopoDS_Compound OldComp;
    BB.MakeCompound( OldComp );
    TopoDS_Iterator iter( Comp );
    for (; iter.More(); iter.Next())
      BB.Add( OldComp, iter.Value() );

    TopoDS_Edge FirstEdge = FindEdgeCloseToBisectorPlane(theFirstVertex,
                                                          OldComp,
                                                          myAxeOfBisPlane.Axis());
    iter.Initialize(OldComp);
    if (!iter.More())
    {
      iter.Initialize(Comp);
      BB.Add( OldComp, iter.Value() );
    }
    TopoDS_Edge LastEdge  = FindEdgeCloseToBisectorPlane(theLastVertex,
                                                          OldComp,
                                                          myAxeOfBisPlane.Axis());
    
    BB.Add(NewWire, FirstEdge);

    if (!FirstEdge.IsSame(LastEdge))
    {
      TopoDS_Vertex aCommonVertex;
      Standard_Boolean CommonVertexExists = FindCommonVertex(FirstEdge, LastEdge,
                                                             theFirstVertex, theLastVertex,
                                                             aCommonVertex);
      if (CommonVertexExists)
        BB.Add(NewWire, LastEdge);
      else
      {
        TopoDS_Vertex Vertex1, Vertex2, V1, V2;
        TopExp::Vertices(FirstEdge, V1, V2);
        Vertex1 = (theFirstVertex.IsSame(V1))? V2 : V1;
        TopExp::Vertices(LastEdge, V1, V2);
        Vertex2 = (theLastVertex.IsSame(V1))? V2 : V1;
        
        TopTools_ListOfShape MiddleEdges;
        if (FindMiddleEdges(Vertex1, Vertex2, myAxeOfBisPlane.Axis(), OldComp, MiddleEdges))
        {
          TopTools_ListIteratorOfListOfShape itl(MiddleEdges);
          for (; itl.More(); itl.Next())
            BB.Add(NewWire, itl.Value());
          BB.Add(NewWire, LastEdge);
        }
        else
        {
          //trim <FirstEdge> and <LastEdge> in the points of extrema
          //these points become new vertex with centre between them
          BRepExtrema_ExtCC Extrema(FirstEdge, LastEdge);
          if (Extrema.IsDone() && Extrema.NbExt() > 0)
          {
            Standard_Integer imin = 1;
            for (i = 2; i <= Extrema.NbExt(); i++)
              if (Extrema.SquareDistance(i) < Extrema.SquareDistance(imin))
                imin = i;
            
            Standard_Real aMinDist = sqrt(Extrema.SquareDistance(imin));
            Standard_Real ParamOnFirstEdge = Extrema.ParameterOnE1(imin);
            Standard_Real ParamOnLastEdge  = Extrema.ParameterOnE2(imin);
            gp_Pnt PointOnFirstEdge = Extrema.PointOnE1(imin);
            gp_Pnt PointOnLastEdge  = Extrema.PointOnE2(imin);
            gp_Pnt MidPnt((PointOnFirstEdge.XYZ() + PointOnLastEdge.XYZ())/2);
            aCommonVertex = BRepLib_MakeVertex(MidPnt);
            BB.UpdateVertex(aCommonVertex, 1.001*aMinDist/2);
            
            UpdateSectionEdge(FirstEdge, theFirstVertex, aCommonVertex, ParamOnFirstEdge);
            UpdateSectionEdge(LastEdge,  theLastVertex,  aCommonVertex, ParamOnLastEdge);
            
            BB.Add(NewWire, LastEdge);
          }
        }
      }
    }

    resWire = NewWire;
    resPlane = gp_Pln(myAxeOfBisPlane);
    return Standard_True;
  }

  //General case: try to find continuous section closest to bisector plane
  TopoDS_Compound OldComp;
  BRep_Builder B;
  B.MakeCompound( OldComp );
  TopoDS_Iterator iter( Comp );
  for (; iter.More(); iter.Next())
    B.Add( OldComp, iter.Value() );

  Standard_Boolean anError = Standard_False;
  //TopoDS_Wire NewWire [2];
  TopTools_SequenceOfShape Wseq;
  for (;;)
  {
    TopExp_Explorer explo( OldComp, TopAbs_EDGE );
    if (!explo.More())
      break;
    TopoDS_Edge FirstEdge = TopoDS::Edge( explo.Current() );
    TopoDS_Wire NewWire = BRepLib_MakeWire( FirstEdge );
    B.Remove( OldComp, FirstEdge );
    if (NewWire.Closed())
    {
      Wseq.Append(NewWire);
      continue;
    }
    
    for (;;)
    {
      TopoDS_Vertex Extremity [2];
      TopExp::Vertices( NewWire, Extremity[0], Extremity[1] );
      if (Extremity[0].IsNull() || Extremity[1].IsNull())
      {
        anError = Standard_True;
        break;
      }
      TopTools_IndexedDataMapOfShapeListOfShape VEmap;
      TopExp::MapShapesAndAncestors( OldComp, TopAbs_VERTEX, TopAbs_EDGE, VEmap );
      TopTools_ListOfShape Vedges [2];
      for (j = 0; j < 2; j++)
        if (VEmap.Contains( Extremity[j] ))
          Vedges[j] = VEmap.FindFromKey( Extremity[j] );
      if (Vedges[0].IsEmpty() && Vedges[1].IsEmpty())
        //no more edges in OldComp to continue NewWire
        break;
      Standard_Boolean Modified = Standard_False;
      for (j = 0; j < 2; j++)
      {
        if (Vedges[j].Extent() == 1)
        {
          const TopoDS_Edge& anEdge = TopoDS::Edge( Vedges[j].First() );
          NewWire = BRepLib_MakeWire( NewWire, anEdge );
          B.Remove( OldComp, anEdge );
          Modified = Standard_True;
        }
      }
      if (!Modified) //only multiple connections
      {
        ind = (Vedges[0].IsEmpty())? 1 : 0;
        TopTools_SequenceOfShape Edges;
        TopTools_ListIteratorOfListOfShape itl( Vedges[ind] );
        for (; itl.More(); itl.Next())
          Edges.Append( itl.Value() );
        Standard_Integer theind=0;
        Standard_Real MinDeviation = RealLast();
        for (j = 1; j <= Edges.Length(); j++)
        {
          TopoDS_Wire aWire = BRepLib_MakeWire( NewWire, TopoDS::Edge(Edges(j)) );
          gp_Pln aPlane;
          Standard_Boolean issing;
          Standard_Real Deviation = ComputeAveragePlaneAndMaxDeviation( aWire, aPlane, issing );
          if (Deviation < MinDeviation)
          {
            MinDeviation = Deviation;
            theind = j;
          }
        }
        NewWire = BRepLib_MakeWire( NewWire, TopoDS::Edge(Edges(theind)) );
        B.Remove( OldComp, Edges(theind) );
      }
      if (NewWire.Closed())
        break;
    }
    Wseq.Append(NewWire);
    if (anError)
      break;
  }
  
  Standard_Real MinAngle = RealLast();
  TopExp_Explorer Explo( OldComp, TopAbs_EDGE );
  if (!anError && !Explo.More()) //wires are built successfully and compound <OldComp> is empty
  {
    if (Wseq.Length() == 1) //only one wire => it becomes result
    {
      resWire = Wseq.First();
      ComputeAveragePlaneAndMaxDeviation( resWire, resPlane, IsSingular );
      return Standard_True;
    }
    else //we must choose the wire which average plane is closest to bisector plane
    {    //(check angle between axes)
      for (i = 1; i <= Wseq.Length(); i++)
      {
        TopoDS_Wire aWire = TopoDS::Wire( Wseq(i) );
        gp_Pln aPln;
        Standard_Boolean issing;
        ComputeAveragePlaneAndMaxDeviation( aWire, aPln, issing );
        if (issing)
          continue;
        
        Standard_Real Angle = aPln.Axis().Angle( myAxeOfBisPlane.Axis() );
        if (Angle > M_PI/2)
          Angle = M_PI - Angle;
        
        if (Angle < MinAngle)
        {
          MinAngle = Angle;
          resWire = aWire;
          resPlane = aPln;
        }
      }
      return Standard_True;
    }
  }
  return Standard_False;
}


// ------------------------------------------------------------------------------------------
// static function: SplitUEdges
// purpose:
// ------------------------------------------------------------------------------------------
Standard_Boolean SplitUEdges(const Handle(TopTools_HArray2OfShape)&     theUEdges, 
                             const BOPDS_PDS&                           theDS,
                             TopTools_DataMapOfShapeListOfShape&        theHistMap) {

  const BOPDS_VectorOfInterfVV& aVVs = theDS->InterfVV();

  BRep_Builder aBB;
  Standard_Integer ueit = 0, upRow, lowCol, upCol;
  TopTools_Array2OfShape aNewVertices(1,2,1,2);
  //
  upRow = theUEdges->UpperRow();
  lowCol = theUEdges->LowerCol();
  upCol = theUEdges->UpperCol();
  //
  for(ueit = theUEdges->LowerRow(); ueit <= upRow; ueit++) {
    const TopoDS_Shape& aE1 = theUEdges->Value(ueit, lowCol);
    const TopoDS_Shape& aE2 = theUEdges->Value(ueit, upCol);

    if(theHistMap.IsBound(aE1) || theHistMap.IsBound(aE2))
      continue;

    Standard_Integer anEIndex1 = theDS->Index(aE1);
    Standard_Integer anEIndex2 = theDS->Index(aE2);

    TopoDS_Vertex aCommonVertex;
    Standard_Real apar1 = 0., apar2 = 0.;
    Standard_Boolean bvertexfound = 
      FindCommonVertex(theDS, anEIndex1, anEIndex2, aCommonVertex, apar1, apar2);
    //
    if(!bvertexfound) {
      TopoDS_Vertex V1 = TopExp::LastVertex(TopoDS::Edge(aE1));
      TopoDS_Vertex V2 = TopExp::FirstVertex(TopoDS::Edge(aE2));
      Standard_Integer vindex1 = theDS->Index(V1);
      Standard_Integer vindex2 = theDS->Index(V2);
      Standard_Integer vvit = 0;
      Standard_Integer aNbVVs = aVVs.Length();

      for(vvit = 0; !bvertexfound && (vvit < aNbVVs); vvit++) {
        //const BOPTools_VVInterference& aVV = aVVs(vvit);
        const BOPDS_InterfVV& aVV = aVVs(vvit);

        if(((vindex1 == aVV.Index1()) && (vindex2 == aVV.Index2())) ||
           ((vindex1 == aVV.Index2()) && (vindex2 == aVV.Index1()))) {

          if(!aVV.HasIndexNew()) {
            continue;
          }
          aCommonVertex = TopoDS::Vertex(theDS->Shape(aVV.IndexNew()));
          bvertexfound = Standard_True;
          apar1 = BRep_Tool::Parameter(V1, TopoDS::Edge(aE1));
          apar2 = BRep_Tool::Parameter(V2, TopoDS::Edge(aE2));
        }
      }
    }

    if(bvertexfound) {
      TopoDS_Vertex aV1, aV2;
      Standard_Real f = 0., l = 0.;
      //
      TopoDS_Edge aNewE1 = TopoDS::Edge(aE1.EmptyCopied());
      TopExp::Vertices(TopoDS::Edge(aE1), aV1, aV2);
      aNewE1.Orientation(TopAbs_FORWARD);
      aV1.Orientation(TopAbs_FORWARD);
      aBB.Add(aNewE1, aV1);
      aCommonVertex.Orientation(TopAbs_REVERSED);
      aBB.Add(aNewE1, aCommonVertex);
      BRep_Tool::Range(TopoDS::Edge(aE1), f, l);
      aBB.Range(aNewE1, f, apar1);

      //
      TopoDS_Edge aNewE2 = TopoDS::Edge(aE2.EmptyCopied());
      TopExp::Vertices(TopoDS::Edge(aE2), aV1, aV2);
      aNewE2.Orientation(TopAbs_FORWARD);
      aCommonVertex.Orientation(TopAbs_FORWARD);
      aBB.Add(aNewE2, aCommonVertex);
      aBB.Add(aNewE2, aV2);
      BRep_Tool::Range(TopoDS::Edge(aE2), f, l);
      aBB.Range(aNewE2, apar2, l);

      TopTools_ListOfShape lst;
      lst.Append(aNewE1);
      theHistMap.Bind(aE1, lst);
      lst.Clear();
      lst.Append(aNewE2);
      theHistMap.Bind(aE2, lst);      
    }
  }
  return Standard_True;
}

// ------------------------------------------------------------------------------------------
// static function: StoreVedgeInHistMap
// purpose:
// ------------------------------------------------------------------------------------------
void StoreVedgeInHistMap(const Handle(TopTools_HArray1OfShape)&     theVEdges,
                         const Standard_Integer                     theIndex,
                         const TopoDS_Shape&                        theNewVshape,
                         TopTools_DataMapOfShapeListOfShape&        theHistMap)
{
  //Replace default value in the map (v-iso edge of face)
  //by intersection of two consecutive faces
  const TopoDS_Shape& aVEdge = theVEdges->Value(theIndex);

  theHistMap.Bound(aVEdge, TopTools_ListOfShape())->Append(theNewVshape);
}

// ------------------------------------------------------------------------------------------
// static function: FindFreeVertices
// purpose:
// ------------------------------------------------------------------------------------------
void FindFreeVertices(const TopoDS_Shape&         theShape,
                      const TopTools_MapOfShape&  theVerticesToAvoid,
                      TopTools_ListOfShape&       theListOfVertex) {

  theListOfVertex.Clear();
  TopTools_IndexedDataMapOfShapeListOfShape aMap;
  TopExp::MapShapesAndAncestors(theShape, TopAbs_VERTEX, TopAbs_EDGE, aMap);
  Standard_Integer i = 0;

  for(i = 1; i <= aMap.Extent(); i++) {
    const TopoDS_Shape& aKey = aMap.FindKey(i);

    if(theVerticesToAvoid.Contains(aKey))
      continue;
    const TopTools_ListOfShape& aList = aMap.FindFromIndex(i);

    if(aList.Extent() < 2) {
      theListOfVertex.Append(aKey);
    }
  }
}

// ------------------------------------------------------------------------------------------
// static function: FindCommonVertex
// purpose:
// ------------------------------------------------------------------------------------------
Standard_Boolean FindCommonVertex(const BOPDS_PDS&         theDS,
                                  const Standard_Integer   theEIndex1,
                                  const Standard_Integer   theEIndex2,
                                  TopoDS_Vertex&           theCommonVertex,
                                  Standard_Real&           theParamOnE1,
                                  Standard_Real&           theParamOnE2) {

  const BOPDS_VectorOfInterfEE& aEEs = theDS->InterfEE();

  Standard_Boolean bvertexfound = Standard_False;
  TopoDS_Vertex aCommonVertex;
  Standard_Integer eeit = 0;

  Standard_Integer aNbEEs;
  aNbEEs = aEEs.Length();
  for(eeit = 0; eeit < aNbEEs; ++eeit) {
    const BOPDS_InterfEE& aEE = aEEs(eeit);

    if((theEIndex1 == aEE.Index1() && theEIndex2 == aEE.Index2()) || 
       (theEIndex1 == aEE.Index2() && theEIndex2 == aEE.Index1())) {

      if(!aEE.HasIndexNew())
        continue;

      IntTools_CommonPrt aCP = aEE.CommonPart();
      if(aCP.Type() == TopAbs_VERTEX)
      {
        theCommonVertex = *(TopoDS_Vertex*)&theDS->Shape(aEE.IndexNew());
        
        if (theEIndex1 == aEE.Index1())
          IntTools_Tools::VertexParameters(aCP, theParamOnE1, theParamOnE2);
        else
          IntTools_Tools::VertexParameters(aCP, theParamOnE2, theParamOnE1);
       
        //
        bvertexfound = Standard_True;
        break;
      }
    }
  }
  return bvertexfound;
}

// ----------------------------------------------------------------------------------------------------
// static function: GetUEdges
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean GetUEdges(const Standard_Integer                     theIndex,
                           const Standard_Integer                     theRank,
                           const Handle(TopTools_HArray2OfShape)&     theUEdges,
                           const TopoDS_Edge&                         theBoundEdge,
                           const TopoDS_Face&                         theFace,
                           TopoDS_Edge&                               theFirstUEdge,
                           TopoDS_Edge&                               theSecondUEdge) {
  const TopoDS_Shape& aUE1 = theUEdges->Value(theIndex, theUEdges->LowerCol() + theRank);
  const TopoDS_Shape& aUE2 = theUEdges->Value(theIndex + 1, theUEdges->LowerCol() + theRank);

  TopoDS_Face aFace = theFace;
  aFace.Orientation(TopAbs_FORWARD);
  TopoDS_Edge E1, E2;
  TopExp_Explorer anExp(aFace, TopAbs_EDGE);

  for(; anExp.More(); anExp.Next()) {
    if(E1.IsNull() && aUE1.IsSame(anExp.Current())) {
      E1 = TopoDS::Edge(anExp.Current());
    }
    else if(E2.IsNull() && aUE2.IsSame(anExp.Current())) {
      E2 = TopoDS::Edge(anExp.Current());
    }
  }

  if(E1.IsNull() || E2.IsNull())
    return Standard_False;

  Standard_Real f, l;
  Handle(Geom2d_Curve) C1 = BRep_Tool::CurveOnSurface(E1, aFace, f, l);

  if(C1.IsNull())
     return Standard_False;
  gp_Pnt2d PU1 = (theRank == 0) ? C1->Value(l) : C1->Value(f);
  Handle(Geom2d_Curve) C2 = BRep_Tool::CurveOnSurface(theBoundEdge, aFace, f, l);

  if(C2.IsNull())
    return Standard_False;
  BRep_Tool::Range(theBoundEdge, f, l);
  gp_Pnt2d pf = C2->Value(f);
  TopoDS_Vertex aV = (theRank == 0) ? TopExp::LastVertex(E1) : TopExp::FirstVertex(E1);
  Standard_Real aTolerance = BRep_Tool::Tolerance(aV);
  BRepAdaptor_Surface aBAS(aFace, Standard_False);

  if(pf.Distance(PU1) > aBAS.UResolution(aTolerance)) {
    TopoDS_Edge atmpE = E1;
    E1 = E2;
    E2 = atmpE;
  }
  theFirstUEdge = E1;
  theSecondUEdge = E2;
  return Standard_True;
}

// ----------------------------------------------------------------------------------------------------
// static function: FillGap
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean FillGap(const TopoDS_Vertex&   theFirstVertex,
                         const TopoDS_Vertex&   theLastVertex,
                         const gp_Pnt2d&        theFirstPoint,
                         const gp_Pnt2d&        theLastPoint,
                         const TopoDS_Face&     theFace,
                         const TopoDS_Compound& theSectionEdges,
                         TopTools_ListOfShape&  theOrderedList) {

  TopTools_IndexedDataMapOfShapeListOfShape aMap;
  TopExp::MapShapesAndAncestors(theSectionEdges, TopAbs_VERTEX, TopAbs_EDGE, aMap);

  if(aMap.IsEmpty()) {
    return Standard_False;
  }

  if(!aMap.Contains(theFirstVertex) || 
     !aMap.Contains(theLastVertex)) {
    return Standard_False;
  }
  TopTools_ListOfShape aListOfEdge;
//  Standard_Integer i = 0;
//  TopoDS_Vertex aCurVertex = theFirstVertex;
  TopTools_MapOfShape aMapToAvoid;

  if(FindNextEdge(theFirstVertex, theLastVertex, aMap, aMapToAvoid, aListOfEdge)) {
    if(!aListOfEdge.IsEmpty()) {
      return CheckAndOrientEdges(aListOfEdge, theFirstPoint, theLastPoint, theFace, theOrderedList);
    }
  }
  return Standard_False;
}

// ----------------------------------------------------------------------------------------------------
// static function: FindNextEdge
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean FindNextEdge(const TopoDS_Vertex&   theFirstVertex,
                              const TopoDS_Vertex&   theLastVertex,
                              const TopTools_IndexedDataMapOfShapeListOfShape& theMapVE,
                              const TopTools_MapOfShape& theMapToAvoid,
                              TopTools_ListOfShape&  theOrderedList) {
  TopoDS_Vertex aCurVertex = theFirstVertex;
  TopTools_MapOfShape aMapToAvoid;
  aMapToAvoid = theMapToAvoid;
  TopTools_ListOfShape aListOfEdge;
  Standard_Integer i = 0;

  for(i = 1; i <= theMapVE.Extent(); i++) {
    if(!theMapVE.Contains(aCurVertex))
      break;
    const TopTools_ListOfShape& lste = theMapVE.FindFromKey(aCurVertex);
    Standard_Boolean befound = Standard_False;

    TopTools_ListIteratorOfListOfShape anIt(lste);

    for(; anIt.More(); anIt.Next()) {
      TopoDS_Shape anEdge = anIt.Value();
      TopoDS_Vertex aSaveCurVertex = aCurVertex;

      if(!aMapToAvoid.Contains(anEdge)) {
        TopoDS_Vertex V1, V2;
        TopExp::Vertices(TopoDS::Edge(anEdge), V1, V2);

        if(!aCurVertex.IsSame(V1)) {
          aCurVertex = V1;
        }
        else if(!aCurVertex.IsSame(V2)) {
          aCurVertex = V2;
        }
        aMapToAvoid.Add(anEdge);
        befound = Standard_True;
        aListOfEdge.Append(anEdge);

        if(!aCurVertex.IsSame(theLastVertex)) {
          TopTools_ListOfShape aListtmp;

          if(!FindNextEdge(aCurVertex, theLastVertex, theMapVE, aMapToAvoid, aListtmp)) {
            aListOfEdge.Clear();
            aCurVertex = aSaveCurVertex;
            continue;
          }
          else {
            aListOfEdge.Append(aListtmp);
            theOrderedList.Append(aListOfEdge);
            return Standard_True;
          }
        }
        break;
      }
    }

    if(aCurVertex.IsSame(theLastVertex))
      break;

    if(!befound) {
      return Standard_False;
    }
  }

  if(aCurVertex.IsSame(theLastVertex)) {
    theOrderedList.Append(aListOfEdge);
    return Standard_True;
  }
  return Standard_False;
}

// ----------------------------------------------------------------------------------------------------
// static function: CheckAndOrientEdges
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean CheckAndOrientEdges(const TopTools_ListOfShape&  theOrderedList,
                                     const gp_Pnt2d&              theFirstPoint,
                                     const gp_Pnt2d&              theLastPoint,
                                     const TopoDS_Face&           theFace,
                                     TopTools_ListOfShape&        theOrientedList) {
  TopTools_ListIteratorOfListOfShape anIt(theOrderedList);

  if(!anIt.More())
    return Standard_True;

  Standard_Real f, l;  
  TopoDS_Edge aEPrev = TopoDS::Edge(anIt.Value());
  anIt.Next();

  Handle(Geom2d_Curve) aCurve = BRep_Tool::CurveOnSurface(aEPrev, theFace, f, l);
  TopoDS_Vertex Vf, Vl;
  TopExp::Vertices(aEPrev, Vf, Vl);
  BRepAdaptor_Surface aBAS(theFace, Standard_False);

  Standard_Real aTolerance1 = (Vf.IsNull()) ? Precision::Confusion() : BRep_Tool::Tolerance(Vf);
  Standard_Real aTolerance2 = (Vl.IsNull()) ? Precision::Confusion() : BRep_Tool::Tolerance(Vl);
  Standard_Real utol = aBAS.UResolution(aTolerance1);
  Standard_Real vtol = aBAS.VResolution(aTolerance1);
  aTolerance1 = (utol > vtol) ? utol : vtol;
  utol = aBAS.UResolution(aTolerance2);
  vtol = aBAS.VResolution(aTolerance2);
  aTolerance2 = (utol > vtol) ? utol : vtol;

  gp_Pnt2d ap = aCurve->Value(f);
  Standard_Boolean bFirstFound = Standard_False;
  Standard_Boolean bLastFound = Standard_False;

  if(ap.Distance(theFirstPoint) < aTolerance1) {
    if(theOrientedList.IsEmpty())
      theOrientedList.Append(aEPrev.Oriented(TopAbs_FORWARD));
    bFirstFound = Standard_True;
  }
  else if(ap.Distance(theLastPoint) < aTolerance1) {
    if(theOrientedList.IsEmpty())
      theOrientedList.Append(aEPrev.Oriented(TopAbs_REVERSED));
    bLastFound = Standard_True;
  }
  ap = aCurve->Value(l);

  if(ap.Distance(theLastPoint) < aTolerance2) {
    if(theOrientedList.IsEmpty())
      theOrientedList.Append(aEPrev.Oriented(TopAbs_FORWARD));
    bLastFound = Standard_True;
  }
  else if(ap.Distance(theFirstPoint) < aTolerance2) {
    if(theOrientedList.IsEmpty())
      theOrientedList.Append(aEPrev.Oriented(TopAbs_REVERSED));
    bFirstFound = Standard_True;
  }

  if (!theOrientedList.IsEmpty())
    aEPrev = TopoDS::Edge (theOrientedList.Last());

  for(; anIt.More(); anIt.Next()) {
    const TopoDS_Edge& aE = TopoDS::Edge(anIt.Value());
    TopoDS_Vertex aV11, aV12;
    TopExp::Vertices(aEPrev, aV11, aV12, Standard_True);
    TopoDS_Vertex aV21, aV22;
    TopExp::Vertices(aE, aV21, aV22, Standard_False);

    TopAbs_Orientation anOri =
      (aV12.IsSame (aV21) || aV11.IsSame (aV22)) ? TopAbs_FORWARD : TopAbs_REVERSED;
    theOrientedList.Append(aE.Oriented(anOri));
    aEPrev = TopoDS::Edge (theOrientedList.Last());

    aTolerance1 = (aV21.IsNull()) ? Precision::Confusion() : BRep_Tool::Tolerance(aV21);
    aTolerance2 = (aV22.IsNull()) ? Precision::Confusion() : BRep_Tool::Tolerance(aV22);
    utol = aBAS.UResolution(aTolerance1);
    vtol = aBAS.VResolution(aTolerance1);
    aTolerance1 = (utol > vtol) ? utol : vtol;
    utol = aBAS.UResolution(aTolerance2);
    vtol = aBAS.VResolution(aTolerance2);
    aTolerance2 = (utol > vtol) ? utol : vtol;
    aCurve = BRep_Tool::CurveOnSurface(aE, theFace, f, l);
    ap = aCurve->Value(f);

    if(ap.Distance(theFirstPoint) < aTolerance1) {
      bFirstFound = Standard_True;
    }
    else if(ap.Distance(theLastPoint) < aTolerance1) {
      bLastFound = Standard_True;
    }
    ap = aCurve->Value(l);

    if(ap.Distance(theFirstPoint) < aTolerance2) {
      bFirstFound = Standard_True;
    }
    else if(ap.Distance(theLastPoint) < aTolerance2) {
      bLastFound = Standard_True;
    }
  }

  return bFirstFound && bLastFound;
}

// ----------------------------------------------------------------------------------------------------
// static function: FindVertex
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean FindVertex(const TopoDS_Edge&                        theEdge,
                            const Standard_Integer                    theRank, 
                            const BOPDS_PDS&                          theDS,
                            const TopTools_DataMapOfShapeListOfShape& theHistMap, 
                            TopoDS_Vertex&                            theVertex,
                            BOPDS_Pave&                               thePave) {

  if(!theHistMap.IsBound(theEdge))
    return Standard_False;

  const TopTools_ListOfShape& lst = theHistMap.Find(theEdge);

  if(lst.IsEmpty())
    return Standard_False;

  TopoDS_Edge aNewEdge = TopoDS::Edge(lst.First());
  Standard_Real f, l;
  BRep_Tool::Range(aNewEdge, f, l);

  if(theRank == 0) {
    thePave.SetParameter(l);
    theVertex = TopExp::LastVertex(aNewEdge);
  }
  else {
    thePave.SetParameter(f);
    theVertex = TopExp::FirstVertex(aNewEdge);
  }
  Standard_Integer anIndex = theDS->Index(theVertex);
  if (anIndex == -1) {
    Standard_Integer i, i1, i2;
    i1=theDS->NbSourceShapes();
    i2=theDS->NbShapes();
    for (i=i1; i<i2; ++i) {
      const TopoDS_Shape& aSx=theDS->Shape(i);
      if(aSx.IsSame(theVertex)) {
        anIndex = i;
        break;
      }
    }
  }

  thePave.SetIndex(anIndex);

  return Standard_True;
}

// ----------------------------------------------------------------------------------------------------
// static function: FindNextVertex
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean FindNextVertex(const Standard_Integer                    theEdgeIndex,
                                const BOPDS_Pave&                         thePrevPave,
                                const BOPDS_PDS&                          theDS,
                                TopoDS_Vertex&                            theNextVertex,
                                BOPDS_Pave&                               thePave) {

  Standard_Boolean bTakePave, bFound;
  BOPDS_Pave aTmpPave;
  BOPDS_ListIteratorOfListOfPave aItP;
  //
  BOPDS_Pave anullpave;
  bFound = Standard_False;
  bTakePave = thePrevPave.IsEqual(anullpave);

  BOPDS_ListOfPave aLP;
  theDS->Paves(theEdgeIndex, aLP);
  aItP.Initialize(aLP);
  for (; aItP.More(); aItP.Next()) {
    aTmpPave = aItP.Value();
    //
    if (bTakePave) {
      if (theDS->IsNewShape(aTmpPave.Index())) {
        theNextVertex = *(TopoDS_Vertex*)&theDS->Shape(aTmpPave.Index());
        thePave = aTmpPave;
        bFound = Standard_True;
        break;
      }
    }
    //
    else if (aTmpPave.IsEqual(thePrevPave)) {
      bTakePave = Standard_True;
    }
  }
  
  return bFound;
}

// ----------------------------------------------------------------------------------------------------
// static function: GetPave
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean GetPave(const Standard_Integer    theEdgeIndex,
                         const Standard_Boolean    isFirst,
                         const BOPDS_PDS&          theDS,
                         BOPDS_Pave&               thePave) {

  Handle(BOPDS_PaveBlock) aPB;
  BOPDS_ListOfPave aLP;
  
  theDS->Paves(theEdgeIndex, aLP);
  if (!aLP.Extent()) {
    return Standard_False;
  }
  //
  if (isFirst) {
    thePave = aLP.First();
  }
  else {
    thePave = aLP.Last();
  }

  return Standard_True;
}

// ----------------------------------------------------------------------------------------------------
// static function: FindFromUEdge
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean FindFromUEdge(const TopoDS_Edge&                        theUE1Old, 
                               const TopoDS_Edge&                        theUE2Old, 
                               const TopoDS_Edge&                        theUE1New, 
                               const TopoDS_Edge&                        theUE2New, 
                               const TopoDS_Face&                        theFace, 
                               const TopoDS_Compound&                    theSecEdges, 
                               const Standard_Integer                    theRank, 
                               const TopoDS_Edge&                        theBoundEdge, 
                               const Standard_Integer                    theBoundEdgeIndex, 
                               const BOPDS_PDS&                          theDS,
                               const TopTools_DataMapOfShapeListOfShape& theHistMap,
                               TopoDS_Compound&                          theSecEdgesNew, 
                               TopTools_ListOfShape&                     theListOfWireEdges, 
                               BOPDS_Pave&                               theFoundPave,
                               Standard_Boolean&                         isOnUEdge) {
  theFoundPave.SetIndex(0);
  theFoundPave.SetParameter(0.);
  isOnUEdge = Standard_True;

  TopoDS_Face aFaceF = theFace;
  aFaceF.Orientation(TopAbs_FORWARD);
  TopoDS_Vertex aPrevVertex, aNextVertex;
  TopoDS_Compound aCompOfSecEdges = theSecEdges;
  TopTools_ListOfShape aListOfWireEdges;
//  BRep_Builder aBB;

  BOPDS_Pave aPave1, aPave2;
  Standard_Real f = 0., l = 0.;
  gp_Pnt2d p1, p2;
  TopoDS_Vertex aFirstV, aLastV;
  BOPDS_Pave atmpPave;

  if(!FindVertex(theUE1Old, theRank, theDS, theHistMap, aPrevVertex, atmpPave)) {
    return Standard_True;
  }

  if(aPrevVertex.IsNull()) {
    return Standard_False;
  }

  aFirstV = aPrevVertex;
  Standard_Boolean bSecFound = Standard_False;
  Handle(Geom2d_Curve) aC1 = BRep_Tool::CurveOnSurface(theUE1New, aFaceF, f, l);
  p1 = (theRank == 0) ? aC1->Value(l) : aC1->Value(f);
  BOPDS_Pave afoundpave;
  BOPDS_ListOfPave aLP;
  theDS->Paves(theBoundEdgeIndex, aLP);
  Standard_Integer nbpave = aLP.Extent();
  Standard_Integer pit = 0;
  
  while(FindNextVertex(theBoundEdgeIndex, aPave1, theDS, aNextVertex, aPave2) && (pit < nbpave)) {
    aLastV = aNextVertex;
    Handle(Geom2d_Curve) aC2 = BRep_Tool::CurveOnSurface(theBoundEdge, aFaceF, f, l);
    p2 = aC2->Value(aPave2.Parameter());
    TopTools_ListOfShape aOrderedList;

    if(FillGap(aFirstV, aLastV, p1, p2, aFaceF, aCompOfSecEdges, aOrderedList)) {
      // remove found edges...
      TopoDS_Compound aComp;
      RemoveEdges(aCompOfSecEdges, aOrderedList, aComp);
      aCompOfSecEdges = aComp;
      aListOfWireEdges.Append(aOrderedList);
      afoundpave = aPave2;
      isOnUEdge = Standard_False;
      bSecFound = Standard_True;
      break;
    }
    aPrevVertex = aNextVertex;
    aPave1 = aPave2;
    pit++;
  }

  if(!bSecFound && FindVertex(theUE2Old, theRank, theDS, theHistMap, aNextVertex, aPave2)) {
    aLastV = aNextVertex;
    Handle(Geom2d_Curve) aC2 = BRep_Tool::CurveOnSurface(theUE2New, aFaceF, f, l);
    p2 = aC2->Value(aPave2.Parameter());
    TopTools_ListOfShape aOrderedList;

    if(FillGap(aFirstV, aLastV, p1, p2, aFaceF, aCompOfSecEdges, aOrderedList)) {
      // remove found edges...
      TopoDS_Compound aComp;

      RemoveEdges(aCompOfSecEdges, aOrderedList, aComp);
      aCompOfSecEdges = aComp;
      aListOfWireEdges.Append(aOrderedList);
      afoundpave = aPave2;
      bSecFound = Standard_True;
      isOnUEdge = Standard_True;
    }
  }

  if(bSecFound) {
    theFoundPave = afoundpave;
    theListOfWireEdges = aListOfWireEdges;
    theSecEdgesNew = aCompOfSecEdges;
  }
  return Standard_True;
}


// ----------------------------------------------------------------------------------------------------
// static function: FindFromVEdge
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean FindFromVEdge(const BOPDS_Pave&                         thePrevPave,
                               const Standard_Boolean&                   isOnUEdge,
                               const TopoDS_Edge&                        theUE1Old, 
                               const TopoDS_Edge&                        theUE2Old, 
                               const TopoDS_Face&                        theFace, 
                               const TopoDS_Compound&                    theSecEdges, 
                               const Standard_Integer                    theRank, 
                               const TopoDS_Edge&                        theBoundEdge, 
                               const Standard_Integer                    theBoundEdgeIndex, 
                               const BOPDS_PDS&                          theDS,
                               const TopTools_DataMapOfShapeListOfShape& theHistMap,
                               TopTools_ListOfShape&                     theListOfWireEdges, 
                               Standard_Boolean&                         isSectionFound) {

  theListOfWireEdges.Clear();
  isSectionFound = Standard_False;
  //
  TopoDS_Face aFaceF = theFace;
  aFaceF.Orientation(TopAbs_FORWARD);
  TopoDS_Vertex aPrevVertex, aNextVertex;
  TopoDS_Compound aCompOfSecEdges = theSecEdges;
  TopTools_ListOfShape aListOfWireEdges;
//  BRep_Builder aBB;

  BOPDS_Pave aPave1, aPave2;

  if(isOnUEdge) {
    TopoDS_Vertex atmpVertex;
    BOPDS_Pave aPaveOfE2;

    if(FindVertex(theUE2Old, theRank, theDS, theHistMap, atmpVertex, aPaveOfE2)) {
      if(thePrevPave.IsEqual(aPaveOfE2))
        return Standard_True;
    }
  }

  Standard_Real f = 0., l = 0.;
  gp_Pnt2d p1(0., 0.), p2(0., 0.);
  TopoDS_Vertex aFirstV, aLastV;
  Handle(Geom2d_Curve) aC1 = BRep_Tool::CurveOnSurface(theUE1Old, aFaceF, f, l);
  Handle(Geom2d_Curve) aC2 = BRep_Tool::CurveOnSurface(theBoundEdge, aFaceF, f, l);
  Standard_Boolean bSecFound = Standard_False;

  aPave1 = thePrevPave;

  if(isOnUEdge) {
    BOPDS_Pave atmpPave;

    if(!GetPave(theBoundEdgeIndex, Standard_True, theDS, atmpPave)) {
      return Standard_False;
    }
    aPave1 = atmpPave;
  }
  p1 = aC2->Value(aPave1.Parameter());
  aPrevVertex = TopoDS::Vertex(theDS->Shape(aPave1.Index()));

  BOPDS_ListOfPave aLP;
  theDS->Paves(theBoundEdgeIndex, aLP);
  Standard_Integer nbpave = aLP.Extent();
  Standard_Integer pit = 0;
  TopTools_Array1OfListOfShape anArrayOfListOfSec(1, nbpave);

  // by pairs non continuously. begin
  Standard_Integer k = 0;
  BOPDS_Pave aFirstPave = aPave1;
  TopoDS_Vertex aFirstVertex = aPrevVertex;
  gp_Pnt2d apfirst = p1;
  BOPDS_ListOfPave aFirstPaves, aLastPaves;
  TColStd_ListOfInteger aListOfFlags;
  Standard_Integer apaircounter = 1;

  for(k = 0; k < nbpave; k++) {
    aPave1 = aFirstPave;
    p1 = apfirst;
    aPrevVertex = aFirstVertex;
    Standard_Boolean bfound = Standard_False;
    pit = 0;

    while(FindNextVertex(theBoundEdgeIndex, aPave1, theDS, aNextVertex, aPave2) && (pit < nbpave)) {
      aFirstV = aPrevVertex;
      aLastV = aNextVertex;
      p2 = aC2->Value(aPave2.Parameter());

      TopTools_ListOfShape aOrderedList;

      if(FillGap(aFirstV, aLastV, p1, p2, aFaceF, aCompOfSecEdges, aOrderedList)) {
        TopoDS_Compound aComp;
        RemoveEdges(aCompOfSecEdges, aOrderedList, aComp);
        aCompOfSecEdges = aComp;

        anArrayOfListOfSec(apaircounter++).Append(aOrderedList);
        aFirstPaves.Append(aFirstPave);
        aLastPaves.Append(aPave2);
        aListOfFlags.Append(1);
        aFirstPave = aPave2;
        aFirstVertex = aNextVertex;
        apfirst = p2;
        aPrevVertex = aNextVertex;
        bSecFound = Standard_True;
        bfound = Standard_True;
      }
      aPave1 = aPave2;
      pit++;
    }

    if(FindVertex(theUE2Old, theRank, theDS, theHistMap, aNextVertex, aPave2)) {
      aFirstV = aPrevVertex;
      aLastV = aNextVertex;
      Handle(Geom2d_Curve) aC3 = BRep_Tool::CurveOnSurface(theUE2Old, aFaceF, f, l);
      p2 = aC3->Value(aPave2.Parameter());

      TopTools_ListOfShape aOrderedList;

      if(FillGap(aFirstV, aLastV, p1, p2, aFaceF, aCompOfSecEdges, aOrderedList)) {
        TopoDS_Compound aComp;
        RemoveEdges(aCompOfSecEdges, aOrderedList, aComp);
        aCompOfSecEdges = aComp;
        anArrayOfListOfSec(apaircounter++).Append(aOrderedList);
        aFirstPaves.Append(aFirstPave);
        aLastPaves.Append(aPave2);
        aListOfFlags.Append(0);
        bSecFound = Standard_True;
        break;
      }
    }

    if(!bfound) {
      if(!FindNextVertex(theBoundEdgeIndex, aFirstPave, theDS, aNextVertex, aPave2)) {
        break;
      }
      aFirstPave = aPave2;
      apfirst = aC2->Value(aPave2.Parameter());
      aFirstVertex = aNextVertex;
    }
  }
  // by pairs non continuously. end

  // by pairs continuously. begin
  aPave1 = thePrevPave;

  if(isOnUEdge) {
    BOPDS_Pave atmpPave;

    if(!GetPave(theBoundEdgeIndex, Standard_True, theDS, atmpPave)) {
      return Standard_False;
    }
    aPave1 = atmpPave;
  }
  p1 = aC2->Value(aPave1.Parameter());
  aPrevVertex = TopoDS::Vertex(theDS->Shape(aPave1.Index()));

  pit = 0;

  while(FindNextVertex(theBoundEdgeIndex, aPave1, theDS, aNextVertex, aPave2) && (pit < nbpave)) {
    aFirstV = aPrevVertex;
    aLastV = aNextVertex;
    p2 = aC2->Value(aPave2.Parameter());

    Standard_Boolean bisinside = Standard_False;
    Standard_Integer apbindex = 0;
    Standard_Integer apbcounter = 1;
    BOPDS_ListIteratorOfListOfPaveBlock aPBIt;
    BOPDS_ListIteratorOfListOfPave aPIt1, aPIt2;
    TColStd_ListIteratorOfListOfInteger aFlagIt;

    for(aPIt1.Initialize(aFirstPaves), aPIt2.Initialize(aLastPaves), aFlagIt.Initialize(aListOfFlags); 
        aPIt1.More() && aPIt2.More() && aFlagIt.More(); 
        aPIt1.Next(), aPIt2.Next(), aFlagIt.Next(), apbcounter++) {

      Standard_Boolean bfin = Standard_False;
      Standard_Boolean blin = Standard_False;

      if(aPave1.IsEqual(aPIt1.Value())) {
        bfin = Standard_True;
      }
      else {
        bfin = (aPave1.Parameter() > aPIt1.Value().Parameter());
      }

      if(aFlagIt.Value()) {
        if(aPave2.IsEqual(aPIt2.Value())) {
          blin = Standard_True;
        }
        else {
          blin = (aPave2.Parameter() < aPIt2.Value().Parameter());
        }
      }
      else {
        if((aPave2.Index() == aPIt2.Value().Index()) && (aPave2.Index() > 0)) {
          Handle(Geom2d_Curve) pc = BRep_Tool::CurveOnSurface(theUE2Old, aFaceF, f, l);
          gp_Pnt2d p3 = pc->Value(aPIt2.Value().Parameter());
          TopoDS_Vertex aV = TopoDS::Vertex(theDS->Shape(aPave2.Index()));
          BRepAdaptor_Surface aBAS(aFaceF, Standard_False);
          Standard_Real aTolerance = BRep_Tool::Tolerance(aV);
          Standard_Real utol = aBAS.UResolution(aTolerance);
          Standard_Real vtol = aBAS.VResolution(aTolerance);
          aTolerance = (utol > vtol) ? utol : vtol;

          if(p2.Distance(p3) < aTolerance)
            blin = Standard_True;
        }
      }

      if(bfin && blin) {
        apbindex = apbcounter;
        bisinside = Standard_True;
        break;
      }
    }

    if(!bisinside) {

      TopTools_ListOfShape aOrderedList;

      if(FillGap(aFirstV, aLastV, p1, p2, aFaceF, aCompOfSecEdges, aOrderedList)) {
        TopoDS_Compound aComp;
        RemoveEdges(aCompOfSecEdges, aOrderedList, aComp);
        aCompOfSecEdges = aComp;
        aListOfWireEdges.Append(aOrderedList);

        bSecFound = Standard_True;
      }
      else {
        TopoDS_Edge aESplit;
        // get split
        aPBIt.Initialize(theDS->PaveBlocks(theBoundEdgeIndex));

        for(; aPBIt.More(); aPBIt.Next()) {
          const Handle(BOPDS_PaveBlock)& aPB1 = aPBIt.Value();
          if (aPB1->OriginalEdge() == theBoundEdgeIndex &&
              aPB1->Pave1().IsEqual(aPave1) &&
              aPB1->Pave2().IsEqual(aPave2) ) {
            if(aPB1->Edge() > 0) {
              aESplit = *(TopoDS_Edge*)&theDS->Shape(aPB1->Edge());
              break;
            }
          }
        }
        
        if(!aESplit.IsNull()) {
          aListOfWireEdges.Append(aESplit);
        }
      }
    }
    else {
      if(apbindex > 0) {
        TopTools_ListOfShape& aListOfSec = anArrayOfListOfSec(apbindex);
        aListOfWireEdges.Append(aListOfSec);
      }
    }
    aPave1 = aPave2;
    aPrevVertex = aNextVertex;
    p1 = p2;
    pit++;
  }

  if(FindVertex(theUE2Old, theRank, theDS, theHistMap, aNextVertex, aPave2)) {
    aFirstV = aPrevVertex;
    aLastV = aNextVertex;
    Handle(Geom2d_Curve) aC3 = BRep_Tool::CurveOnSurface(theUE2Old, aFaceF, f, l);
    p2 = aC3->Value(aPave2.Parameter());

    Standard_Boolean bisinside = Standard_False;
    Standard_Integer apbindex = 0;
    Standard_Integer apbcounter = 1;
    BOPDS_ListIteratorOfListOfPaveBlock aPBIt;
    BOPDS_ListIteratorOfListOfPave aPIt1, aPIt2;
    TColStd_ListIteratorOfListOfInteger aFlagIt;

    for(aPIt1.Initialize(aFirstPaves), aPIt2.Initialize(aLastPaves), aFlagIt.Initialize(aListOfFlags); 
        aPIt1.More() && aPIt2.More() && aFlagIt.More(); 
        aPIt1.Next(), aPIt2.Next(), aFlagIt.Next(), apbcounter++) {

      Standard_Boolean bfin = Standard_False;
      Standard_Boolean blin = Standard_False;

      if(aPave1.IsEqual(aPIt1.Value())) {
        bfin = Standard_True;
      }
      else {
        bfin = (aPave1.Parameter() > aPIt1.Value().Parameter());
      }

      if(aFlagIt.Value()) {
        if(aPave2.IsEqual(aPIt2.Value())) {
          blin = Standard_True;
        }
        else {
          blin = (aPave2.Parameter() < aPIt2.Value().Parameter());
        }
      }
      else {
        blin = Standard_True;
      }

      if(bfin && blin) {
        apbindex = apbcounter;
        bisinside = Standard_True;
        break;
      }
    }

    if(!bisinside) {

      TopTools_ListOfShape aOrderedList;

      if(FillGap(aFirstV, aLastV, p1, p2, aFaceF, aCompOfSecEdges, aOrderedList)) {
        TopoDS_Compound aComp;
        RemoveEdges(aCompOfSecEdges, aOrderedList, aComp);
        aCompOfSecEdges = aComp;
        aListOfWireEdges.Append(aOrderedList);

        bSecFound = Standard_True;
      }
      else {
        //add split
        TopoDS_Edge aESplit;
        // get split
        if(!GetPave(theBoundEdgeIndex, Standard_False, theDS, aPave2))
          return Standard_False;
        //
        aPBIt.Initialize(theDS->PaveBlocks(theBoundEdgeIndex));
        for(; aPBIt.More(); aPBIt.Next()) {
          const Handle(BOPDS_PaveBlock)& aPB1 = aPBIt.Value();
          if (aPB1->OriginalEdge() == theBoundEdgeIndex &&
              aPB1->Pave1().IsEqual(aPave1) &&
              aPB1->Pave2().IsEqual(aPave2) ) {
            if(aPB1->Edge() > 0) {
              aESplit = *(TopoDS_Edge*)&theDS->Shape(aPB1->Edge());
              break;
            }
          }
        }

        if(!aESplit.IsNull()) {
          aListOfWireEdges.Append(aESplit);
        }
      }
    }
    else {
      if(apbindex > 0) {
        TopTools_ListOfShape& aListOfSec = anArrayOfListOfSec(apbindex);
        aListOfWireEdges.Append(aListOfSec);
      }
    }
  }
  else {
    //add split
    TopoDS_Edge aESplit;
    // get split
    if(!GetPave(theBoundEdgeIndex, Standard_False, theDS, aPave2))
      return Standard_False;

    BOPDS_ListIteratorOfListOfPaveBlock aPBIt;
    aPBIt.Initialize(theDS->PaveBlocks(theBoundEdgeIndex));
    for(; aPBIt.More(); aPBIt.Next()) {
      const Handle(BOPDS_PaveBlock)& aPB1 = aPBIt.Value();
      if (aPB1->OriginalEdge() == theBoundEdgeIndex &&
          aPB1->Pave1().IsEqual(aPave1) &&
          aPB1->Pave2().IsEqual(aPave2) ) {
        if(aPB1->Edge() > 0) {
          aESplit = *(TopoDS_Edge*)&theDS->Shape(aPB1->Edge());
          break;
        }
      }
    }

    if(!aESplit.IsNull()) {
      aListOfWireEdges.Append(aESplit);
    }
  }
  
  // by pairs continuously. end
  theListOfWireEdges = aListOfWireEdges;
  isSectionFound = bSecFound;
  return Standard_True;
}

// ----------------------------------------------------------------------------------------------------
// static function: RemoveEdges
// purpose:
// ----------------------------------------------------------------------------------------------------
void RemoveEdges(const TopoDS_Compound&      theSourceComp,
                 const TopTools_ListOfShape& theListToRemove,
                 TopoDS_Compound&            theResultComp) {
  BRep_Builder aBB;
  TopoDS_Compound aComp;
  aBB.MakeCompound(aComp);
  TopExp_Explorer anExp(theSourceComp, TopAbs_EDGE);

  for(; anExp.More(); anExp.Next()) {
    Standard_Boolean bfound = Standard_False;
    TopTools_ListIteratorOfListOfShape anIt(theListToRemove);
    
    for(; !bfound && anIt.More(); anIt.Next()) {
      bfound = anExp.Current().IsSame(anIt.Value());
    }

    if(!bfound) {
      aBB.Add(aComp, anExp.Current());
    }
  }
  theResultComp = aComp;
}

// ----------------------------------------------------------------------------------------------------
// static function: FilterSectionEdges
// purpose:
// ----------------------------------------------------------------------------------------------------
Standard_Boolean FilterSectionEdges(const BOPDS_VectorOfCurve&       theBCurves,
                                    const TopoDS_Face&               theSecPlane,
                                    const BOPDS_PDS&                 theDS,
                                    TopoDS_Compound&                 theResult) {

  theResult.Nullify();

  BRep_Builder aBB;
  aBB.MakeCompound(theResult);
  Standard_Integer aNbCurves = theBCurves.Length();
  Standard_Integer cit = 0;
  BOPDS_ListIteratorOfListOfPaveBlock aPBIt;
  
  for(cit = 0; cit < aNbCurves; ++cit) {
    const BOPDS_Curve& aBCurve = theBCurves(cit);
    const BOPDS_ListOfPaveBlock& aSectEdges = aBCurve.PaveBlocks();

    aPBIt.Initialize(aSectEdges);
    for (; aPBIt.More(); aPBIt.Next()) {
      const Handle(BOPDS_PaveBlock)& aPB = aPBIt.Value();
      Standard_Integer nSect = aPB->Edge();
      const TopoDS_Shape& aS = theDS->Shape(nSect);
      TopoDS_Edge anEdge = TopoDS::Edge(aS);
      Standard_Boolean bAddEdge = Standard_True;

      if(!theSecPlane.IsNull()) {
        IntTools_BeanFaceIntersector anIntersector(anEdge, theSecPlane);
        Standard_Real f = 0., l = 0.;
        BRep_Tool::Range(anEdge, f, l);
        anIntersector.SetBeanParameters(f, l);
        //
        Handle(IntTools_Context) aContext = new IntTools_Context;
        anIntersector.SetContext(aContext);
        //
        anIntersector.Perform();

        if(anIntersector.IsDone()) {
          bAddEdge = Standard_False;
          Standard_Integer r = 0;

          for(r = 1; r <= anIntersector.Result().Length(); r++) {
            const IntTools_Range& aRange = anIntersector.Result().Value(r);

            if(((aRange.First() - f) < Precision::PConfusion()) &&
               ((l - aRange.Last()) < Precision::PConfusion())) {
              bAddEdge = Standard_True;
              break;
            }//if(((aRange.First() - f) < Precision::PConfusion()) &&
          }//for(r = 1; r <= anIntersector.Result().Length(); r++) {
        }//if(anIntersector.IsDone()) {
      }//if(!theSecPlane.IsNull()) {

      if(bAddEdge) {
        aBB.Add(theResult, aS);
      }
    }//for (; aPBIt.More(); aPBIt.Next()) {
  }//for(cit = 0; cit < aNbCurves; ++cit) {

  return Standard_True;
}


//=======================================================================
//function : ComputeAveragePlaneAndMaxDeviation
//purpose  : 
//=======================================================================
static Standard_Real ComputeAveragePlaneAndMaxDeviation(const TopoDS_Shape& aWire,
                                                        gp_Pln& thePlane,
                                                        Standard_Boolean& IsSingular)
{
  Standard_Integer N = 40;
  Standard_Integer nedges = aWire.NbChildren();

  TColgp_Array1OfPnt Pnts( 1, nedges*N );
  Standard_Integer ind = 1, i;
  for (TopoDS_Iterator iter (aWire); iter.More(); iter.Next())
    {
      const TopoDS_Edge& anEdge = TopoDS::Edge( iter.Value() );
      BRepAdaptor_Curve aCurve(anEdge);
      GCPnts_UniformAbscissa Distribution( aCurve, N+1 );
      for (i = 1; i <= N; i++)
        {
          Standard_Real par = Distribution.Parameter(i);
          Pnts( ind++ ) = aCurve.Value(par);
        }
    }

  gp_Ax2 Axe;
  GeomLib::AxeOfInertia( Pnts, Axe, IsSingular );
  if (IsSingular)
    return -1;

  thePlane = gp_Pln( Axe );
  Standard_Real MaxDeviation = 0;
  for (i = 1; i <= Pnts.Length(); i++)
    {
      Standard_Real dist = thePlane.Distance( Pnts(i) );
      if (dist > MaxDeviation)
        MaxDeviation = dist;
    }
  return MaxDeviation;
}


static void UpdateSectionEdge(TopoDS_Edge&         theEdge,
                              const TopoDS_Vertex& theConstVertex,
                              TopoDS_Vertex&       theVertex,
                              const Standard_Real  theParam)
{
  TopoDS_Edge F_Edge = theEdge;
  F_Edge.Orientation(TopAbs_FORWARD);
  
  TopAbs_Orientation OrOfVertex;
  TopoDS_Vertex V1, V2, AnotherVertex;
  TopExp::Vertices(F_Edge, V1, V2);
  if (theConstVertex.IsSame(V1))
  {
    //OrOfConst = TopAbs_FORWARD;
    OrOfVertex = TopAbs_REVERSED;
    AnotherVertex = V2;
  }
  else
  {
    //OrOfConst = TopAbs_REVERSED;
    OrOfVertex = TopAbs_FORWARD;
    AnotherVertex = V1;
  }

  BRep_Builder BB;
  Standard_Real fpar, lpar;
  BRep_Tool::Range(F_Edge, fpar, lpar);
  if (OrOfVertex == TopAbs_FORWARD)
    fpar = theParam;
  else
    lpar = theParam;
  BB.Range(F_Edge, fpar, lpar);

  F_Edge.Free(Standard_True);
  BB.Remove(F_Edge, AnotherVertex);
  theVertex.Orientation(OrOfVertex);
  BB.Add(F_Edge, theVertex);
}

//Finds the edge connected to <theVertex> in the compound <theComp>
//that is closest to bisector plane angularly.
//Removes found edge from <theComp>
//<theAxis> is the axis of bisector plane
static TopoDS_Edge FindEdgeCloseToBisectorPlane(const TopoDS_Vertex& theVertex,
                                                TopoDS_Compound&     theComp,
                                                const gp_Ax1&        theAxis)
{
  TopTools_IndexedDataMapOfShapeListOfShape VEmap;
  TopExp::MapShapesAndAncestors( theComp, TopAbs_VERTEX, TopAbs_EDGE, VEmap );
  
  TopoDS_Edge MinEdge;
  if (!VEmap.Contains(theVertex))
    return MinEdge;
  
  BRep_Builder BB;
  
  const TopTools_ListOfShape& Edges = VEmap.FindFromKey(theVertex);
  if (Edges.Extent() == 1)
    MinEdge = TopoDS::Edge(Edges.First());
  else
  {
    TopTools_ListIteratorOfListOfShape itl(Edges);
    Standard_Real MinAngle = RealLast();
    for (; itl.More(); itl.Next())
    {
      const TopoDS_Edge& anEdge = TopoDS::Edge(itl.Value());
      TopoDS_Wire aWire;
      BB.MakeWire(aWire);
      BB.Add(aWire, anEdge);
      gp_Pln aPln;
      Standard_Boolean issing;
      ComputeAveragePlaneAndMaxDeviation( aWire, aPln, issing );
      Standard_Real anAngle;
      if (issing) //edge is a segment of line
      {
        //<anAngle> is angle between <anEdge> and its projection on bisector plane
        BRepAdaptor_Curve BAcurve(anEdge);
        gp_Pnt FirstPnt = BAcurve.Value(BAcurve.FirstParameter());
        gp_Pnt LastPnt  = BAcurve.Value(BAcurve.LastParameter());
        gp_Vec EdgeVec(FirstPnt, LastPnt);
        gp_Ax1 EdgeAxis(FirstPnt, EdgeVec);
        anAngle = EdgeAxis.Direction().Angle(theAxis.Direction());
        if (anAngle > M_PI/2)
          anAngle = M_PI - anAngle;
        anAngle = M_PI/2 - anAngle;
      }
      else
      {
        anAngle = aPln.Axis().Angle( theAxis );
        if (anAngle > M_PI/2)
          anAngle = M_PI - anAngle;
      }
      
      if (anAngle < MinAngle)
      {
        MinAngle = anAngle;
        MinEdge  = anEdge;
      }
    }
  } //else (more than one edge)

  BB.Remove(theComp, MinEdge);
  return MinEdge;
}

static Standard_Boolean FindMiddleEdges(const TopoDS_Vertex&  theVertex1,
                                        const TopoDS_Vertex&  theVertex2,
                                        const gp_Ax1&         theAxis,
                                        TopoDS_Compound&      theComp,
                                        TopTools_ListOfShape& theElist)
{
  TopTools_IndexedDataMapOfShapeListOfShape VEmap;
  TopExp::MapShapesAndAncestors( theComp, TopAbs_VERTEX, TopAbs_EDGE, VEmap );
  if (VEmap.IsEmpty())
    return Standard_False;

  if (!VEmap.Contains(theVertex1) ||
      !VEmap.Contains(theVertex2))
    return Standard_False;

  TopoDS_Vertex CurVertex = theVertex1;
  for (;;)
  {
    TopoDS_Edge CurEdge;
    
    CurEdge = FindEdgeCloseToBisectorPlane(CurVertex, theComp, theAxis);
    if (CurEdge.IsNull())
      return Standard_False;
    
    TopoDS_Vertex V1, V2;
    TopExp::Vertices(CurEdge, V1, V2);
    CurVertex = (V1.IsSame(CurVertex))? V2 : V1;

    theElist.Append(CurEdge);
    if (CurVertex.IsSame(theVertex2))
      return Standard_True;
  }
}

static Standard_Boolean FindCommonVertex(const TopoDS_Edge&   theFirstEdge,
                                         const TopoDS_Edge&   theLastEdge,
                                         const TopoDS_Vertex& theFirstVertex,
                                         const TopoDS_Vertex& theLastVertex,
                                         TopoDS_Vertex&       theCommonVertex)
{
  if (!theFirstVertex.IsSame(theLastVertex))
  {
    Standard_Boolean CommonVertexExists = TopExp::CommonVertex(theFirstEdge,
                                                               theLastEdge,
                                                               theCommonVertex);
    return CommonVertexExists;
  }

  TopoDS_Vertex V1, V2, V3, V4;
  TopExp::Vertices(theFirstEdge, V1, V2);
  TopExp::Vertices(theLastEdge, V3, V4);

  if (V1.IsSame(theFirstVertex))
  {
    if (V2.IsSame(V3) ||
        V2.IsSame(V4))
    {
      theCommonVertex = V2;
      return Standard_True;
    }
  }
  else
  {
    if (V1.IsSame(V3) ||
        V1.IsSame(V4))
    {
      theCommonVertex = V1;
      return Standard_True;
    }
  }

  return Standard_False;
}
