src/BRepTools/BRepTools_WireExplorer.cxx

// Created on: 1993-01-21
// Created by: Remi LEQUETTE
// Copyright (c) 1993-1999 Matra Datavision
// Copyright (c) 1999-2014 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 <BRep_Tool.hxx>
#include <BRepAdaptor_Surface.hxx>
#include <BRepTools.hxx>
#include <BRepTools_WireExplorer.hxx>
#include <Geom2d_Curve.hxx>
#include <Geom_Surface.hxx>
#include <GeomAdaptor_Surface.hxx>
#include <gp_Pnt2d.hxx>
#include <Precision.hxx>
#include <Standard_DomainError.hxx>
#include <Standard_NoMoreObject.hxx>
#include <Standard_NoSuchObject.hxx>
#include <TopExp.hxx>
#include <TopExp_Explorer.hxx>
#include <TopoDS.hxx>
#include <TopoDS_Edge.hxx>
#include <TopoDS_Face.hxx>
#include <TopoDS_Iterator.hxx>
#include <TopoDS_Vertex.hxx>
#include <TopoDS_Wire.hxx>
#include <TopTools_DataMapIteratorOfDataMapOfShapeListOfShape.hxx>
#include <TopTools_ListIteratorOfListOfShape.hxx>
#include <TopTools_ListOfShape.hxx>
#include <TopTools_MapIteratorOfMapOfShape.hxx>
#include <TopTools_MapOfShape.hxx>

//=======================================================================
// forward declarations of aux functions
//=======================================================================
static Standard_Boolean SelectDouble(TopTools_MapOfShape& Doubles,
				     TopTools_ListOfShape& L,
				     TopoDS_Edge&          E);

static Standard_Boolean SelectDegenerated(TopTools_ListOfShape& L,
					  TopoDS_Edge&          E);

static Standard_Real GetNextParamOnPC(const Handle(Geom2d_Curve)& aPC,
				      const gp_Pnt2d& aPRef,
				      const Standard_Real& fP,
				      const Standard_Real& lP,
				      const Standard_Real& tolU,
				      const Standard_Real& tolV,
				      const Standard_Boolean& reverse);

//=======================================================================
//function : BRepTools_WireExplorer
//purpose  :
//=======================================================================
BRepTools_WireExplorer::BRepTools_WireExplorer()
: myReverse(Standard_False),
  myTolU(0.0),
  myTolV(0.0)
{
}

//=======================================================================
//function : BRepTools_WireExplorer
//purpose  :
//=======================================================================
BRepTools_WireExplorer::BRepTools_WireExplorer(const TopoDS_Wire& W)
{
  TopoDS_Face F = TopoDS_Face();
  Init(W,F);
}

//=======================================================================
//function : BRepTools_WireExplorer
//purpose  :
//=======================================================================
BRepTools_WireExplorer::BRepTools_WireExplorer(const TopoDS_Wire& W,
					       const TopoDS_Face& F)
{
  Init(W,F);
}

//=======================================================================
//function : Init
//purpose  :
//=======================================================================
void  BRepTools_WireExplorer::Init(const TopoDS_Wire& W)
{
  TopoDS_Face F = TopoDS_Face();
  Init(W,F);
}

//=======================================================================
//function : Init
//purpose  :
//=======================================================================
void  BRepTools_WireExplorer::Init(const TopoDS_Wire& W,
                                   const TopoDS_Face& F)
{
  myEdge = TopoDS_Edge();
  myVertex = TopoDS_Vertex();
  myMap.Clear();
  myDoubles.Clear();

  if (W.IsNull())
    return;

  Standard_Real UMin(0.0), UMax(0.0), VMin(0.0), VMax(0.0);
  if (!F.IsNull())
  {
    // For the faces based on Cone, BSpline and Bezier compute the
    // UV bounds to precise the UV tolerance values
    const GeomAbs_SurfaceType aSurfType = BRepAdaptor_Surface(F, Standard_False).GetType();
    if (aSurfType == GeomAbs_Cone ||
        aSurfType == GeomAbs_BSplineSurface ||
        aSurfType == GeomAbs_BezierSurface)
    {
      BRepTools::UVBounds(F, UMin, UMax, VMin, VMax);
    }
  }

  Init(W, F, UMin, UMax, VMin, VMax);
}

//=======================================================================
//function : Init
//purpose  :
//=======================================================================
void  BRepTools_WireExplorer::Init(const TopoDS_Wire& W,
                                   const TopoDS_Face& F,
                                   const Standard_Real UMin,
                                   const Standard_Real UMax,
                                   const Standard_Real VMin,
                                   const Standard_Real VMax)
{
  myEdge = TopoDS_Edge();
  myVertex = TopoDS_Vertex();
  myMap.Clear();
  myDoubles.Clear();

  if (W.IsNull())
    return;

  myFace = F;
  Standard_Real dfVertToler = 0.;
  myReverse = Standard_False;

  if (!myFace.IsNull())
  {
    TopLoc_Location aL;
    const Handle(Geom_Surface)& aSurf = BRep_Tool::Surface(myFace, aL);
    GeomAdaptor_Surface aGAS(aSurf);
    TopExp_Explorer anExp(W, TopAbs_VERTEX);
    for (; anExp.More(); anExp.Next())
    {
      const TopoDS_Vertex& aV = TopoDS::Vertex(anExp.Current());
      dfVertToler = Max(BRep_Tool::Tolerance(aV), dfVertToler);
    }
    if (dfVertToler < Precision::Confusion())
    {
      // Use tolerance of edges
      for (TopoDS_Iterator it(W); it.More(); it.Next())
        dfVertToler = Max(BRep_Tool::Tolerance(TopoDS::Edge(it.Value())), dfVertToler);

      if (dfVertToler < Precision::Confusion())
        // empty wire
        return;
    }
    myTolU = 2. * aGAS.UResolution(dfVertToler);
    myTolV = 2. * aGAS.VResolution(dfVertToler);

    // uresolution for cone with infinite vmin vmax is too small.
    if (aGAS.GetType() == GeomAbs_Cone)
    {
      gp_Pnt aP;
      gp_Vec aD1U, aD1V;
      aGAS.D1(UMin, VMin, aP, aD1U, aD1V);
      Standard_Real tol1, tol2, maxtol = .0005*(UMax - UMin);
      Standard_Real a = aD1U.Magnitude();

      if (a <= Precision::Confusion())
        tol1 = maxtol;
      else
        tol1 = Min(maxtol, dfVertToler / a);

      aGAS.D1(UMin, VMax, aP, aD1U, aD1V);
      a = aD1U.Magnitude();
      if (a <= Precision::Confusion())
        tol2 = maxtol;
      else
        tol2 = Min(maxtol, dfVertToler / a);

      myTolU = 2. * Max(tol1, tol2);
    }

    if (aGAS.GetType() == GeomAbs_BSplineSurface ||
      aGAS.GetType() == GeomAbs_BezierSurface)
    {
      Standard_Real maxTol = Max(myTolU, myTolV);
      gp_Pnt aP;
      gp_Vec aDU, aDV;
      aGAS.D1((UMax - UMin) / 2., (VMax - VMin) / 2., aP, aDU, aDV);
      Standard_Real mod = Sqrt(aDU*aDU + aDV*aDV);
      if (mod > gp::Resolution())
      {
        if (mod * maxTol / dfVertToler < 1.5)
        {
          maxTol = 1.5 * dfVertToler / mod;
        }
        myTolU = maxTol;
        myTolV = maxTol;
      }
    }

    myReverse = (myFace.Orientation() == TopAbs_REVERSED);
  }

  // map of vertices to know if the wire is open
  TopTools_IndexedMapOfShape vmap;
  //  map of infinite edges
  TopTools_MapOfShape anInfEmap;

  // list the vertices
  TopoDS_Vertex V1, V2;
  TopTools_ListOfShape empty;

  TopoDS_Iterator it(W);
  while (it.More())
  {
    const TopoDS_Edge& E = TopoDS::Edge(it.Value());
    TopAbs_Orientation Eori = E.Orientation();
    if (Eori == TopAbs_INTERNAL || Eori == TopAbs_EXTERNAL)
    {
      it.Next();
      continue;
    }
    TopExp::Vertices(E, V1, V2, Standard_True);

    if (!V1.IsNull())
    {
      if (!myMap.IsBound(V1))
        myMap.Bind(V1, empty);
      myMap(V1).Append(E);

      // add or remove in the vertex map
      V1.Orientation(TopAbs_FORWARD);
      Standard_Integer currsize = vmap.Extent(),
                       ind = vmap.Add(V1);
      if (currsize >= ind)
      {
        vmap.RemoveKey(V1);
      }
    }

    if (!V2.IsNull())
    {
      V2.Orientation(TopAbs_REVERSED);
      Standard_Integer currsize = vmap.Extent(),
                       ind = vmap.Add(V2);
      if (currsize >= ind)
      {
        vmap.RemoveKey(V2);
      }
    }

    if (V1.IsNull() || V2.IsNull())
    {
      Standard_Real aF = 0., aL = 0.;
      BRep_Tool::Range(E, aF, aL);

      if (Eori == TopAbs_FORWARD)
      {
        if (aF == -Precision::Infinite())
          anInfEmap.Add(E);
      }
      else
      { // Eori == TopAbs_REVERSED
        if (aL == Precision::Infinite())
          anInfEmap.Add(E);
      }
    }
    it.Next();
  }

  //Construction of the set of double edges.
  TopoDS_Iterator it2(W);
  TopTools_MapOfShape emap;
  while (it2.More()) {
    if (!emap.Add(it2.Value()))
      myDoubles.Add(it2.Value());
    it2.Next();
  }

  // if vmap is not empty the wire is open, let us find the first vertex
  if (!vmap.IsEmpty()) {
    //TopTools_MapIteratorOfMapOfShape itt(vmap);
    //while (itt.Key().Orientation() != TopAbs_FORWARD) {
    //  itt.Next();
    //  if (!itt.More()) break;
    //}
    //if (itt.More()) V1 = TopoDS::Vertex(itt.Key());
    Standard_Integer ind = 0;
    for (ind = 1; ind <= vmap.Extent(); ++ind)
    {
      if (vmap(ind).Orientation() == TopAbs_FORWARD)
      {
        V1 = TopoDS::Vertex(vmap(ind));
        break;
      }
    }
  }
  else {
    //   The wire is infinite Try to find the first vertex. It may be NULL.
    if (!anInfEmap.IsEmpty()) {
      TopTools_MapIteratorOfMapOfShape itt(anInfEmap);

      for (; itt.More(); itt.Next()) {
        TopoDS_Edge        anEdge = TopoDS::Edge(itt.Key());
        TopAbs_Orientation anOri = anEdge.Orientation();
        Standard_Real      aF;
        Standard_Real      aL;

        BRep_Tool::Range(anEdge, aF, aL);
        if ((anOri == TopAbs_FORWARD  && aF == -Precision::Infinite()) ||
          (anOri == TopAbs_REVERSED && aL == Precision::Infinite())) {
          myEdge = anEdge;
          myVertex = TopoDS_Vertex();

          return;
        }
      }
    }

    // use the first vertex in iterator
    it.Initialize(W);
    while (it.More()) {
      const TopoDS_Edge& E = TopoDS::Edge(it.Value());
      TopAbs_Orientation Eori = E.Orientation();
      if (Eori == TopAbs_INTERNAL || Eori == TopAbs_EXTERNAL) {
        // JYL 10-03-97 : waiting for correct processing
        // of INTERNAL/EXTERNAL edges
        it.Next();
        continue;
      }
      TopExp::Vertices(E, V1, V2, Standard_True);
      break;
    }
  }

  if (V1.IsNull()) return;
  if (!myMap.IsBound(V1)) return;

  TopTools_ListOfShape& l = myMap(V1);
  myEdge = TopoDS::Edge(l.First());
  l.RemoveFirst();
  myVertex = TopExp::FirstVertex(myEdge, Standard_True);

}

//=======================================================================
//function : More
//purpose  :
//=======================================================================
Standard_Boolean  BRepTools_WireExplorer::More()const
{
  return !myEdge.IsNull();
}

//=======================================================================
//function : Next
//purpose  :
//=======================================================================
void  BRepTools_WireExplorer::Next()
{
  myVertex = TopExp::LastVertex (myEdge, Standard_True);

  if (myVertex.IsNull()) {
     myEdge = TopoDS_Edge();
     return;
  }
  if (!myMap.IsBound(myVertex)) {
     myEdge = TopoDS_Edge();
     return;
  }

  TopTools_ListOfShape& l = myMap(myVertex);

  if (l.IsEmpty()) {
    myEdge = TopoDS_Edge();
  }
  else if (l.Extent() == 1) {
//  Modified by Sergey KHROMOV - Fri Jun 21 10:28:01 2002 OCC325 Begin
    TopoDS_Vertex aV1;
    TopoDS_Vertex aV2;
    TopoDS_Edge   aNextEdge = TopoDS::Edge(l.First());

    TopExp::Vertices(aNextEdge, aV1, aV2, Standard_True);

    if (!aV1.IsSame(myVertex)) {
      myEdge = TopoDS_Edge();
      return;
    }
    if (!myFace.IsNull() && aV1.IsSame(aV2)) {
      Handle(Geom2d_Curve) aPrevPC;
      Handle(Geom2d_Curve) aNextPC;
      Standard_Real        aPar11, aPar12;
      Standard_Real        aPar21, aPar22;
      Standard_Real        aPrevPar;
      Standard_Real        aNextFPar;
      Standard_Real        aNextLPar;

      aPrevPC = BRep_Tool::CurveOnSurface(myEdge, myFace, aPar11, aPar12);
      aNextPC = BRep_Tool::CurveOnSurface(aNextEdge, myFace, aPar21, aPar22);

      if (aPrevPC.IsNull() || aNextPC.IsNull()) {
	      myEdge = TopoDS_Edge();
	      return;
      }

      if (myEdge.Orientation() == TopAbs_FORWARD)
	      aPrevPar = aPar12;
      else
	      aPrevPar = aPar11;

      if (aNextEdge.Orientation() == TopAbs_FORWARD) {
	      aNextFPar = aPar21;
	      aNextLPar = aPar22;
      } else {
	      aNextFPar = aPar22;
	      aNextLPar = aPar21;
      }

      gp_Pnt2d aPPrev  = aPrevPC->Value(aPrevPar);
      gp_Pnt2d aPNextF = aNextPC->Value(aNextFPar);
      gp_Pnt2d aPNextL = aNextPC->Value(aNextLPar);

      if (aPPrev.SquareDistance(aPNextF) > aPPrev.SquareDistance(aPNextL)) {
	      myEdge = TopoDS_Edge();
	      return;
      }
    }
//  Modified by Sergey KHROMOV - Fri Jun 21 11:08:16 2002 End
    myEdge = TopoDS::Edge(l.First());
    l.Clear();
  }
  else {
    if (myFace.IsNull()) {
      // Without Face - try to return edges
      // as logically as possible
      // At first degenerated edges.
      TopoDS_Edge E = myEdge;
      if (SelectDegenerated(l,E)) {
	      myEdge = E;
	      return;
      }
      // At second double edges.
      E = myEdge;
      if (SelectDouble(myDoubles,l,E)) {
	      myEdge = E;
	      return;
      }

      TopTools_ListIteratorOfListOfShape it(l);
      Standard_Boolean notfound = Standard_True;
      while (it.More()) {
	      if (!it.Value().IsSame(myEdge)) {
	        myEdge = TopoDS::Edge(it.Value());
	        l.Remove(it);
	        notfound = Standard_False;
	        break;
	      }
	      it.Next();
      }

      if(notfound) {
	      myEdge = TopoDS_Edge();
	      return;
      }

    }
    else
    {
      // If we have more than one edge attached to the list
      // probably wire that we explore contains a loop or loops.
      Standard_Real dfFPar = 0., dfLPar = 0.;
      Handle(Geom2d_Curve) aPCurve = BRep_Tool::CurveOnSurface (myEdge, myFace, dfFPar, dfLPar);
      if(aPCurve.IsNull())
      {
        myEdge = TopoDS_Edge();
        return;
      }
      // Note: current < myVertex > which is last on < myEdge >
      //       equals in 2D to following 2D points:
      //       edge is FORWARD  - point with MAX parameter on PCurve;
      //       edge is REVERSED - point with MIN parameter on PCurve.

      // Get 2D point equals to < myVertex > in 2D for current edge.
      gp_Pnt2d PRef;
      if( myEdge.Orientation() == TopAbs_REVERSED )
        aPCurve->D0(dfFPar, PRef);
      else
        aPCurve->D0(dfLPar, PRef);

      // Get next 2D point from current edge's PCurve with parameter
      // F + dP (REV) or L - dP (FOR)
      Standard_Boolean isrevese = ( myEdge.Orientation() == TopAbs_REVERSED );
      Standard_Real dfMPar = GetNextParamOnPC(aPCurve,PRef,dfFPar,dfLPar,myTolU,myTolV,isrevese);

      gp_Pnt2d PRefm;
      aPCurve->D0(dfMPar, PRefm);
      // Get vector from PRef to PRefm
      gp_Vec2d anERefDir(PRef,PRefm);
      if (anERefDir.SquareMagnitude() < gp::Resolution())
      {
        myEdge = TopoDS_Edge();
        return;
      }

      // Search the list of edges looking for the edge having hearest
      // 2D point of connected vertex to current one and smallest angle.
      // First process all degenerated edges, then - all others.

      TopTools_ListIteratorOfListOfShape it;
      Standard_Integer k = 1, kMin = 0, iDone = 0;
      Standard_Boolean isDegenerated = Standard_True;
      Standard_Real dmin = RealLast();
      Standard_Real dfMinAngle = 3.0*M_PI, dfCurAngle = 3.0*M_PI;

      for(iDone = 0; iDone < 2; iDone++)
      {
        it.Initialize(l);
        while( it.More() )
        {
	        const TopoDS_Edge& E = TopoDS::Edge(it.Value());
	        if( E.IsSame(myEdge) )
	        {
	          it.Next();
	          k++;
	          continue;
	        }

	        TopoDS_Vertex aVert1, aVert2;
	        TopExp::Vertices (E, aVert1, aVert2, Standard_True);
	        if( aVert1.IsNull() || aVert2.IsNull() )
          {
            it.Next();
            k++;
            continue;
          }

	        aPCurve = BRep_Tool::CurveOnSurface (E, myFace, dfFPar, dfLPar);
	        if( aPCurve.IsNull() )
          {
            it.Next();
            k++;
            continue;
          }

	        gp_Pnt2d aPEb, aPEe;
	        if( aVert1.IsSame(aVert2) == isDegenerated )
	        {
	          if( E.Orientation() == TopAbs_REVERSED )
	            aPCurve->D0(dfLPar, aPEb);
	          else
	            aPCurve->D0(dfFPar, aPEb);

	          if( Abs(dfLPar-dfFPar) > Precision::PConfusion() )
	          {
		          isrevese = ( E.Orientation() == TopAbs_REVERSED );
		          isrevese = !isrevese;
		          Standard_Real aEPm = GetNextParamOnPC(aPCurve,aPEb,dfFPar,dfLPar,myTolU,myTolV,isrevese);

		          aPCurve->D0 (aEPm, aPEe);
              if(aPEb.SquareDistance(aPEe) <= gp::Resolution())
              {
                //seems to be very short curve
                gp_Vec2d aD;
                aPCurve->D1(aEPm, aPEe, aD);
	              if( E.Orientation() == TopAbs_REVERSED )
                  aPEe.SetXY(aPEb.XY()-aD.XY());
	              else
                  aPEe.SetXY(aPEb.XY()+aD.XY());

                if(aPEb.SquareDistance(aPEe) <= gp::Resolution())
                {
                  it.Next();
                  k++;
                  continue;
                }
              }
		          gp_Vec2d anEDir(aPEb, aPEe);
		          dfCurAngle = Abs( anEDir.Angle(anERefDir) );
	          }

	          if( dfCurAngle <= dfMinAngle )
	          {
		          Standard_Real d = PRef.SquareDistance(aPEb);
		          if( d <= Precision::PConfusion() )
		            d = 0.;
		          if( Abs(aPEb.X()-PRef.X()) < myTolU  &&  Abs(aPEb.Y()-PRef.Y()) < myTolV )
		          {
		            if( d <= dmin )
		            {
			            dfMinAngle = dfCurAngle;
			            kMin = k;
			            dmin = d;
		            }
		          }
	          }
	        }
	        it.Next();
	        k++;
        }// while it

        if( kMin == 0 )
        {
	        isDegenerated = Standard_False;
	        k = 1;
	        dmin = RealLast();
        }
        else
          break;
      }// for iDone

      if(kMin == 0)
      {
        // probably unclosed in 2d space wire
        myEdge = TopoDS_Edge();
        return;
      }

      // Selection the edge.
      it.Initialize(l);
      k = 1;
      while( it.More() )
      {
        if( k == kMin )
        {
          myEdge = TopoDS::Edge(it.Value());
          l.Remove(it);
          break;
        }
        it.Next();
        k++;
      }
    }//else face != NULL && l > 1
  }//else l > 1
}

//=======================================================================
//function : Current
//purpose  :
//=======================================================================
const TopoDS_Edge&  BRepTools_WireExplorer::Current()const
{
  return myEdge;
}

//=======================================================================
//function : Orientation
//purpose  :
//=======================================================================
TopAbs_Orientation BRepTools_WireExplorer::Orientation() const
{
  if (myVertex.IsNull()
  && !myEdge.IsNull())
  {
    // infinite edge
    return TopAbs_FORWARD;
  }

  TopoDS_Iterator it(myEdge,Standard_False);
  while (it.More()) {
    if (myVertex.IsSame(it.Value()))
      return it.Value().Orientation();
    it.Next();
  }
  throw Standard_NoSuchObject("BRepTools_WireExplorer::Orientation");
}

//=======================================================================
//function : CurrentVertex
//purpose  :
//=======================================================================
const TopoDS_Vertex& BRepTools_WireExplorer::CurrentVertex() const
{
  return myVertex;
}

//=======================================================================
//function : Clear
//purpose  :
//=======================================================================

void BRepTools_WireExplorer::Clear()
{
  myMap.Clear();
  myDoubles.Clear();
  myEdge = TopoDS_Edge();
  myFace = TopoDS_Face();
  myVertex = TopoDS_Vertex();
}


//=======================================================================
//function : SelectDouble
//purpose  :
//=======================================================================

Standard_Boolean SelectDouble(TopTools_MapOfShape& Doubles,
			      TopTools_ListOfShape& L,
			      TopoDS_Edge&          E)
{
  TopTools_ListIteratorOfListOfShape it(L);

  for (; it.More(); it.Next()) {
    const TopoDS_Shape& CE = it.Value();
    if (Doubles.Contains(CE) && (!E.IsSame(CE))) {
      E = TopoDS::Edge(CE);
      L.Remove(it);
      return 1;
    }
  }
  return 0;
}

//=======================================================================
//function : SelectDegenerated
//purpose  :
//=======================================================================

Standard_Boolean SelectDegenerated(TopTools_ListOfShape& L,
				   TopoDS_Edge&          E)
{
  TopTools_ListIteratorOfListOfShape it(L);
  while (it.More()) {
    if (!it.Value().IsSame(E)) {
      E = TopoDS::Edge(it.Value());
      if (BRep_Tool::Degenerated(E)) {
	L.Remove(it);
	return 1;
      }
    }
    it.Next();
  }
  return 0;
}

//=======================================================================
//function : GetNextParamOnPC
//purpose  :
//=======================================================================
Standard_Real GetNextParamOnPC(const Handle(Geom2d_Curve)& aPC,
			       const gp_Pnt2d& aPRef,
			       const Standard_Real& fP,
			       const Standard_Real& lP,
			       const Standard_Real& tolU,
			       const Standard_Real& tolV,
			       const Standard_Boolean& reverse)
{
  Standard_Real result = ( reverse ) ? fP : lP;
  Standard_Real dP = Abs( lP - fP ) / 1000.; // was / 16.;
  if( reverse )
    {
      Standard_Real startPar = fP;
      Standard_Boolean nextPntOnEdge = Standard_False;
      while( !nextPntOnEdge && startPar < lP )
	{
	  gp_Pnt2d pnt;
	  startPar += dP;
	  aPC->D0(startPar, pnt);
	  if( Abs( aPRef.X() - pnt.X() ) < tolU && Abs( aPRef.Y() - pnt.Y() ) < tolV )
	    continue;
	  else
	    {
	      result = startPar;
	      nextPntOnEdge = Standard_True;
	      break;
	    }
	}

      if( !nextPntOnEdge )
	result = lP;

      if( result > lP )
	result = lP;
    }
  else
    {
      Standard_Real startPar = lP;
      Standard_Boolean nextPntOnEdge = Standard_False;
      while( !nextPntOnEdge && startPar > fP )
	{
	  gp_Pnt2d pnt;
	  startPar -= dP;
	  aPC->D0(startPar, pnt);
	  if( Abs( aPRef.X() - pnt.X() ) < tolU && Abs( aPRef.Y() - pnt.Y() ) < tolV )
	    continue;
	  else
	    {
	      result = startPar;
	      nextPntOnEdge = Standard_True;
	      break;
	    }
	}

      if( !nextPntOnEdge )
	result = fP;

      if( result < fP )
	result = fP;
    }

  return result;
}