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ProjLib_ComputeApproxOnPolarSurface.cxx

// Author:  Bruno DUMORTIER
//          <dub@fuegox>
#include <ProjLib_ComputeApproxOnPolarSurface.hxx>
#include <AppCont_Function2d.hxx>
#include <ElSLib.hxx>
#include <ElCLib.hxx>
#include <BSplCLib.hxx>
#include <PLib.hxx>
#include <Standard_NoSuchObject.hxx>
#include <Geom_UndefinedDerivative.hxx>
#include <gp_Trsf.hxx>
#include <Precision.hxx>
#include <Approx_FitAndDivide2d.hxx>
#include <math.hxx>
#include <AppParCurves_MultiCurve.hxx>
#include <Geom_Surface.hxx>
#include <Geom2d_BSplineCurve.hxx>
#include <Geom2d_BezierCurve.hxx>
#include <Geom2d_Line.hxx>
#include <Geom2d_Circle.hxx>
#include <Geom2d_Ellipse.hxx>
#include <Geom2d_Hyperbola.hxx>
#include <Geom2d_Parabola.hxx>
#include <Geom2d_TrimmedCurve.hxx>
#include <Geom_BSplineSurface.hxx>
#include <Geom_BezierSurface.hxx>
#include <Geom_BSplineCurve.hxx>
#include <Geom_BezierCurve.hxx>
#include <Geom_TrimmedCurve.hxx>

#include <TColgp_Array1OfPnt2d.hxx>
#include <TColgp_Array2OfPnt2d.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <TColgp_SequenceOfPnt2d.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColStd_Array1OfInteger.hxx>
#include <TColStd_SequenceOfReal.hxx>
#include <TColStd_ListOfTransient.hxx>

#include <GeomAbs_SurfaceType.hxx>
#include <GeomAbs_CurveType.hxx>
#include <Handle_Adaptor3d_HCurve.hxx>
#include <Handle_Adaptor3d_HSurface.hxx>
#include <Adaptor3d_Surface.hxx>
#include <Adaptor3d_Curve.hxx>
#include <Adaptor3d_HSurface.hxx>
#include <Adaptor3d_HCurve.hxx>
#include <Adaptor2d_HCurve2d.hxx>
#include <Geom2dAdaptor_Curve.hxx>
#include <Geom2dAdaptor_HCurve.hxx>
#include <GeomAdaptor_HCurve.hxx>
#include <GeomAdaptor.hxx>
#include <GeomAdaptor_Surface.hxx>
#include <TColgp_SequenceOfPnt.hxx>

#include <gp_Pnt.hxx>
#include <gp_Pnt2d.hxx>
#include <gp_Vec2d.hxx>
#include <Extrema_GenLocateExtPS.hxx>
#include <Extrema_ExtPS.hxx>
#include <GCPnts_QuasiUniformAbscissa.hxx>
#include <Standard_DomainError.hxx>
//#include <GeomLib_IsIso.hxx>
//#include <GeomLib_CheckSameParameter.hxx>

#ifdef DEB
#ifdef DRAW
#include <DrawTrSurf.hxx>
#endif
static Standard_Integer NbFunc   = 1;
static Standard_Integer compteur = 0;
#endif

//=======================================================================
//function : Value
//purpose  : (OCC217 - apo)- Compute Point2d that project on polar surface(<Surf>) 3D<Curve>
//            <InitCurve2d> use for calculate start 2D point.
//=======================================================================

static gp_Pnt2d Function_Value(const Standard_Real U,
                         const Handle(Adaptor3d_HSurface)& Surf,    
                         const Handle(Adaptor3d_HCurve)& Curve,
                         const Handle(Adaptor2d_HCurve2d)& InitCurve2d,
                               //OCC217
                         const Standard_Real DistTol3d, const Standard_Real tolU, const Standard_Real tolV)
                         //const Standard_Real Tolerance)
{
  //OCC217
  //Standard_Real Tol3d = 100*Tolerance;

  gp_Pnt2d p2d = InitCurve2d->Value(U) ;
  gp_Pnt p = Curve->Value(U);
//  Curve->D0(U,p) ;
  Standard_Real Uinf, Usup, Vinf, Vsup;
  Uinf = Surf->Surface().FirstUParameter();
  Usup = Surf->Surface().LastUParameter();
  Vinf = Surf->Surface().FirstVParameter();
  Vsup = Surf->Surface().LastVParameter();
  Standard_Integer decalU = 0, decalV = 0;
  Standard_Real U0 = p2d.X(), V0 = p2d.Y();
  
  GeomAbs_SurfaceType Type = Surf->GetType();
  if((Type != GeomAbs_BSplineSurface) && 
     (Type != GeomAbs_BezierSurface)  &&
     (Type != GeomAbs_OffsetSurface)    ) {
    Standard_Real S, T;
    switch (Type) {
//    case GeomAbs_Plane:
//      {
//    gp_Pln Plane = Surf->Plane();
//    ElSLib::Parameters( Plane, p, S, T);
//    break;
//      }
    case GeomAbs_Cylinder:
      {
      gp_Cylinder Cylinder = Surf->Cylinder();
      ElSLib::Parameters( Cylinder, p, S, T);
      if(U0 < Uinf) decalU = -int((Uinf - U0)/(2*PI))-1;
      if(U0 > Usup) decalU =  int((U0 - Usup)/(2*PI))+1;
      S += decalU*2*PI;
      break;
      }
    case GeomAbs_Cone:
      {
      gp_Cone Cone = Surf->Cone();
      ElSLib::Parameters( Cone, p, S, T);
      if(U0 < Uinf) decalU = -int((Uinf - U0)/(2*PI))-1;
      if(U0 > Usup) decalU =  int((U0 - Usup)/(2*PI))+1;
      S += decalU*2*PI;
      break;
      }
    case GeomAbs_Sphere:
      {
      gp_Sphere Sphere = Surf->Sphere();
      ElSLib::Parameters( Sphere, p, S, T);
      if(U0 < Uinf) decalU = -int((Uinf - U0)/(2*PI))-1;
      if(U0 > Usup) decalU =  int((U0 - Usup)/(2*PI))+1;
      S += decalU*2*PI;
      if(V0 < Vinf) decalV = -int((Vinf - V0)/(2*PI))-1;
      if(V0 > (Vsup+(Vsup-Vinf))) decalV =  int((V0 - Vsup+(Vsup-Vinf))/(2*PI))+1;
      T += decalV*2*PI;
      if(0.4*PI < Abs(U0 - S) && Abs(U0 - S) < 1.6*PI) {
        T = PI - T;
        if(U0 < S)
          S -= PI;
        else
          S += PI;
      }
      break;
      }
    case GeomAbs_Torus:
      {
      gp_Torus Torus = Surf->Torus();
      ElSLib::Parameters( Torus, p, S, T);
      if(U0 < Uinf) decalU = -int((Uinf - U0)/(2*PI))-1;
      if(U0 > Usup) decalU =  int((U0 - Usup)/(2*PI))+1;
      if(V0 < Vinf) decalV = -int((Vinf - V0)/(2*PI))-1;
      if(V0 > Vsup) decalV =  int((V0 - Vsup)/(2*PI))+1;
      S += decalU*2*PI; T += decalV*2*PI;
      break;
      }
    default:
      Standard_NoSuchObject::Raise("ProjLib_ComputeApproxOnPolarSurface::Value");
    }
    return gp_Pnt2d(S, T);
  }
  
  //////////////////
  Standard_Real DistMin = RealLast();
  //OCC217
  //Standard_Real tolU,tolV ;
  //tolU = Tolerance;
  //tolV = Tolerance;
  
  Standard_Real uperiod =0, vperiod = 0, u, v;
  // U0 et V0 sont les points dans la periode pour initialiser 
  // (periode ou est u et v),
  // U1 et V1 sont les points pour construire les poles
  
  if(Surf->IsUPeriodic() || Surf->IsUClosed()) {
    uperiod =  Surf->LastUParameter() - Surf->FirstUParameter();
  }
  if(Surf->IsVPeriodic() || Surf->IsVClosed()) {
    vperiod = Surf->LastVParameter() - Surf->FirstVParameter();
  } 
  if(U0 < Uinf)
    if(!uperiod)
      U0 = Uinf;
    else {
      decalU = int((Uinf - U0)/uperiod)+1;
      U0 += decalU*uperiod;
    }
  if(U0 > Usup)
    if(!uperiod)
      U0 = Usup;
    else {
      decalU = -(int((U0 - Usup)/uperiod)+1);
      U0 += decalU*uperiod;
    }
  if(V0 < Vinf)
    if(!vperiod)
      V0 = Vinf;
    else {
      decalV = int((Vinf - V0)/vperiod)+1;
      V0 += decalV*vperiod;
    }
  if(V0 > Vsup)
    if(!vperiod)
      V0 = Vsup;
    else {
      decalV = -int((V0 - Vsup)/vperiod)-1;
      V0 += decalV*vperiod;
    }
  
  // On reduit la surface autour de U0
  Standard_Real uLittle = (Usup - Uinf)/10, vLittle = (Vsup - Vinf)/10;
  Standard_Real uInfLi = 0, vInfLi = 0,uSupLi = 0, vSupLi = 0;
  if((U0 - Uinf) > uLittle) uInfLi = U0 - uLittle; else uInfLi = Uinf;
  if((V0 - Vinf) > vLittle) vInfLi = V0 - vLittle; else vInfLi = Vinf;
  if((Usup - U0) > uLittle) uSupLi = U0 + uLittle; else uSupLi = Usup;
  if((Vsup - V0) > vLittle) vSupLi = V0 + vLittle; else vSupLi = Vsup;
  
  //  const Adaptor3d_Surface GAS = Surf->Surface();

  GeomAdaptor_Surface SurfLittle;
  if (Type == GeomAbs_BSplineSurface) {
    Handle(Geom_Surface) GBSS(Surf->Surface().BSpline());
    SurfLittle.Load(GBSS, uInfLi, uSupLi, vInfLi, vSupLi);
  }
  else if (Type == GeomAbs_BezierSurface) {
    Handle(Geom_Surface) GS(Surf->Surface().Bezier());
    SurfLittle.Load(GS, uInfLi, uSupLi, vInfLi, vSupLi);
  }
  else if (Type == GeomAbs_OffsetSurface) {
    Handle(Geom_Surface) GS = GeomAdaptor::MakeSurface(Surf->Surface());
    SurfLittle.Load(GS, uInfLi, uSupLi, vInfLi, vSupLi);
  }
  else {
    Standard_NoSuchObject::Raise("");
  }

  Extrema_GenLocateExtPS  locext(p, SurfLittle, U0, V0, tolU, tolV);
  if (locext.IsDone()) {
    DistMin = locext.Value();
    if (DistMin < DistTol3d) {
      (locext.Point()).Parameter(u, v);
      gp_Pnt2d pnt(u - decalU*uperiod,v - decalV*vperiod);
      return pnt;
    }
  } 
  
  Extrema_ExtPS  ext(p, SurfLittle, tolU, tolV) ;
  if (ext.IsDone() && ext.NbExt()>=1 ) {
    DistMin = ext.Value(1);
    Standard_Integer GoodValue = 1;
    for ( Standard_Integer i = 2 ; i <= ext.NbExt() ; i++ ) 
      if( DistMin > ext.Value(i)) {
      DistMin = ext.Value(i);
      GoodValue = i;
      }
    if (DistMin < DistTol3d) {
      (ext.Point(GoodValue)).Parameter(u,v);
      gp_Pnt2d pnt(u - decalU*uperiod,v - decalV*vperiod);
      return pnt;
    }
  }
  
  return p2d;
}


//=======================================================================
//function : ProjLib_PolarFunction
//purpose  : (OCC217 - apo)- This class produce interface to call "gp_Pnt2d Function_Value(...)"
//=======================================================================

class ProjLib_PolarFunction : public AppCont_Function2d
{
  Handle(Adaptor3d_HCurve)           myCurve;
  Handle(Adaptor2d_HCurve2d)         myInitialCurve2d ;
  Handle(Adaptor3d_HSurface)         mySurface ;
  //OCC217
  Standard_Real                      myTolU, myTolV; 
  Standard_Real                      myDistTol3d; 
  //Standard_Real                    myTolerance ; 
  
  public :
  
  ProjLib_PolarFunction(const Handle(Adaptor3d_HCurve) & C, 
                  const Handle(Adaptor3d_HSurface)& Surf,
                  const Handle(Adaptor2d_HCurve2d)& InitialCurve2d,
                  //OCC217
                  const Standard_Real Tol3d) :
                  //const Standard_Real Tolerance) :
  myCurve(C),
  myInitialCurve2d(InitialCurve2d),
  mySurface(Surf),
  //OCC217        
  myTolU(Surf->UResolution(Tol3d)),
  myTolV(Surf->VResolution(Tol3d)),
  myDistTol3d(100.0*Tol3d){} ;
  //myTolerance(Tolerance){} ;
  
  ~ProjLib_PolarFunction() {}
  
  Standard_Real FirstParameter() const
    {return (myCurve->FirstParameter()+1.e-9);}
  
  Standard_Real LastParameter() const
    {return (myCurve->LastParameter()-1.e-9);}
  
  gp_Pnt2d Value(const Standard_Real t) const {
    return Function_Value
      (t,mySurface,myCurve,myInitialCurve2d,myDistTol3d,myTolU,myTolV) ;  //OCC217
      //(t,mySurface,myCurve,myInitialCurve2d,myTolerance) ;
  }
  
//  Standard_Boolean D1(const Standard_Real t, gp_Pnt2d& P, gp_Vec2d& V) const
  Standard_Boolean D1(const Standard_Real , gp_Pnt2d& , gp_Vec2d& ) const
    {return Standard_False;}
};

//=======================================================================
//function : ProjLib_ComputeApproxOnPolarSurface
//purpose  : 
//=======================================================================

ProjLib_ComputeApproxOnPolarSurface::ProjLib_ComputeApproxOnPolarSurface(){}


//=======================================================================
//function : ProjLib_ComputeApproxOnPolarSurface
//purpose  : 
//=======================================================================

ProjLib_ComputeApproxOnPolarSurface::ProjLib_ComputeApproxOnPolarSurface
(const Handle(Adaptor2d_HCurve2d)& InitialCurve2d,
 const Handle(Adaptor3d_HCurve)& Curve,
 const Handle(Adaptor3d_HSurface)& S,
 const Standard_Real tol3d):myProjIsDone(Standard_False)  //OCC217
 //const Standard_Real tolerance):myProjIsDone(Standard_False)
{
  myTolerance = tol3d; //OCC217
  //myTolerance = Max(Tolerance,Precision::PApproximation());
  myBSpline = Perform(InitialCurve2d,Curve,S);
}
//=======================================================================
//function : ProjLib_ComputeApproxOnPolarSurface
//purpose  : Traite le cas de la couture
//=======================================================================

ProjLib_ComputeApproxOnPolarSurface::ProjLib_ComputeApproxOnPolarSurface
(const Handle(Adaptor2d_HCurve2d)& InitialCurve2d,
 const Handle(Adaptor2d_HCurve2d)& InitialCurve2dBis,
 const Handle(Adaptor3d_HCurve)& Curve,
 const Handle(Adaptor3d_HSurface)& S,
 const Standard_Real tol3d):myProjIsDone(Standard_False)  //OCC217
 //const Standard_Real tolerance):myProjIsDone(Standard_False)
{// InitialCurve2d et InitialCurve2dBis sont les deux pcurves de la couture
  myTolerance = tol3d; //OCC217
  //myTolerance = Max(tolerance,Precision::PApproximation());
  Handle(Geom2d_BSplineCurve) bsc = Perform(InitialCurve2d,Curve,S);
  if(myProjIsDone) {
    gp_Pnt2d P2dproj, P2d, P2dBis;
    P2dproj = bsc->StartPoint();
    P2d    = InitialCurve2d->Value(InitialCurve2d->FirstParameter());
    P2dBis = InitialCurve2dBis->Value(InitialCurve2dBis->FirstParameter());

    Standard_Real Dist, DistBis;
    Dist    = P2dproj.Distance(P2d);
    DistBis = P2dproj.Distance(P2dBis);
    if( Dist < DistBis)  {
      // myBSpline2d est bien la pcurve recherche. On la translate pour avoir myCurve2d
      myBSpline = bsc;
      Handle(Geom2d_Geometry) GG = myBSpline->Translated(P2d, P2dBis);
      my2ndCurve = Handle(Geom2d_Curve)::DownCast(GG);
    }
    else {
      my2ndCurve = bsc;
      Handle(Geom2d_Geometry) GG = my2ndCurve->Translated(P2dBis, P2d);
      myBSpline = Handle(Geom2d_BSplineCurve)::DownCast(GG);
    }
  }
}

//=======================================================================
//function : ProjLib_ComputeApproxOnPolarSurface
//purpose  : cas sans courbe d'initialisation
//=======================================================================

ProjLib_ComputeApproxOnPolarSurface::ProjLib_ComputeApproxOnPolarSurface
(const Handle(Adaptor3d_HCurve)& Curve,
 const Handle(Adaptor3d_HSurface)& S,
 const Standard_Real tol3d):myProjIsDone(Standard_False)  //OCC217
 //const Standard_Real tolerance):myProjIsDone(Standard_False)
{
  myTolerance = tol3d; //OCC217
  //myTolerance = Max(tolerance,Precision::PApproximation());
  const Handle_Adaptor2d_HCurve2d InitCurve2d ;
  myBSpline = Perform(InitCurve2d,Curve,S);  
} 

static Handle(Geom2d_BSplineCurve) Concat(Handle(Geom2d_BSplineCurve) C1,
                                Handle(Geom2d_BSplineCurve) C2)
{
  Standard_Integer deg, deg1, deg2;
  deg1 = C1->Degree();
  deg2 = C2->Degree();
  
  if ( deg1 < deg2) {
    C1->IncreaseDegree(deg2);
    deg = deg2;
  }
  else if ( deg2 < deg1) {
    C2->IncreaseDegree(deg1);
    deg = deg1;
  }
  else deg = deg1;

  Standard_Integer np1,np2,nk1,nk2,np,nk;
  np1 = C1->NbPoles();
  nk1 = C1->NbKnots();
  np2 = C2->NbPoles();
  nk2 = C2->NbKnots();
  nk = nk1 + nk2 -1;
  np = np1 + np2 -1;

  TColStd_Array1OfReal    K1(1,nk1); C1->Knots(K1);
  TColStd_Array1OfInteger M1(1,nk1); C1->Multiplicities(M1);
  TColgp_Array1OfPnt2d    P1(1,np1); C1->Poles(P1);
  TColStd_Array1OfReal    K2(1,nk2); C2->Knots(K2);
  TColStd_Array1OfInteger M2(1,nk2); C2->Multiplicities(M2);
  TColgp_Array1OfPnt2d    P2(1,np2); C2->Poles(P2);

  // Compute the new BSplineCurve
  TColStd_Array1OfReal    K(1,nk);
  TColStd_Array1OfInteger M(1,nk);
  TColgp_Array1OfPnt2d    P(1,np);

  Standard_Integer i, count = 0;
  // Set Knots and Mults
  for ( i = 1; i <= nk1; i++) {
    count++;
    K(count) = K1(i);
    M(count) = M1(i);
  }
  M(count) = deg;
  for ( i = 2; i <= nk2; i++) {
    count++;
    K(count) = K2(i);
    M(count) = M2(i);
  }
  // Set the Poles
  count = 0;
  for (i = 1; i <= np1; i++) {
    count++;
    P(count) = P1(i);
  }
  for (i = 2; i <= np2; i++) {
    count++;
    P(count) = P2(i);
  }

  Handle(Geom2d_BSplineCurve) BS = 
    new Geom2d_BSplineCurve(P,K,M,deg);
  return BS;
}


//=======================================================================
//function : Perform
//purpose  : 
//=======================================================================
Handle(Geom2d_BSplineCurve) ProjLib_ComputeApproxOnPolarSurface::Perform
(const Handle(Adaptor2d_HCurve2d)& InitialCurve2d,
 const Handle(Adaptor3d_HCurve)& Curve,
 const Handle(Adaptor3d_HSurface)& S) 
{
  //OCC217
  Standard_Real Tol3d = myTolerance; 
  Standard_Real ParamTol = Precision::PApproximation();

  Handle(Adaptor2d_HCurve2d) AHC2d = InitialCurve2d;
  Handle(Adaptor3d_HCurve) AHC = Curve;
  
// si la courbe 3d est une BSpline de degré C0, on la découpe en bout de degré C1
// -> bug cts18237
  GeomAbs_CurveType typeCurve = Curve->GetType();
  if(typeCurve == GeomAbs_BSplineCurve) {
    TColStd_ListOfTransient LOfBSpline2d;
    Handle(Geom_BSplineCurve) BSC = Curve->BSpline();
    Standard_Integer nbInter = Curve->NbIntervals(GeomAbs_C1);
    if(nbInter > 1) {
      Standard_Integer i, j;
      Handle(Geom_TrimmedCurve) GTC;
      Handle(Geom2d_TrimmedCurve) G2dTC;
      TColStd_Array1OfReal Inter(1,nbInter+1);
      Curve->Intervals(Inter,GeomAbs_C1);
      Standard_Real firstinter = Inter.Value(1), secondinter = Inter.Value(2);
      // initialisation 3d
      GTC = new Geom_TrimmedCurve(BSC, firstinter, secondinter);
      AHC = new GeomAdaptor_HCurve(GTC);
      
      // s'il y a une courbe d'initialisation : 
      // - soit c'est une BSpline C0, avec discontinuité aux même paramètres de noeuds
      // et on prend les bouts C1
      // - soit c'est une courbe C1 et on en prend les bouts qui nous intéresse
      // et sinon on en créer une.
      
      // initialisation 2d
      Standard_Integer nbInter2d;
      Standard_Boolean C2dIsToCompute;
      C2dIsToCompute = InitialCurve2d.IsNull();
      Handle(Geom2d_BSplineCurve) BSC2d;
      Handle(Geom2d_Curve) G2dC;
      
      if(!C2dIsToCompute) {
      nbInter2d = InitialCurve2d->NbIntervals(GeomAbs_C1);
      TColStd_Array1OfReal Inter2d(1,nbInter2d+1);
      InitialCurve2d->Intervals(Inter2d,GeomAbs_C1);
      j = 1;
      for(i = 1,j = 1;i <= nbInter;i++)
        if(Abs(Inter.Value(i) - Inter2d.Value(j)) < ParamTol) { //OCC217
        //if(Abs(Inter.Value(i) - Inter2d.Value(j)) < myTolerance) {
          if (j > nbInter2d) break;
          j++;
        }
      if(j != (nbInter2d+1)) {
        C2dIsToCompute = Standard_True;
      }
      }
      
      if(C2dIsToCompute) {
      AHC2d = BuildInitialCurve2d(AHC, S);
      }
      else {
      typeCurve = InitialCurve2d->GetType();
      switch (typeCurve) {
      case GeomAbs_Line: {
        G2dC = new Geom2d_Line(InitialCurve2d->Line());
        break;
      }
      case GeomAbs_Circle: {
        G2dC = new Geom2d_Circle(InitialCurve2d->Circle());
        break;
      }
      case GeomAbs_Ellipse: {
        G2dC = new Geom2d_Ellipse(InitialCurve2d->Ellipse());
        break;
      }
      case GeomAbs_Hyperbola: {
        G2dC = new Geom2d_Hyperbola(InitialCurve2d->Hyperbola());
        break;
      }
      case GeomAbs_Parabola: {
        G2dC = new Geom2d_Parabola(InitialCurve2d->Parabola());
        break;
      }
      case GeomAbs_BezierCurve: {
        G2dC = InitialCurve2d->Bezier();
        break;
      }
      case GeomAbs_BSplineCurve: {
        G2dC = InitialCurve2d->BSpline();
        break;
      }
#ifndef DEB
      default:
        break;
#endif
      }
      gp_Pnt2d fp2d = G2dC->Value(firstinter), lp2d = G2dC->Value(secondinter);
      gp_Pnt fps, lps, fpc, lpc;
      S->D0(fp2d.X(), fp2d.Y(), fps);
      S->D0(lp2d.X(), lp2d.Y(), lps);
      Curve->D0(firstinter, fpc);
      Curve->D0(secondinter, lpc);
      //OCC217
      if((fps.IsEqual(fpc, Tol3d)) &&
         (lps.IsEqual(lpc, Tol3d))) {
      //if((fps.IsEqual(fpc, myTolerance)) &&
      //   (lps.IsEqual(lpc, myTolerance))) {
        G2dTC = new Geom2d_TrimmedCurve(G2dC, firstinter, secondinter);
        Geom2dAdaptor_Curve G2dAC(G2dTC);
        AHC2d = new Geom2dAdaptor_HCurve(G2dAC);
        myProjIsDone = Standard_True;
      }
      else {
        AHC2d = BuildInitialCurve2d(AHC, S);
        C2dIsToCompute = Standard_True;
      }
      }
      
      if(myProjIsDone) {
      BSC2d = ProjectUsingInitialCurve2d(AHC, S, AHC2d);  
      if(BSC2d.IsNull()) return Handle(Geom2d_BSplineCurve)(); //IFV
      LOfBSpline2d.Append(BSC2d);
      }
      else {
      return Handle(Geom2d_BSplineCurve)();
      }
      


      Standard_Real iinter, ip1inter;
      Standard_Integer nbK2d, deg;
      nbK2d = BSC2d->NbKnots(); deg = BSC2d->Degree();

      for(i = 2;i <= nbInter;i++) {
      iinter = Inter.Value(i);
      ip1inter = Inter.Value(i+1);
      // cas général 3d
      GTC->SetTrim(iinter, ip1inter);
      AHC = new GeomAdaptor_HCurve(GTC);
      
      // cas général 2d
      if(C2dIsToCompute) {
        AHC2d = BuildInitialCurve2d(AHC, S);
      }
      else {
        gp_Pnt2d fp2d = G2dC->Value(iinter), lp2d = G2dC->Value(ip1inter);
        gp_Pnt fps, lps, fpc, lpc;
        S->D0(fp2d.X(), fp2d.Y(), fps);
        S->D0(lp2d.X(), lp2d.Y(), lps);
        Curve->D0(iinter, fpc);
        Curve->D0(ip1inter, lpc);
        //OCC217
        if((fps.IsEqual(fpc, Tol3d)) &&
           (lps.IsEqual(lpc, Tol3d))) {
        //if((fps.IsEqual(fpc, myTolerance)) &&
        //   (lps.IsEqual(lpc, myTolerance))) {
          G2dTC->SetTrim(iinter, ip1inter);
          Geom2dAdaptor_Curve G2dAC(G2dTC);
          AHC2d = new Geom2dAdaptor_HCurve(G2dAC);
          myProjIsDone = Standard_True;
        }
        else {
          AHC2d = BuildInitialCurve2d(AHC, S);
        }
      }
      if(myProjIsDone) {
        BSC2d = ProjectUsingInitialCurve2d(AHC, S, AHC2d);  
        if(BSC2d.IsNull()) {
          return Handle(Geom2d_BSplineCurve)();
        }
        LOfBSpline2d.Append(BSC2d);
        nbK2d += BSC2d->NbKnots() - 1;
        deg = Max(deg, BSC2d->Degree());
      }
      else {
        return Handle(Geom2d_BSplineCurve)();
      }
      }

      Standard_Integer NbC = LOfBSpline2d.Extent();
      Handle(Geom2d_BSplineCurve) CurBS;
      CurBS = Handle(Geom2d_BSplineCurve)::DownCast(LOfBSpline2d.First());
      LOfBSpline2d.RemoveFirst();
      for (Standard_Integer ii = 2; ii <= NbC; ii++) {
      Handle(Geom2d_BSplineCurve) BS = 
        Handle(Geom2d_BSplineCurve)::DownCast(LOfBSpline2d.First());
      CurBS = Concat(CurBS,BS);
      LOfBSpline2d.RemoveFirst();
      }
      return CurBS;
    }
  }
  
  if(InitialCurve2d.IsNull()) {
    AHC2d = BuildInitialCurve2d(Curve, S);
    if(!myProjIsDone) 
      return Handle(Geom2d_BSplineCurve)(); 
  }
  return ProjectUsingInitialCurve2d(AHC, S, AHC2d);    
}

//=======================================================================
//function : ProjLib_BuildInitialCurve2d
//purpose  : 
//=======================================================================

Handle(Adaptor2d_HCurve2d) 
     ProjLib_ComputeApproxOnPolarSurface::
     BuildInitialCurve2d(const Handle(Adaptor3d_HCurve)&   Curve,
                   const Handle(Adaptor3d_HSurface)& Surf)
{
  //  faire la discretisation de Curve avec quasiuniform deflection
  //  densifier a NbOfPnts points aux moins
  myProjIsDone = Standard_False;
  
  //OCC217
  Standard_Real Tol3d = myTolerance; 
  Standard_Real TolU = Surf->UResolution(Tol3d), TolV = Surf->VResolution(Tol3d);
  Standard_Real DistTol3d = 100.0*Tol3d;

  // NON myTol est une Tol2d !!!!
  //Standard_Real TolU = myTolerance, TolV = myTolerance;
  //Standard_Real Tol3d = 100*myTolerance; // Au hazard Balthazar.

  Standard_Integer NbOfPnts = 61; 
  GCPnts_QuasiUniformAbscissa QUA(Curve->GetCurve(),NbOfPnts);
  TColgp_Array1OfPnt Pts(1,NbOfPnts);
  TColStd_Array1OfReal Param(1,NbOfPnts);
  Standard_Integer i, j;
  for( i = 1; i <= NbOfPnts ; i++ ) { 
    Param(i) = QUA.Parameter(i);
    Pts(i) = Curve->Value(Param(i));
  }
  
  TColgp_Array1OfPnt2d Pts2d(1,NbOfPnts);
  TColStd_Array1OfInteger Mult(1,NbOfPnts);
  Mult.Init(1);
  Mult(1) = Mult(NbOfPnts) = 2;
  
  Standard_Real Vinf, Vsup;
  Vinf = Surf->Surface().FirstVParameter();
  Vsup = Surf->Surface().LastVParameter();
  GeomAbs_SurfaceType Type = Surf->GetType();
  if((Type != GeomAbs_BSplineSurface) && (Type != GeomAbs_BezierSurface) &&
     (Type != GeomAbs_OffsetSurface)) {
    Standard_Real S, T;
//    Standard_Integer usens = 0, vsens = 0; 
    // pour savoir comment on est par rapport a la periode
    switch (Type) {
//    case GeomAbs_Plane:
//      {
//    gp_Pln Plane = Surf->Plane();
//    for ( i = 1 ; i <= NbOfPnts ; i++) { 
//      ElSLib::Parameters( Plane, Pts(i), S, T);
//      Pts2d(i).SetCoord(S,T);
//    }
//    myProjIsDone = Standard_True;
//    break;
//      }
    case GeomAbs_Cylinder:
      {
//    Standard_Real Sloc, Tloc;
      Standard_Real Sloc;
      Standard_Integer usens = 0;
      gp_Cylinder Cylinder = Surf->Cylinder();
      ElSLib::Parameters( Cylinder, Pts(1), S, T);
      Pts2d(1).SetCoord(S,T);
      for ( i = 2 ; i <= NbOfPnts ; i++) { 
        Sloc = S;
        ElSLib::Parameters( Cylinder, Pts(i), S, T);
        if(Abs(Sloc - S) > PI)
          if(Sloc > S)
            usens++;
          else
            usens--;
        Pts2d(i).SetCoord(S+usens*2*PI,T);
      }
      myProjIsDone = Standard_True;
      break;
      }
    case GeomAbs_Cone:
      {
//    Standard_Real Sloc, Tloc;
      Standard_Real Sloc;
      Standard_Integer usens = 0;
      gp_Cone Cone = Surf->Cone();
      ElSLib::Parameters( Cone, Pts(1), S, T);
      Pts2d(1).SetCoord(S,T);
      for ( i = 2 ; i <= NbOfPnts ; i++) { 
        Sloc = S;
        ElSLib::Parameters( Cone, Pts(i), S, T);
        if(Abs(Sloc - S) > PI)
          if(Sloc > S)
            usens++;
          else
            usens--;
        Pts2d(i).SetCoord(S+usens*2*PI,T);
      }
      myProjIsDone = Standard_True;
      break;
      }
    case GeomAbs_Sphere:
      {
      Standard_Real Sloc, Tloc;
      Standard_Integer usens = 0, vsens = 0; //usens marche ici par demi periode
      Standard_Boolean vparit = Standard_False;
      gp_Sphere Sphere = Surf->Sphere();
      ElSLib::Parameters( Sphere, Pts(1), S, T);
      Pts2d(1).SetCoord(S,T);
      for ( i = 2 ; i <= NbOfPnts ; i++) { 
        Sloc = S;Tloc = T;
        ElSLib::Parameters( Sphere, Pts(i), S, T);
        if(1.6*PI < Abs(Sloc - S))
          if(Sloc > S)
            usens += 2;
          else
            usens -= 2;
        if(1.6*PI > Abs(Sloc - S) && Abs(Sloc - S) > 0.4*PI) {
          vparit = !vparit;
          if(Sloc > S)
            usens++;
          else
            usens--;
          if(Abs(Tloc - Vsup) < (Vsup - Vinf)/5)
            vsens++;
          else
            vsens--;
        }
        if(vparit) {
          Pts2d(i).SetCoord(S+usens*PI,(PI - T)*(vsens-1));
        }     
        else {
          Pts2d(i).SetCoord(S+usens*PI,T+vsens*PI);
          
        }
      }
      myProjIsDone = Standard_True;
      break;
      }
    case GeomAbs_Torus:
      {
      Standard_Real Sloc, Tloc;
      Standard_Integer usens = 0, vsens = 0;
      gp_Torus Torus = Surf->Torus();
      ElSLib::Parameters( Torus, Pts(1), S, T);
      Pts2d(1).SetCoord(S,T);
      for ( i = 2 ; i <= NbOfPnts ; i++) { 
        Sloc = S; Tloc = T;
        ElSLib::Parameters( Torus, Pts(i), S, T);
        if(Abs(Sloc - S) > PI)
          if(Sloc > S)
            usens++;
          else
            usens--;
        if(Abs(Tloc - T) > PI)
          if(Tloc > T)
            vsens++;
          else
            vsens--;
        Pts2d(i).SetCoord(S+usens*2*PI,T+vsens*2*PI);
      }
      myProjIsDone = Standard_True;
      break;
      }
    default:
      Standard_NoSuchObject::Raise("ProjLib_ComputeApproxOnPolarSurface::BuildInitialCurve2d");
    }
  }
  else {
    Standard_Real Uinf = Surf->Surface().FirstUParameter();
    Standard_Real Usup = Surf->Surface().LastUParameter();
    
    myProjIsDone = Standard_False;
    Standard_Real DistMin = 1.e+100, u = 0., v = 0.;
    gp_Pnt pntproj;

    TColgp_SequenceOfPnt2d Sols;
    Standard_Boolean areManyZeros = Standard_False;
    
    Curve->D0(Param.Value(1), pntproj) ;
    Extrema_ExtPS  aExtPS(pntproj, Surf->Surface(), TolU, TolV) ;

    if( aExtPS.IsDone() && aExtPS.NbExt() >= 1 ) {

      Standard_Integer GoodValue = 1;

      for ( i = 1 ; i <= aExtPS.NbExt() ; i++ ) {
      if( aExtPS.Value(i) < DistTol3d ) {
        if( Abs( aExtPS.Value(i) ) <= 1.e-9 ) {
          aExtPS.Point(i).Parameter(u,v);
          gp_Pnt2d p2d(u,v);
          Standard_Boolean isSame = Standard_False;
          for( j = 1; j <= Sols.Length(); j++ ) {
            if( p2d.Distance( Sols.Value(j) ) <= 1.e-9 ) {
            isSame = Standard_True;
            break;
            }
          }
          if( !isSame ) Sols.Append( p2d );
        }
        if( DistMin > aExtPS.Value(i) ) {
          DistMin = aExtPS.Value(i);
          GoodValue = i;
        }
      }
      }

      if( Sols.Length() > 1 ) areManyZeros = Standard_True;

      if( DistMin <= DistTol3d ) {
      if( !areManyZeros ) {
        aExtPS.Point(GoodValue).Parameter(u,v);
        Pts2d(1).SetCoord(u,v);
        myProjIsDone = Standard_True;
      }
      else {
        Standard_Integer nbSols = Sols.Length();
        Standard_Real DistMax = -1.e+100;
        for( i = 1; i <= nbSols; i++ ) {
          const gp_Pnt2d& aP1 = Sols.Value(i);
          for( j = i+1; j <= nbSols; j++ ) {
            const gp_Pnt2d& aP2 = Sols.Value(j);
            Standard_Real aDist = aP1.Distance(aP2);
            if( aDist > DistMax ) DistMax = aDist;
          }
        }
        if( DistMax > Max(TolU,TolV) ) {
          Standard_Integer tPp = 0;
          for( i = 1; i <= 5; i++ ) {
            Standard_Integer nbExtOk = 0;
            Standard_Integer indExt = 0;
            Standard_Integer iT = 1 + (NbOfPnts - 1)/5*i;
            Curve->D0( Param.Value(iT), pntproj );
            Extrema_ExtPS aTPS( pntproj, Surf->Surface(), TolU, TolV );
            DistMin = 1.e+100;
            if( aTPS.IsDone() && aTPS.NbExt() >= 1 ) {
            for( j = 1 ; j <= aTPS.NbExt() ; j++ ) {
              if( aTPS.Value(j) < DistTol3d ) {
                nbExtOk++;
                if( aTPS.Value(j) < DistMin ) {
                  DistMin = aTPS.Value(j);
                  indExt = j;
                }
              }
            }
            }
            if( nbExtOk == 1 ) {
            tPp = iT;
            aTPS.Point(indExt).Parameter(u,v);
            break;
            }
          }

          if( tPp != 0 ) {
            gp_Pnt2d aPp = gp_Pnt2d(u,v);
            gp_Pnt2d aPn;
            j = 1;
            Standard_Boolean isFound = Standard_False;
            while( !isFound ) { 
            Curve->D0( Param.Value(tPp+j), pntproj );
            Extrema_ExtPS aTPS( pntproj, Surf->Surface(), TolU, TolV );
            DistMin = 1.e+100;
            Standard_Integer indExt = 0;
            if( aTPS.IsDone() && aTPS.NbExt() >= 1 ) {
              for( i = 1 ; i <= aTPS.NbExt() ; i++ ) {
                if( aTPS.Value(i) < DistTol3d && aTPS.Value(i) < DistMin ) {
                  DistMin = aTPS.Value(i);
                  indExt = i;
                  isFound = Standard_True;
                }
              }
            }
            if( isFound ) {
              aTPS.Point(indExt).Parameter(u,v);
              aPn = gp_Pnt2d(u,v);
              break;
            }
            j++;
            if( (tPp+j) > NbOfPnts ) break;
            }

            if( isFound ) {
            gp_Vec2d atV(aPp,aPn);
            Standard_Boolean isChosen = Standard_False;
            for( i = 1; i <= nbSols; i++ ) {
              const gp_Pnt2d& aP1 = Sols.Value(i);
              gp_Vec2d asV(aP1,aPp);
              if( asV.Dot(atV) > 0. ) {
                isChosen = Standard_True;
                Pts2d(1).SetCoord(aP1.X(),aP1.Y());
                myProjIsDone = Standard_True;
                break;
              }
            }
            if( !isChosen ) {
              aExtPS.Point(GoodValue).Parameter(u,v);
              Pts2d(1).SetCoord(u,v);
              myProjIsDone = Standard_True;
            }
            }
            else {
            aExtPS.Point(GoodValue).Parameter(u,v);
            Pts2d(1).SetCoord(u,v);
            myProjIsDone = Standard_True;
            }
          }
          else {
            aExtPS.Point(GoodValue).Parameter(u,v);
            Pts2d(1).SetCoord(u,v);
            myProjIsDone = Standard_True;
          }
        }
        else {
          aExtPS.Point(GoodValue).Parameter(u,v);
          Pts2d(1).SetCoord(u,v);
          myProjIsDone = Standard_True;
        }
      }
      }
      
      //  calcule des points suivants avec GenLocate_ExtPS
      // (et stocke le resultat et le parametre chacun dans une sequence)
      Standard_Integer usens = 0, vsens = 0; 
      // pour savoir comment on est par rapport a la periode
      Standard_Real U0 = u, V0 = v, U1 = u, V1 = v, uperiod =0, vperiod = 0;
      // U0 et V0 sont les points dans la periode pour initialiser 
      // (periode ou sont u et v),
      // U1 et V1 sont les points pour construire les poles


      if(Surf->IsUPeriodic() || Surf->IsUClosed()) {
      uperiod = Surf->LastUParameter() - Surf->FirstUParameter(); 
      }

      if(Surf->IsVPeriodic() || Surf->IsVClosed()) {
      vperiod = Surf->LastVParameter() - Surf->FirstVParameter(); 
      } 
      
      for ( i = 2 ; i <= NbOfPnts ; i++) 
      if(myProjIsDone) {
        myProjIsDone = Standard_False;
        DistMin = RealLast();
        Curve->D0(Param.Value(i), pntproj);
        Extrema_GenLocateExtPS  aLocateExtPS
          (pntproj, Surf->Surface(), U0, V0, TolU, TolV) ;
        
        if (aLocateExtPS.IsDone())
          if (aLocateExtPS.Value() < DistTol3d) {  //OCC217
          //if (aLocateExtPS.Value() < Tol3d) {
            (aLocateExtPS.Point()).Parameter(U0,V0);
            U1 = U0 + usens*uperiod;
            V1 = V0 + vsens*vperiod;
            Pts2d(i).SetCoord(U1,V1);
            myProjIsDone = Standard_True;
          }
        if(!myProjIsDone && uperiod) {
          Standard_Real Uinf, Usup, Uaux;
          Uinf = Surf->Surface().FirstUParameter();
          Usup = Surf->Surface().LastUParameter();
          if((Usup - U0) > (U0 - Uinf)) 
            Uaux = 2*Uinf - U0 + uperiod;
          else 
            Uaux = 2*Usup - U0 - uperiod;
          Extrema_GenLocateExtPS  locext(pntproj, 
                                 Surf->Surface(), 
                                 Uaux, V0, TolU, TolV);
          if (locext.IsDone())
            if (locext.Value() < DistTol3d) {  //OCC217
            //if (locext.Value() < Tol3d) {
            (locext.Point()).Parameter(u,v);
            if((Usup - U0) > (U0 - Uinf)) 
              usens--;
            else 
              usens++;
            U0 = u; V0 = v;
            U1 = U0 + usens*uperiod;
            V1 = V0 + vsens*vperiod;
            Pts2d(i).SetCoord(U1,V1);
            myProjIsDone = Standard_True;
            }
        }
        if(!myProjIsDone && vperiod) {
          Standard_Real Vinf, Vsup, Vaux;
          Vinf = Surf->Surface().FirstVParameter();
          Vsup = Surf->Surface().LastVParameter();
          if((Vsup - V0) > (V0 - Vinf)) 
            Vaux = 2*Vinf - V0 + vperiod;
          else 
            Vaux = 2*Vsup - V0 - vperiod;
          Extrema_GenLocateExtPS  locext(pntproj, 
                                 Surf->Surface(), 
                                 U0, Vaux, TolU, TolV) ;
          if (locext.IsDone())
            if (locext.Value() < DistTol3d) {  //OCC217
            //if (locext.Value() < Tol3d) {
            (locext.Point()).Parameter(u,v);
            if((Vsup - V0) > (V0 - Vinf)) 
              vsens--;
            else 
              vsens++;
            U0 = u; V0 = v;
            U1 = U0 + usens*uperiod;
            V1 = V0 + vsens*vperiod;
            Pts2d(i).SetCoord(U1,V1);
            myProjIsDone = Standard_True;
            }
        }   
        if(!myProjIsDone && uperiod && vperiod) {
          Standard_Real Uaux, Vaux;
          if((Usup - U0) > (U0 - Uinf)) 
            Uaux = 2*Uinf - U0 + uperiod;
          else 
            Uaux = 2*Usup - U0 - uperiod;
          if((Vsup - V0) > (V0 - Vinf)) 
            Vaux = 2*Vinf - V0 + vperiod;
          else 
            Vaux = 2*Vsup - V0 - vperiod;
          Extrema_GenLocateExtPS  locext(pntproj, 
                                 Surf->Surface(), 
                                 Uaux, Vaux, TolU, TolV);
          if (locext.IsDone())
            if (locext.Value() < DistTol3d) {
            //if (locext.Value() < Tol3d) {
            (locext.Point()).Parameter(u,v);
            if((Usup - U0) > (U0 - Uinf)) 
              usens--;
            else 
              usens++;
            if((Vsup - V0) > (V0 - Vinf)) 
              vsens--;
            else 
              vsens++;
            U0 = u; V0 = v;
            U1 = U0 + usens*uperiod;
            V1 = V0 + vsens*vperiod;
            Pts2d(i).SetCoord(U1,V1);
            myProjIsDone = Standard_True;
            }
        }
        if(!myProjIsDone) {
          Extrema_ExtPS ext(pntproj, Surf->Surface(), TolU, TolV) ;
          if (ext.IsDone()) {
            DistMin = ext.Value(1);
            Standard_Integer GoodValue = 1;
            for ( j = 2 ; j <= ext.NbExt() ; j++ )
            if( DistMin > ext.Value(j)) {
              DistMin = ext.Value(j);
              GoodValue = j;
            }
            if (DistMin < DistTol3d) {
            //if (DistMin < Tol3d) {
            (ext.Point(GoodValue)).Parameter(u,v);
            if(uperiod)
              if((U0 - u) > (2*uperiod/3)) {
                usens++;
              }
              else
                if((u - U0) > (2*uperiod/3)) {
                  usens--;
                }
            if(vperiod)
              if((V0 - v) > (vperiod/2)) {
                vsens++;
              }
              else
                if((v - V0) > (vperiod/2)) {
                  vsens--;
                }
            U0 = u; V0 = v;
            U1 = U0 + usens*uperiod;
            V1 = V0 + vsens*vperiod;
            Pts2d(i).SetCoord(U1,V1);
            myProjIsDone = Standard_True;
            }
          }
        }
      }
      else break;
    }    
  }
  // -- On transforme Pnts2d en Geom2d_BSplineCurve, a l'aide de Param et de Mult
  if(myProjIsDone) {
    myBSpline = new Geom2d_BSplineCurve(Pts2d,Param,Mult,1);
    Geom2dAdaptor_Curve GAC(myBSpline);
    Handle(Adaptor2d_HCurve2d) IC2d = new Geom2dAdaptor_HCurve(GAC);
#ifdef DEB
//    char name [100];
//    sprintf(name,"%s_%d","build",compteur++);
//    DrawTrSurf::Set(name,myBSpline);
#endif
    return IC2d;
  }
  else {
//  Modified by Sergey KHROMOV - Thu Apr 18 10:57:50 2002 Begin
//     Standard_NoSuchObject_Raise_if(1,"ProjLib_Compu: build echec");
//  Modified by Sergey KHROMOV - Thu Apr 18 10:57:51 2002 End
    return Handle(Adaptor2d_HCurve2d)();
  }
  myProjIsDone = Standard_False;
//  Modified by Sergey KHROMOV - Thu Apr 18 10:58:01 2002 Begin
//   Standard_NoSuchObject_Raise_if(1,"ProjLib_ComputeOnPS: build echec");
//  Modified by Sergey KHROMOV - Thu Apr 18 10:58:02 2002 End
  return Handle(Adaptor2d_HCurve2d)();
}




//=======================================================================
//function : ProjLib_ProjectUsingInitialCurve2d
//purpose  : 
//=======================================================================
Handle(Geom2d_BSplineCurve) 
     ProjLib_ComputeApproxOnPolarSurface::
     ProjectUsingInitialCurve2d(const Handle(Adaptor3d_HCurve)& Curve,
                        const Handle(Adaptor3d_HSurface)& Surf,
                        const Handle(Adaptor2d_HCurve2d)& InitCurve2d) 
{  
  //OCC217
  Standard_Real Tol3d = myTolerance;
  Standard_Real DistTol3d = 1.0*Tol3d;
  Standard_Real TolU = Surf->UResolution(Tol3d), TolV = Surf->VResolution(Tol3d);
  Standard_Real Tol2d = Sqrt(TolU*TolU + TolV*TolV);

  Standard_Integer i;
  GeomAbs_SurfaceType TheTypeS = Surf->GetType();
  GeomAbs_CurveType TheTypeC = Curve->GetType();
//  Handle(Standard_Type) TheTypeS = Surf->DynamicType();
//  Handle(Standard_Type) TheTypeC = Curve->DynamicType();   // si on a :
//  if(TheTypeS == STANDARD_TYPE(Geom_BSplineSurface)) {
  if(TheTypeS == GeomAbs_Plane) {
    Standard_Real S, T;
    gp_Pln Plane = Surf->Plane();
    if(TheTypeC == GeomAbs_BSplineCurve) {
      Handle(Geom_BSplineCurve) BSC = Curve->BSpline();
      TColgp_Array1OfPnt2d Poles2d(1,Curve->NbPoles());
      for(i = 1;i <= Curve->NbPoles();i++) {
      ElSLib::Parameters( Plane, BSC->Pole(i), S, T);
      Poles2d(i).SetCoord(S,T);
      }
      TColStd_Array1OfReal Knots(1, BSC->NbKnots());
      BSC->Knots(Knots);
      TColStd_Array1OfInteger Mults(1, BSC->NbKnots());
      BSC->Multiplicities(Mults);
      if(BSC->IsRational()) {
      TColStd_Array1OfReal Weights(1, BSC->NbPoles());
      BSC->Weights(Weights); 
      return new Geom2d_BSplineCurve(Poles2d, Weights, Knots, Mults,
                               BSC->Degree(), BSC->IsPeriodic()) ;
      }
      return new Geom2d_BSplineCurve(Poles2d, Knots, Mults,
                             BSC->Degree(), BSC->IsPeriodic()) ;
      
    }
    if(TheTypeC == GeomAbs_BezierCurve) {
      Handle(Geom_BezierCurve) BC = Curve->Bezier();
      TColgp_Array1OfPnt2d Poles2d(1,Curve->NbPoles());
      for(i = 1;i <= Curve->NbPoles();i++) {
      ElSLib::Parameters( Plane, BC->Pole(i), S, T);
      Poles2d(i).SetCoord(S,T);
      }
      TColStd_Array1OfReal Knots(1, 2);
      Knots.SetValue(1,0.0);
      Knots.SetValue(2,1.0);
      TColStd_Array1OfInteger Mults(1, 2);
      Mults.Init(BC->NbPoles());
      if(BC->IsRational()) {
      TColStd_Array1OfReal Weights(1, BC->NbPoles());
      BC->Weights(Weights); 
      return new Geom2d_BSplineCurve(Poles2d, Weights, Knots, Mults,
                               BC->Degree(), BC->IsPeriodic()) ;
      }
      return new Geom2d_BSplineCurve(Poles2d, Knots, Mults,
                             BC->Degree(), BC->IsPeriodic()) ;
    }
  }
  if(TheTypeS == GeomAbs_BSplineSurface) {
    Handle(Geom_BSplineSurface) BSS = Surf->BSpline();
    if((BSS->MaxDegree() == 1) &&
       (BSS->NbUPoles() == 2) &&
       (BSS->NbVPoles() == 2)) {
      gp_Pnt p11 = BSS->Pole(1,1);
      gp_Pnt p12 = BSS->Pole(1,2);
      gp_Pnt p21 = BSS->Pole(2,1);
      gp_Pnt p22 = BSS->Pole(2,2);
      gp_Vec V1(p11,p12);
      gp_Vec V2(p21,p22);
      if(V1.IsEqual(V2,Tol3d,Tol3d/(p11.Distance(p12)*180/PI))){  //OCC217
      //if(V1.IsEqual(V2,myTolerance,myTolerance/(p11.Distance(p12)*180/PI))){
      //  alors la surface polaire est plane
      //  et l'on se contente de projeter les poles de Curve
      Standard_Integer DistMin = IntegerLast();
      Standard_Real u,v;
      //OCC217
      //Standard_Real TolU = Surf->UResolution(myTolerance)
      //  , TolV = Surf->VResolution(myTolerance);
//    gp_Pnt pntproj;
      if(TheTypeC == GeomAbs_BSplineCurve) {
        Handle(Geom_BSplineCurve) BSC = Curve->BSpline();
        TColgp_Array1OfPnt2d Poles2d(1,Curve->NbPoles());
        for(i = 1;i <= Curve->NbPoles();i++) {
          myProjIsDone = Standard_False;
          DistMin = IntegerLast();
          Extrema_GenLocateExtPS  extrloc(BSC->Pole(i),Surf->Surface(),(p11.X()+p22.X())/2,
                                  (p11.Y()+p22.Y())/2,TolU,TolV) ;
          if (extrloc.IsDone()) {
            DistMin = (Standard_Integer ) extrloc.Value();
            if (DistMin < DistTol3d) {  //OCC217
            //if (DistMin < myTolerance) {
            (extrloc.Point()).Parameter(u,v);
            Poles2d(i).SetCoord(u,v);
            myProjIsDone = Standard_True;
            }
            else break;
          }
          else break;
          if(!myProjIsDone) 
            break;
        }
        if(myProjIsDone) {
          TColStd_Array1OfReal Knots(1, BSC->NbKnots());
          BSC->Knots(Knots);
          TColStd_Array1OfInteger Mults(1, BSC->NbKnots());
          BSC->Multiplicities(Mults);
          if(BSC->IsRational()) {
            TColStd_Array1OfReal Weights(1, BSC->NbPoles());
            BSC->Weights(Weights); 
            return new Geom2d_BSplineCurve(Poles2d, Weights, Knots, Mults,
                                   BSC->Degree(), BSC->IsPeriodic()) ;
          }
          return new Geom2d_BSplineCurve(Poles2d, Knots, Mults,
                                 BSC->Degree(), BSC->IsPeriodic()) ;
          
          
        }
      } 
      if(TheTypeC == GeomAbs_BezierCurve) {
        Handle(Geom_BezierCurve) BC = Curve->Bezier();
        TColgp_Array1OfPnt2d Poles2d(1,Curve->NbPoles());
        for(i = 1;i <= Curve->NbPoles();i++) {
          DistMin = IntegerLast();
          Extrema_GenLocateExtPS  extrloc(BC->Pole(i),Surf->Surface(),0.5,
                                  0.5,TolU,TolV) ;
          if (extrloc.IsDone()) {
            DistMin = (Standard_Integer ) extrloc.Value();
            if (DistMin < DistTol3d) {  //OCC217
            //if (DistMin < myTolerance) {
            (extrloc.Point()).Parameter(u,v);
            Poles2d(i).SetCoord(u,v);
            myProjIsDone = Standard_True;
            }
            else break;
          }
          else break;
          if(myProjIsDone) 
            myProjIsDone = Standard_False;
          else break;
        }
        if(myProjIsDone) {
          TColStd_Array1OfReal Knots(1, 2);
          Knots.SetValue(1,0.0);
          Knots.SetValue(2,1.0);
          TColStd_Array1OfInteger Mults(1, 2);
          Mults.Init(BC->NbPoles());
          if(BC->IsRational()) {
            TColStd_Array1OfReal Weights(1, BC->NbPoles());
            BC->Weights(Weights); 
            return new Geom2d_BSplineCurve(Poles2d, Weights, Knots, Mults,
                                        BC->Degree(), BC->IsPeriodic()) ;
          }
          return new Geom2d_BSplineCurve(Poles2d, Knots, Mults,
                                      BC->Degree(), BC->IsPeriodic()) ;
        }
      } 
      }
    }
  }
  else if(TheTypeS == GeomAbs_BezierSurface) {
    Handle(Geom_BezierSurface) BS = Surf->Bezier();
    if((BS->MaxDegree() == 1) &&
       (BS->NbUPoles() == 2) &&
       (BS->NbVPoles() == 2)) {
      gp_Pnt p11 = BS->Pole(1,1);
      gp_Pnt p12 = BS->Pole(1,2);
      gp_Pnt p21 = BS->Pole(2,1);
      gp_Pnt p22 = BS->Pole(2,2);
      gp_Vec V1(p11,p12);
      gp_Vec V2(p21,p22);
      if(V1.IsEqual(V2,Tol3d,Tol3d/(p11.Distance(p12)*180/PI))){ //OCC217
      //if(V1.IsEqual(V2,myTolerance,myTolerance/(p11.Distance(p12)*180/PI))){ 
      //    et l'on se contente de projeter les poles de Curve
      Standard_Integer DistMin = IntegerLast();
      Standard_Real u,v;
        //OCC217
      //Standard_Real TolU = Surf->UResolution(myTolerance)
      //  , TolV = Surf->VResolution(myTolerance);

//    gp_Pnt pntproj;
      if(TheTypeC == GeomAbs_BSplineCurve) {
        Handle(Geom_BSplineCurve) BSC = Curve->BSpline();
        TColgp_Array1OfPnt2d Poles2d(1,Curve->NbPoles());
        for(i = 1;i <= Curve->NbPoles();i++) {
          myProjIsDone = Standard_False;
          DistMin = IntegerLast();
          Extrema_GenLocateExtPS  extrloc(BSC->Pole(i),Surf->Surface(),(p11.X()+p22.X())/2,
                                  (p11.Y()+p22.Y())/2,TolU,TolV) ;
          if (extrloc.IsDone()) {
            DistMin = (Standard_Integer ) extrloc.Value();
            if (DistMin < DistTol3d) {  //OCC217
            //if (DistMin < myTolerance) {
            (extrloc.Point()).Parameter(u,v);
            Poles2d(i).SetCoord(u,v);
            myProjIsDone = Standard_True;
            }
            else break;
          }
          else break;
          if(!myProjIsDone) 
            break;
        }
        if(myProjIsDone) {
          TColStd_Array1OfReal Knots(1, BSC->NbKnots());
          BSC->Knots(Knots);
          TColStd_Array1OfInteger Mults(1, BSC->NbKnots());
          BSC->Multiplicities(Mults);
          if(BSC->IsRational()) {
            TColStd_Array1OfReal Weights(1, BSC->NbPoles());
            BSC->Weights(Weights); 
            return new Geom2d_BSplineCurve(Poles2d, Weights, Knots, Mults,
                                        BSC->Degree(), BSC->IsPeriodic()) ;
          }
          return new Geom2d_BSplineCurve(Poles2d, Knots, Mults,
                                      BSC->Degree(), BSC->IsPeriodic()) ;
          
          
        }
      } 
      if(TheTypeC == GeomAbs_BezierCurve) {
        Handle(Geom_BezierCurve) BC = Curve->Bezier();
        TColgp_Array1OfPnt2d Poles2d(1,Curve->NbPoles());
        for(i = 1;i <= Curve->NbPoles();i++) {
          DistMin = IntegerLast();
          Extrema_GenLocateExtPS  extrloc(BC->Pole(i),Surf->Surface(),0.5,
                                  0.5,TolU,TolV) ;
          if (extrloc.IsDone()) {
            DistMin = (Standard_Integer ) extrloc.Value();
            if (DistMin < DistTol3d) {  //OCC217
            //if (DistMin < myTolerance) {
            (extrloc.Point()).Parameter(u,v);
            Poles2d(i).SetCoord(u,v);
            myProjIsDone = Standard_True;
            }
            else break;
          }
          else break;
          if(myProjIsDone) 
            myProjIsDone = Standard_False;
          else break;
        }
        if(myProjIsDone) {
          TColStd_Array1OfReal Knots(1, 2);
          Knots.SetValue(1,0.0);
          Knots.SetValue(2,1.0);
          TColStd_Array1OfInteger Mults(1, 2);
          Mults.Init(BC->NbPoles());
          if(BC->IsRational()) {
            TColStd_Array1OfReal Weights(1, BC->NbPoles());
            BC->Weights(Weights); 
            return new Geom2d_BSplineCurve(Poles2d, Weights, Knots, Mults,
                                        BC->Degree(), BC->IsPeriodic()) ;
          }
          return new Geom2d_BSplineCurve(Poles2d, Knots, Mults,
                                      BC->Degree(), BC->IsPeriodic()) ;
        }
      } 
      }
    }
  }

  ProjLib_PolarFunction F(Curve, Surf, InitCurve2d, Tol3d) ;  //OCC217
  //ProjLib_PolarFunction F(Curve, Surf, InitCurve2d, myTolerance) ;

#ifdef DEB
  Standard_Integer Nb = 50;
  
  Standard_Real U, U1, U2;
  U1 = F.FirstParameter();
  U2 = F.LastParameter();
  
  TColgp_Array1OfPnt2d    DummyPoles(1,Nb+1);
  TColStd_Array1OfReal    DummyKnots(1,Nb+1);
  TColStd_Array1OfInteger DummyMults(1,Nb+1);
  DummyMults.Init(1);
  DummyMults(1) = 2;
  DummyMults(Nb+1) = 2;
  for (Standard_Integer ij = 0; ij <= Nb; ij++) {
    U = (Nb-ij)*U1 + ij*U2;
    U /= Nb;
    DummyPoles(ij+1) = F.Value(U);
    DummyKnots(ij+1) = ij;
  }
  Handle(Geom2d_BSplineCurve) DummyC2d =
    new Geom2d_BSplineCurve(DummyPoles, DummyKnots, DummyMults, 1);
  Standard_CString Temp = "bs2d";
#ifdef DRAW
  DrawTrSurf::Set(Temp,DummyC2d);
#endif
//  DrawTrSurf::Set((Standard_CString ) "bs2d",DummyC2d);
  Handle(Geom2dAdaptor_HCurve) DDD = 
    Handle(Geom2dAdaptor_HCurve)::DownCast(InitCurve2d);
  
  Temp = "initc2d";
#ifdef DRAW
  DrawTrSurf::Set(Temp,DDD->ChangeCurve2d().Curve());
#endif
//  DrawTrSurf::Set((Standard_CString ) "initc2d",DDD->ChangeCurve2d().Curve());
#endif

  Standard_Integer Deg1,Deg2;
//  Deg1 = 8;
//  Deg2 = 8;
  Deg1 = 2; //IFV
  Deg2 = 8; //IFV 

  Approx_FitAndDivide2d Fit(F,Deg1,Deg2,Tol3d,Tol2d, //OCC217
  //Approx_FitAndDivide2d Fit(F,Deg1,Deg2,myTolerance,myTolerance,
                      Standard_True);

  if(Fit.IsAllApproximated()) {
    Standard_Integer i;
    Standard_Integer NbCurves = Fit.NbMultiCurves();
    Standard_Integer MaxDeg = 0;
    // Pour transformer la MultiCurve en BSpline, il faut que toutes 
    // les Bezier la constituant aient le meme degre -> Calcul de MaxDeg
    Standard_Integer NbPoles  = 1;
    for (i = 1; i <= NbCurves; i++) {
      Standard_Integer Deg = Fit.Value(i).Degree();
      MaxDeg = Max ( MaxDeg, Deg);
    }

    NbPoles = MaxDeg * NbCurves + 1;               //Poles sur la BSpline
    TColgp_Array1OfPnt2d  Poles( 1, NbPoles);
      
    TColgp_Array1OfPnt2d TempPoles( 1, MaxDeg + 1);//pour augmentation du degre
    
    TColStd_Array1OfReal Knots( 1, NbCurves + 1);  //Noeuds de la BSpline
    
    Standard_Integer Compt = 1;
    for (i = 1; i <= NbCurves; i++) {
      Fit.Parameters(i, Knots(i), Knots(i+1)); 
      AppParCurves_MultiCurve MC = Fit.Value( i);       //Charge la Ieme Curve
      TColgp_Array1OfPnt2d Poles2d( 1, MC.Degree() + 1);//Recupere les poles
      MC.Curve(1, Poles2d);
      
      //Augmentation eventuelle du degre
      Standard_Integer Inc = MaxDeg - MC.Degree();
      if ( Inc > 0) {
//    BSplCLib::IncreaseDegree( Inc, Poles2d, PLib::NoWeights(), 
      BSplCLib::IncreaseDegree( MaxDeg, Poles2d, PLib::NoWeights(), 
                   TempPoles, PLib::NoWeights());
      //mise a jour des poles de la PCurve
      for (Standard_Integer j = 1 ; j <= MaxDeg + 1; j++) {
        Poles.SetValue( Compt, TempPoles( j));
        Compt++;
      }
      }
      else {
      //mise a jour des poles de la PCurve
      for (Standard_Integer j = 1 ; j <= MaxDeg + 1; j++) {
        Poles.SetValue( Compt, Poles2d( j));
        Compt++;
      }
      } 
      
      Compt--;
    }
    
    //mise a jour des fields de ProjLib_Approx
    Standard_Integer NbKnots = NbCurves + 1;
    
    // les noeuds debut et fin ne sont pas corrects : Cf: ouverture de 
    // l intervalle
    Knots( 1) -= 1.e-9;
    Knots(NbKnots) += 1.e-9; 
    
    
    TColStd_Array1OfInteger   Mults( 1, NbKnots);
    Mults.Init(MaxDeg);
    Mults.SetValue( 1, MaxDeg + 1);
    Mults.SetValue(NbKnots, MaxDeg + 1);
    myProjIsDone = Standard_True;
    Handle(Geom2d_BSplineCurve) Dummy =
      new Geom2d_BSplineCurve(Poles,Knots,Mults,MaxDeg);
    
    // try to smoother the Curve GeomAbs_C1.

    Standard_Boolean OK = Standard_True;

    for (Standard_Integer ij = 2; ij < NbKnots; ij++) {
      OK = OK && Dummy->RemoveKnot(ij,MaxDeg-1,Tol3d);  //OCC217
      //OK = OK && Dummy->RemoveKnot(ij,MaxDeg-1,myTolerance);
    }
#ifdef DEB
    if (!OK) {
      cout << "ProjLib_ComputeApproxOnPolarSurface : Smoothing echoue"<<endl;
    }
#endif 
    return Dummy;
  }
  return Handle(Geom2d_BSplineCurve)();
}

//=======================================================================
//function : BSpline
//purpose  : 
//=======================================================================

Handle(Geom2d_BSplineCurve)  
     ProjLib_ComputeApproxOnPolarSurface::BSpline() const 
     
{
//  Modified by Sergey KHROMOV - Thu Apr 18 11:16:46 2002 End
//   Standard_NoSuchObject_Raise_if
//     (!myProjIsDone,
//      "ProjLib_ComputeApproxOnPolarSurface:BSpline");
//  Modified by Sergey KHROMOV - Thu Apr 18 11:16:47 2002 End
  return myBSpline ;
}

//=======================================================================
//function : Curve2d
//purpose  : 
//=======================================================================

Handle(Geom2d_Curve)  
     ProjLib_ComputeApproxOnPolarSurface::Curve2d() const 
     
{
  Standard_NoSuchObject_Raise_if
    (!myProjIsDone,
     "ProjLib_ComputeApproxOnPolarSurface:2ndCurve2d");
  return my2ndCurve ;
}


//=======================================================================
//function : IsDone
//purpose  : 
//=======================================================================

Standard_Boolean ProjLib_ComputeApproxOnPolarSurface::IsDone() const 
     
{
  return myProjIsDone;
}

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