[occt.git] / src / ApproxInt / ApproxInt_Approx.gxx

// Created on: 1993-03-30
// Created by: Laurent BUCHARD
// 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 <AppParCurves_Constraint.hxx>
#include <GeomAbs_SurfaceType.hxx>
#include <IntSurf_Quadric.hxx>
#include <gp_Trsf.hxx>
#include <gp_Trsf2d.hxx>
#include <IntSurf_PntOn2S.hxx>
#include <Precision.hxx>
#include <ApproxInt_KnotTools.hxx>

// If quantity of points is less than aMinNbPointsForApprox
// then interpolation is used.
const Standard_Integer aMinNbPointsForApprox = 5;

// This constant should be removed in the future.
const Standard_Real RatioTol = 1.5 ;

//=======================================================================
//function : ComputeTrsf3d
//purpose  : 
//=======================================================================
static void ComputeTrsf3d(const Handle(TheWLine)& theline,
                          Standard_Real& theXo,
                          Standard_Real& theYo,
                          Standard_Real& theZo)
{
  const Standard_Integer aNbPnts = theline->NbPnts();
  Standard_Real aXmin = RealLast(), aYmin = RealLast(), aZmin = RealLast();
  for(Standard_Integer i=1;i<=aNbPnts;i++)
  {
    const gp_Pnt P = theline->Point(i).Value();
    aXmin = Min(P.X(), aXmin);
    aYmin = Min(P.Y(), aYmin);
    aZmin = Min(P.Z(), aZmin);
  }

  theXo = -aXmin;
  theYo = -aYmin;
  theZo = -aZmin;
}

//=======================================================================
//function : ComputeTrsf2d
//purpose  : 
//=======================================================================
static void ComputeTrsf2d(const Handle(TheWLine)& theline,
                          const Standard_Boolean onFirst,
                          Standard_Real& theUo,
                          Standard_Real& theVo)
{ 
  const Standard_Integer aNbPnts = theline->NbPnts();
  Standard_Real aUmin = RealLast(), aVmin = RealLast();

  // pointer to a member-function
  void (IntSurf_PntOn2S::* pfunc)(Standard_Real&,Standard_Real&) const;

  if (onFirst)
    pfunc = &IntSurf_PntOn2S::ParametersOnS1;
  else
    pfunc = &IntSurf_PntOn2S::ParametersOnS2;
  
  for(Standard_Integer i=1; i<=aNbPnts; i++)
  {
    const IntSurf_PntOn2S POn2S = theline->Point(i);
    Standard_Real  U,V;
    (POn2S.*pfunc)(U,V);
    aUmin = Min(U, aUmin);
    aVmin = Min(V, aVmin);
  }

  theUo = -aUmin;
  theVo = -aVmin;
}

//=======================================================================
//function : Parameters
//purpose  :
//=======================================================================
void ApproxInt_Approx::Parameters(const ApproxInt_TheMultiLine& Line,
                       const Standard_Integer firstP,
                       const Standard_Integer lastP,
                       const Approx_ParametrizationType Par,
                       math_Vector& TheParameters)
{
  Standard_Integer i, j, nbP2d, nbP3d;
  Standard_Real dist;

  if (Par == Approx_ChordLength || Par == Approx_Centripetal) {
    nbP3d = ApproxInt_TheMultiLineTool::NbP3d(Line);
    nbP2d = ApproxInt_TheMultiLineTool::NbP2d(Line);
    Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
    if (nbP3d == 0) mynbP3d = 1;
    if (nbP2d == 0) mynbP2d = 1;

    TheParameters(firstP) = 0.0;
    dist = 0.0;
    TColgp_Array1OfPnt tabP(1, mynbP3d);
    TColgp_Array1OfPnt tabPP(1, mynbP3d);
    TColgp_Array1OfPnt2d tabP2d(1, mynbP2d);
    TColgp_Array1OfPnt2d tabPP2d(1, mynbP2d);

    for (i = firstP+1; i <= lastP; i++) {
      if (nbP3d != 0 && nbP2d != 0) ApproxInt_TheMultiLineTool::Value(Line, i-1, tabP, tabP2d);
      else if (nbP2d != 0)          ApproxInt_TheMultiLineTool::Value(Line, i-1, tabP2d);
      else if (nbP3d != 0)          ApproxInt_TheMultiLineTool::Value(Line, i-1, tabP);

      if (nbP3d != 0 && nbP2d != 0) ApproxInt_TheMultiLineTool::Value(Line, i, tabPP, tabPP2d);
      else if (nbP2d != 0)          ApproxInt_TheMultiLineTool::Value(Line, i, tabPP2d);
      else if (nbP3d != 0)          ApproxInt_TheMultiLineTool::Value(Line, i, tabPP);
      dist = 0;
      for (j = 1; j <= nbP3d; j++) {
        const gp_Pnt &aP1 = tabP(j),
                     &aP2 = tabPP(j);
        dist += aP2.SquareDistance(aP1);
      }
      for (j = 1; j <= nbP2d; j++) {
        const gp_Pnt2d &aP12d = tabP2d(j),
                       &aP22d = tabPP2d(j);

        dist += aP22d.SquareDistance(aP12d);
      }

      dist = Sqrt(dist);
      if(Par == Approx_ChordLength)
      {
        TheParameters(i) = TheParameters(i - 1) + dist;
      }
      else
      {// Par == Approx_Centripetal
        TheParameters(i) = TheParameters(i - 1) + Sqrt(dist);
      }
    }
    for (i = firstP; i <= lastP; i++) TheParameters(i) /= TheParameters(lastP);
  }
  else {
    for (i = firstP; i <= lastP; i++) {
      TheParameters(i) = (Standard_Real(i)-firstP)/
        (Standard_Real(lastP)-Standard_Real(firstP));
    }
  }
}

//=======================================================================
//function : Default constructor
//purpose  : 
//=======================================================================
ApproxInt_Approx::ApproxInt_Approx():
                      myComputeLine(4, 8, 0.001, 0.001, 5),
                      myComputeLineBezier(4, 8, 0.001, 0.001, 5),
                      myWithTangency(Standard_True),
                      myTol3d(0.001),
                      myTol2d(0.001),
                      myDegMin(4),
                      myDegMax(8),
                      myNbIterMax(5),
                      myTolReached3d(0.0),
                      myTolReached2d(0.0)
{
  myComputeLine.SetContinuity(2);
  //myComputeLineBezier.SetContinuity(2);
}

//=======================================================================
//function : Perform
//purpose  : Build without surfaces information.
//=======================================================================
void ApproxInt_Approx::Perform(const Handle(TheWLine)& theline,
                               const Standard_Boolean ApproxXYZ,
                               const Standard_Boolean ApproxU1V1,
                               const Standard_Boolean ApproxU2V2,
                               const Standard_Integer indicemin,
                               const Standard_Integer indicemax)
{
  // Prepare DS.
  prepareDS(ApproxXYZ, ApproxU1V1, ApproxU2V2, indicemin, indicemax);

  const Standard_Integer nbpntbez = myData.indicemax - myData.indicemin;
  if(nbpntbez < aMinNbPointsForApprox) 
    myData.myBezierApprox = Standard_False;
  else 
    myData.myBezierApprox = Standard_True;

  // Fill data structure.
  fillData(theline);

  // Build knots.
  buildKnots(theline, NULL);
  if (myKnots.Length() == 2 &&
      indicemax - indicemin > 2 * myData.myNbPntMax)
  {
    // At least 3 knots for BrepApprox.
    myKnots.ChangeLast() = (indicemax - indicemin) / 2;
    myKnots.Append(indicemax);
  }

  myComputeLine.Init      (myDegMin, myDegMax, myTol3d, myTol2d, myNbIterMax, Standard_True, myData.parametrization);
  myComputeLineBezier.Init(myDegMin, myDegMax, myTol3d, myTol2d, myNbIterMax, Standard_True, myData.parametrization);

  buildCurve(theline, NULL);
}

//=======================================================================
//function : Perform
//purpose  : Definition of next steps according to surface types
//            (i.e. coordination algorithm).
//=======================================================================
void ApproxInt_Approx::Perform(const ThePSurface& Surf1,
                               const ThePSurface& Surf2,
                               const Handle(TheWLine)& theline,
                               const Standard_Boolean ApproxXYZ,
                               const Standard_Boolean ApproxU1V1,
                               const Standard_Boolean ApproxU2V2,
                               const Standard_Integer indicemin,
                               const Standard_Integer indicemax) 
{

  myTolReached3d = myTolReached2d = 0.;

  const GeomAbs_SurfaceType typeS1 = ThePSurfaceTool::GetType(Surf1);
  const GeomAbs_SurfaceType typeS2 = ThePSurfaceTool::GetType(Surf2);

  const Standard_Boolean isQuadric = ((typeS1 == GeomAbs_Plane) ||
                                      (typeS1 == GeomAbs_Cylinder) ||
                                      (typeS1 == GeomAbs_Sphere) ||
                                      (typeS1 == GeomAbs_Cone) ||
                                      (typeS2 == GeomAbs_Plane) ||
                                      (typeS2 == GeomAbs_Cylinder) ||
                                      (typeS2 == GeomAbs_Sphere) ||
                                      (typeS2 == GeomAbs_Cone));

  if(isQuadric)
  {
    IntSurf_Quadric Quad;
    Standard_Boolean SecondIsImplicit=Standard_False;
    switch (typeS1)
    {
    case GeomAbs_Plane:
      Quad.SetValue(ThePSurfaceTool::Plane(Surf1));
      break;

    case GeomAbs_Cylinder:
      Quad.SetValue(ThePSurfaceTool::Cylinder(Surf1));
      break;

    case GeomAbs_Sphere:
      Quad.SetValue(ThePSurfaceTool::Sphere(Surf1));
      break;

    case GeomAbs_Cone:
      Quad.SetValue(ThePSurfaceTool::Cone(Surf1));
      break;

    default:
      {
        SecondIsImplicit = Standard_True;
        switch (typeS2)
        {
        case GeomAbs_Plane:
          Quad.SetValue(ThePSurfaceTool::Plane(Surf2));
          break;

        case GeomAbs_Cylinder:
          Quad.SetValue(ThePSurfaceTool::Cylinder(Surf2));
          break;

        case GeomAbs_Sphere:
          Quad.SetValue(ThePSurfaceTool::Sphere(Surf2));
          break;

        case GeomAbs_Cone:
          Quad.SetValue(ThePSurfaceTool::Cone(Surf2));
          break;

        default:
          break;
        }//switch (typeS2)
      }

      break;
    }//switch (typeS1)

    Perform(Quad, (SecondIsImplicit? Surf1: Surf2), theline,
            ApproxXYZ, ApproxU1V1, ApproxU2V2,
            indicemin, indicemax, !SecondIsImplicit);

    return;
  }

  // Here, isQuadric == FALSE.

  // Prepare DS.
  prepareDS(ApproxXYZ, ApproxU1V1, ApproxU2V2, indicemin, indicemax);

  // Non-analytical case: Param-Param perform.
  ApproxInt_ThePrmPrmSvSurfaces myPrmPrmSvSurfaces(Surf1,Surf2);

  Standard_Integer nbpntbez = indicemax-indicemin;

  if(nbpntbez < aMinNbPointsForApprox)
  {
    myData.myBezierApprox = Standard_False;
  }
  else 
  {
    myData.myBezierApprox = Standard_True;
  }

  // Fill data structure.
  fillData(theline);

  const Standard_Boolean cut = myData.myBezierApprox;
  const Standard_Address ptrsvsurf = &myPrmPrmSvSurfaces;

  // Build knots.
  buildKnots(theline, ptrsvsurf);

  myComputeLine.Init      ( myDegMin, myDegMax, myTol3d, myTol2d,
                            myNbIterMax, cut, myData.parametrization);
  myComputeLineBezier.Init( myDegMin, myDegMax, myTol3d, myTol2d,
                            myNbIterMax, cut, myData.parametrization);

  buildCurve(theline, ptrsvsurf);
}

//=======================================================================
//function : Perform
//purpose  : Analytic-Param perform.
//=======================================================================
void ApproxInt_Approx::Perform(const TheISurface& ISurf,
                               const ThePSurface& PSurf,
                               const Handle(TheWLine)& theline,
                               const Standard_Boolean ApproxXYZ,
                               const Standard_Boolean ApproxU1V1,
                               const Standard_Boolean ApproxU2V2,
                               const Standard_Integer indicemin,
                               const Standard_Integer indicemax,
                               const Standard_Boolean isTheQuadFirst)
{
  // Prepare DS.
  prepareDS(ApproxXYZ, ApproxU1V1, ApproxU2V2, indicemin, indicemax);

  // Non-analytical case: Analytic-Param perform.
  ApproxInt_TheImpPrmSvSurfaces myImpPrmSvSurfaces = 
                          isTheQuadFirst? ApproxInt_TheImpPrmSvSurfaces(ISurf, PSurf):
                                          ApproxInt_TheImpPrmSvSurfaces(PSurf, ISurf);

  myImpPrmSvSurfaces.SetUseSolver(Standard_False);

  const Standard_Integer nbpntbez = indicemax-indicemin;
  if(nbpntbez < aMinNbPointsForApprox)
  {
    myData.myBezierApprox = Standard_False;
  }
  else 
  {
    myData.myBezierApprox = Standard_True;
  }

  const Standard_Boolean cut = myData.myBezierApprox;
  const Standard_Address ptrsvsurf = &myImpPrmSvSurfaces;

  // Fill data structure.
  fillData(theline);

  // Build knots.
  buildKnots(theline, ptrsvsurf);

  myComputeLine.Init      ( myDegMin, myDegMax, myTol3d, myTol2d,
                            myNbIterMax, cut, myData.parametrization);
  myComputeLineBezier.Init( myDegMin, myDegMax, myTol3d, myTol2d,
                            myNbIterMax, cut, myData.parametrization);

  buildCurve(theline, ptrsvsurf);
}

//=======================================================================
//function : SetParameters
//purpose  : 
//=======================================================================
void ApproxInt_Approx::SetParameters( const Standard_Real Tol3d,
                                      const Standard_Real Tol2d,
                                      const Standard_Integer DegMin,
                                      const Standard_Integer DegMax,
                                      const Standard_Integer NbIterMax,
                                      const Standard_Integer NbPntMax,
                                      const Standard_Boolean ApproxWithTangency,
                                      const Approx_ParametrizationType Parametrization)
{
  myData.myNbPntMax = NbPntMax;
  myWithTangency = ApproxWithTangency;
  myTol3d        = Tol3d/RatioTol;
  myTol2d        = Tol2d/RatioTol;
  myDegMin       = DegMin;
  myDegMax       = DegMax;
  myNbIterMax    = NbIterMax;

  myComputeLine.Init      ( myDegMin, myDegMax, myTol3d, myTol2d,
                            myNbIterMax, Standard_True, Parametrization);
  myComputeLineBezier.Init( myDegMin, myDegMax, myTol3d, myTol2d,
                            myNbIterMax, Standard_True, Parametrization);

  if(!ApproxWithTangency)
  { 
    myComputeLine.SetConstraints(AppParCurves_PassPoint,AppParCurves_PassPoint);
    myComputeLineBezier.SetConstraints(AppParCurves_PassPoint,AppParCurves_PassPoint);
  }
  
  myData.myBezierApprox = Standard_True;
}

//=======================================================================
//function : NbMultiCurves
//purpose  :
//=======================================================================
Standard_Integer ApproxInt_Approx::NbMultiCurves() const
{
  return 1;
}

//=======================================================================
//function : UpdateTolReached
//purpose  :
//=======================================================================
void ApproxInt_Approx::UpdateTolReached()
{
  if (myData.myBezierApprox)
  {
    const Standard_Integer NbCurves = myComputeLineBezier.NbMultiCurves() ;
    for (Standard_Integer ICur = 1 ; ICur <= NbCurves ; ICur++)
    {
      Standard_Real Tol3D, Tol2D ;
      myComputeLineBezier.Error (ICur, Tol3D, Tol2D) ;
      myTolReached3d = Max(myTolReached3d, Tol3D);
      myTolReached2d = Max(myTolReached2d, Tol2D);
    }
  }
  else
  {
    myComputeLine.Error (myTolReached3d, myTolReached2d);
  }
}

//=======================================================================
//function : TolReached3d
//purpose  :
//=======================================================================
Standard_Real ApproxInt_Approx::TolReached3d() const
{
  return myTolReached3d * RatioTol;
}

//=======================================================================
//function : TolReached2d
//purpose  :
//=======================================================================
Standard_Real ApproxInt_Approx::TolReached2d() const
{
  return myTolReached2d * RatioTol;
}

//=======================================================================
//function : IsDone
//purpose  :
//=======================================================================
Standard_Boolean ApproxInt_Approx::IsDone() const
{
  if(myData.myBezierApprox)
  { 
    return(myComputeLineBezier.NbMultiCurves() > 0);
  }
  else
  {
    return(myComputeLine.IsToleranceReached());
  }
}

//=======================================================================
//function : Value
//purpose  :
//=======================================================================
const AppParCurves_MultiBSpCurve& ApproxInt_Approx::Value(const Standard_Integer ) const
{
  if(myData.myBezierApprox)
  { 
    return(myBezToBSpl.Value());
  }
  else
  { 
    return(myComputeLine.Value());
  }
}

//=======================================================================
//function : fillData
//purpose  : Fill ApproxInt data structure.
//=======================================================================
void ApproxInt_Approx::fillData(const Handle(TheWLine)& theline)
{
  if(myData.ApproxXYZ)
    ComputeTrsf3d(theline, myData.Xo, myData.Yo, myData.Zo);
  else
    myData.Xo = myData.Yo = myData.Zo = 0.0;

  if(myData.ApproxU1V1)
    ComputeTrsf2d(theline, Standard_True, myData.U1o, myData.V1o);
  else
    myData.U1o = myData.V1o = 0.0;

  if(myData.ApproxU2V2)
    ComputeTrsf2d(theline, Standard_False, myData.U2o, myData.V2o);
  else
    myData.U2o = myData.V2o = 0.0;
}

//=======================================================================
//function : prepareDS
//purpose  :
//=======================================================================
void ApproxInt_Approx::prepareDS(const Standard_Boolean theApproxXYZ,
                                 const Standard_Boolean theApproxU1V1,
                                 const Standard_Boolean theApproxU2V2,
                                 const Standard_Integer theIndicemin,
                                 const Standard_Integer theIndicemax)
{
  myTolReached3d = myTolReached2d = 0.0;
  myData.ApproxU1V1 = theApproxU1V1;
  myData.ApproxU2V2 = theApproxU2V2;
  myData.ApproxXYZ = theApproxXYZ;
  myData.indicemin = theIndicemin;
  myData.indicemax = theIndicemax;
  myData.parametrization = myComputeLineBezier.Parametrization();
}

//=======================================================================
//function : buildKnots
//purpose  :
//=======================================================================
void ApproxInt_Approx::buildKnots(const Handle(TheWLine)& theline,
                                  const Standard_Address thePtrSVSurf)
{
  myKnots.Clear();
  if(!myData.myBezierApprox)
  {
    myKnots.Append(myData.indicemin);
    myKnots.Append(myData.indicemax);
    return;
  }

  const ApproxInt_TheMultiLine aTestLine( theline, thePtrSVSurf,
                                          ((myData.ApproxXYZ)? 1 : 0),
                                          ((myData.ApproxU1V1)? 1: 0) + ((myData.ApproxU2V2)? 1: 0),
                                          myData.ApproxU1V1, myData.ApproxU2V2,
                                          myData.Xo, myData.Yo, myData.Zo,
                                          myData.U1o, myData.V1o, myData.U2o, myData.V2o,
                                          myData.ApproxU1V1,
                                          myData.indicemin, myData.indicemax);

  const Standard_Integer  nbp3d = aTestLine.NbP3d(),
                          nbp2d = aTestLine.NbP2d();
  TColgp_Array1OfPnt aTabPnt3d(1, Max(1, nbp3d));
  TColgp_Array1OfPnt2d aTabPnt2d(1, Max(1, nbp2d));
  TColgp_Array1OfPnt aPntXYZ(myData.indicemin, myData.indicemax);
  TColgp_Array1OfPnt2d aPntU1V1(myData.indicemin, myData.indicemax);
  TColgp_Array1OfPnt2d aPntU2V2(myData.indicemin, myData.indicemax);

  for(Standard_Integer i = myData.indicemin; i <= myData.indicemax; ++i)
  {
    if (nbp3d != 0 && nbp2d != 0) aTestLine.Value(i, aTabPnt3d, aTabPnt2d);
    else if (nbp2d != 0)          aTestLine.Value(i, aTabPnt2d);
    else if (nbp3d != 0)          aTestLine.Value(i, aTabPnt3d);
    //
    if(nbp3d > 0)
    {
      aPntXYZ(i) = aTabPnt3d(1);
    }
    if(nbp2d > 1)
    {
      aPntU1V1(i) = aTabPnt2d(1);
      aPntU2V2(i) = aTabPnt2d(2);
    }
    else if(nbp2d > 0)
    {
      if(myData.ApproxU1V1)
      {
        aPntU1V1(i) = aTabPnt2d(1);
      }
      else
      {
        aPntU2V2(i) = aTabPnt2d(1);
      }
    }
  }

  Standard_Integer aMinNbPnts = myData.myNbPntMax;

  // Expected parametrization.
  math_Vector aPars(myData.indicemin, myData.indicemax);
  Parameters(aTestLine, myData.indicemin, myData.indicemax, myData.parametrization, aPars);

  ApproxInt_KnotTools::BuildKnots(aPntXYZ, aPntU1V1, aPntU2V2, aPars,
    myData.ApproxXYZ, myData.ApproxU1V1, myData.ApproxU2V2, aMinNbPnts, myKnots);
}

//=======================================================================
//function : buildCurve
//purpose  :
//=======================================================================
void ApproxInt_Approx::buildCurve(const Handle(TheWLine)& theline,
                                  const Standard_Address thePtrSVSurf)
{
  if(myData.myBezierApprox)
  {
    myBezToBSpl.Reset();
  }

  Standard_Integer kind = myKnots.Lower();
  Standard_Integer imin = 0, imax = 0;
  Standard_Boolean OtherInter = Standard_False;
  do
  {
    // Base cycle: iterate over knots.
    imin = myKnots(kind);
    imax = myKnots(kind+1);
    ApproxInt_TheMultiLine myMultiLine(theline, thePtrSVSurf,
                                       ((myData.ApproxXYZ)? 1 : 0),
                                       ((myData.ApproxU1V1)? 1: 0) + ((myData.ApproxU2V2)? 1: 0),
                                       myData.ApproxU1V1, myData.ApproxU2V2,
                                       myData.Xo, myData.Yo, myData.Zo, myData.U1o, myData.V1o,
                                       myData.U2o, myData.V2o, myData.ApproxU1V1, imin, imax);

    if(myData.myBezierApprox)
    {
      myComputeLineBezier.Perform(myMultiLine);
      if (myComputeLineBezier.NbMultiCurves() == 0)
        return;
    }
    else
    {
      myComputeLine.Perform(myMultiLine);
    }

    UpdateTolReached();

    Standard_Integer indice3d = 1, indice2d1 = 2, indice2d2 = 3;
    if(!myData.ApproxXYZ)  { indice2d1--; indice2d2--; } 
    if(!myData.ApproxU1V1) { indice2d2--; } 
    if(myData.ApproxXYZ)
    { 
      if(myData.myBezierApprox)
      {
        for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--)
        {
          myComputeLineBezier.ChangeValue(nbmc).Transform(indice3d, -myData.Xo, 1.0, -myData.Yo, 1.0, -myData.Zo, 1.0);
        }
      }
      else
      {
        myComputeLine.ChangeValue().Transform(indice3d, -myData.Xo, 1.0, -myData.Yo, 1.0, -myData.Zo, 1.0);
      }
    }
    if(myData.ApproxU1V1)
    {
      if(myData.myBezierApprox) {
        for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--)
        {
          myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d1, -myData.U1o, 1.0, -myData.V1o, 1.0);
        }
      }
      else
      {
        myComputeLine.ChangeValue().Transform2d(indice2d1, -myData.U1o, 1.0, -myData.V1o, 1.0);
      }
    }
    if(myData.ApproxU2V2)
    {
      if(myData.myBezierApprox)
      {
        for(Standard_Integer nbmc = myComputeLineBezier.NbMultiCurves() ; nbmc>=1; nbmc--)
        {
          myComputeLineBezier.ChangeValue(nbmc).Transform2d(indice2d2, -myData.U2o, 1.0, -myData.V2o, 1.0);
        }
      }
      else
      {
        myComputeLine.ChangeValue().Transform2d(indice2d2, -myData.U2o, 1.0, -myData.V2o, 1.0);
      }
    }

    OtherInter = Standard_False;
    if(myData.myBezierApprox)
    {
      for(Standard_Integer nbmc = 1; 
        nbmc <= myComputeLineBezier.NbMultiCurves();
        nbmc++)
      {
          myBezToBSpl.Append(myComputeLineBezier.Value(nbmc));
      }
      kind++;
      if(kind < myKnots.Upper())
      {
        OtherInter = Standard_True;
      }
    }
  }
  while(OtherInter);

  if(myData.myBezierApprox)
  {
    myBezToBSpl.Perform();
  }
}