OCCT

// Copyright (c) 1995-1999 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 <Approx_ParametrizationType.hxx>
#include <TColStd_Array1OfReal.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <TColgp_Array1OfPnt2d.hxx>
#include <gp_Pnt.hxx>
#include <gp_Pnt2d.hxx>
#include <gp_Vec.hxx>
#include <gp_Vec2d.hxx>
#include <TColgp_Array1OfVec.hxx>
#include <TColgp_Array1OfVec2d.hxx>
#include <AppParCurves_Constraint.hxx>
#include <AppParCurves_HArray1OfConstraintCouple.hxx>
#include <AppParCurves_MultiPoint.hxx>
#include <Precision.hxx>
#include <math_IntegerVector.hxx>
#include <math_Gauss.hxx>
#include <math_Uzawa.hxx>
#include <Approx_MCurvesToBSpCurve.hxx>
#include <AppParCurves_ConstraintCouple.hxx>

#include <stdio.h>

#ifdef OCCT_DEBUG
static Standard_Boolean mydebug = Standard_False;

#include <Geom_BezierCurve.hxx>
#include <Geom2d_BezierCurve.hxx>
#ifdef DRAW
#include <DrawTrSurf.hxx>
#include <Draw.hxx>
#include <Draw_Appli.hxx>
#endif

static void DUMP(const MultiLine& Line)
{
  Standard_Integer i, j, nbP2d, nbP3d, firstP, lastP;
  gp_Pnt P1;
  gp_Pnt2d P12d;

  firstP = LineTool::FirstPoint(Line);
  lastP  = LineTool::LastPoint(Line);

  nbP3d = LineTool::NbP3d(Line);
  nbP2d = LineTool::NbP2d(Line);
  Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
  if (nbP3d == 0) mynbP3d = 1;
  if (nbP2d == 0) mynbP2d = 1;
  
  TColgp_Array1OfPnt tabP(1, mynbP3d);
  TColgp_Array1OfPnt2d tabP2d(1, mynbP2d);
  
  std::cout <<"DUMP de la MultiLine entre "<<firstP <<" et "<<lastP<<": "<<std::endl;
  for (i = firstP; i <= lastP; i++) {
    if (nbP3d != 0 && nbP2d != 0) LineTool::Value(Line, i, tabP, tabP2d);
    else if (nbP2d != 0)          LineTool::Value(Line, i, tabP2d);
    else if (nbP3d != 0)          LineTool::Value(Line, i, tabP);
    
    std::cout << "point "<<i<<":"<< std::endl;
    for (j = 1; j <= nbP3d; j++) {
      P1 = tabP(j);
      std::cout <<P1.X()<<" "<<P1.Y()<<" "<<P1.Z()<<std::endl;
    }
    for (j = 1; j <= nbP2d; j++) {
      P12d = tabP2d(j);
      std::cout <<P12d.X()<<" "<<P12d.Y()<<std::endl;
    }
  }

}

static void DUMP(const AppParCurves_MultiCurve& C) {
  static Standard_Integer nbappel = 0;
  Standard_Integer i;
  Standard_Integer nbpoles = C.NbPoles();

  Handle(Geom_BezierCurve) BSp;
  Handle(Geom2d_BezierCurve) BSp2d;

  TColgp_Array1OfPnt tabPoles(1, nbpoles);
  TColgp_Array1OfPnt2d tabPoles2d(1, nbpoles);
  char solname[100];

  nbappel++;
  for (i = 1; i <= C.NbCurves(); i++) {
    if (C.Dimension(i) == 3) {
      C.Curve(i, tabPoles);
      BSp = new Geom_BezierCurve(tabPoles);
      sprintf(solname, "%s%i%s_%i", "c", i, "3d", nbappel);
#ifdef DRAW
      char* Temp = solname;
      DrawTrSurf::Set(Temp, BSp);
//      DrawTrSurf::Set(solname, BSp);
#endif
    }
    else {
      C.Curve(i, tabPoles2d);
      BSp2d = new Geom2d_BezierCurve(tabPoles2d);
      sprintf(solname, "%s%i%s_%i", "c", i, "2d", nbappel);
#ifdef DRAW
      char* Temp = solname;
      DrawTrSurf::Set(Temp, BSp2d);
//      DrawTrSurf::Set(solname, BSp2d);
#endif
    }
  }
#ifdef DRAW
  dout.Flush();
#endif
}

#endif

static Standard_Boolean CheckMultiCurve(const AppParCurves_MultiCurve& theMultiCurve,
                                        const MultiLine& theLine,
                                        const Standard_Integer theIndfirst,
                                        const Standard_Integer theIndlast,
                                        Standard_Integer& theIndbad)
{
  const Standard_Integer nbp3d = LineTool::NbP3d(theLine);
  const Standard_Integer nbp2d = LineTool::NbP2d(theLine);

  const Standard_Real coeff = 4.; //2*2
  
  if (nbp3d > 1) //only simple cases are analysed
    return Standard_True;

  const Standard_Real MinScalProd = -0.9;
  constexpr Standard_Real SqTol3d = Precision::SquareConfusion();

  theIndbad = 0;
  Standard_Integer indbads [4];
  indbads[1] = indbads[2] = indbads[3] = 0;
  
  Standard_Integer NbCur = theMultiCurve.NbCurves();
  Standard_Boolean LoopFound = Standard_False;

  Standard_Integer aNbP3d = Max(nbp3d, 1);
  Standard_Integer aNbP2d = Max(nbp2d, 1);
  
  TColgp_Array1OfPnt tabP(1, aNbP3d);
  TColgp_Array1OfPnt2d tabP2d(1, aNbP2d);
  
#ifdef DRAW
  char* name = new char[100];
  Standard_Integer nbbc = 1;
  Standard_Integer indc = 1;
#endif
  if (theMultiCurve.Dimension(1) == 3 /*myNbP3d == 1*/)
  {
    TColgp_Array1OfPnt aPoles(1, theMultiCurve.NbPoles());
    theMultiCurve.Curve(1, aPoles);
#ifdef DRAW
    Handle(Geom_Curve) theBezier = new Geom_BezierCurve(aPoles);
    sprintf(name, "bc3d_%d_%d", indc, nbbc);
    DrawTrSurf::Set(name, theBezier);
#endif
    gp_Vec FirstVec, SecondVec;
    Standard_Integer indp = 2;
    while (indp <= aPoles.Upper())
    {
      FirstVec = gp_Vec(aPoles(1), aPoles(indp++));
      Standard_Real aLength = FirstVec.Magnitude();
      if (aLength > gp::Resolution())
      {
        FirstVec /= aLength;
        break;
      }
    }
    gp_Pnt MidPnt = aPoles(indp-1);
    //for (Standard_Integer k = 3; k <= aPoles.Upper(); k++)
    while (indp <= aPoles.Upper())
    {
      SecondVec = gp_Vec(MidPnt, aPoles(indp));
      Standard_Real aLength = SecondVec.Magnitude();
      if (aLength <= gp::Resolution())
      {
        indp++;
        continue;
      }
      SecondVec /= aLength;
      Standard_Real ScalProd = FirstVec * SecondVec;
      if (ScalProd < MinScalProd)
      {
#ifdef DRAW
        std::cout<<"ScalProd("<<indp-2<<","<<indp-1<<")-("<<indp-1<<","<<indp<<") = "<<ScalProd<<std::endl;
#endif
        LoopFound = Standard_True;
        break;
      }
      FirstVec = SecondVec;
      MidPnt = aPoles(indp);
      indp++;
    }
    //Check: may be it is a real loop
    if (LoopFound)
    {
#ifdef DRAW
      for (Standard_Integer ipoint = theIndfirst; ipoint <= theIndlast; ipoint++)
      {
        LineTool::Value(theLine, ipoint, tabP);
        gp_Pnt aPnt = tabP(1);
        sprintf(name, "p%d", ipoint);
        DrawTrSurf::Set(name, aPnt);
      }
#endif
      for (Standard_Integer FirstInd = theIndfirst;
           FirstInd <= theIndlast - 2; FirstInd++)
      {
        LineTool::Value(theLine, FirstInd, tabP);
        gp_Pnt FirstPnt = tabP(1);
        for (Standard_Integer k = FirstInd+1; k < theIndlast; k++)
        {
          LineTool::Value(theLine, k, tabP);
          gp_Pnt Pnt1 = tabP(1);
          LineTool::Value(theLine, k+1, tabP);
          gp_Pnt Pnt2 = tabP(1);
          if (FirstPnt.SquareDistance(Pnt1) <= SqTol3d ||
              FirstPnt.SquareDistance(Pnt2) <= SqTol3d)
          {
            LoopFound = Standard_False;
            break;
          }
          gp_Vec Vec1(FirstPnt, Pnt1);
          Vec1.Normalize();
          gp_Vec Vec2(FirstPnt, Pnt2);
          Vec2.Normalize();
          Standard_Real ScalProd = Vec1 * Vec2;
          if (ScalProd < MinScalProd)
          {
            LoopFound = Standard_False;
            break;
          }
        }
        if (LoopFound == Standard_False)
          break;
      }
    }
    if (LoopFound)
    {
      //search <indbad>
      Standard_Real MaxSqDist = 0.;
      Standard_Real MinSqDist = RealLast();
      for (Standard_Integer k = theIndfirst+1; k <= theIndlast; k++)
      {
        LineTool::Value(theLine, k-1, tabP);
        gp_Pnt PrevPnt = tabP(1);
        LineTool::Value(theLine, k, tabP);
        gp_Pnt CurPnt  = tabP(1);
        Standard_Real aSqDist = PrevPnt.SquareDistance(CurPnt);
        if (aSqDist > MaxSqDist)
        {
          MaxSqDist = aSqDist;
          indbads[1] = k;
        }
        if (aSqDist > gp::Resolution() &&
            aSqDist < MinSqDist)
          MinSqDist = aSqDist;
      }
      Standard_Real Relation = MaxSqDist / MinSqDist;
      if (Relation < coeff)
        LoopFound = Standard_False;
      else
        for (Standard_Integer indcur = 2; indcur <= NbCur; indcur++)
        {
          MaxSqDist = 0.;
          for (Standard_Integer k = theIndfirst+1; k <= theIndlast; k++)
          {
            LineTool::Value(theLine, k-1, tabP2d);
            gp_Pnt2d PrevPnt = tabP2d(indcur-1);
            LineTool::Value(theLine, k, tabP2d);
            gp_Pnt2d CurPnt  = tabP2d(indcur-1);
            Standard_Real aSqDist = PrevPnt.SquareDistance(CurPnt);
            if (aSqDist > MaxSqDist)
            {
              MaxSqDist = aSqDist;
              indbads[indcur] = k;
            }
          }
        }
    }
  } //if (myNbP3d == 1)
  else //2d case
  {
    TColgp_Array1OfPnt2d aPoles2d(1, theMultiCurve.NbPoles());
    theMultiCurve.Curve(1, aPoles2d);
#ifdef DRAW
    Handle(Geom2d_Curve) theBezier2d = new Geom2d_BezierCurve(aPoles2d);
    sprintf(name, "bc2d_%d_%d", indc, nbbc);
    DrawTrSurf::Set(name, theBezier2d);
#endif
    const Standard_Real aSqNormToler = Epsilon(1.0)*Epsilon(1.0);
    gp_Vec2d FirstVec(aPoles2d(1), aPoles2d(2)), SecondVec;
    Standard_Real aVecSqNorm = FirstVec.SquareMagnitude();
    if (aVecSqNorm < aSqNormToler)
    {
      theIndbad = theIndfirst + 1;
      return Standard_False;
    }

    FirstVec /= Sqrt(aSqNormToler);
    gp_Pnt2d MidPnt = aPoles2d(2);
    for (Standard_Integer k = 3; k <= aPoles2d.Upper(); k++)
    {
      SecondVec.SetXY(aPoles2d(k).XY() - MidPnt.XY());
      aVecSqNorm = SecondVec.SquareMagnitude();
      if (aVecSqNorm < aSqNormToler)
      {
        theIndbad = theIndfirst + k - 1;
        return Standard_False;
      }

      SecondVec /= Sqrt(aVecSqNorm);
      Standard_Real ScalProd = FirstVec * SecondVec;
      if (ScalProd < MinScalProd)
      {
#ifdef DRAW
        std::cout<<"ScalProd("<<k-2<<","<<k-1<<")-("<<k-1<<","<<k<<") = "<<ScalProd<<std::endl;
#endif
        LoopFound = Standard_True;
        break;
      }
      FirstVec = SecondVec;
      MidPnt = aPoles2d(k);
    }
    //Check: may be it is a real loop
    if (LoopFound)
    {
#ifdef DRAW
      for (Standard_Integer ipoint = theIndfirst; ipoint <= theIndlast; ipoint++)
      {
        LineTool::Value(theLine, ipoint, tabP2d);
        gp_Pnt2d aPnt2d = tabP2d(1);
        sprintf(name, "p%d", ipoint);
        DrawTrSurf::Set(name, aPnt2d);
      }
#endif
      for (Standard_Integer FirstInd = theIndfirst;
           FirstInd <= theIndlast - 2; FirstInd++)
      {
        LineTool::Value(theLine, FirstInd, tabP2d);
        gp_Pnt2d FirstPnt = tabP2d(1);
        for (Standard_Integer k = FirstInd+1; k < theIndlast; k++)
        {
          LineTool::Value(theLine, k, tabP2d);
          gp_Pnt2d Pnt1 = tabP2d(1);
          LineTool::Value(theLine, k+1, tabP2d);
          gp_Pnt2d Pnt2 = tabP2d(1);
          if (FirstPnt.SquareDistance(Pnt1) <= SqTol3d ||
              FirstPnt.SquareDistance(Pnt2) <= SqTol3d)
          {
            LoopFound = Standard_False;
            break;
          }
          gp_Vec2d Vec1(FirstPnt, Pnt1);
          Vec1.Normalize();
          gp_Vec2d Vec2(FirstPnt, Pnt2);
          Vec2.Normalize();
          Standard_Real ScalProd = Vec1 * Vec2;
          if (ScalProd < MinScalProd)
          {
            LoopFound = Standard_False;
            break;
          }
        }
        if (LoopFound == Standard_False)
          break;
      }
    }
    if (LoopFound)
    {
      //search <indbad>
      for (Standard_Integer indcur = 1; indcur <= NbCur; indcur++)
      {
        Standard_Real MaxSqDist = 0.;
        Standard_Real MinSqDist = RealLast();
        for (Standard_Integer k = theIndfirst+1; k <= theIndlast; k++)
        {
          LineTool::Value(theLine, k-1, tabP2d);
          gp_Pnt2d PrevPnt = tabP2d(indcur);
          LineTool::Value(theLine, k, tabP2d);
          gp_Pnt2d CurPnt  = tabP2d(indcur);
          Standard_Real aSqDist = PrevPnt.SquareDistance(CurPnt);
          if (aSqDist > MaxSqDist)
          {
            MaxSqDist = aSqDist;
            indbads[indcur] = k;
          }
          if (aSqDist > gp::Resolution() &&
              aSqDist < MinSqDist)
            MinSqDist = aSqDist;
        }
        Standard_Real Relation = MaxSqDist / MinSqDist;
        if (Relation < coeff)
          LoopFound = Standard_False;
      }
    }
  }

  //Define <indbad>
  for (Standard_Integer i = 1; i <= 3; i++)
    if (indbads[i] != 0)
    {
      theIndbad = indbads[i];
      break;
    }

  if (!LoopFound)
    theIndbad = 0;
  
  return (!LoopFound);
}

void Approx_ComputeLine::FirstTangencyVector(const MultiLine&       Line,
					     const Standard_Integer index,
					     math_Vector&           V) const 
{

  Standard_Integer i, j, nbP2d, nbP3d;
  nbP3d = LineTool::NbP3d(Line);
  nbP2d = LineTool::NbP2d(Line);
  Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
  if (nbP3d == 0) mynbP3d = 1;
  if (nbP2d == 0) mynbP2d = 1;
  Standard_Boolean Ok=Standard_False;
  TColgp_Array1OfVec TabV(1, mynbP3d);
  TColgp_Array1OfVec2d TabV2d(1, mynbP2d);
 
  if (nbP3d != 0 && nbP2d != 0)
    Ok = LineTool::Tangency(Line, index, TabV, TabV2d);
  else if (nbP2d != 0)
    Ok = LineTool::Tangency(Line, index, TabV2d);
  else if (nbP3d != 0)
    Ok = LineTool::Tangency(Line, index, TabV);

  if (Ok) {
    if (nbP3d != 0) {
      j = 1;
      for (i = TabV.Lower(); i <= TabV.Upper(); i++) {
	V(j)   = TabV(i).X();
	V(j+1) = TabV(i).Y();
	V(j+2) = TabV(i).Z();
	j += 3;
      }
    }
    if (nbP2d != 0) {
      j = nbP3d*3+1;
      for (i = TabV2d.Lower(); i <= TabV2d.Upper(); i++) {
	V(j)   = TabV2d(i).X();
	V(j+1) = TabV2d(i).Y();
	j += 2;
      }
    }
  }
  else {

    // recherche d un vecteur tangent par construction d une parabole:
    AppParCurves_Constraint firstC, lastC;
    firstC = lastC = AppParCurves_PassPoint;
    Standard_Integer nbpoles = 3;
    math_Vector mypar(index, index+2);
    Parameters(Line, index, index+2, mypar);
    Approx_ParLeastSquareOfMyGradient 
      LSQ(Line, index, index+2, firstC, lastC, mypar, nbpoles);
    AppParCurves_MultiCurve C = LSQ.BezierValue();
    
    gp_Pnt myP;
    gp_Vec myV;
    gp_Pnt2d myP2d;
    gp_Vec2d myV2d;
    j = 1;
    for (i = 1; i <= nbP3d; i++) {
      C.D1(i, 0.0, myP, myV);
      V(j)   = myV.X();
      V(j+1) = myV.Y();
      V(j+2) = myV.Z();
      j += 3;
    }
    j = nbP3d*3+1;
    for (i = nbP3d+1; i <= nbP3d+nbP2d; i++) {
      C.D1(i, 0.0, myP2d, myV2d);
      V(j)   = myV2d.X();
      V(j+1) = myV2d.Y();
      j += 2;
    }
  }
}


void Approx_ComputeLine::LastTangencyVector(const MultiLine&       Line,
					    const Standard_Integer index,
					    math_Vector&           V) const
{
  Standard_Integer i, j, nbP2d, nbP3d;
  nbP3d = LineTool::NbP3d(Line);
  nbP2d = LineTool::NbP2d(Line);
  Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
  if (nbP3d == 0) mynbP3d = 1;
  if (nbP2d == 0) mynbP2d = 1;
  Standard_Boolean Ok=Standard_False;
  TColgp_Array1OfVec TabV(1, mynbP3d);
  TColgp_Array1OfVec2d TabV2d(1, mynbP2d);

 
  if (nbP3d != 0 && nbP2d != 0)
    Ok = LineTool::Tangency(Line, index, TabV, TabV2d);
  else if (nbP2d != 0)
    Ok = LineTool::Tangency(Line, index, TabV2d);
  else if (nbP3d != 0)
    Ok = LineTool::Tangency(Line, index, TabV);

  if (Ok) {
    if (nbP3d != 0) {
      j = 1;
      for (i = TabV.Lower(); i <= TabV.Upper(); i++) {
	V(j)   = TabV(i).X();
	V(j+1) = TabV(i).Y();
	V(j+2) = TabV(i).Z();
	j += 3;
      }
    }
    if (nbP2d != 0) {
      j = nbP3d*3+1;
      for (i = TabV2d.Lower(); i <= TabV2d.Upper(); i++) {
	V(j)   = TabV2d(i).X();
	V(j+1) = TabV2d(i).Y();
	j += 2;
      }
    }
  }
  else {

    // recherche d un vecteur tangent par construction d une parabole:
    AppParCurves_Constraint firstC, lastC;
    firstC = lastC = AppParCurves_PassPoint;
    Standard_Integer nbpoles = 3;
    math_Vector mypar(index-2, index);
    Parameters(Line, index-2, index, mypar);
    Approx_ParLeastSquareOfMyGradient 
      LSQ(Line, index-2, index, firstC, lastC, mypar, nbpoles);
    AppParCurves_MultiCurve C = LSQ.BezierValue();
    
    gp_Pnt myP;
    gp_Vec myV;
    gp_Pnt2d myP2d;
    gp_Vec2d myV2d;
    j = 1;
    for (i = 1; i <= nbP3d; i++) {
      C.D1(i, 1.0, myP, myV);
      V(j)   = myV.X();
      V(j+1) = myV.Y();
      V(j+2) = myV.Z();
      j += 3;
    }
    j = nbP3d*3+1;
    for (i = nbP3d+1; i <= nbP3d+nbP2d; i++) {
      C.D1(i, 1.0, myP2d, myV2d);
      V(j)   = myV2d.X();
      V(j+1) = myV2d.Y();
      j += 2;
    }
  }

}



Standard_Real Approx_ComputeLine::
  SearchFirstLambda(const MultiLine&            Line, 
		    const math_Vector&          TheParam,
		    const math_Vector&          V,
		    const Standard_Integer      index) const 
{

  // dq/dw = lambda* V = (p2-p1)/(u2-u1)
  
  Standard_Integer nbP2d, nbP3d;
  gp_Pnt P1, P2;
  gp_Pnt2d P12d, P22d;
  nbP3d = LineTool::NbP3d(Line);
  nbP2d = LineTool::NbP2d(Line);
  Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
  if (nbP3d == 0) mynbP3d = 1;
  if (nbP2d == 0) mynbP2d = 1;
  TColgp_Array1OfPnt tabP1(1, mynbP3d), tabP2(1, mynbP3d);
  TColgp_Array1OfPnt2d tabP12d(1, mynbP2d), tabP22d(1, mynbP2d);
 

  if (nbP3d != 0 && nbP2d != 0) LineTool::Value(Line, index, tabP1, tabP12d);
  else if (nbP2d != 0)          LineTool::Value(Line, index, tabP12d);
  else if (nbP3d != 0)          LineTool::Value(Line, index, tabP1);

  if (nbP3d != 0 && nbP2d != 0) LineTool::Value(Line, index+1, tabP2, tabP22d);
  else if (nbP2d != 0)          LineTool::Value(Line, index+1, tabP22d);
  else if (nbP3d != 0)          LineTool::Value(Line, index+1, tabP2);
				     

  Standard_Real U1 = TheParam(index), U2 = TheParam(index+1);
  Standard_Real lambda, S;					  
  Standard_Integer low = V.Lower();
 
  if (nbP3d != 0) {
    P1 = tabP1(1);
    P2 = tabP2(1);
    gp_Vec P1P2(P1, P2), myV;
    myV.SetCoord(V(low), V(low+1), V(low+2));
    lambda = (P1P2.Magnitude())/(myV.Magnitude()*(U2-U1));
    S = (P1P2.Dot(myV)> 0.0) ? 1.0 : -1.0;
  }
  else {
    P12d = tabP12d(1);
    P22d = tabP22d(1);
    gp_Vec2d P1P2(P12d, P22d), myV;
    myV.SetCoord(V(low), V(low+1));
    lambda = (P1P2.Magnitude())/(myV.Magnitude()*(U2-U1));
    S = (P1P2.Dot(myV)> 0.0) ? 1.0 : -1.0;
  }
  return (S*lambda);

}


Standard_Real Approx_ComputeLine::
 SearchLastLambda(const MultiLine&            Line, 
		  const math_Vector&          TheParam,
		  const math_Vector&          V,
		  const Standard_Integer      index) const
{
  // dq/dw = lambda* V = (p2-p1)/(u2-u1)
  
  Standard_Integer nbP2d, nbP3d;
  gp_Pnt P1, P2;
  gp_Pnt2d P12d, P22d;
  nbP3d = LineTool::NbP3d(Line);
  nbP2d = LineTool::NbP2d(Line);
  Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
  if (nbP3d == 0) mynbP3d = 1;
  if (nbP2d == 0) mynbP2d = 1;
  TColgp_Array1OfPnt tabP(1, mynbP3d), tabP2(1, mynbP3d);
  TColgp_Array1OfPnt2d tabP2d(1, mynbP2d), tabP22d(1, mynbP2d);
 
  if (nbP3d != 0 && nbP2d != 0) LineTool::Value(Line, index-1, tabP, tabP2d);
  else if (nbP2d != 0)          LineTool::Value(Line, index-1, tabP2d);
  else if (nbP3d != 0)          LineTool::Value(Line, index-1, tabP);

  if (nbP3d != 0 && nbP2d != 0) LineTool::Value(Line, index, tabP2, tabP22d);
  else if (nbP2d != 0)          LineTool::Value(Line, index, tabP22d);
  else if (nbP3d != 0)          LineTool::Value(Line, index, tabP2);


  Standard_Real U1 = TheParam(index-1), U2 = TheParam(index);
  Standard_Real lambda, S;
  Standard_Integer low = V.Lower();

  if (nbP3d != 0) {
    P1 = tabP(1);
    P2 = tabP2(1);
    gp_Vec P1P2(P1, P2), myV;
    myV.SetCoord(V(low), V(low+1), V(low+2));
    lambda = (P1P2.Magnitude())/(myV.Magnitude()*(U2-U1));
    S = (P1P2.Dot(myV)> 0.0) ? 1.0 : -1.0;
  }
  else {
    P12d = tabP2d(1);
    P22d = tabP22d(1);
    gp_Vec2d P1P2(P12d, P22d), myV;
    myV.SetCoord(V(low), V(low+1));
    lambda = (P1P2.Magnitude())/(myV.Magnitude()*(U2-U1));
    S = (P1P2.Dot(myV)> 0.0) ? 1.0 : -1.0;
  }

  return (S*lambda);
}



Approx_ComputeLine::Approx_ComputeLine
                    (const MultiLine& Line,
		     const math_Vector& Parameters,
		     const Standard_Integer degreemin,
		     const Standard_Integer degreemax,
		     const Standard_Real Tolerance3d,
		     const Standard_Real Tolerance2d,
		     const Standard_Integer NbIterations,
		     const Standard_Boolean cutting,
		     const Standard_Boolean Squares)
: myMultiLineNb (0),
  myIsClear (Standard_False)
{
  myfirstParam = new TColStd_HArray1OfReal(Parameters.Lower(), 
					   Parameters.Upper());
  for (Standard_Integer i = Parameters.Lower(); i <= Parameters.Upper(); i++) {
    myfirstParam->SetValue(i, Parameters(i));
  }
  myConstraints = new AppParCurves_HArray1OfConstraintCouple(1, 2);
  Par = Approx_IsoParametric;
  mydegremin = degreemin;
  mydegremax = degreemax;
  mytol3d = Tolerance3d;
  mytol2d = Tolerance2d;
  mysquares = Squares;
  mycut = cutting;
  myitermax = NbIterations;
  alldone = Standard_False;
  myfirstC = AppParCurves_TangencyPoint;
  mylastC = AppParCurves_TangencyPoint;
  Perform(Line);
}


Approx_ComputeLine::Approx_ComputeLine
                    (const math_Vector& Parameters,
		     const Standard_Integer degreemin,
		     const Standard_Integer degreemax,
		     const Standard_Real Tolerance3d,
		     const Standard_Real Tolerance2d,
		     const Standard_Integer NbIterations,
		     const Standard_Boolean cutting,
		     const Standard_Boolean Squares)
: myMultiLineNb (0),
  myIsClear (Standard_False)
{
  myfirstParam = new TColStd_HArray1OfReal(Parameters.Lower(), 
					   Parameters.Upper());
  for (Standard_Integer i = Parameters.Lower(); i <= Parameters.Upper(); i++) {
    myfirstParam->SetValue(i, Parameters(i));
  }
  myfirstC = AppParCurves_TangencyPoint;
  mylastC = AppParCurves_TangencyPoint;
  myConstraints = new AppParCurves_HArray1OfConstraintCouple(1, 2);
  Par = Approx_IsoParametric;
  mydegremin = degreemin;
  mydegremax = degreemax;
  mytol3d = Tolerance3d;
  mytol2d = Tolerance2d;
  mysquares = Squares;
  mycut = cutting;
  myitermax = NbIterations;
  alldone = Standard_False;
}

Approx_ComputeLine::Approx_ComputeLine
                    (const Standard_Integer degreemin,
		     const Standard_Integer degreemax,
		     const Standard_Real Tolerance3d,
		     const Standard_Real Tolerance2d,
		     const Standard_Integer NbIterations,
		     const Standard_Boolean cutting,
		     const Approx_ParametrizationType parametrization,
		     const Standard_Boolean Squares)
: myMultiLineNb (0),
  myIsClear (Standard_False)
{
  myConstraints = new AppParCurves_HArray1OfConstraintCouple(1, 2);
  Par = parametrization;
  mydegremin = degreemin;
  mydegremax = degreemax;
  mytol3d = Tolerance3d;
  mytol2d = Tolerance2d;
  mysquares = Squares;
  mycut = cutting;
  myitermax = NbIterations;
  myfirstC = AppParCurves_TangencyPoint;
  mylastC = AppParCurves_TangencyPoint;
  alldone = Standard_False;
}


Approx_ComputeLine::Approx_ComputeLine
                    (const MultiLine& Line,
		     const Standard_Integer degreemin,
		     const Standard_Integer degreemax,
		     const Standard_Real Tolerance3d,
		     const Standard_Real Tolerance2d,
		     const Standard_Integer NbIterations,
		     const Standard_Boolean cutting,
		     const Approx_ParametrizationType parametrization,
		     const Standard_Boolean Squares)
: myMultiLineNb (0),
  myIsClear (Standard_False)
{
  myConstraints = new AppParCurves_HArray1OfConstraintCouple(1, 2);
  alldone = Standard_False;
  mydegremin = degreemin;
  mydegremax = degreemax;
  mytol3d = Tolerance3d;
  mytol2d = Tolerance2d;
  mysquares = Squares;
  mycut = cutting;
  myitermax = NbIterations;
  Par = parametrization;
  myfirstC = AppParCurves_TangencyPoint;
  mylastC = AppParCurves_TangencyPoint;

  Perform(Line);
}



void Approx_ComputeLine::Perform(const MultiLine& Line)
{
#ifdef OCCT_DEBUG
  if (mydebug) DUMP(Line);
#endif
  if (!myIsClear)
  {
    myMultiCurves.Clear();
    myPar.Clear();
    Tolers3d.Clear();
    Tolers2d.Clear();
    myMultiLineNb = 0;
  }
  else myIsClear = Standard_False;

  Standard_Integer i, nbp, Thefirstpt, Thelastpt, oldlastpt;
  Standard_Boolean Finish = Standard_False,
          begin = Standard_True, Ok = Standard_False, 
          GoUp = Standard_False, Interpol;
  Standard_Real thetol3d, thetol2d;
  Approx_Status MyStatus;
//  gp_Vec V13d, V23d;
//  gp_Vec2d V2d;
  Thefirstpt = LineTool::FirstPoint(Line);
  Thelastpt  = LineTool::LastPoint(Line);
  Standard_Integer myfirstpt = Thefirstpt; 
  Standard_Integer mylastpt = Thelastpt;

  AppParCurves_ConstraintCouple myCouple1(myfirstpt, myfirstC);
  AppParCurves_ConstraintCouple myCouple2(mylastpt, mylastC);
  myConstraints->SetValue(1, myCouple1);
  myConstraints->SetValue(2, myCouple2);

  math_Vector TheParam(Thefirstpt, Thelastpt);


  if (!mycut) {
    if(myfirstParam.IsNull()) {
      Parameters(Line, Thefirstpt, Thelastpt, TheParam);
    }
    else {
      for (i = myfirstParam->Lower(); i <= myfirstParam->Upper(); i++) {
	TheParam(i+Thefirstpt-1) = myfirstParam->Value(i);
      }
    }
    TheMultiCurve = AppParCurves_MultiCurve();
    MultiLine anOtherLine0;
    Standard_Boolean isOtherLine0Made = Standard_False;
    Standard_Integer indbad = 0;
    alldone = Compute(Line, myfirstpt, mylastpt, TheParam, thetol3d, thetol2d, indbad);
    if (indbad != 0)
    {
      isOtherLine0Made = LineTool::MakeMLOneMorePoint(Line, myfirstpt, mylastpt, indbad, anOtherLine0);
    }
    if (isOtherLine0Made)
    {
      myIsClear = Standard_True;
      //++myMultiLineNb;
      Perform(anOtherLine0);
      alldone = Standard_True;
    }
    if(!alldone && TheMultiCurve.NbCurves() > 0) {
#ifdef OCCT_DEBUG
      if (mydebug) DUMP(TheMultiCurve);
#endif
      myMultiCurves.Append(TheMultiCurve);
      Tolers3d.Append(currenttol3d);
      Tolers2d.Append(currenttol2d);
      Standard_Integer mylen = mylastpt-myfirstpt+1;
      Standard_Integer myParLen = myParameters->Length();
      Standard_Integer aLen = (myParLen > mylen)? myParLen : mylen;
      Handle(TColStd_HArray1OfReal) ThePar =
        new TColStd_HArray1OfReal(myfirstpt, myfirstpt+aLen-1);
      for (i = 0; i < aLen; i++)
        ThePar->SetValue(myfirstpt+i, myParameters->Value(myParameters->Lower()+i));
      myPar.Append(ThePar);
    }
  }
  else {
    while (!Finish) {
      oldlastpt = mylastpt;
      // Gestion du decoupage de la multiline pour approximer:
      if(!begin) {
	if (!GoUp) {
	  if (Ok) {
	    // Calcul de la partie a approximer.
	    myfirstpt = mylastpt;
	    mylastpt  = Thelastpt;
	    if (myfirstpt == Thelastpt) {
	      Finish = Standard_True;
	      alldone = Standard_True;
	      return;
	    }
	  }
	  else {
	    nbp = mylastpt - myfirstpt + 1;
	    MyStatus = LineTool::WhatStatus(Line, myfirstpt, mylastpt);
	    if (MyStatus == Approx_NoPointsAdded && nbp <= mydegremax+1) {
	      Interpol = ComputeCurve(Line, myfirstpt, mylastpt);
	      if (Interpol) {
		if (mylastpt == Thelastpt) {
		  Finish = Standard_True;
		  alldone = Standard_True;
		  return;
		}
	      }
	    }
	    mylastpt = Standard_Integer((myfirstpt + mylastpt)/2);
	  }
	}
	GoUp = Standard_False;
      }
      
      // Verification du nombre de points restants par rapport au degre
      // demande.
      // ==============================================================
      nbp = mylastpt - myfirstpt + 1;
      MyStatus = LineTool::WhatStatus(Line, myfirstpt, mylastpt);
      if (nbp <= mydegremax+5 ) {
	// Rajout necessaire de points si possible.
	// ========================================
	GoUp = Standard_False;
	Ok = Standard_True;
	if (MyStatus == Approx_PointsAdded) {
	  // Appel recursif du decoupage:
	  GoUp = Standard_True;

	  MultiLine anOtherLine1 = LineTool::MakeMLBetween(Line, myfirstpt, mylastpt, nbp-1);
	  
	  Standard_Integer nbpdsotherligne = LineTool::FirstPoint (anOtherLine1) - LineTool::LastPoint (anOtherLine1);

	  //-- Si MakeML a echoue   on retourne une ligne vide
	  if ((nbpdsotherligne == 0) || myMultiLineNb >= 3)
	  {
	    //-- cout<<" ** ApproxComputeLine MakeML Echec ** LBR lbr "<<endl;
	    if (myfirstpt == mylastpt) break;  // Pour etre sur de ne pas 
	    // planter la station !!
	    myCouple1.SetIndex(myfirstpt);
	    myCouple2.SetIndex(mylastpt);
	    myConstraints->SetValue(1, myCouple1);
	    myConstraints->SetValue(2, myCouple2);

	    math_Vector Param(myfirstpt, mylastpt);
	    Approx_ParametrizationType SavePar = Par;
	    Par = Approx_IsoParametric;
	    Parameters(Line, myfirstpt, mylastpt, Param);
	    TheMultiCurve = AppParCurves_MultiCurve();
            MultiLine anOtherLine2;
            Standard_Boolean isOtherLine2Made = Standard_False;
            Standard_Integer indbad = 0;
	    Ok = Compute(Line, myfirstpt, mylastpt, Param, thetol3d, thetol2d, indbad);
            if (indbad != 0)
            {
              isOtherLine2Made = LineTool::MakeMLOneMorePoint(Line, myfirstpt, mylastpt, indbad, anOtherLine2);
            }
            if (isOtherLine2Made)
            {
              myIsClear = Standard_True;
              //++myMultiLineNb;
              Par = SavePar;
              Perform(anOtherLine2);
              Ok = Standard_True;
            }

	    if (!Ok) {
	      Standard_Real tt3d = currenttol3d, tt2d = currenttol2d;
	      Handle(TColStd_HArray1OfReal) saveParameters = myParameters;
	      AppParCurves_MultiCurve saveMultiCurve = TheMultiCurve;

	      if(SavePar != Approx_IsoParametric)
		Par = SavePar;
	      else
		Par = Approx_ChordLength;

	      Parameters(Line, myfirstpt, mylastpt, Param);
        isOtherLine2Made = Standard_False;
              indbad = 0;
	      Ok = Compute(Line, myfirstpt, mylastpt, Param, thetol3d, thetol2d, indbad);
              if (indbad != 0)
              {
                isOtherLine2Made = LineTool::MakeMLOneMorePoint (Line, myfirstpt, mylastpt, indbad, anOtherLine2);
              }
              if (isOtherLine2Made)
              {
                myIsClear = Standard_True;
                //++myMultiLineNb;
                Perform (anOtherLine2);
                Ok = Standard_True;
              }
	      
	      if (!Ok && tt3d <= currenttol3d && tt2d <= currenttol2d) {
		currenttol3d = tt3d; currenttol2d = tt2d;
		myParameters = saveParameters;
		TheMultiCurve = saveMultiCurve;
	      }
	    }
	    Par = SavePar;
            if (myfirstpt == Thelastpt)
            {
              Finish = Standard_True;
              alldone = Standard_True;
              return;
            }

	    oldlastpt = mylastpt;
	    if (!Ok) {
	      tolreached = Standard_False;
	      if (TheMultiCurve.NbCurves() == 0) {
		myMultiCurves.Clear();
		return;
	      }
#ifdef OCCT_DEBUG
              if (mydebug) DUMP(TheMultiCurve);
#endif
              MultiLine anOtherLine3;
              Standard_Boolean isOtherLine3Made = Standard_False;
              Standard_Integer indbad2 = 0;
              if (!CheckMultiCurve(TheMultiCurve, Line,
                                   myfirstpt, mylastpt,
                                   indbad2))
              {
                isOtherLine3Made = LineTool::MakeMLOneMorePoint (Line, myfirstpt, mylastpt, indbad2, anOtherLine3);
              }
              if (isOtherLine3Made)
              {
                myIsClear = Standard_True;
                //++myMultiLineNb;
                Perform(anOtherLine3);
                myfirstpt = mylastpt;
                mylastpt = Thelastpt;
              }
              else
              {
                myMultiCurves.Append(TheMultiCurve);
                Tolers3d.Append(currenttol3d);
                Tolers2d.Append(currenttol2d);
                Standard_Integer mylen = oldlastpt-myfirstpt+1;
                Standard_Integer myParLen = myParameters->Length();
                Standard_Integer aLen = (myParLen > mylen)? myParLen : mylen;
                Handle(TColStd_HArray1OfReal) ThePar =
                  new TColStd_HArray1OfReal(myfirstpt, myfirstpt+aLen-1);
                for (i = 0; i < aLen; i++)
                  ThePar->SetValue(myfirstpt+i, myParameters->Value(myParameters->Lower()+i));
                myPar.Append(ThePar);
              }
	    } 
	    myfirstpt = oldlastpt;
	    mylastpt = Thelastpt;
	    
	  }
	  else
	  {
	    myIsClear = Standard_True;
	    ++myMultiLineNb;
	    Perform(anOtherLine1);
	    myfirstpt = mylastpt;
	    mylastpt = Thelastpt;
	  }
	}
	
        if  (MyStatus == Approx_NoPointsAdded && !begin) {
	  // On rend la meilleure approximation obtenue precedemment.
	  // ========================================================
	  GoUp = Standard_True;
	  tolreached = Standard_False;
	  if (TheMultiCurve.NbCurves() == 0) {
	    myMultiCurves.Clear();
	    return;
	  }
#ifdef OCCT_DEBUG
      if (mydebug) DUMP(TheMultiCurve);
#endif
	  myMultiCurves.Append(TheMultiCurve);
	  Tolers3d.Append(currenttol3d);
	  Tolers2d.Append(currenttol2d);
          Standard_Integer mylen = oldlastpt-myfirstpt+1;
          Standard_Integer myParLen = myParameters->Length();
          Standard_Integer aLen = (myParLen > mylen)? myParLen : mylen;
          Handle(TColStd_HArray1OfReal) ThePar =
            new TColStd_HArray1OfReal(myfirstpt, myfirstpt+aLen-1);
          for (i = 0; i < aLen; i++)
            ThePar->SetValue(myfirstpt+i, myParameters->Value(myParameters->Lower()+i));
	  myPar.Append(ThePar);

	  myfirstpt = oldlastpt;
	  mylastpt = Thelastpt;
	}
	
	else if (MyStatus == Approx_NoApproximation) {
	  // On ne fait pas d approximation entre myfirstpt et mylastpt.
	  // ===========================================================
	  // On stocke pour pouvoir en informer l utilisateur.
	  GoUp = Standard_True;
	  myfirstpt = mylastpt;
	  mylastpt = Thelastpt;
	}
      }
      
      if (myfirstpt == Thelastpt) {
	Finish = Standard_True;
	alldone = Standard_True;
	return;
      }
      if (!GoUp) {
	if (myfirstpt == mylastpt) break;  // Pour etre sur de ne pas 
	                                   // planter la station !!
	myCouple1.SetIndex(myfirstpt);
	myCouple2.SetIndex(mylastpt);
	myConstraints->SetValue(1, myCouple1);
	myConstraints->SetValue(2, myCouple2);
	
	// Calcul des parametres sur ce nouvel intervalle.
	// On recupere les parametres initiaux lors du decoupage.

	math_Vector Param(myfirstpt, mylastpt);
	if (begin) {
	  if(myfirstParam.IsNull()) {
	    Parameters(Line, myfirstpt, mylastpt, Param);
	  }
	  else {
	    for (i = myfirstParam->Lower(); i <= myfirstParam->Upper(); i++) {
	      Param(i) = myfirstParam->Value(i);
	    }
	    myfirstParam.Nullify();
	  }
	  TheParam = Param;
	  begin = Standard_False;
	}
	else {
	  Standard_Real pfirst = TheParam.Value(myfirstpt);
	  Standard_Real plast = TheParam.Value(mylastpt);
	  for (i = myfirstpt; i <= mylastpt; i++) {
	    Param(i) = (TheParam.Value(i)-pfirst)/(plast-pfirst);
	  }
	}

	TheMultiCurve = AppParCurves_MultiCurve();
        Standard_Integer indbad = 0;
	Ok = Compute(Line, myfirstpt, mylastpt, Param, thetol3d, thetol2d, indbad);
        if (myfirstpt == Thelastpt)
        {
          Finish = Standard_True;
          alldone = Standard_True;
          return;
        }
      }
    }
  }
}



const TColStd_Array1OfReal& Approx_ComputeLine::Parameters(const Standard_Integer Index) const
{
  return (myPar.Value(Index))->Array1();
}


Standard_Integer Approx_ComputeLine::NbMultiCurves()const
{
  return myMultiCurves.Length();
}

AppParCurves_MultiCurve& Approx_ComputeLine::ChangeValue(const Standard_Integer Index)
{
  return myMultiCurves.ChangeValue(Index);
}


const AppParCurves_MultiCurve& Approx_ComputeLine::Value(const Standard_Integer Index)
const
{
  return myMultiCurves.Value(Index);
}


const AppParCurves_MultiBSpCurve& Approx_ComputeLine::SplineValue()
{
  Approx_MCurvesToBSpCurve Trans;
  Trans.Perform(myMultiCurves);
  myspline = Trans.Value();
  return myspline;
}





void Approx_ComputeLine::Parameters(const MultiLine& Line, 
			       const Standard_Integer firstP,
			       const Standard_Integer lastP,
			       math_Vector& TheParameters) const
{
  Standard_Integer i, j, nbP2d, nbP3d;
  Standard_Real dist;

  if(Par == Approx_ChordLength || Par == Approx_Centripetal)
  {
    nbP3d = LineTool::NbP3d(Line);
    nbP2d = LineTool::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) LineTool::Value(Line, i - 1, tabP, tabP2d);
      else if(nbP2d != 0)          LineTool::Value(Line, i - 1, tabP2d);
      else if(nbP3d != 0)          LineTool::Value(Line, i - 1, tabP);

      if(nbP3d != 0 && nbP2d != 0) LineTool::Value(Line, i, tabPP, tabPP2d);
      else if(nbP2d != 0)          LineTool::Value(Line, i, tabPP2d);
      else if(nbP3d != 0)          LineTool::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));
    }
  }
}  


Standard_Boolean Approx_ComputeLine::Compute(const MultiLine& Line,
					     const Standard_Integer fpt,
					     const Standard_Integer lpt,
                                             math_Vector&     Para,
					     Standard_Real&   TheTol3d,
					     Standard_Real&   TheTol2d,
                                             Standard_Integer& indbad)
{
  indbad = 0;
  Standard_Integer deg, i;
  Standard_Boolean mydone;
  Standard_Real Fv;
  Standard_Integer nbp = lpt-fpt+1;

  math_Vector ParSav(Para.Lower(), Para.Upper());
  for (i = Para.Lower(); i <= Para.Upper(); i++) {
    ParSav(i) = Para(i);
  }
  Standard_Integer Mdegmax = mydegremax;
  if(nbp < Mdegmax+5 && mycut) { 
    Mdegmax = nbp - 5;
  }
  if(Mdegmax < mydegremin)  { 
    Mdegmax = mydegremin;
  }
  
  currenttol3d = currenttol2d = RealLast();
  for (deg = Min(nbp-1,mydegremin); deg <= Mdegmax; deg++) {
    AppParCurves_MultiCurve mySCU(deg+1);
    if (mysquares) {
      Approx_ParLeastSquareOfMyGradient SQ(Line, fpt, lpt, 
					   myfirstC, mylastC, Para, deg+1);
      mydone = SQ.IsDone();
      mySCU = SQ.BezierValue();
      SQ.Error(Fv, TheTol3d, TheTol2d);
    }
    else {
      Approx_MyGradient GRAD(Line, fpt, lpt, myConstraints, 
			     Para, deg, mytol3d, mytol2d, myitermax);
      mydone = GRAD.IsDone();
      mySCU = GRAD.Value();
      if (mySCU.NbCurves() == 0)
	continue;
      TheTol3d = GRAD.MaxError3d();
      TheTol2d = GRAD.MaxError2d();
    }      
    Standard_Real uu1 = Para(Para.Lower()), uu2;
    Standard_Boolean restau = Standard_False;
    for ( i = Para.Lower()+1; i <= Para.Upper(); i++) {
      uu2 =  Para(i);
      if (uu2 <= uu1) {
	restau = Standard_True;
//	cout << "restau = Standard_True" << endl;
	break;
      }
      uu1 = uu2;
    }
    if (restau) {
      for (i = Para.Lower(); i <= Para.Upper(); i++) {
	Para(i) = ParSav(i);
      }
    }
    if (mydone) {
      if (TheTol3d <= mytol3d && TheTol2d <= mytol2d) {
	// Stockage de la multicurve approximee.
	tolreached = Standard_True;
#ifdef OCCT_DEBUG
        if (mydebug) DUMP(mySCU);
#endif
        if (!CheckMultiCurve(mySCU, Line,
                             fpt, lpt,
                             indbad))
        {
          return Standard_False;
        }
        else
        {
          myMultiCurves.Append(mySCU);
          // Stockage des parametres de la partie de MultiLine approximee:
          // A ameliorer !! (bq trop de recopies)
          Handle(TColStd_HArray1OfReal) ThePar = 
            new TColStd_HArray1OfReal(Para.Lower(), Para.Upper());
          for (i = Para.Lower(); i <= Para.Upper(); i++) {
            ThePar->SetValue(i, Para(i));
          }
          myPar.Append(ThePar);
          Tolers3d.Append(TheTol3d);
          Tolers2d.Append(TheTol2d);
          return Standard_True;
        }
      }
    }

    if (TheTol3d <= currenttol3d && TheTol2d <= currenttol2d) {
      TheMultiCurve = mySCU;
      currenttol3d = TheTol3d;
      currenttol2d = TheTol2d;
      myParameters = new TColStd_HArray1OfReal(Para.Lower(), Para.Upper());
      for (i = Para.Lower(); i <= Para.Upper(); i++) {
	myParameters->SetValue(i, Para(i));
      }
    }

  }

  return Standard_False;
}




Standard_Boolean  Approx_ComputeLine::ComputeCurve(const MultiLine& Line,
				      const Standard_Integer firstpt,
				      const Standard_Integer lastpt)
{
  Standard_Integer i, j, nbP3d, nbP2d, deg;
  gp_Vec V13d, V23d;
  gp_Vec2d V12d, V22d;
  gp_Pnt P1, P2;
  gp_Pnt2d P12d, P22d;
  Standard_Boolean Tangent1, Tangent2, mydone= Standard_False;
#ifdef OCCT_DEBUG
  Standard_Boolean Parallel;
#endif
  Standard_Integer myfirstpt = firstpt, mylastpt = lastpt;
  Standard_Integer nbp = lastpt-firstpt+1;
  math_Vector Para(firstpt, lastpt);

  Parameters(Line, firstpt, lastpt, Para);

  nbP3d = LineTool::NbP3d(Line);
  nbP2d = LineTool::NbP2d(Line);
  Standard_Integer mynbP3d = nbP3d, mynbP2d = nbP2d;
  if (nbP3d == 0) mynbP3d = 1 ;
  if (nbP2d == 0) mynbP2d = 1 ;


  TColgp_Array1OfVec tabV1(1, mynbP3d), tabV2(1, mynbP3d);
  TColgp_Array1OfPnt tabP1(1, mynbP3d), tabP2(1, mynbP3d), tabP(1, mynbP3d);
  TColgp_Array1OfVec2d tabV12d(1, mynbP2d), tabV22d(1, mynbP2d);
  TColgp_Array1OfPnt2d tabP12d(1, mynbP2d), tabP22d(1, mynbP2d), tabP2d(1, mynbP2d);

  if (nbP3d != 0 && nbP2d != 0) {
    LineTool::Value(Line, myfirstpt,tabP1,tabP12d);
    LineTool::Value(Line, mylastpt,tabP2,tabP22d);
    Tangent1 = LineTool::Tangency(Line, myfirstpt,tabV1,tabV12d);
    Tangent2 = LineTool::Tangency(Line, mylastpt,tabV2,tabV22d);
  }
  else if (nbP2d != 0) {
    LineTool::Value(Line, myfirstpt,tabP12d);
    LineTool::Value(Line, mylastpt,tabP22d);
    Tangent1 = LineTool::Tangency(Line, myfirstpt, tabV12d);
    Tangent2 = LineTool::Tangency(Line, mylastpt, tabV22d);
  }
  else {
    LineTool::Value(Line, myfirstpt,tabP1);
    LineTool::Value(Line, mylastpt,tabP2);
    Tangent1 = LineTool::Tangency(Line, myfirstpt, tabV1);
    Tangent2 = LineTool::Tangency(Line, mylastpt, tabV2);
  }
  if (nbp == 2) {
    // S il n y a que 2 points, on verifie quand meme que les tangentes sont 
    // alignees.
#ifdef OCCT_DEBUG
    Parallel = Standard_True;
#endif
    if (Tangent1) {
      for (i = 1; i <= nbP3d; i++) {
	gp_Vec PVec(tabP1(i), tabP2(i));
	V13d = tabV1(i);
	if (!PVec.IsParallel(V13d, Precision::Angular())) {
#ifdef OCCT_DEBUG
	  Parallel = Standard_False;
#endif
	  break;
	}
      }
      for (i = 1; i <= nbP2d; i++) {
	gp_Vec2d PVec2d(tabP12d(i), tabP22d(i));
	V12d = tabV12d(i);
	if (!PVec2d.IsParallel(V12d, Precision::Angular())) {
#ifdef OCCT_DEBUG
	  Parallel = Standard_False;
#endif
	  break;
	}
      }
    }	

    if (Tangent2) {
      for (i = 1; i <= nbP3d; i++) {
	gp_Vec PVec(tabP1(i), tabP2(i));
	V23d = tabV2(i);
	if (!PVec.IsParallel(V23d, Precision::Angular())) {
#ifdef OCCT_DEBUG
	  Parallel = Standard_False;
#endif
	  break;
	}
      }
      for (i = 1; i <= nbP2d; i++) {
	gp_Vec2d PVec2d(tabP12d(i), tabP22d(i));
	V22d = tabV22d(i);
	if (!PVec2d.IsParallel(V22d, Precision::Angular())) {
#ifdef OCCT_DEBUG
	  Parallel = Standard_False;
#endif
	  break;
	}
      }
    }

#ifdef OCCT_DEBUG
    if (!Parallel) {
      if (mydebug) std::cout <<"droite mais tangentes pas vraiment paralleles!!"<< std::endl;
    }
#endif
    AppParCurves_MultiCurve mySCU(mydegremin+1);
    if (nbP3d != 0 && nbP2d != 0) {
      AppParCurves_MultiPoint MPole1(tabP1, tabP12d);
      AppParCurves_MultiPoint MPole2(tabP2, tabP22d);
      mySCU.SetValue(1, MPole1);
      mySCU.SetValue(mydegremin+1, MPole2);
      for (i = 2; i <= mydegremin; i++) {
	for (j = 1; j<= nbP3d; j++) {
	  P1 = tabP1(j);
	  P2 = tabP2(j);
	  tabP(j).SetXYZ(P1.XYZ()+(i-1)*(P2.XYZ()-P1.XYZ())/mydegremin);
	}
	for (j = 1; j<= nbP2d; j++) {
	  P12d = tabP12d(j);
	  P22d = tabP22d(j);
	  tabP2d(j).SetXY(P12d.XY()+(i-1)*(P22d.XY()-P12d.XY())/mydegremin);
	}
	AppParCurves_MultiPoint MPole(tabP, tabP2d);
	mySCU.SetValue(i, MPole);
      }

    }
    else if (nbP3d != 0) {
      AppParCurves_MultiPoint MPole1(tabP1);
      AppParCurves_MultiPoint MPole2(tabP2);
      mySCU.SetValue(1, MPole1);
      mySCU.SetValue(mydegremin+1, MPole2);
      for (i = 2; i <= mydegremin; i++) {
	for (j = 1; j<= nbP3d; j++) {
	  P1 = tabP1(j);
	  P2 = tabP2(j);
	  tabP(j).SetXYZ(P1.XYZ()+(i-1)*(P2.XYZ()-P1.XYZ())/mydegremin);
	}
	AppParCurves_MultiPoint MPole(tabP);
	mySCU.SetValue(i, MPole);
      }
    }
    else if (nbP2d != 0) {
      AppParCurves_MultiPoint MPole1(tabP12d);
      AppParCurves_MultiPoint MPole2(tabP22d);
      mySCU.SetValue(1, MPole1);
      mySCU.SetValue(mydegremin+1, MPole2);
      for (i = 2; i <= mydegremin; i++) {
	for (j = 1; j<= nbP2d; j++) {
	  P12d = tabP12d(j);
	  P22d = tabP22d(j);
	  tabP2d(j).SetXY(P12d.XY()+(i-1)*(P22d.XY()-P12d.XY())/mydegremin);
	}
	AppParCurves_MultiPoint MPole(tabP2d);
	mySCU.SetValue(i, MPole);
      }
    }
    mydone = Standard_True;
    // Stockage de la multicurve approximee.
    tolreached = Standard_True;
#ifdef OCCT_DEBUG
      if (mydebug) DUMP(mySCU);
#endif
    myMultiCurves.Append(mySCU);
    Handle(TColStd_HArray1OfReal) ThePar = new TColStd_HArray1OfReal(Para.Lower(), Para.Upper());
    for (i = Para.Lower(); i <= Para.Upper(); i++) {
      ThePar->SetValue(i, Para(i));
    }
    myPar.Append(ThePar);
    Tolers3d.Append(Precision::Confusion());
    Tolers2d.Append(Precision::PConfusion());
    return mydone;
  }

  // avec les tangentes.
  deg = nbp+1;
  AppParCurves_MultiCurve mySCU(deg+1);
  AppParCurves_Constraint Cons = AppParCurves_TangencyPoint;
  Standard_Real lambda1, lambda2;
  math_Vector V1(1, nbP3d*3+nbP2d*2);
  math_Vector V2(1, nbP3d*3+nbP2d*2);
  FirstTangencyVector(Line, myfirstpt, V1);
  lambda1 = SearchFirstLambda(Line, Para, V1, myfirstpt);
  
  LastTangencyVector(Line, mylastpt, V2);
  lambda2 = SearchLastLambda(Line, Para, V2, mylastpt);
  
  Approx_ParLeastSquareOfMyGradient 
    LSQ(Line, myfirstpt, mylastpt, 
	Cons, Cons, Para, deg+1);
  
  lambda1 = lambda1/deg;
  lambda2 = lambda2/deg;
  LSQ.Perform(Para, V1, V2, lambda1, lambda2);
  mydone = LSQ.IsDone();
  mySCU = LSQ.BezierValue();
  
  if (mydone) {
    Standard_Real Fv, TheTol3d, TheTol2d;
    LSQ.Error(Fv, TheTol3d, TheTol2d);  

    // Stockage de la multicurve approximee.
    tolreached = Standard_True;
#ifdef OCCT_DEBUG
      if (mydebug) DUMP(mySCU);
#endif
    myMultiCurves.Append(mySCU);
    Handle(TColStd_HArray1OfReal) ThePar = 
      new TColStd_HArray1OfReal(Para.Lower(), Para.Upper());
    for (i = Para.Lower(); i <= Para.Upper(); i++) {
      ThePar->SetValue(i, Para(i));
    }
    myPar.Append(ThePar);
    Tolers3d.Append(TheTol3d);
    Tolers2d.Append(TheTol2d);
    return Standard_True;
  }
  return mydone;
}



void Approx_ComputeLine::Init(const Standard_Integer degreemin,
			      const Standard_Integer degreemax,
			      const Standard_Real Tolerance3d,
			      const Standard_Real Tolerance2d,
			      const Standard_Integer NbIterations,
			      const Standard_Boolean cutting,
			      const Approx_ParametrizationType parametrization,
			      const Standard_Boolean Squares)
{
  mydegremin = degreemin;
  mydegremax = degreemax;
  mytol3d = Tolerance3d;
  mytol2d = Tolerance2d;
  Par = parametrization;
  mysquares = Squares;
  mycut = cutting;
  myitermax = NbIterations;
}



void Approx_ComputeLine::SetDegrees(const Standard_Integer degreemin,
				    const Standard_Integer degreemax)
{
  mydegremin = degreemin;
  mydegremax = degreemax;
}


void Approx_ComputeLine::SetTolerances(const Standard_Real Tolerance3d,
				       const Standard_Real Tolerance2d)
{
  mytol3d = Tolerance3d;
  mytol2d = Tolerance2d;
}


void Approx_ComputeLine::SetConstraints(const AppParCurves_Constraint FirstC,
					const AppParCurves_Constraint LastC)
{
  myfirstC = FirstC;
  mylastC = LastC;
}



Standard_Boolean Approx_ComputeLine::IsAllApproximated()
const {
  return alldone;
}

Standard_Boolean Approx_ComputeLine::IsToleranceReached()
const {
  return tolreached;
}

void Approx_ComputeLine::Error(const Standard_Integer Index,
			       Standard_Real& tol3d,
			       Standard_Real& tol2d) const
{
  tol3d = Tolers3d.Value(Index);
  tol2d = Tolers2d.Value(Index);
}

Approx_ParametrizationType Approx_ComputeLine::Parametrization() const
{
  return Par;
}