[occt.git] / src / AppParCurves / AppParCurves_BSpGradient.gxx

// 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.

// lpa, le 11/09/91


// Application de la methode du gradient corrige pour minimiser 
// F  = somme(||C(ui, Poles(ui)) - ptli||2.
// La methode de gradient conjugue est programmee dans la bibliotheque 
// mathematique: math_BFGS.


#define No_Standard_RangeError
#define No_Standard_OutOfRange

#include <AppParCurves_Constraint.hxx>
#include <AppParCurves_ConstraintCouple.hxx>
#include <math_BFGS.hxx>
#include <StdFail_NotDone.hxx>
#include <AppParCurves_MultiPoint.hxx>
#include <gp_Pnt.hxx>
#include <gp_Pnt2d.hxx>
#include <gp_Vec.hxx>
#include <gp_Vec2d.hxx>
#include <TColgp_Array1OfPnt.hxx>
#include <TColgp_Array1OfPnt2d.hxx>
#include <TColgp_Array1OfVec.hxx>
#include <TColgp_Array1OfVec2d.hxx>

static AppParCurves_Constraint FirstConstraint
  (const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
   const Standard_Integer FirstPoint)
{
  Standard_Integer i, myindex;
  Standard_Integer low = TheConstraints->Lower(), upp= TheConstraints->Upper();
  AppParCurves_ConstraintCouple mycouple;
  AppParCurves_Constraint Cons = AppParCurves_NoConstraint;

  for (i = low; i <= upp; i++) {
    mycouple = TheConstraints->Value(i);
    Cons = mycouple.Constraint();
    myindex = mycouple.Index();
    if (myindex == FirstPoint) {
      break;
    }
  }
  return Cons;
}


static AppParCurves_Constraint LastConstraint
  (const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
   const Standard_Integer LastPoint)
{
  Standard_Integer i, myindex;
  Standard_Integer low = TheConstraints->Lower(), upp= TheConstraints->Upper();
  AppParCurves_ConstraintCouple mycouple;
  AppParCurves_Constraint Cons = AppParCurves_NoConstraint;

  for (i = low; i <= upp; i++) {
    mycouple = TheConstraints->Value(i);
    Cons = mycouple.Constraint();
    myindex = mycouple.Index();
    if (myindex == LastPoint) {
      break;
    }
  }
  return Cons;
}


AppParCurves_BSpGradient::
   AppParCurves_BSpGradient(const MultiLine& SSP,
         const Standard_Integer FirstPoint,
         const Standard_Integer LastPoint,
	 const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
         math_Vector& Parameters,
	 const TColStd_Array1OfReal& Knots,
	 const TColStd_Array1OfInteger& Mults,
         const Standard_Integer Deg,
	 const Standard_Real Tol3d,
	 const Standard_Real Tol2d,
	 const Standard_Integer NbIterations):
	 ParError(FirstPoint, LastPoint,0.0),
         mylambda1(0.0),
         mylambda2(0.0),
         myIsLambdaDefined(Standard_False)
{
  Perform(SSP, FirstPoint, LastPoint, TheConstraints, Parameters, 
	  Knots, Mults, Deg, Tol3d, Tol2d, NbIterations);
}


AppParCurves_BSpGradient::
   AppParCurves_BSpGradient(const MultiLine& SSP,
         const Standard_Integer FirstPoint,
         const Standard_Integer LastPoint,
	 const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
         math_Vector& Parameters,
	 const TColStd_Array1OfReal& Knots,
	 const TColStd_Array1OfInteger& Mults,
         const Standard_Integer Deg,
	 const Standard_Real Tol3d,
	 const Standard_Real Tol2d,
	 const Standard_Integer NbIterations,
	 const Standard_Real lambda1,
	 const Standard_Real lambda2):
	 ParError(FirstPoint, LastPoint,0.0),
         mylambda1(lambda1),
         mylambda2(lambda2),
         myIsLambdaDefined(Standard_True)
{
  Perform(SSP, FirstPoint, LastPoint, TheConstraints, Parameters, 
	  Knots, Mults, Deg, Tol3d, Tol2d, NbIterations);
}


void AppParCurves_BSpGradient::
  Perform(const MultiLine& SSP,
         const Standard_Integer FirstPoint,
         const Standard_Integer LastPoint,
	 const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
         math_Vector& Parameters,
	 const TColStd_Array1OfReal& Knots,
	 const TColStd_Array1OfInteger& Mults,
         const Standard_Integer Deg,
	 const Standard_Real Tol3d,
	 const Standard_Real Tol2d,
	 const Standard_Integer NbIterations)
{

//  Standard_Boolean grad = Standard_True;
  Standard_Integer i, j, k, i2, l;
  Standard_Real UF, DU, Fval = 0.0, FU, DFU;
  Standard_Integer nbP3d = ToolLine::NbP3d(SSP);
  Standard_Integer nbP2d = ToolLine::NbP2d(SSP);
  Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
  Standard_Integer nbP = nbP3d + nbP2d;
//  gp_Pnt Pt, P1, P2;
  gp_Pnt Pt;
//  gp_Pnt2d Pt2d, P12d, P22d;
  gp_Pnt2d Pt2d;
//  gp_Vec V1, V2, MyV;
  gp_Vec V1, MyV;
//  gp_Vec2d V12d, V22d, MyV2d;
  gp_Vec2d V12d, MyV2d;
  Done = Standard_False;
  
  if (nbP3d == 0) mynbP3d = 1;
  if (nbP2d == 0) mynbP2d = 1;
  TColgp_Array1OfPnt TabP(1, mynbP3d);
  TColgp_Array1OfPnt2d TabP2d(1, mynbP2d);
  TColgp_Array1OfVec TabV(1, mynbP3d);
  TColgp_Array1OfVec2d TabV2d(1, mynbP2d);

  // Calcul de la fonction F= somme(||C(ui)-Ptli||2):
  // Appel a une fonction heritant de MultipleVarFunctionWithGradient
  // pour calculer F et grad_F.
  // ================================================================

  Standard_Integer nbpoles = -Deg -1;
  for (i = Mults.Lower() ;i <= Mults.Upper(); i++) {
    nbpoles += Mults(i);
  }

  TColgp_Array1OfPnt   TabPole(1, nbpoles);
  TColgp_Array1OfPnt2d TabPole2d(1, nbpoles);
  TColgp_Array1OfPnt    ThePoles(1, (nbpoles)*mynbP3d);
  TColgp_Array1OfPnt2d  ThePoles2d(1, (nbpoles)*mynbP2d);


  AppParCurves_Constraint 
    FirstCons = FirstConstraint(TheConstraints, FirstPoint), 
    LastCons  = LastConstraint(TheConstraints, LastPoint);


  AppParCurves_BSpParFunction MyF(SSP, FirstPoint,LastPoint, TheConstraints, 
				  Parameters, Knots, Mults, nbpoles);


  if (FirstCons >= AppParCurves_TangencyPoint ||
      LastCons >= AppParCurves_TangencyPoint) {

    if (!myIsLambdaDefined) {
      AppParCurves_BSpParLeastSquare thefitt(SSP, Knots, Mults, FirstPoint,
					     LastPoint, FirstCons, LastCons, 
					     Parameters, nbpoles);
      if (FirstCons >= AppParCurves_TangencyPoint) {
	mylambda1 = thefitt.FirstLambda();
	MyF.SetFirstLambda(mylambda1);
      }
      if (LastCons >= AppParCurves_TangencyPoint) {
	mylambda2 = thefitt.LastLambda();
	MyF.SetLastLambda(mylambda2);
      }
    }
    else {
      MyF.SetFirstLambda(mylambda1);
      MyF.SetLastLambda(mylambda2);
    }
  }


  MyF.Value(Parameters, Fval);
  MError3d = MyF.MaxError3d();
  MError2d = MyF.MaxError2d();
  SCU = MyF.CurveValue();

  if (MError3d > Tol3d || MError2d > Tol2d) {

    // Stockage des Poles des courbes pour projeter:
    // ============================================
    i2 = 0;
    for (k = 1; k <= nbP3d; k++) {
      SCU.Curve(k, TabPole);
      for (j=1; j<=nbpoles; j++) ThePoles(j+i2) = TabPole(j);
      i2 += nbpoles;
    }
    i2 = 0;
    for (k = 1; k <= nbP2d; k++) {
      SCU.Curve(nbP3d+k, TabPole2d);
      for (j=1; j<=nbpoles; j++) ThePoles2d(j+i2) = TabPole2d(j);
      i2 += nbpoles;
    }
    
    //  Une iteration rapide de projection est faite par la methode de 
    //  Rogers & Fog 89, methode equivalente a Hoschek 88 qui ne necessite pas
    //  le calcul de D2.
    
    const math_Matrix& A = MyF.FunctionMatrix();
    const math_Matrix& DA = MyF.DerivativeFunctionMatrix();
    const math_IntegerVector& Index = MyF.Index();
    Standard_Real aa, da, a, b, c, d , e , f, px, py, pz;
    Standard_Integer indexdeb, indexfin;

    for (j = FirstPoint+1; j <= LastPoint-1; j++) {
      
      UF = Parameters(j);
      if (nbP3d != 0 && nbP2d != 0) ToolLine::Value(SSP, j, TabP, TabP2d);
      else if (nbP2d != 0)          ToolLine::Value(SSP, j, TabP2d);
      else                          ToolLine::Value(SSP, j, TabP);
      
      FU = 0.0;
      DFU = 0.0;
      i2 = 0;
      
      indexdeb = Index(j) + 1;
      indexfin = indexdeb + Deg;

      for (k = 1; k <= nbP3d; k++) {
	a = b = c = d = e = f = 0.0;
	for (l = indexdeb; l <= indexfin; l++) {
	  Pt = ThePoles(l+i2); 
	  px = Pt.X(); py = Pt.Y(); pz = Pt.Z();
	  aa = A(j, l); da = DA(j, l);
	  a += aa* px; d += da* px;
	  b += aa* py; e += da* py;
	  c += aa* pz; f += da* pz;
	}
	Pt.SetCoord(a, b, c);
	V1.SetCoord(d, e, f);
	i2 += nbpoles;

	MyV = gp_Vec(Pt, TabP(k));
	FU += MyV*V1;
	DFU += V1.SquareMagnitude();
      }
      i2 = 0;
      for (k = 1; k <= nbP2d; k++) {
	a = b = d = e = 0.0;
	for (l = indexdeb; l <= indexfin; l++) {
	  Pt2d = ThePoles2d(l+i2); 
	  px = Pt2d.X(); py = Pt2d.Y();
	  aa = A(j, l); da = DA(j, l);
	  a += aa* px; d += da* px;
	  b += aa* py; e += da* py;
	}
	Pt2d.SetCoord(a, b);
	V12d.SetCoord(d, e);
	i2 += nbpoles;

	MyV2d = gp_Vec2d(Pt2d, TabP2d(k));
	FU += MyV2d*V12d;
	DFU += V12d.SquareMagnitude();
      }
      
      if (DFU >= RealEpsilon()) {
	DU = FU/DFU;
	DU = Sign(Min(5.e-02, Abs(DU)), DU);
	UF += DU;
	Parameters(j) = UF;
      }
    }
    
    MyF.Value(Parameters, Fval);
    MError3d = MyF.MaxError3d();
    MError2d = MyF.MaxError2d();
  }


  if (MError3d<= Tol3d && MError2d <= Tol2d) {
    Done = Standard_True;
  }
  else if (NbIterations != 0) {
    // NbIterations de gradient conjugue:
    // =================================
    Standard_Real Eps = 1.e-07;
    AppParCurves_BSpGradient_BFGS FResol(MyF, Parameters, Tol3d, 
					 Tol2d, Eps, NbIterations);
  }

  SCU = MyF.CurveValue();


  AvError = 0.;
  for (j = FirstPoint; j <= LastPoint; j++) {  
    Parameters(j) = MyF.NewParameters()(j);
    // Recherche des erreurs maxi et moyenne a un index donne:
    for (k = 1; k <= nbP; k++) {
      ParError(j) = Max(ParError(j), MyF.Error(j, k));
    }
    AvError += ParError(j);
  }
  AvError = AvError/(LastPoint-FirstPoint+1);


  MError3d = MyF.MaxError3d();
  MError2d = MyF.MaxError2d();
  if (MError3d <= Tol3d && MError2d <= Tol2d) {
    Done = Standard_True;
  }

}


AppParCurves_MultiBSpCurve AppParCurves_BSpGradient::Value() const {
  return SCU;
}


Standard_Boolean AppParCurves_BSpGradient::IsDone() const {
  return Done;
}


Standard_Real AppParCurves_BSpGradient::Error(const Standard_Integer Index) const {
  return ParError(Index);
}

Standard_Real AppParCurves_BSpGradient::AverageError() const {
  return AvError;
}

Standard_Real AppParCurves_BSpGradient::MaxError3d() const {
  return MError3d;
}

Standard_Real AppParCurves_BSpGradient::MaxError2d() const {
  return MError2d;
}
Commit	Line	Data
b311480e	1	// Copyright (c) 1995-1999 Matra Datavision
973c2be1	2	// Copyright (c) 1999-2014 OPEN CASCADE SAS
b311480e	3	//
973c2be1	4	// This file is part of Open CASCADE Technology software library.
b311480e	5	//
d5f74e42	6	// This library is free software; you can redistribute it and/or modify it under
d5f74e42	7	// the terms of the GNU Lesser General Public License version 2.1 as published
973c2be1	8	// by the Free Software Foundation, with special exception defined in the file
	9	// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
	10	// distribution for complete text of the license and disclaimer of any warranty.
b311480e	11	//
973c2be1	12	// Alternatively, this file may be used under the terms of Open CASCADE
973c2be1	13	// commercial license or contractual agreement.
b311480e	14
7fd59977	15	// lpa, le 11/09/91
	16
	17
	18	// Application de la methode du gradient corrige pour minimiser
	19	// F = somme(\|\|C(ui, Poles(ui)) - ptli\|\|2.
	20	// La methode de gradient conjugue est programmee dans la bibliotheque
	21	// mathematique: math_BFGS.
	22
	23
	24	#define No_Standard_RangeError
	25	#define No_Standard_OutOfRange
	26
	27	#include <AppParCurves_Constraint.hxx>
	28	#include <AppParCurves_ConstraintCouple.hxx>
	29	#include <math_BFGS.hxx>
	30	#include <StdFail_NotDone.hxx>
	31	#include <AppParCurves_MultiPoint.hxx>
	32	#include <gp_Pnt.hxx>
	33	#include <gp_Pnt2d.hxx>
	34	#include <gp_Vec.hxx>
	35	#include <gp_Vec2d.hxx>
	36	#include <TColgp_Array1OfPnt.hxx>
	37	#include <TColgp_Array1OfPnt2d.hxx>
	38	#include <TColgp_Array1OfVec.hxx>
	39	#include <TColgp_Array1OfVec2d.hxx>
	40
7fd59977	41	static AppParCurves_Constraint FirstConstraint
	42	(const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
	43	const Standard_Integer FirstPoint)
	44	{
	45	Standard_Integer i, myindex;
	46	Standard_Integer low = TheConstraints->Lower(), upp= TheConstraints->Upper();
	47	AppParCurves_ConstraintCouple mycouple;
	48	AppParCurves_Constraint Cons = AppParCurves_NoConstraint;
	49
	50	for (i = low; i <= upp; i++) {
	51	mycouple = TheConstraints->Value(i);
	52	Cons = mycouple.Constraint();
	53	myindex = mycouple.Index();
	54	if (myindex == FirstPoint) {
	55	break;
	56	}
	57	}
	58	return Cons;
	59	}
	60
	61
	62	static AppParCurves_Constraint LastConstraint
	63	(const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
	64	const Standard_Integer LastPoint)
	65	{
	66	Standard_Integer i, myindex;
	67	Standard_Integer low = TheConstraints->Lower(), upp= TheConstraints->Upper();
	68	AppParCurves_ConstraintCouple mycouple;
	69	AppParCurves_Constraint Cons = AppParCurves_NoConstraint;
	70
	71	for (i = low; i <= upp; i++) {
	72	mycouple = TheConstraints->Value(i);
	73	Cons = mycouple.Constraint();
	74	myindex = mycouple.Index();
	75	if (myindex == LastPoint) {
	76	break;
	77	}
	78	}
	79	return Cons;
	80	}
	81
	82
	83
	84
	85
	86	AppParCurves_BSpGradient::
	87	AppParCurves_BSpGradient(const MultiLine& SSP,
	88	const Standard_Integer FirstPoint,
	89	const Standard_Integer LastPoint,
	90	const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
	91	math_Vector& Parameters,
	92	const TColStd_Array1OfReal& Knots,
	93	const TColStd_Array1OfInteger& Mults,
	94	const Standard_Integer Deg,
	95	const Standard_Real Tol3d,
	96	const Standard_Real Tol2d,
	97	const Standard_Integer NbIterations):
89bc1237	98	ParError(FirstPoint, LastPoint,0.0),
	99	mylambda1(0.0),
	100	mylambda2(0.0),
	101	myIsLambdaDefined(Standard_False)
7fd59977	102	{
	103	Perform(SSP, FirstPoint, LastPoint, TheConstraints, Parameters,
	104	Knots, Mults, Deg, Tol3d, Tol2d, NbIterations);
	105	}
	106
	107
	108	AppParCurves_BSpGradient::
	109	AppParCurves_BSpGradient(const MultiLine& SSP,
	110	const Standard_Integer FirstPoint,
	111	const Standard_Integer LastPoint,
	112	const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
	113	math_Vector& Parameters,
	114	const TColStd_Array1OfReal& Knots,
	115	const TColStd_Array1OfInteger& Mults,
	116	const Standard_Integer Deg,
	117	const Standard_Real Tol3d,
	118	const Standard_Real Tol2d,
	119	const Standard_Integer NbIterations,
	120	const Standard_Real lambda1,
	121	const Standard_Real lambda2):
89bc1237	122	ParError(FirstPoint, LastPoint,0.0),
	123	mylambda1(lambda1),
	124	mylambda2(lambda2),
	125	myIsLambdaDefined(Standard_True)
7fd59977	126	{
7fd59977	127	Perform(SSP, FirstPoint, LastPoint, TheConstraints, Parameters,
	128	Knots, Mults, Deg, Tol3d, Tol2d, NbIterations);
	129	}
	130
	131
	132
	133
	134
	135
	136
	137	void AppParCurves_BSpGradient::
	138	Perform(const MultiLine& SSP,
	139	const Standard_Integer FirstPoint,
	140	const Standard_Integer LastPoint,
	141	const Handle(AppParCurves_HArray1OfConstraintCouple)& TheConstraints,
	142	math_Vector& Parameters,
	143	const TColStd_Array1OfReal& Knots,
	144	const TColStd_Array1OfInteger& Mults,
	145	const Standard_Integer Deg,
	146	const Standard_Real Tol3d,
	147	const Standard_Real Tol2d,
	148	const Standard_Integer NbIterations)
	149	{
	150
	151	// Standard_Boolean grad = Standard_True;
	152	Standard_Integer i, j, k, i2, l;
	153	Standard_Real UF, DU, Fval = 0.0, FU, DFU;
	154	Standard_Integer nbP3d = ToolLine::NbP3d(SSP);
	155	Standard_Integer nbP2d = ToolLine::NbP2d(SSP);
	156	Standard_Integer mynbP3d=nbP3d, mynbP2d=nbP2d;
	157	Standard_Integer nbP = nbP3d + nbP2d;
	158	// gp_Pnt Pt, P1, P2;
	159	gp_Pnt Pt;
	160	// gp_Pnt2d Pt2d, P12d, P22d;
	161	gp_Pnt2d Pt2d;
	162	// gp_Vec V1, V2, MyV;
	163	gp_Vec V1, MyV;
	164	// gp_Vec2d V12d, V22d, MyV2d;
	165	gp_Vec2d V12d, MyV2d;
	166	Done = Standard_False;
	167
	168	if (nbP3d == 0) mynbP3d = 1;
	169	if (nbP2d == 0) mynbP2d = 1;
	170	TColgp_Array1OfPnt TabP(1, mynbP3d);
	171	TColgp_Array1OfPnt2d TabP2d(1, mynbP2d);
	172	TColgp_Array1OfVec TabV(1, mynbP3d);
	173	TColgp_Array1OfVec2d TabV2d(1, mynbP2d);
	174
	175	// Calcul de la fonction F= somme(\|\|C(ui)-Ptli\|\|2):
	176	// Appel a une fonction heritant de MultipleVarFunctionWithGradient
	177	// pour calculer F et grad_F.
	178	// ================================================================
	179
	180	Standard_Integer nbpoles = -Deg -1;
	181	for (i = Mults.Lower() ;i <= Mults.Upper(); i++) {
	182	nbpoles += Mults(i);
	183	}
	184
	185	TColgp_Array1OfPnt TabPole(1, nbpoles);
	186	TColgp_Array1OfPnt2d TabPole2d(1, nbpoles);
	187	TColgp_Array1OfPnt ThePoles(1, (nbpoles)*mynbP3d);
	188	TColgp_Array1OfPnt2d ThePoles2d(1, (nbpoles)*mynbP2d);
	189
	190
191	AppParCurves_Constraint
192	FirstCons = FirstConstraint(TheConstraints, FirstPoint),
193	LastCons = LastConstraint(TheConstraints, LastPoint);
194
195
196	AppParCurves_BSpParFunction MyF(SSP, FirstPoint,LastPoint, TheConstraints,
197	Parameters, Knots, Mults, nbpoles);
198
199
200
201	if (FirstCons >= AppParCurves_TangencyPoint \|\|
202	LastCons >= AppParCurves_TangencyPoint) {
203
89bc1237	204	if (!myIsLambdaDefined) {
7fd59977	205	AppParCurves_BSpParLeastSquare thefitt(SSP, Knots, Mults, FirstPoint,
	206	LastPoint, FirstCons, LastCons,
	207	Parameters, nbpoles);
	208	if (FirstCons >= AppParCurves_TangencyPoint) {
	209	mylambda1 = thefitt.FirstLambda();
	210	MyF.SetFirstLambda(mylambda1);
	211	}
	212	if (LastCons >= AppParCurves_TangencyPoint) {
	213	mylambda2 = thefitt.LastLambda();
	214	MyF.SetLastLambda(mylambda2);
	215	}
	216	}
	217	else {
	218	MyF.SetFirstLambda(mylambda1);
	219	MyF.SetLastLambda(mylambda2);
	220	}
	221	}
	222
	223
	224	MyF.Value(Parameters, Fval);
	225	MError3d = MyF.MaxError3d();
	226	MError2d = MyF.MaxError2d();
	227	SCU = MyF.CurveValue();
	228
	229	if (MError3d > Tol3d \|\| MError2d > Tol2d) {
	230
	231	// Stockage des Poles des courbes pour projeter:
	232	// ============================================
	233	i2 = 0;
	234	for (k = 1; k <= nbP3d; k++) {
	235	SCU.Curve(k, TabPole);
	236	for (j=1; j<=nbpoles; j++) ThePoles(j+i2) = TabPole(j);
	237	i2 += nbpoles;
	238	}
	239	i2 = 0;
	240	for (k = 1; k <= nbP2d; k++) {
	241	SCU.Curve(nbP3d+k, TabPole2d);
	242	for (j=1; j<=nbpoles; j++) ThePoles2d(j+i2) = TabPole2d(j);
	243	i2 += nbpoles;
	244	}
	245
	246	// Une iteration rapide de projection est faite par la methode de
	247	// Rogers & Fog 89, methode equivalente a Hoschek 88 qui ne necessite pas
	248	// le calcul de D2.
	249
	250	const math_Matrix& A = MyF.FunctionMatrix();
	251	const math_Matrix& DA = MyF.DerivativeFunctionMatrix();
	252	const math_IntegerVector& Index = MyF.Index();
	253	Standard_Real aa, da, a, b, c, d , e , f, px, py, pz;
	254	Standard_Integer indexdeb, indexfin;
	255
	256	for (j = FirstPoint+1; j <= LastPoint-1; j++) {
	257
	258	UF = Parameters(j);
	259	if (nbP3d != 0 && nbP2d != 0) ToolLine::Value(SSP, j, TabP, TabP2d);
	260	else if (nbP2d != 0) ToolLine::Value(SSP, j, TabP2d);
	261	else ToolLine::Value(SSP, j, TabP);
	262
	263	FU = 0.0;
	264	DFU = 0.0;
	265	i2 = 0;
	266
	267	indexdeb = Index(j) + 1;
	268	indexfin = indexdeb + Deg;
269
270	for (k = 1; k <= nbP3d; k++) {
271	a = b = c = d = e = f = 0.0;
272	for (l = indexdeb; l <= indexfin; l++) {
273	Pt = ThePoles(l+i2);
274	px = Pt.X(); py = Pt.Y(); pz = Pt.Z();
275	aa = A(j, l); da = DA(j, l);
276	a += aa* px; d += da* px;
277	b += aa* py; e += da* py;
278	c += aa* pz; f += da* pz;
279	}
280	Pt.SetCoord(a, b, c);
281	V1.SetCoord(d, e, f);
282	i2 += nbpoles;
283
284	MyV = gp_Vec(Pt, TabP(k));
285	FU += MyV*V1;
286	DFU += V1.SquareMagnitude();
287	}
288	i2 = 0;
289	for (k = 1; k <= nbP2d; k++) {
290	a = b = d = e = 0.0;
291	for (l = indexdeb; l <= indexfin; l++) {
292	Pt2d = ThePoles2d(l+i2);
293	px = Pt2d.X(); py = Pt2d.Y();
294	aa = A(j, l); da = DA(j, l);
295	a += aa* px; d += da* px;
296	b += aa* py; e += da* py;
297	}
298	Pt2d.SetCoord(a, b);
299	V12d.SetCoord(d, e);
300	i2 += nbpoles;
301
302	MyV2d = gp_Vec2d(Pt2d, TabP2d(k));
303	FU += MyV2d*V12d;
304	DFU += V12d.SquareMagnitude();
305	}
306
307	if (DFU >= RealEpsilon()) {
308	DU = FU/DFU;
309	DU = Sign(Min(5.e-02, Abs(DU)), DU);
310	UF += DU;
311	Parameters(j) = UF;
312	}
313	}
314
315	MyF.Value(Parameters, Fval);
316	MError3d = MyF.MaxError3d();
317	MError2d = MyF.MaxError2d();
318	}
319
320
321	if (MError3d<= Tol3d && MError2d <= Tol2d) {
322	Done = Standard_True;
323	}
324	else if (NbIterations != 0) {
325	// NbIterations de gradient conjugue:
326	// =================================
327	Standard_Real Eps = 1.e-07;
328	AppParCurves_BSpGradient_BFGS FResol(MyF, Parameters, Tol3d,
329	Tol2d, Eps, NbIterations);
330	}
331
332	SCU = MyF.CurveValue();
333
334
335	AvError = 0.;
336	for (j = FirstPoint; j <= LastPoint; j++) {
337	Parameters(j) = MyF.NewParameters()(j);
338	// Recherche des erreurs maxi et moyenne a un index donne:
339	for (k = 1; k <= nbP; k++) {
340	ParError(j) = Max(ParError(j), MyF.Error(j, k));
341	}
342	AvError += ParError(j);
343	}
344	AvError = AvError/(LastPoint-FirstPoint+1);
345
346
347	MError3d = MyF.MaxError3d();
348	MError2d = MyF.MaxError2d();
349	if (MError3d <= Tol3d && MError2d <= Tol2d) {
350	Done = Standard_True;
351	}
352
353	}
354
355
356
357	AppParCurves_MultiBSpCurve AppParCurves_BSpGradient::Value() const {
358	return SCU;
359	}
360
361
362	Standard_Boolean AppParCurves_BSpGradient::IsDone() const {
363	return Done;
364	}
365
366
367	Standard_Real AppParCurves_BSpGradient::Error(const Standard_Integer Index) const {
368	return ParError(Index);
369	}
370
371	Standard_Real AppParCurves_BSpGradient::AverageError() const {
372	return AvError;
373	}
374
375	Standard_Real AppParCurves_BSpGradient::MaxError3d() const {
376	return MError3d;
377	}
378
379	Standard_Real AppParCurves_BSpGradient::MaxError2d() const {
380	return MError2d;
381	}
382
383