// Created on: 1996-07-03
// Created by: Joelle CHAUVET
// Copyright (c) 1996-1999 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 <AdvApp2Var_ApproxAFunc2Var.hxx>
#include <AdvApp2Var_EvaluatorFunc2Var.hxx>
#include <AdvApp2Var_Criterion.hxx>
#include <AdvApp2Var_Context.hxx>
#include <AdvApp2Var_Patch.hxx>
#include <AdvApp2Var_Network.hxx>
#include <AdvApp2Var_Node.hxx>
#include <AdvApp2Var_Iso.hxx>
#include <AdvApp2Var_Strip.hxx>
#include <AdvApp2Var_Framework.hxx>
#include <AdvApprox_Cutting.hxx>

#include <Standard_ConstructionError.hxx>
#include <Standard_OutOfRange.hxx>
#include <TColStd_HArray1OfInteger.hxx>
#include <TColStd_HArray2OfInteger.hxx>
#include <TColStd_HArray1OfReal.hxx>
#include <TColStd_HArray2OfReal.hxx>

#include <gp_XY.hxx>
#include <gp_Pnt2d.hxx>
#include <gp_Pnt.hxx>
#include <TColgp_HArray2OfPnt.hxx>

#include <Convert_GridPolynomialToPoles.hxx>

#include <Geom_BezierSurface.hxx>
#include <Geom_BSplineSurface.hxx>


//=======================================================================
//function : AdvApp2Var_ApproxAFunc2Var
//purpose  : 
//=======================================================================

AdvApp2Var_ApproxAFunc2Var::AdvApp2Var_ApproxAFunc2Var(
                           const Standard_Integer Num1DSS,
                           const Standard_Integer Num2DSS,
                           const Standard_Integer Num3DSS,
                           const Handle(TColStd_HArray1OfReal)& OneDTol,
                           const Handle(TColStd_HArray1OfReal)& TwoDTol,
                           const Handle(TColStd_HArray1OfReal)& ThreeDTol,
                           const Handle(TColStd_HArray2OfReal)& OneDTolFr,
                           const Handle(TColStd_HArray2OfReal)& TwoDTolFr,
                           const Handle(TColStd_HArray2OfReal)& ThreeDTolFr,
                           const Standard_Real FirstInU,
                           const Standard_Real LastInU,
                           const Standard_Real FirstInV,
                           const Standard_Real LastInV,
                           const GeomAbs_IsoType FavorIso,
                           const GeomAbs_Shape ContInU,
                           const GeomAbs_Shape ContInV,
                           const Standard_Integer PrecisCode,
                           const Standard_Integer MaxDegInU,
                           const Standard_Integer MaxDegInV,
                           const Standard_Integer MaxPatch,
                           const AdvApp2Var_EvaluatorFunc2Var& Func,
                           AdvApprox_Cutting& UChoice,
                           AdvApprox_Cutting& VChoice)
: my1DTolerances  (OneDTol),
  my2DTolerances  (TwoDTol),
  my3DTolerances  (ThreeDTol),
  my1DTolOnFront  (OneDTolFr),
  my2DTolOnFront  (TwoDTolFr),
  my3DTolOnFront  (ThreeDTolFr),
  myFirstParInU   (FirstInU),
  myLastParInU    (LastInU),
  myFirstParInV   (FirstInV),
  myLastParInV    (LastInV),
  myFavoriteIso   (FavorIso),
  myContInU       (ContInU),
  myContInV       (ContInV),
  myPrecisionCode (PrecisCode),
  myMaxDegInU     (MaxDegInU),
  myMaxDegInV     (MaxDegInV),
  myMaxPatches    (MaxPatch),
  myDone          (Standard_False),
  myHasResult     (Standard_False),
  myDegreeInU     (0),
  myDegreeInV     (0),
  myCriterionError(0.0)
{
  myNumSubSpaces[0] = Num1DSS;
  myNumSubSpaces[1] = Num2DSS;
  myNumSubSpaces[2] = Num3DSS;

  Init();
  Perform(UChoice, VChoice, Func);
  ConvertBS();
}

//=======================================================================
//function : AdvApp2Var_ApproxAFunc2Var
//purpose  : 
//=======================================================================

 AdvApp2Var_ApproxAFunc2Var::AdvApp2Var_ApproxAFunc2Var(
                      const Standard_Integer Num1DSS,
                      const Standard_Integer Num2DSS,
                      const Standard_Integer Num3DSS,
                      const Handle(TColStd_HArray1OfReal)& OneDTol,
                      const Handle(TColStd_HArray1OfReal)& TwoDTol,
                      const Handle(TColStd_HArray1OfReal)& ThreeDTol,
                      const Handle(TColStd_HArray2OfReal)& OneDTolFr,
                      const Handle(TColStd_HArray2OfReal)& TwoDTolFr,
                      const Handle(TColStd_HArray2OfReal)& ThreeDTolFr,
                      const Standard_Real FirstInU,
                      const Standard_Real LastInU,
                      const Standard_Real FirstInV,
                      const Standard_Real LastInV,
                      const GeomAbs_IsoType FavorIso,
                      const GeomAbs_Shape ContInU,
                      const GeomAbs_Shape ContInV,
                      const Standard_Integer PrecisCode,
                      const Standard_Integer MaxDegInU,
                      const Standard_Integer MaxDegInV,
                      const Standard_Integer MaxPatch,
                      const AdvApp2Var_EvaluatorFunc2Var& Func,
                      const AdvApp2Var_Criterion& Crit,
                      AdvApprox_Cutting& UChoice,
                      AdvApprox_Cutting& VChoice)
: my1DTolerances  (OneDTol),
  my2DTolerances  (TwoDTol),
  my3DTolerances  (ThreeDTol),
  my1DTolOnFront  (OneDTolFr),
  my2DTolOnFront  (TwoDTolFr),
  my3DTolOnFront  (ThreeDTolFr),
  myFirstParInU   (FirstInU),
  myLastParInU    (LastInU),
  myFirstParInV   (FirstInV),
  myLastParInV    (LastInV),
  myFavoriteIso   (FavorIso),
  myContInU       (ContInU),
  myContInV       (ContInV),
  myPrecisionCode (PrecisCode),
  myMaxDegInU     (MaxDegInU),
  myMaxDegInV     (MaxDegInV),
  myMaxPatches    (MaxPatch),
  myDone          (Standard_False),
  myHasResult     (Standard_False),
  myDegreeInU     (0),
  myDegreeInV     (0),
  myCriterionError(0.0)
{
  myNumSubSpaces[0] = Num1DSS;
  myNumSubSpaces[1] = Num2DSS;
  myNumSubSpaces[2] = Num3DSS;

  Init();
  Perform(UChoice, VChoice, Func, Crit);
  ConvertBS();
}

//=======================================================================
//function : Init
//purpose  : Initialisation of the approximation
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::Init()
{
  Standard_Integer ifav,iu=0,iv=0,ndu,ndv;
  switch (myFavoriteIso) {
  case GeomAbs_IsoU :
    ifav = 1;
    break;
  case GeomAbs_IsoV :
    ifav = 2;
    break;
  default :
    ifav = 2;
    break;
  }
  switch (myContInU) {
  case GeomAbs_C0 :
    iu = 0;
    break;
  case GeomAbs_C1 :
    iu = 1;
    break;
  case GeomAbs_C2 :
    iu = 2;
    break;
  default :
    throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : UContinuity Error");
  }
  switch (myContInV) {
  case GeomAbs_C0 :
    iv = 0;
    break;
  case GeomAbs_C1 :
    iv = 1;
    break;
  case GeomAbs_C2 :
    iv = 2;
    break;
  default :
    throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : VContinuity Error");
  }
  ndu = Max(myMaxDegInU+1,2*iu+2);
  ndv = Max(myMaxDegInV+1,2*iv+2);
  if (ndu<2*iu+2)
    throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : UMaxDegree Error");
  if (ndv<2*iv+2)
    throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : VMaxDegree Error");
  myPrecisionCode = Max(0,Min(myPrecisionCode,3));
  AdvApp2Var_Context Conditions(ifav,iu,iv,ndu,ndv,
				myPrecisionCode,
				myNumSubSpaces[0],
                                myNumSubSpaces[1],
                                myNumSubSpaces[2],
                                my1DTolerances,
                                my2DTolerances,
                                my3DTolerances,
                                my1DTolOnFront,
                                my2DTolOnFront,
                                my3DTolOnFront);
  myConditions = Conditions;
  InitGrid(1);
}


//=======================================================================
//function : InitGrid
//purpose  : Initialisation of the approximation with regular cuttings
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::InitGrid(const Standard_Integer NbInt)
{
  Standard_Integer iu=myConditions.UOrder(),iv=myConditions.VOrder(),iint;

  AdvApp2Var_Patch M0(myFirstParInU,myLastParInU,myFirstParInV,myLastParInV,iu,iv);

  AdvApp2Var_SequenceOfPatch Net;
  Net.Append(M0);

  TColStd_SequenceOfReal TheU,TheV;
  TheU.Append(myFirstParInU);
  TheV.Append(myFirstParInV);
  TheU.Append(myLastParInU);
  TheV.Append(myLastParInV);

  AdvApp2Var_Network Result(Net,TheU,TheV);


  gp_XY UV1(myFirstParInU,myFirstParInV);
  AdvApp2Var_Node C1(UV1,iu,iv);
  gp_XY UV2(myLastParInU,myFirstParInV);
  AdvApp2Var_Node C2(UV2,iu,iv);
  gp_XY UV4(myLastParInU,myLastParInV);
  AdvApp2Var_Node C4(UV4,iu,iv);
  gp_XY UV3(myFirstParInU,myLastParInV);
  AdvApp2Var_Node C3(UV3,iu,iv);
  AdvApp2Var_SequenceOfNode Bag;
  Bag.Append(C1);
  Bag.Append(C2);
  Bag.Append(C3);
  Bag.Append(C4);

  AdvApp2Var_Iso V0(GeomAbs_IsoV,myFirstParInV,
		    myFirstParInU,myLastParInU,myFirstParInV,myLastParInV,
		    1,iu,iv);
  AdvApp2Var_Iso V1(GeomAbs_IsoV,myLastParInV,
		    myFirstParInU,myLastParInU,myFirstParInV,myLastParInV,
		    2,iu,iv);
  AdvApp2Var_Iso U0(GeomAbs_IsoU,myFirstParInU,
		    myFirstParInU,myLastParInU,myFirstParInV,myLastParInV,
		    3,iu,iv);
  AdvApp2Var_Iso U1(GeomAbs_IsoU,myLastParInU,
		    myFirstParInU,myLastParInU,myFirstParInV,myLastParInV,
		    4,iu,iv);

  AdvApp2Var_Strip BU0,BV0;
  BU0.Append(V0);
  BU0.Append(V1);
  BV0.Append(U0);
  BV0.Append(U1);

  AdvApp2Var_SequenceOfStrip UStrip,VStrip;
  UStrip.Append(BU0);
  VStrip.Append(BV0);

  AdvApp2Var_Framework Constraints(Bag,UStrip,VStrip);

// regular cutting if NbInt>1
  Standard_Real deltu = (myLastParInU-myFirstParInU)/NbInt,
                deltv = (myLastParInV-myFirstParInV)/NbInt;
  for (iint=1;iint<=NbInt-1;iint++) {
    Result.UpdateInU(myFirstParInU+iint*deltu);
    Constraints.UpdateInU(myFirstParInU+iint*deltu);
    Result.UpdateInV(myFirstParInV+iint*deltv);
    Constraints.UpdateInV(myFirstParInV+iint*deltv);
  }
  myResult = Result;
  myConstraints = Constraints;
}

//=======================================================================
//function : Perform
//purpose  : Computation of the approximation
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::Perform(const AdvApprox_Cutting& UChoice,
					 const AdvApprox_Cutting& VChoice,
					 const AdvApp2Var_EvaluatorFunc2Var& Func)
{
  ComputePatches(UChoice,VChoice,Func);
  myHasResult = myDone = Standard_True;
  Compute3DErrors();
}

//=======================================================================
//function : Perform
//purpose  : Computation of the approximation
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::Perform(const AdvApprox_Cutting& UChoice,
					 const AdvApprox_Cutting& VChoice,
					 const AdvApp2Var_EvaluatorFunc2Var& Func,
					 const AdvApp2Var_Criterion& Crit)
{
  ComputePatches(UChoice,VChoice,Func,Crit);
  myHasResult = myDone = Standard_True;
  Compute3DErrors();
  ComputeCritError();
}

//=======================================================================
//function : ComputePatches
//purpose  : Computation of the polynomial approximations
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::ComputePatches(const AdvApprox_Cutting& UChoice,
						const AdvApprox_Cutting& VChoice,
					 const AdvApp2Var_EvaluatorFunc2Var& Func)
{
  Standard_Real Udec, Vdec;
  Standard_Boolean Umore, Vmore;
  Standard_Integer NbPatch, NbU, NbV, NumDec;
  Standard_Integer FirstNA;

  while (myResult.FirstNotApprox(FirstNA)) {

// complete the set of constraints 
    ComputeConstraints(UChoice, VChoice, Func);

// discretization of constraints relative to the square
    myResult(FirstNA).Discretise(myConditions,myConstraints,Func);
    if ( ! myResult(FirstNA).IsDiscretised() ) {
      myHasResult =  myDone = Standard_False;
      throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : Surface Discretisation Error");
    }

// calculate the number and the type of autorized cuts
// depending on the max number of squares and the validity of next cuts.
    NbU = myResult.NbPatchInU();
    NbV = myResult.NbPatchInV();
    NbPatch = NbU*NbV;
    Umore = UChoice.Value(myResult(FirstNA).U0(), myResult(FirstNA).U1(),Udec);
    Vmore = VChoice.Value(myResult(FirstNA).V0(), myResult(FirstNA).V1(),Vdec);

    NumDec = 0;
    if ( ((NbPatch+NbV)<=myMaxPatches) && ((NbPatch+NbU)>myMaxPatches)
         && (Umore) ) NumDec = 1;
    if ( ((NbPatch+NbV)>myMaxPatches) && ((NbPatch+NbU)<=myMaxPatches) 
         && (Vmore) ) NumDec = 2;
    if ( ((NbPatch+NbV)<=myMaxPatches) && ((NbPatch+NbU)<=myMaxPatches) ) {
      if ( Umore ) NumDec = 3;
      if ( (NbV>NbU) && Vmore ) NumDec = 4;
    }
    if ( (NbU+1)*(NbV+1)<=myMaxPatches ) {
      if ( !Umore && !Vmore ) NumDec=0;
      if ( Umore && !Vmore ) NumDec=3;
      if ( !Umore && Vmore ) NumDec=4;
      if ( Umore && Vmore ) NumDec=5;
    }

// approximation of the square
    myResult(FirstNA).MakeApprox(myConditions,myConstraints,NumDec);

    if ( ! myResult(FirstNA).IsApproximated() ) {
      switch (myResult(FirstNA).CutSense()) {
      case 0 :
//	It is not possible to cut : the result is preserved
        if ( myResult(FirstNA).HasResult()) {
	  myResult(FirstNA).OverwriteApprox();
        }
        else {
          myHasResult =  myDone = Standard_False;
          throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : Surface Approximation Error");
        }
	break;
      case 1 :
//      It is necessary to cut in U
	myResult.UpdateInU(Udec);
	myConstraints.UpdateInU(Udec);
	break;
      case 2 :
//      It is necessary to cut in V
	myResult.UpdateInV(Vdec);
	myConstraints.UpdateInV(Vdec);
	break;
      case 3 :
//      It is necesary to cut in U and V
	myResult.UpdateInU(Udec);
	myConstraints.UpdateInU(Udec);
	myResult.UpdateInV(Vdec);
	myConstraints.UpdateInV(Vdec);
	break;
      default :
        myHasResult =  myDone = Standard_False;
        throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : Surface Approximation Error");
      }
    }
  }
}

//=======================================================================
//function : ComputePatches
//purpose  : Computation of the polynomial approximations
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::ComputePatches(const AdvApprox_Cutting& UChoice,
					 const AdvApprox_Cutting& VChoice,
					 const AdvApp2Var_EvaluatorFunc2Var& Func,
					 const AdvApp2Var_Criterion& Crit)
{
  Standard_Real Udec, Vdec, CritValue, m1=0.;
  Standard_Boolean Umore, Vmore, CritAbs = (Crit.Type() == AdvApp2Var_Absolute);
  Standard_Integer NbPatch, NbU, NbV, NbInt, NumDec;
  Standard_Integer FirstNA, decision=0;

  while (myResult.FirstNotApprox(FirstNA)) {

// complete the set of constraints 
    ComputeConstraints(UChoice, VChoice, Func, Crit);
    if (decision>0) {
      m1 = 0.;
    }

// discretize the constraints relative to the square
    myResult(FirstNA).Discretise(myConditions,myConstraints,Func);
    if ( ! myResult(FirstNA).IsDiscretised() ) {
      myHasResult =  myDone = Standard_False;
      throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : Surface Discretisation Error");
    }

// calculate the number and type of autorized cuts
// depending on the max number of squares and the validity of next cuts
    NbU = myResult.NbPatchInU();
    NbV = myResult.NbPatchInV();
    NbPatch = NbU*NbV;
    NbInt = NbU;
    Umore = UChoice.Value(myResult(FirstNA).U0(), myResult(FirstNA).U1(),Udec);
    Vmore = VChoice.Value(myResult(FirstNA).V0(), myResult(FirstNA).V1(),Vdec);

    NumDec = 0;
    if ( ((NbPatch+NbV)<=myMaxPatches) && ((NbPatch+NbU)>myMaxPatches)
         && (Umore) ) NumDec = 1;
    if ( ((NbPatch+NbV)>myMaxPatches) && ((NbPatch+NbU)<=myMaxPatches) 
         && (Vmore) ) NumDec = 2;
    if ( ((NbPatch+NbV)<=myMaxPatches) && ((NbPatch+NbU)<=myMaxPatches) ) {
      if ( Umore ) NumDec = 3;
      if ( (NbV>NbU) && Vmore ) NumDec = 4;
    }
    if ( (NbU+1)*(NbV+1)<=myMaxPatches ) {
      if ( !Umore && !Vmore ) NumDec=0;
      if ( Umore && !Vmore ) NumDec=1;
      if ( !Umore && Vmore ) NumDec=2;
      if ( Umore && Vmore ) NumDec=5;
    }

// approximation of the square
    if ( CritAbs ) {
      myResult(FirstNA).MakeApprox(myConditions,myConstraints,0);
    }
    else {
      myResult(FirstNA).MakeApprox(myConditions,myConstraints,NumDec);
    }
    if (NumDec>=3) NumDec = NumDec - 2;

// evaluation of the criterion on the square
    if ( myResult(FirstNA).HasResult() ) {
      Crit.Value(myResult(FirstNA),myConditions);
      CritValue = myResult(FirstNA).CritValue();
      if (m1<CritValue) m1 = CritValue;
    }
// is it necessary to cut ?
    decision = myResult(FirstNA).CutSense(Crit,NumDec);
    Standard_Boolean Regular = (Crit.Repartition() ==  AdvApp2Var_Regular);
//    Standard_Boolean Regular = Standard_True;
    if (Regular && decision>0) {
      NbInt++;
      InitGrid(NbInt);
    }
    else {
      switch (decision) {
      case 0 :
//	Impossible to cut : the result is preserved
	if ( myResult(FirstNA).HasResult() ) {
	  myResult(FirstNA).OverwriteApprox();
	}
	else {
	  myHasResult =  myDone = Standard_False;
	  throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : Surface Approximation Error");
	}
	break;
      case 1 :
//      It is necessary to cut in U
	myResult.UpdateInU(Udec);
	myConstraints.UpdateInU(Udec);
	break;
      case 2 :
//      It is necessary to cut in V
	myResult.UpdateInV(Vdec);
	myConstraints.UpdateInV(Vdec);
	break;
      case 3 :
//      It is necessary to cut in U and V
	myResult.UpdateInU(Udec);
	myConstraints.UpdateInU(Udec);
	myResult.UpdateInV(Vdec);
	myConstraints.UpdateInV(Vdec);
	break;
	default :
	myHasResult =  myDone = Standard_False;
	throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : Surface Approximation Error");
      }
    }
  }
}

//=======================================================================
//function : ComputeConstraints without Criterion
//purpose  : Approximation of the constraints
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::ComputeConstraints(const AdvApprox_Cutting& UChoice,
					 const AdvApprox_Cutting& VChoice,
					 const AdvApp2Var_EvaluatorFunc2Var& Func)
{
  Standard_Real dec;
  Standard_Boolean more;
  Standard_Integer ind1, ind2, NbPatch, NbU, NbV;
  AdvApp2Var_Iso Is;
  Standard_Integer indN1, indN2;
  Standard_Integer iu = myConditions.UOrder(), iv = myConditions.VOrder();
  AdvApp2Var_Node N1(iu,iv), N2(iu,iv);

  while ( myConstraints.FirstNotApprox(ind1, ind2, Is) ) {

// approximation of iso and calculation of constraints at extremities
    indN1 = myConstraints.FirstNode(Is.Type(),ind1,ind2);
    N1 = myConstraints.Node(indN1);
    indN2 = myConstraints.LastNode(Is.Type(),ind1,ind2);
    N2 = myConstraints.Node(indN2);

    Is.MakeApprox(myConditions,
		  myFirstParInU, myLastParInU,
		  myFirstParInV, myLastParInV,
		  Func, N1 , N2);

    if (Is.IsApproximated()) {
// iso is approached at the required tolerance
      myConstraints.ChangeIso(ind1,ind2,Is);
      myConstraints.ChangeNode(indN1) = N1;
      myConstraints.ChangeNode(indN2) = N2;
    }

    else {
// Approximation is not satisfactory
      NbU = myResult.NbPatchInU();
      NbV = myResult.NbPatchInV();
      if (Is.Type()==GeomAbs_IsoV) {
	NbPatch = (NbU+1)*NbV;
	more = UChoice.Value(Is.T0(),Is.T1(),dec);
      }
      else {
	NbPatch = (NbV+1)*NbU;
	more = VChoice.Value(Is.T0(),Is.T1(),dec);
      }

      if (NbPatch<=myMaxPatches && more) {
//	It is possible to cut iso
	if (Is.Type()==GeomAbs_IsoV) {
	  myResult.UpdateInU(dec);
	  myConstraints.UpdateInU(dec);
	}
	else {
	  myResult.UpdateInV(dec);
	  myConstraints.UpdateInV(dec);
	}
      }

      else {
//	It is not possible to cut : the result is preserved
	if (Is.HasResult()) {
	  Is.OverwriteApprox();
	  myConstraints.ChangeIso(ind1,ind2,Is);
	  myConstraints.ChangeNode(indN1) = N1;
	  myConstraints.ChangeNode(indN2) = N2;	
	}
	else {
	  myHasResult =  myDone = Standard_False;
	  throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : Curve Approximation Error");
	}
      }
    }
  }
}


//=======================================================================
//function : ComputeConstraints with Criterion
//purpose  : Approximation of the constraints
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::ComputeConstraints(const AdvApprox_Cutting& UChoice,
					 const AdvApprox_Cutting& VChoice,
					 const AdvApp2Var_EvaluatorFunc2Var& Func,
					 const AdvApp2Var_Criterion& Crit)
{
  Standard_Real dec;
  Standard_Boolean more, CritRel = (Crit.Type() == AdvApp2Var_Relative);
  Standard_Integer ind1, ind2, NbPatch, NbU, NbV;
  AdvApp2Var_Iso Is;
  Standard_Integer indN1, indN2;
  Standard_Integer iu = myConditions.UOrder(), iv = myConditions.VOrder();
  AdvApp2Var_Node N1(iu,iv), N2(iu,iv);

    while ( myConstraints.FirstNotApprox(ind1, ind2, Is) ) {

// approximation of the iso and calculation of constraints at the extremities
      indN1 = myConstraints.FirstNode(Is.Type(),ind1,ind2);
      N1 = myConstraints.Node(indN1);
      indN2 = myConstraints.LastNode(Is.Type(),ind1,ind2);
      N2 = myConstraints.Node(indN2);

      Is.MakeApprox(myConditions,
                    myFirstParInU, myLastParInU,
                    myFirstParInV, myLastParInV,
                    Func, N1 , N2);

      if (Is.IsApproximated()) {
// iso is approached at the required tolerance
	myConstraints.ChangeIso(ind1,ind2,Is);
	myConstraints.ChangeNode(indN1) = N1;
	myConstraints.ChangeNode(indN2) = N2;
      }

      else {
// Approximation is not satisfactory
	NbU = myResult.NbPatchInU();
	NbV = myResult.NbPatchInV();
	if (Is.Type()==GeomAbs_IsoV) {
	  NbPatch = (NbU+1)*NbV;
	  more = UChoice.Value(Is.T0(),Is.T1(),dec);
	}
	else {
	  NbPatch = (NbV+1)*NbU;
	  more = VChoice.Value(Is.T0(),Is.T1(),dec);
	}

//      To force Overwrite if the criterion is Absolute
	more = more && (CritRel);

	if (NbPatch<=myMaxPatches && more) {
//	It is possible to cut iso
	  if (Is.Type()==GeomAbs_IsoV) {
	    myResult.UpdateInU(dec);
	    myConstraints.UpdateInU(dec);
	  }
	  else {
	    myResult.UpdateInV(dec);
	    myConstraints.UpdateInV(dec);
	  }
	}

	else {
//	It is not possible to cut: the result is preserved
          if (Is.HasResult()) {
	    Is.OverwriteApprox();
	    myConstraints.ChangeIso(ind1,ind2,Is);
	    myConstraints.ChangeNode(indN1) = N1;
	    myConstraints.ChangeNode(indN2) = N2;	
          }
          else {
	    myHasResult =  myDone = Standard_False;
	    throw Standard_ConstructionError("AdvApp2Var_ApproxAFunc2Var : Curve Approximation Error");
          }
	}
      }
    }
}

//=======================================================================
//function : Compute3DErrors
//purpose  : Computation of the 3D errors
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::Compute3DErrors()
{

  Standard_Integer iesp,ipat;
  Standard_Real error_max,error_moy,error_U0,error_V0,error_U1,error_V1;
  Standard_Real Tol,F1Tol,F2Tol,F3Tol,F4Tol;
  if ( myNumSubSpaces[2] > 0 ) {
    my3DMaxError = new (TColStd_HArray1OfReal) (1,myNumSubSpaces[2]);
    my3DAverageError = new (TColStd_HArray1OfReal) (1,myNumSubSpaces[2]);
    my3DUFrontError = new (TColStd_HArray1OfReal) (1,myNumSubSpaces[2]);
    my3DVFrontError = new (TColStd_HArray1OfReal) (1,myNumSubSpaces[2]);
    for (iesp=1;iesp<=myNumSubSpaces[2];iesp++) {
      error_max = 0;
      error_moy = 0.;
      error_U0 = 0.;
      error_V0 = 0.;
      error_U1 = 0.;
      error_V1 = 0.;
      Tol = my3DTolerances->Value(iesp);
      F1Tol = my3DTolOnFront->Value(iesp,1);
      F2Tol = my3DTolOnFront->Value(iesp,2);
      F3Tol = my3DTolOnFront->Value(iesp,3);
      F4Tol = my3DTolOnFront->Value(iesp,4);
      for (ipat=1;ipat<=myResult.NbPatch();ipat++) {
	error_max = Max((myResult(ipat).MaxErrors())->Value(iesp),error_max);
	error_U0 = Max((myResult(ipat).IsoErrors())->Value(iesp,3),error_U0);
	error_U1 = Max((myResult(ipat).IsoErrors())->Value(iesp,4),error_U1);
	error_V0 = Max((myResult(ipat).IsoErrors())->Value(iesp,1),error_V0);
	error_V1 = Max((myResult(ipat).IsoErrors())->Value(iesp,2),error_V1);
	error_moy += (myResult(ipat).AverageErrors())->Value(iesp);
      }
      my3DMaxError->SetValue(iesp,error_max);
      my3DUFrontError->SetValue(iesp,Max(error_U0,error_U1));
      my3DVFrontError->SetValue(iesp,Max(error_V0,error_V1));
      error_moy /= (Standard_Real) myResult.NbPatch();
      my3DAverageError->SetValue(iesp,error_moy);
      if ( error_max>Tol 
	  || error_U0>F3Tol || error_U1>F4Tol 
	  || error_V0>F1Tol || error_V1>F2Tol) {
	myDone = Standard_False;
      }
    }
  }
}


//=======================================================================
//function : ComputeCritError
//purpose  : Computation of the max value of the Criterion
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::ComputeCritError()
{

  Standard_Integer iesp,ipat;
  Standard_Real crit_max;
  if ( myNumSubSpaces[2] > 0 ) {
    for (iesp=1;iesp<=myNumSubSpaces[2];iesp++) {
      crit_max = 0.;
      for (ipat=1;ipat<=myResult.NbPatch();ipat++) {
	crit_max = Max((myResult(ipat).CritValue()),crit_max);
      }
      myCriterionError = crit_max;
    }
  }
}

//=======================================================================
//function : ConvertBS
//purpose  : Convertion of the approximation in BSpline Surface
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::ConvertBS()
{
 // Homogeneization of degrees
  Standard_Integer iu = myConditions.UOrder(), iv = myConditions.VOrder();
  Standard_Integer ncfu = myConditions.ULimit(), ncfv = myConditions.VLimit();
  myResult.SameDegree(iu,iv,ncfu,ncfv);
  myDegreeInU = ncfu - 1;
  myDegreeInV = ncfv - 1;

 // Calculate resulting surfaces 
  mySurfaces = new ( TColGeom_HArray1OfSurface) (1,  myNumSubSpaces[2]);

  Standard_Integer j;
  TColStd_Array1OfReal UKnots (1, myResult.NbPatchInU()+1);
  for (j=1; j<=UKnots.Length(); j++) { UKnots.SetValue(j, myResult.UParameter(j)); } 
 
  TColStd_Array1OfReal VKnots (1, myResult.NbPatchInV()+1);
  for (j=1; j<=VKnots.Length(); j++) { VKnots.SetValue(j, myResult.VParameter(j)); }

 // Prepare data for conversion grid of polynoms --> poles
  Handle(TColStd_HArray1OfReal) Uint1 = 
    new (TColStd_HArray1OfReal) (1,2);
  Uint1->SetValue(1, -1);
  Uint1->SetValue(2, 1);
  Handle(TColStd_HArray1OfReal) Vint1 = 
    new (TColStd_HArray1OfReal) (1,2);
  Vint1->SetValue(1, -1);
  Vint1->SetValue(2, 1);

  Handle(TColStd_HArray1OfReal) Uint2 = 
    new (TColStd_HArray1OfReal) (1,myResult.NbPatchInU()+1);
  for (j=1; j<=Uint2->Length(); j++) { Uint2->SetValue(j, myResult.UParameter(j)); } 
  Handle(TColStd_HArray1OfReal) Vint2 = 
    new (TColStd_HArray1OfReal) (1,myResult.NbPatchInV()+1);
  for (j=1; j<=Vint2->Length(); j++) { Vint2->SetValue(j, myResult.VParameter(j)); } 

  Standard_Integer nmax = myResult.NbPatchInU()*myResult.NbPatchInV(),
                   Size_eq = myConditions.ULimit() * myConditions.VLimit() * 3;

  Handle(TColStd_HArray2OfInteger) NbCoeff = 
    new (TColStd_HArray2OfInteger) (1, nmax, 1, 2);
  Handle(TColStd_HArray1OfReal) Poly = 
    new (TColStd_HArray1OfReal) (1, nmax * Size_eq);

  Standard_Integer SSP, i;
  for (SSP=1; SSP <= myNumSubSpaces[2]; SSP++) { 

    // Creation of the grid of polynoms
    Standard_Integer n=0,icf=1,ieq;
    for (j=1; j<=myResult.NbPatchInV(); j++) {
      for (i=1; i<=myResult.NbPatchInU(); i++) {
	n++;
	NbCoeff->SetValue(n,1, myResult.Patch(i,j).NbCoeffInU());
	NbCoeff->SetValue(n,2, myResult.Patch(i,j).NbCoeffInV());
	for (ieq=1; ieq<=Size_eq;ieq++) {
	  Poly->SetValue(icf,(myResult.Patch(i,j).Coefficients(SSP,myConditions))
                                  ->Value(ieq));
	  icf++;
	}
      }
    }
  
    // Conversion into poles
    Convert_GridPolynomialToPoles CvP (myResult.NbPatchInU(),myResult.NbPatchInV(),
				       iu,iv,myMaxDegInU,myMaxDegInV,NbCoeff,
				       Poly,Uint1,Vint1,Uint2,Vint2);
    if ( !CvP.IsDone() ) { myDone = Standard_False; }
   
    // Conversion into BSpline
    mySurfaces->ChangeValue(SSP) = new (Geom_BSplineSurface) 
	( CvP.Poles()->Array2(),   
	  CvP.UKnots()->Array1(),  CvP.VKnots()->Array1(),
	  CvP.UMultiplicities()->Array1(), CvP.VMultiplicities()->Array1(),
	  CvP.UDegree(), CvP.VDegree() );
  }
}

//=======================================================================
//function : MaxError
//purpose  : 
//=======================================================================

Handle(TColStd_HArray1OfReal)
 AdvApp2Var_ApproxAFunc2Var::MaxError(const Standard_Integer Dimension) const
{
  Handle (TColStd_HArray1OfReal) EPtr;
  if (Dimension <1 || Dimension >3) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::MaxError : Dimension must be equal to 1,2 or 3 !");
  }
  switch (Dimension) {
  case 1:
    EPtr = my1DMaxError;
    break;
  case 2:
    EPtr = my2DMaxError;
    break;
  case 3:
    EPtr = my3DMaxError;
    break;
  }
  return EPtr;
}

//=======================================================================
//function : AverageError
//purpose  : 
//=======================================================================

Handle(TColStd_HArray1OfReal)
 AdvApp2Var_ApproxAFunc2Var::AverageError(const Standard_Integer Dimension) const 
{
  Handle (TColStd_HArray1OfReal) EPtr;
  if (Dimension <1 || Dimension >3) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::AverageError : Dimension must be equal to 1,2 or 3 !");
  }
  switch (Dimension) {
  case 1:
    EPtr = my1DAverageError;
    break;
  case 2:
    EPtr = my2DAverageError;
    break;
  case 3:
    EPtr = my3DAverageError;
    break;
  }
  return EPtr;
}

//=======================================================================
//function : UFrontError
//purpose  : 
//=======================================================================

Handle(TColStd_HArray1OfReal)
 AdvApp2Var_ApproxAFunc2Var::UFrontError(const Standard_Integer Dimension) const 
{
  Handle (TColStd_HArray1OfReal) EPtr;
  if (Dimension <1 || Dimension >3) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::UFrontError : Dimension must be equal to 1,2 or 3 !");
  }
  switch (Dimension) {
  case 1:
    EPtr = my1DUFrontError;
    break;
  case 2:
    EPtr = my2DUFrontError;
    break;
  case 3:
    EPtr = my3DUFrontError;
    break;
  }
  return EPtr;
}

//=======================================================================
//function : VFrontError
//purpose  : 
//=======================================================================

Handle(TColStd_HArray1OfReal)
 AdvApp2Var_ApproxAFunc2Var::VFrontError(const Standard_Integer Dimension) const 
{
  Handle (TColStd_HArray1OfReal) EPtr;
  if (Dimension <=0 || Dimension >3) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::VFrontError : Dimension must be equal to 1,2 or 3 !");
  }
  switch (Dimension) {
  case 1:
    EPtr = my1DVFrontError;
    break;
  case 2:
    EPtr = my2DVFrontError;
    break;
  case 3:
    EPtr = my3DVFrontError;
    break;
  }
  return EPtr;
}

//=======================================================================
//function : MaxError
//purpose  : 
//=======================================================================

Standard_Real
 AdvApp2Var_ApproxAFunc2Var::MaxError(const Standard_Integer Dimension,
				      const Standard_Integer SSPIndex) const 
{
  if (Dimension !=3 || SSPIndex !=1) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::MaxError: ONE Surface 3D only !");
  }
  Handle (TColStd_HArray1OfReal) EPtr = MaxError(Dimension);
  return EPtr->Value(SSPIndex);
}

//=======================================================================
//function : AverageError
//purpose  : 
//=======================================================================

Standard_Real
 AdvApp2Var_ApproxAFunc2Var::AverageError(const Standard_Integer Dimension,
					  const Standard_Integer SSPIndex) const 
{
  if (Dimension !=3 || SSPIndex !=1) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::AverageError : ONE Surface 3D only !");
  }
  Handle (TColStd_HArray1OfReal) EPtr = AverageError(Dimension);
  return EPtr->Value(SSPIndex);
}

//=======================================================================
//function : UFrontError
//purpose  : 
//=======================================================================

Standard_Real
 AdvApp2Var_ApproxAFunc2Var::UFrontError(const Standard_Integer Dimension,
					 const Standard_Integer SSPIndex) const 
{
  if (Dimension !=3 || SSPIndex !=1) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::UFrontError : ONE Surface 3D only !");
  }
  Handle (TColStd_HArray1OfReal) EPtr = UFrontError(Dimension);
  return EPtr->Value(SSPIndex);
}

//=======================================================================
//function : VFrontError
//purpose  : 
//=======================================================================

Standard_Real
 AdvApp2Var_ApproxAFunc2Var::VFrontError(const Standard_Integer Dimension,
					 const Standard_Integer SSPIndex) const 
{
  if (Dimension !=3 || SSPIndex !=1) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::VFrontError : ONE Surface 3D only !");
  }
  Handle (TColStd_HArray1OfReal) EPtr = VFrontError(Dimension);
  return EPtr->Value(SSPIndex);
}


//=======================================================================
//function : CritError
//purpose  : 
//=======================================================================

Standard_Real
 AdvApp2Var_ApproxAFunc2Var::CritError(const Standard_Integer Dimension,
				       const Standard_Integer SSPIndex) const 
{
  if (Dimension !=3 || SSPIndex !=1) {
    throw Standard_OutOfRange("AdvApp2Var_ApproxAFunc2Var::CritError: ONE Surface 3D only !");
  }
  return myCriterionError;
}

//=======================================================================
//function : Dump
//purpose  : 
//=======================================================================

void AdvApp2Var_ApproxAFunc2Var::Dump(Standard_OStream& o) const 
{
  Standard_Integer iesp=1,NbKU,NbKV,ik;
  o<<std::endl;
  if (!myHasResult) { o<<"No result"<<std::endl; }
  else {
    o<<"There is a result";
    if (myDone) {
      o<<" within the requested tolerance "<<my3DTolerances->Value(iesp)<<std::endl;
    }
    else if (my3DMaxError->Value(iesp)>my3DTolerances->Value(iesp)) {
      o<<" WITHOUT the requested tolerance "<<my3DTolerances->Value(iesp)<<std::endl;
    }
    else {
      o<<" WITHOUT the requested continuities "<<std::endl;
    }
    o<<std::endl;
    o<<"Result max error :"<<my3DMaxError->Value(iesp)<<std::endl;
    o<<"Result average error :"<<my3DAverageError->Value(iesp)<<std::endl;
    o<<"Result max error on U frontiers :"<<my3DUFrontError->Value(iesp)<<std::endl;
    o<<"Result max error on V frontiers :"<<my3DVFrontError->Value(iesp)<<std::endl;
    o<<std::endl;
    o<<"Degree of Bezier patches in U : "<<myDegreeInU
      <<"  in V : "<<myDegreeInV<<std::endl;
    o<<std::endl;
    Handle(Geom_BSplineSurface) S
      = Handle(Geom_BSplineSurface)::DownCast(mySurfaces->Value(iesp));
    o<<"Number of poles in U : "<<S->NbUPoles()
      <<"  in V : "<<S->NbVPoles()<<std::endl;
    o<<std::endl;
    NbKU = S->NbUKnots();
    NbKV = S->NbVKnots();
    o<<"Number of knots in U : "<<NbKU<<std::endl;
    for (ik=1;ik<=NbKU;ik++) {
      o<<"   "<<ik<<" : "<<S->UKnot(ik)<<"   mult : "<<S->UMultiplicity(ik)<<std::endl;
    }
    o<<std::endl;
    o<<"Number of knots in V : "<<NbKV<<std::endl;
    for (ik=1;ik<=NbKV;ik++) {
      o<<"   "<<ik<<" : "<<S->VKnot(ik)<<"   mult : "<<S->VMultiplicity(ik)<<std::endl;
    }
    o<<std::endl;
  }
}
