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.

// lpa, le 11/09/91

// Application of the corrected gradient method to minimize
// F  = sum(||C(ui, Poles(ui)) - ptli||2.
// The conjugate gradient method is implemented in the mathematical
// library: math_BFGS.
// This algorithm must be called only when dealing with a set
// of constrained points (other than at extremities). Indeed, the call to the
// function F to minimize implies a call to ParLeastSquare and ResConstraint.
// If this is not the case, the call to ResConstraint is equivalent to a
// second least squares resolution, thus wasting a lot of time.

#define No_Standard_RangeError
#define No_Standard_OutOfRange

#include <AppParCurves_Constraint.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 <NCollection_Array1.hxx>
#include <BSplCLib.hxx>
#include <PLib.hxx>

// #define AppParCurves_Gradient_BFGS BFGS_/**/AppParCurves_Gradient

AppParCurves_Gradient::AppParCurves_Gradient(
  const MultiLine&                                                       SSP,
  const int                                                              FirstPoint,
  const int                                                              LastPoint,
  const occ::handle<NCollection_HArray1<AppParCurves_ConstraintCouple>>& TheConstraints,
  math_Vector&                                                           Parameters,
  const int                                                              Deg,
  const double                                                           Tol3d,
  const double                                                           Tol2d,
  const int                                                              NbIterations)
    : ParError(FirstPoint, LastPoint, 0.0),
      AvError(0.0),
      MError3d(0.0),
      MError2d(0.0)
{

  //  bool grad = true;
  int    j, k, i2, l;
  double UF, DU, Fval = 0.0, FU, DFU;
  int    nbP3d   = ToolLine::NbP3d(SSP);
  int    nbP2d   = ToolLine::NbP2d(SSP);
  int    mynbP3d = nbP3d, mynbP2d = nbP2d;
  int    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 = false;

  if (nbP3d == 0)
    mynbP3d = 1;
  if (nbP2d == 0)
    mynbP2d = 1;
  NCollection_Array1<gp_Pnt>   TabP(1, mynbP3d);
  NCollection_Array1<gp_Pnt2d> TabP2d(1, mynbP2d);
  NCollection_Array1<gp_Vec>   TabV(1, mynbP3d);
  NCollection_Array1<gp_Vec2d> TabV2d(1, mynbP2d);

  // Calculation of the function F= sum(||C(ui)-Ptli||2):
  // Call to a function inheriting from MultipleVarFunctionWithGradient
  // to compute F and grad_F.
  // ================================================================

  AppParCurves_ParFunction MyF(SSP, FirstPoint, LastPoint, TheConstraints, Parameters, Deg);

  if (!MyF.Value(Parameters, Fval))
  {
    Done = false;
    return;
  }

  SCU                              = MyF.CurveValue();
  int                          deg = SCU.NbPoles() - 1;
  NCollection_Array1<gp_Pnt>   TabPole(1, deg + 1), TabCoef(1, deg + 1);
  NCollection_Array1<gp_Pnt2d> TabPole2d(1, deg + 1), TabCoef2d(1, deg + 1);
  NCollection_Array1<gp_Pnt>   TheCoef(1, (deg + 1) * mynbP3d);
  NCollection_Array1<gp_Pnt2d> TheCoef2d(1, (deg + 1) * mynbP2d);

  // Storage of curve poles for projection:
  // ============================================
  i2 = 0;
  for (k = 1; k <= nbP3d; k++)
  {
    SCU.Curve(k, TabPole);
    BSplCLib::PolesCoefficients(TabPole, PLib::NoWeights(), TabCoef, PLib::NoWeights());
    for (j = 1; j <= deg + 1; j++)
      TheCoef(j + i2) = TabCoef(j);
    i2 += deg + 1;
  }
  i2 = 0;
  for (k = 1; k <= nbP2d; k++)
  {
    SCU.Curve(nbP3d + k, TabPole2d);
    BSplCLib::PolesCoefficients(TabPole2d, PLib::NoWeights(), TabCoef2d, PLib::NoWeights());
    for (j = 1; j <= deg + 1; j++)
      TheCoef2d(j + i2) = TabCoef2d(j);
    i2 += deg + 1;
  }

  //  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.

  // Iteration de Projection:
  // =======================
  for (j = FirstPoint + 1; j <= LastPoint - 1; j++)
  {
    UF = Parameters(j);
    if (nbP != 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;
    for (k = 1; k <= nbP3d; k++)
    {
      for (l = 1; l <= deg + 1; l++)
        TabCoef(l) = TheCoef(l + i2);
      i2 += deg + 1;
      BSplCLib::CoefsD1(UF, TabCoef, BSplCLib::NoWeights(), Pt, V1);
      MyV = gp_Vec(Pt, TabP(k));
      FU += MyV * V1;
      DFU += V1.SquareMagnitude();
    }
    i2 = 0;
    for (k = 1; k <= nbP2d; k++)
    {
      for (l = 1; l <= deg + 1; l++)
        TabCoef2d(l) = TheCoef2d(l + i2);
      i2 += deg + 1;
      BSplCLib::CoefsD1(UF, TabCoef2d, BSplCLib::NoWeights(), Pt2d, V12d);
      MyV2d = gp_Vec2d(Pt2d, TabP2d(k));
      FU += MyV2d * V12d;
      DFU += V12d.SquareMagnitude();
    }

    if (DFU >= RealEpsilon())
    {
      DU = FU / DFU;
      DU = std::copysign(std::min(5.e-02, std::abs(DU)), DU);
      UF += DU;
      Parameters(j) = UF;
    }
  }

  if (!MyF.Value(Parameters, Fval))
  {
    SCU  = AppParCurves_MultiCurve();
    Done = false;
    return;
  }
  MError3d = MyF.MaxError3d();
  MError2d = MyF.MaxError2d();

  if (MError3d <= Tol3d && MError2d <= Tol2d)
  {
    Done = true;
    SCU  = MyF.CurveValue();
  }
  else if (NbIterations != 0)
  {
    // NbIterations de gradient conjugue:
    // =================================
    double                     Eps = 1.e-07;
    AppParCurves_Gradient_BFGS FResol(MyF, Parameters, Tol3d, Tol2d, Eps, NbIterations);
    Parameters = MyF.NewParameters();
    SCU        = MyF.CurveValue();
  }

  AvError = 0.;
  for (j = FirstPoint; j <= LastPoint; j++)
  {
    // Recherche des erreurs maxi et moyenne a un index donne:
    for (k = 1; k <= nbP; k++)
    {
      ParError(j) = std::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 = true;
  }
}

AppParCurves_MultiCurve AppParCurves_Gradient::Value() const
{
  return SCU;
}

bool AppParCurves_Gradient::IsDone() const
{
  return Done;
}

double AppParCurves_Gradient::Error(const int Index) const
{
  return ParError(Index);
}

double AppParCurves_Gradient::AverageError() const
{
  return AvError;
}

double AppParCurves_Gradient::MaxError3d() const
{
  return MError3d;
}

double AppParCurves_Gradient::MaxError2d() const
{
  return MError2d;
}