// Created on: 1997-10-22
// Created by: Philippe MANGIN
// Copyright (c) 1997-1999 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.

#ifndef _PLib_HermitJacobi_HeaderFile
#define _PLib_HermitJacobi_HeaderFile

#include "Standard.hxx"

#include "NCollection_Array1.hxx"
#include "Standard_Integer.hxx"
#include "GeomAbs_Shape.hxx"
#include "PLib_JacobiPolynomial.hxx"

//! This class provides method to work with Jacobi Polynomials
//! relatively to an order of constraint
//! q = myWorkDegree-2*(myNivConstr+1)
//! Jk(t) for k=0,q compose the Jacobi Polynomial base relatively to the weight W(t)
//! iorder is the integer value for the constraints:
//! iorder = 0 <=> ConstraintOrder = GeomAbs_C0
//! iorder = 1 <=> ConstraintOrder = GeomAbs_C1
//! iorder = 2 <=> ConstraintOrder = GeomAbs_C2
//! P(t) = H(t) + W(t) * Q(t) Where W(t) = (1-t**2)**(2*iordre+2)
//! the coefficients JacCoeff represents P(t) JacCoeff are stored as follow:
//! @code
//! c0(1)      c0(2) ....       c0(Dimension)
//! c1(1)      c1(2) ....       c1(Dimension)
//!
//! cDegree(1) cDegree(2) ....  cDegree(Dimension)
//! @endcode
//! The coefficients
//! @code
//! c0(1)                  c0(2) ....            c0(Dimension)
//! c2*ordre+1(1)                ...          c2*ordre+1(dimension)
//! @endcode
//! represents the part of the polynomial in the
//! Hermit's base: H(t)
//! @code
//! H(t) = c0H00(t) + c1H01(t) + ...c(iordre)H(0 ;iorder)+ c(iordre+1)H10(t)+...
//! @endcode
//! The following coefficients represents the part of the
//! polynomial in the Jacobi base ie Q(t)
//! @code
//! Q(t) = c2*iordre+2  J0(t) + ...+ cDegree JDegree-2*iordre-2
//! @endcode
class PLib_HermitJacobi
{

public:
  //! Initialize the polynomial class
  //! Degree has to be <= 30
  //! ConstraintOrder has to be GeomAbs_C0
  //! GeomAbs_C1
  //! GeomAbs_C2
  Standard_EXPORT PLib_HermitJacobi(const int WorkDegree, const GeomAbs_Shape ConstraintOrder);

  //! This method computes the maximum error on the polynomial
  //! W(t) Q(t) obtained by missing the coefficients of JacCoeff from
  //! NewDegree +1 to Degree
  Standard_EXPORT double MaxError(const int Dimension,
                                  double&   HermJacCoeff,
                                  const int NewDegree) const;

  //! Compute NewDegree <= MaxDegree so that MaxError is lower
  //! than Tol.
  //! MaxError can be greater than Tol if it is not possible
  //! to find a NewDegree <= MaxDegree.
  //! In this case NewDegree = MaxDegree
  Standard_EXPORT void ReduceDegree(const int    Dimension,
                                    const int    MaxDegree,
                                    const double Tol,
                                    double&      HermJacCoeff,
                                    int&         NewDegree,
                                    double&      MaxError) const;

  Standard_EXPORT double AverageError(const int Dimension,
                                      double&   HermJacCoeff,
                                      const int NewDegree) const;

  //! Convert the polynomial P(t) = H(t) + W(t) Q(t) in the canonical base.
  Standard_EXPORT void ToCoefficients(const int                         Dimension,
                                      const int                         Degree,
                                      const NCollection_Array1<double>& HermJacCoeff,
                                      NCollection_Array1<double>&       Coefficients) const;

  //! Compute the values of the basis functions in u
  Standard_EXPORT void D0(const double U, NCollection_Array1<double>& BasisValue) const;

  //! Compute the values and the derivatives values of
  //! the basis functions in u
  Standard_EXPORT void D1(const double                U,
                          NCollection_Array1<double>& BasisValue,
                          NCollection_Array1<double>& BasisD1) const;

  //! Compute the values and the derivatives values of
  //! the basis functions in u
  Standard_EXPORT void D2(const double                U,
                          NCollection_Array1<double>& BasisValue,
                          NCollection_Array1<double>& BasisD1,
                          NCollection_Array1<double>& BasisD2) const;

  //! Compute the values and the derivatives values of
  //! the basis functions in u
  Standard_EXPORT void D3(const double                U,
                          NCollection_Array1<double>& BasisValue,
                          NCollection_Array1<double>& BasisD1,
                          NCollection_Array1<double>& BasisD2,
                          NCollection_Array1<double>& BasisD3) const;

  //! returns WorkDegree
  int WorkDegree() const noexcept { return myJacobi.WorkDegree(); }

  //! returns NivConstr
  int NivConstr() const noexcept { return myJacobi.NivConstr(); }

protected:
  //! Compute the values and the derivatives values of
  //! the basis functions in u
  Standard_EXPORT void D0123(const int                   NDerive,
                             const double                U,
                             NCollection_Array1<double>& BasisValue,
                             NCollection_Array1<double>& BasisD1,
                             NCollection_Array1<double>& BasisD2,
                             NCollection_Array1<double>& BasisD3) const;

private:
  const PLib_JacobiPolynomial myJacobi;
};

#endif // _PLib_HermitJacobi_HeaderFile