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: More...

#include <PLib_HermitJacobi.hxx>

Public Member Functions
	PLib_HermitJacobi (const int WorkDegree, const GeomAbs_Shape ConstraintOrder)
	Initialize the polynomial class Degree has to be <= 30 ConstraintOrder has to be GeomAbs_C0 GeomAbs_C1 GeomAbs_C2.
double	MaxError (const int Dimension, double &HermJacCoeff, const int NewDegree) const
	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.
void	ReduceDegree (const int Dimension, const int MaxDegree, const double Tol, double &HermJacCoeff, int &NewDegree, double &MaxError) 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.
double	AverageError (const int Dimension, double &HermJacCoeff, const int NewDegree) const
void	ToCoefficients (const int Dimension, const int Degree, const NCollection_Array1< double > &HermJacCoeff, NCollection_Array1< double > &Coefficients) const
	Convert the polynomial P(t) = H(t) + W(t) Q(t) in the canonical base.
void	D0 (const double U, NCollection_Array1< double > &BasisValue) const
	Compute the values of the basis functions in u.
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.
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.
void	D3 (const double U, NCollection_Array1< double > &BasisValue, NCollection_Array1< double > &BasisD1, NCollection_Array1< double > &BasisD2, NCollection_Array1< double > &BasisD3) const
	Compute the values and the derivatives values of the basis functions in u.
int	WorkDegree () const noexcept
	returns WorkDegree
int	NivConstr () const noexcept
	returns NivConstr

Protected Member Functions
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
	Compute the values and the derivatives values of the basis functions in u.

Detailed Description

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:

c0(1)      c0(2) ....       c0(Dimension)
c1(1)      c1(2) ....       c1(Dimension)
 
cDegree(1) cDegree(2) ....  cDegree(Dimension)

The coefficients

c0(1) c0(2) .... c0(Dimension)

c2*ordre+1(1) ... c2*ordre+1(dimension)

represents the part of the polynomial in the Hermit's base: H(t)

H(t) = c0H00(t) + c1H01(t) + ...c(iordre)H(0 ;iorder)+ c(iordre+1)H10(t)+...

c

const GLubyte * c

Definition OpenGl_glext.h:21581

t

GLdouble GLdouble t

Definition OpenGl_glext.h:330

The following coefficients represents the part of the polynomial in the Jacobi base ie Q(t)

Q(t) = c2*iordre+2 J0(t) + ...+ cDegree JDegree-2*iordre-2

Constructor & Destructor Documentation

◆ PLib_HermitJacobi()

PLib_HermitJacobi::PLib_HermitJacobi	(	const int	WorkDegree,
		const GeomAbs_Shape	ConstraintOrder )

Initialize the polynomial class Degree has to be <= 30 ConstraintOrder has to be GeomAbs_C0 GeomAbs_C1 GeomAbs_C2.

Member Function Documentation

◆ AverageError()

double PLib_HermitJacobi::AverageError	(	const int	Dimension,
		double &	HermJacCoeff,
		const int	NewDegree ) const

◆ D0()

void PLib_HermitJacobi::D0	(	const double	U,
		NCollection_Array1< double > &	BasisValue ) const

Compute the values of the basis functions in u.

◆ D0123()

void PLib_HermitJacobi::D0123	(	const int	NDerive,
		const double	U,
		NCollection_Array1< double > &	BasisValue,
		NCollection_Array1< double > &	BasisD1,
		NCollection_Array1< double > &	BasisD2,
		NCollection_Array1< double > &	BasisD3 ) const

protected

Compute the values and the derivatives values of the basis functions in u.

◆ D1()

void PLib_HermitJacobi::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.

◆ D2()

void PLib_HermitJacobi::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.

◆ D3()

void PLib_HermitJacobi::D3	(	const double	U,
		NCollection_Array1< double > &	BasisValue,
		NCollection_Array1< double > &	BasisD1,
		NCollection_Array1< double > &	BasisD2,
		NCollection_Array1< double > &	BasisD3 ) const

Compute the values and the derivatives values of the basis functions in u.

◆ MaxError()

double PLib_HermitJacobi::MaxError	(	const int	Dimension,
		double &	HermJacCoeff,
		const int	NewDegree ) const

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.

◆ NivConstr()

int PLib_HermitJacobi::NivConstr ( ) const

inlinenoexcept

returns NivConstr

◆ ReduceDegree()

void PLib_HermitJacobi::ReduceDegree	(	const int	Dimension,
		const int	MaxDegree,
		const double	Tol,
		double &	HermJacCoeff,
		int &	NewDegree,
		double &	MaxError ) 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.

◆ ToCoefficients()

void PLib_HermitJacobi::ToCoefficients	(	const int	Dimension,
		const int	Degree,
		const NCollection_Array1< double > &	HermJacCoeff,
		NCollection_Array1< double > &	Coefficients ) const

Convert the polynomial P(t) = H(t) + W(t) Q(t) in the canonical base.

◆ WorkDegree()

int PLib_HermitJacobi::WorkDegree ( ) const

inlinenoexcept

returns WorkDegree

The documentation for this class was generated from the following file:

PLib_HermitJacobi.hxx

Public Member Functions

Protected Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ PLib_HermitJacobi()

Member Function Documentation

◆ AverageError()

◆ D0()

◆ D0123()

◆ D1()

◆ D2()

◆ D3()

◆ MaxError()

◆ NivConstr()

◆ ReduceDegree()

◆ ToCoefficients()

◆ WorkDegree()