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 weigth 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) = R(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_JacobiPolynomial.hxx>

Inheritance diagram for PLib_JacobiPolynomial:

[legend]

Public Member Functions
	PLib_JacobiPolynomial (const Standard_Integer WorkDegree, const GeomAbs_Shape ConstraintOrder)
	Initialize the polynomial class Degree has to be <= 30 ConstraintOrder has to be GeomAbs_C0 GeomAbs_C1 GeomAbs_C2.

void	Points (const Standard_Integer NbGaussPoints, TColStd_Array1OfReal &TabPoints) const
	returns the Jacobi Points for Gauss integration ie the positive values of the Legendre roots by increasing values NbGaussPoints is the number of points chosen for the integral computation. TabPoints (0,NbGaussPoints/2) TabPoints (0) is loaded only for the odd values of NbGaussPoints The possible values for NbGaussPoints are : 8, 10, 15, 20, 25, 30, 35, 40, 50, 61 NbGaussPoints must be greater than Degree

void	Weights (const Standard_Integer NbGaussPoints, TColStd_Array2OfReal &TabWeights) const
	returns the Jacobi weigths for Gauss integration only for the positive values of the Legendre roots in the order they are given by the method Points NbGaussPoints is the number of points chosen for the integral computation. TabWeights (0,NbGaussPoints/2,0,Degree) TabWeights (0,.) are only loaded for the odd values of NbGaussPoints The possible values for NbGaussPoints are : 8 , 10 , 15 ,20 ,25 , 30, 35 , 40 , 50 , 61 NbGaussPoints must be greater than Degree

void	MaxValue (TColStd_Array1OfReal &TabMax) const
	this method loads for k=0,q the maximum value of abs ( W(t)Jk(t) )for t bellonging to [-1,1] This values are loaded is the array TabMax(0,myWorkDegree-2(myNivConst+1)) MaxValue ( me ; TabMaxPointer : in out Real );

Standard_Real	MaxError (const Standard_Integer Dimension, Standard_Real &JacCoeff, const Standard_Integer 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 Standard_Integer Dimension, const Standard_Integer MaxDegree, const Standard_Real Tol, Standard_Real &JacCoeff, Standard_Integer &NewDegree, Standard_Real &MaxError) const override
	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_Real	AverageError (const Standard_Integer Dimension, Standard_Real &JacCoeff, const Standard_Integer NewDegree) const

void	ToCoefficients (const Standard_Integer Dimension, const Standard_Integer Degree, const TColStd_Array1OfReal &JacCoeff, TColStd_Array1OfReal &Coefficients) const override
	Convert the polynomial P(t) = R(t) + W(t) Q(t) in the canonical base.

void	D0 (const Standard_Real U, TColStd_Array1OfReal &BasisValue) override
	Compute the values of the basis functions in u.

void	D1 (const Standard_Real U, TColStd_Array1OfReal &BasisValue, TColStd_Array1OfReal &BasisD1) override
	Compute the values and the derivatives values of the basis functions in u.

void	D2 (const Standard_Real U, TColStd_Array1OfReal &BasisValue, TColStd_Array1OfReal &BasisD1, TColStd_Array1OfReal &BasisD2) override
	Compute the values and the derivatives values of the basis functions in u.

void	D3 (const Standard_Real U, TColStd_Array1OfReal &BasisValue, TColStd_Array1OfReal &BasisD1, TColStd_Array1OfReal &BasisD2, TColStd_Array1OfReal &BasisD3) override
	Compute the values and the derivatives values of the basis functions in u.

Standard_Integer	WorkDegree () const override
	returns WorkDegree

Standard_Integer	NivConstr () const
	returns NivConstr

Public Member Functions inherited from PLib_Base
Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor.

	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing.

Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter.

virtual	~Standard_Transient ()
	Destructor must be virtual.

virtual const opencascade::handle< Standard_Type > &	DynamicType () const
	Returns a type descriptor about this object.

Standard_Boolean	IsInstance (const opencascade::handle< Standard_Type > &theType) const
	Returns a true value if this is an instance of Type.

Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName.

Standard_Boolean	IsKind (const opencascade::handle< Standard_Type > &theType) const
	Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Boolean	IsKind (const Standard_CString theTypeName) const
	Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Transient *	This () const
	Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero.

Standard_Integer	GetRefCount () const noexcept
	Get the reference counter of this object.

void	IncrementRefCounter () noexcept
	Increments the reference counter of this object.

Standard_Integer	DecrementRefCounter () noexcept
	Decrements the reference counter of this object; returns the decremented value.

virtual void	Delete () const
	Memory deallocator for transient classes.

Additional Inherited Members
Public Types inherited from Standard_Transient
typedef void	base_type
	Returns a type descriptor about this object.

Static Public Member Functions inherited from Standard_Transient
static constexpr const char *	get_type_name ()
	Returns a type descriptor about this object.

static const opencascade::handle< Standard_Type > &	get_type_descriptor ()
	Returns type descriptor of Standard_Transient class.

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 weigth 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) = R(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 canonical base: R(t) R(t) = c0 + c1 t + ...+ c2*iordre+1 t**2*iordre+1 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_JacobiPolynomial()

PLib_JacobiPolynomial::PLib_JacobiPolynomial	(	const Standard_Integer	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()

Standard_Real PLib_JacobiPolynomial::AverageError	(	const Standard_Integer	Dimension,
		Standard_Real &	JacCoeff,
		const Standard_Integer	NewDegree ) const

◆ D0()

void PLib_JacobiPolynomial::D0	(	const Standard_Real	U,
		TColStd_Array1OfReal &	BasisValue )

overridevirtual

Compute the values of the basis functions in u.

Implements PLib_Base.

◆ D1()

void PLib_JacobiPolynomial::D1	(	const Standard_Real	U,
		TColStd_Array1OfReal &	BasisValue,
		TColStd_Array1OfReal &	BasisD1 )

overridevirtual

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

Implements PLib_Base.

◆ D2()

void PLib_JacobiPolynomial::D2	(	const Standard_Real	U,
		TColStd_Array1OfReal &	BasisValue,
		TColStd_Array1OfReal &	BasisD1,
		TColStd_Array1OfReal &	BasisD2 )

overridevirtual

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

Implements PLib_Base.

◆ D3()

void PLib_JacobiPolynomial::D3	(	const Standard_Real	U,
		TColStd_Array1OfReal &	BasisValue,
		TColStd_Array1OfReal &	BasisD1,
		TColStd_Array1OfReal &	BasisD2,
		TColStd_Array1OfReal &	BasisD3 )

overridevirtual

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

Implements PLib_Base.

◆ MaxError()

Standard_Real PLib_JacobiPolynomial::MaxError	(	const Standard_Integer	Dimension,
		Standard_Real &	JacCoeff,
		const Standard_Integer	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.

◆ MaxValue()

void PLib_JacobiPolynomial::MaxValue ( TColStd_Array1OfReal & TabMax ) const

this method loads for k=0,q the maximum value of abs ( W(t)*Jk(t) )for t bellonging to [-1,1] This values are loaded is the array TabMax(0,myWorkDegree-2*(myNivConst+1)) MaxValue ( me ; TabMaxPointer : in out Real );

◆ NivConstr()

Standard_Integer PLib_JacobiPolynomial::NivConstr ( ) const

returns NivConstr

◆ Points()

void PLib_JacobiPolynomial::Points	(	const Standard_Integer	NbGaussPoints,
		TColStd_Array1OfReal &	TabPoints ) const

returns the Jacobi Points for Gauss integration ie the positive values of the Legendre roots by increasing values NbGaussPoints is the number of points chosen for the integral computation. TabPoints (0,NbGaussPoints/2) TabPoints (0) is loaded only for the odd values of NbGaussPoints The possible values for NbGaussPoints are : 8, 10, 15, 20, 25, 30, 35, 40, 50, 61 NbGaussPoints must be greater than Degree

◆ ReduceDegree()

void PLib_JacobiPolynomial::ReduceDegree	(	const Standard_Integer	Dimension,
		const Standard_Integer	MaxDegree,
		const Standard_Real	Tol,
		Standard_Real &	JacCoeff,
		Standard_Integer &	NewDegree,
		Standard_Real &	MaxError ) const

overridevirtual

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.

Implements PLib_Base.

◆ ToCoefficients()

void PLib_JacobiPolynomial::ToCoefficients	(	const Standard_Integer	Dimension,
		const Standard_Integer	Degree,
		const TColStd_Array1OfReal &	JacCoeff,
		TColStd_Array1OfReal &	Coefficients ) const

overridevirtual

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

Implements PLib_Base.

◆ Weights()

void PLib_JacobiPolynomial::Weights	(	const Standard_Integer	NbGaussPoints,
		TColStd_Array2OfReal &	TabWeights ) const

returns the Jacobi weigths for Gauss integration only for the positive values of the Legendre roots in the order they are given by the method Points NbGaussPoints is the number of points chosen for the integral computation. TabWeights (0,NbGaussPoints/2,0,Degree) TabWeights (0,.) are only loaded for the odd values of NbGaussPoints The possible values for NbGaussPoints are : 8 , 10 , 15 ,20 ,25 , 30, 35 , 40 , 50 , 61 NbGaussPoints must be greater than Degree

◆ WorkDegree()

Standard_Integer PLib_JacobiPolynomial::WorkDegree ( ) const

overridevirtual

returns WorkDegree

Implements PLib_Base.

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

PLib_JacobiPolynomial.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PLib_JacobiPolynomial()

Member Function Documentation

◆ AverageError()

◆ D0()

◆ D1()

◆ D2()

◆ D3()

◆ MaxError()

◆ MaxValue()

◆ NivConstr()

◆ Points()

◆ ReduceDegree()

◆ ToCoefficients()

◆ Weights()

◆ WorkDegree()