PLib_JacobiPolynomial Class Reference

This class provides method to work with Jacobi Polynomials relativly to an order of constraint q = myWorkDegree-2*(myNivConstr+1) Jk(t) for k=0,q compose the Jacobi Polynomial base relativly 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:
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## 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. More...

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 choosen 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 More...

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 choosen 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 More...

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 ); More...

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. More...

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. More...

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. More...

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

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. More...

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. More...

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. More...

Standard_Integer WorkDegree () const override
returns WorkDegree More...

Standard_Integer NivConstr () const
returns NivConstr More...

Public Member Functions inherited from MMgt_TShared
virtual void Delete () const override
Memory deallocator for transient classes. More...

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

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

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

virtual ~Standard_Transient ()
Destructor must be virtual. More...

virtual const opencascade::handle< Standard_Type > & DynamicType () const

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

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

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. More...

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. More...

Standard_TransientThis () 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. More...

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

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

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

Public Types inherited from Standard_Transient
typedef void base_type

Static Public Member Functions inherited from Standard_Transient
static const char * get_type_name ()

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

## Detailed Description

This class provides method to work with Jacobi Polynomials relativly to an order of constraint q = myWorkDegree-2*(myNivConstr+1) Jk(t) for k=0,q compose the Jacobi Polynomial base relativly 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 ( 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

 Standard_Real PLib_JacobiPolynomial::AverageError ( const Standard_Integer Dimension, Standard_Real & JacCoeff, const Standard_Integer NewDegree ) const
 void PLib_JacobiPolynomial::D0 ( const Standard_Real U, TColStd_Array1OfReal & BasisValue )
overridevirtual

Compute the values of the basis functions in u.

Implements PLib_Base.

 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.

 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.

 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.

 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.

 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 );

 Standard_Integer PLib_JacobiPolynomial::NivConstr ( ) const

returns NivConstr

 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 choosen 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 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.

 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.

 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 choosen 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

 Standard_Integer PLib_JacobiPolynomial::WorkDegree ( ) const
overridevirtual

returns WorkDegree

Implements PLib_Base.

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