Open CASCADE Technology  7.7.0.dev
Public Member Functions

PLib_HermitJacobi Class Reference

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) = 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>

Inheritance diagram for PLib_HermitJacobi:
Inheritance graph
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Public Member Functions

 PLib_HermitJacobi (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...
 
Standard_Real MaxError (const Standard_Integer Dimension, Standard_Real &HermJacCoeff, 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 &HermJacCoeff, 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 &HermJacCoeff, const Standard_Integer NewDegree) const
 
void ToCoefficients (const Standard_Integer Dimension, const Standard_Integer Degree, const TColStd_Array1OfReal &HermJacCoeff, TColStd_Array1OfReal &Coefficients) const override
 Convert the polynomial P(t) = H(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 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 void Delete () const
 Memory deallocator for transient classes. More...
 
virtual const opencascade::handle< Standard_Type > & DynamicType () const
 Returns a type descriptor about this object. More...
 
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...
 

Additional Inherited Members

- Public Types inherited from Standard_Transient
typedef void base_type
 Returns a type descriptor about this object. More...
 
- Static Public Member Functions inherited from Standard_Transient
static const char * get_type_name ()
 Returns a type descriptor about this object. More...
 
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 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) = 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)+...

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 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_HermitJacobi::AverageError ( const Standard_Integer  Dimension,
Standard_Real HermJacCoeff,
const Standard_Integer  NewDegree 
) const

◆ D0()

void PLib_HermitJacobi::D0 ( const Standard_Real  U,
TColStd_Array1OfReal BasisValue 
)
overridevirtual

Compute the values of the basis functions in u.

Implements PLib_Base.

◆ D1()

void PLib_HermitJacobi::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_HermitJacobi::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_HermitJacobi::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_HermitJacobi::MaxError ( const Standard_Integer  Dimension,
Standard_Real HermJacCoeff,
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.

◆ NivConstr()

Standard_Integer PLib_HermitJacobi::NivConstr ( ) const

returns NivConstr

◆ ReduceDegree()

void PLib_HermitJacobi::ReduceDegree ( const Standard_Integer  Dimension,
const Standard_Integer  MaxDegree,
const Standard_Real  Tol,
Standard_Real HermJacCoeff,
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_HermitJacobi::ToCoefficients ( const Standard_Integer  Dimension,
const Standard_Integer  Degree,
const TColStd_Array1OfReal HermJacCoeff,
TColStd_Array1OfReal Coefficients 
) const
overridevirtual

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

Implements PLib_Base.

◆ WorkDegree()

Standard_Integer PLib_HermitJacobi::WorkDegree ( ) const
overridevirtual

returns WorkDegree

Implements PLib_Base.


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