Open CASCADE Technology Reference Manual 8.0.0
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Public Member Functions | Protected 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 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)
NCollection_ForwardRangeIterator
STL input iterator that wraps an OCCT More()/Next() iterator.
Definition NCollection_ForwardRange.hxx:142

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

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:
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