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>
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 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 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 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 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 Standard_Transient | |
| Standard_Transient () | |
| Empty constructor. More... | |
| Standard_Transient (const Standard_Transient &) | |
| Copy constructor – does nothing. More... | |
| Standard_Transient & | operator= (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_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. 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) = 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()
|
overridevirtual |
Compute the values of the basis functions in u.
Implements PLib_Base.
◆ D1()
|
overridevirtual |
Compute the values and the derivatives values of the basis functions in u.
Implements PLib_Base.
◆ D2()
|
overridevirtual |
Compute the values and the derivatives values of the basis functions in u.
Implements PLib_Base.
◆ D3()
|
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()
|
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()
|
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()
|
overridevirtual |
returns WorkDegree
Implements PLib_Base.
The documentation for this class was generated from the following file:
