PLib means Polynomial functions library. This pk provides basic computation functions for polynomial functions. Note: weight arrays can be passed by pointer for some functions so that NULL pointer is valid. That means no weights passed. More...

#include <PLib.hxx>

Static Public Member Functions
static TColStd_Array1OfReal *	NoWeights ()
	Used as argument for a non rational functions. More...

static TColStd_Array2OfReal *	NoWeights2 ()
	Used as argument for a non rational functions. More...

static void	SetPoles (const TColgp_Array1OfPnt &Poles, TColStd_Array1OfReal &FP)
	Copy in FP the coordinates of the poles. More...

static void	SetPoles (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, TColStd_Array1OfReal &FP)
	Copy in FP the coordinates of the poles. More...

static void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array1OfPnt &Poles)
	Get from FP the coordinates of the poles. More...

static void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array1OfPnt &Poles, TColStd_Array1OfReal &Weights)
	Get from FP the coordinates of the poles. More...

static void	SetPoles (const TColgp_Array1OfPnt2d &Poles, TColStd_Array1OfReal &FP)
	Copy in FP the coordinates of the poles. More...

static void	SetPoles (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, TColStd_Array1OfReal &FP)
	Copy in FP the coordinates of the poles. More...

static void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array1OfPnt2d &Poles)
	Get from FP the coordinates of the poles. More...

static void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array1OfPnt2d &Poles, TColStd_Array1OfReal &Weights)
	Get from FP the coordinates of the poles. More...

static Standard_Real	Bin (const Standard_Integer N, const Standard_Integer P)
	Returns the Binomial Cnp. N should be <= BSplCLib::MaxDegree(). More...

static void	RationalDerivative (const Standard_Integer Degree, const Standard_Integer N, const Standard_Integer Dimension, Standard_Real &Ders, Standard_Real &RDers, const Standard_Boolean All=Standard_True)
	Computes the derivatives of a ratio at order <N> in dimension <Dimension>. More...

static void	RationalDerivatives (const Standard_Integer DerivativesRequest, const Standard_Integer Dimension, Standard_Real &PolesDerivatives, Standard_Real &WeightsDerivatives, Standard_Real &RationalDerivates)
	Computes DerivativesRequest derivatives of a ratio at of a BSpline function of degree <Degree> dimension <Dimension>. More...

static void	EvalPolynomial (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real &PolynomialCoeff, Standard_Real &Results)
	Performs Horner method with synthethic division for derivatives parameter <U>, with <Degree> and <Dimension>. PolynomialCoeff are stored in the following fashion c0(1) c0(2) .... c0(Dimension) c1(1) c1(2) .... c1(Dimension) More...

static void	NoDerivativeEvalPolynomial (const Standard_Real U, const Standard_Integer Degree, const Standard_Integer Dimension, const Standard_Integer DegreeDimension, Standard_Real &PolynomialCoeff, Standard_Real &Results)
	Same as above with DerivativeOrder = 0;. More...

static void	EvalPoly2Var (const Standard_Real U, const Standard_Real V, const Standard_Integer UDerivativeOrder, const Standard_Integer VDerivativeOrder, const Standard_Integer UDegree, const Standard_Integer VDegree, const Standard_Integer Dimension, Standard_Real &PolynomialCoeff, Standard_Real &Results)
	Applies EvalPolynomial twice to evaluate the derivative of orders UDerivativeOrder in U, VDerivativeOrder in V at parameters U,V. More...

static Standard_Integer	EvalLagrange (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real &ValueArray, Standard_Real &ParameterArray, Standard_Real &Results)
	Performs the Lagrange Interpolation of given series of points with given parameters with the requested derivative order Results will store things in the following format with d = DerivativeOrder. More...

static Standard_Integer	EvalCubicHermite (const Standard_Real U, const Standard_Integer DerivativeOrder, const Standard_Integer Dimension, Standard_Real &ValueArray, Standard_Real &DerivativeArray, Standard_Real &ParameterArray, Standard_Real &Results)
	Performs the Cubic Hermite Interpolation of given series of points with given parameters with the requested derivative order. ValueArray stores the value at the first and last parameter. It has the following format : [0], [Dimension-1] : value at first param [Dimension], [Dimension + Dimension-1] : value at last param Derivative array stores the value of the derivatives at the first parameter and at the last parameter in the following format [0], [Dimension-1] : derivative at first param [Dimension], [Dimension + Dimension-1] : derivative at last param. More...

static Standard_Boolean	HermiteCoefficients (const Standard_Real FirstParameter, const Standard_Real LastParameter, const Standard_Integer FirstOrder, const Standard_Integer LastOrder, math_Matrix &MatrixCoefs)
	This build the coefficient of Hermite's polynomes on [FirstParameter, LastParameter]. More...

static void	CoefficientsPoles (const TColgp_Array1OfPnt &Coefs, const TColStd_Array1OfReal WCoefs, TColgp_Array1OfPnt &Poles, TColStd_Array1OfReal WPoles)

static void	CoefficientsPoles (const TColgp_Array1OfPnt2d &Coefs, const TColStd_Array1OfReal WCoefs, TColgp_Array1OfPnt2d &Poles, TColStd_Array1OfReal WPoles)

static void	CoefficientsPoles (const TColStd_Array1OfReal &Coefs, const TColStd_Array1OfReal WCoefs, TColStd_Array1OfReal &Poles, TColStd_Array1OfReal WPoles)

static void	CoefficientsPoles (const Standard_Integer dim, const TColStd_Array1OfReal &Coefs, const TColStd_Array1OfReal WCoefs, TColStd_Array1OfReal &Poles, TColStd_Array1OfReal WPoles)

static void	Trimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array1OfPnt &Coeffs, TColStd_Array1OfReal *WCoeffs)

static void	Trimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array1OfPnt2d &Coeffs, TColStd_Array1OfReal *WCoeffs)

static void	Trimming (const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &Coeffs, TColStd_Array1OfReal *WCoeffs)

static void	Trimming (const Standard_Real U1, const Standard_Real U2, const Standard_Integer dim, TColStd_Array1OfReal &Coeffs, TColStd_Array1OfReal *WCoeffs)

static void	CoefficientsPoles (const TColgp_Array2OfPnt &Coefs, const TColStd_Array2OfReal WCoefs, TColgp_Array2OfPnt &Poles, TColStd_Array2OfReal WPoles)

static void	UTrimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array2OfPnt &Coeffs, TColStd_Array2OfReal *WCoeffs)

static void	VTrimming (const Standard_Real V1, const Standard_Real V2, TColgp_Array2OfPnt &Coeffs, TColStd_Array2OfReal *WCoeffs)

static Standard_Boolean	HermiteInterpolate (const Standard_Integer Dimension, const Standard_Real FirstParameter, const Standard_Real LastParameter, const Standard_Integer FirstOrder, const Standard_Integer LastOrder, const TColStd_Array2OfReal &FirstConstr, const TColStd_Array2OfReal &LastConstr, TColStd_Array1OfReal &Coefficients)
	Compute the coefficients in the canonical base of the polynomial satisfying the given constraints at the given parameters The array FirstContr(i,j) i=1,Dimension j=0,FirstOrder contains the values of the constraint at parameter FirstParameter idem for LastConstr. More...

static void	JacobiParameters (const GeomAbs_Shape ConstraintOrder, const Standard_Integer MaxDegree, const Standard_Integer Code, Standard_Integer &NbGaussPoints, Standard_Integer &WorkDegree)
	Compute the number of points used for integral computations (NbGaussPoints) and the degree of Jacobi Polynomial (WorkDegree). ConstraintOrder has to be GeomAbs_C0, GeomAbs_C1 or GeomAbs_C2 Code: Code d' init. des parametres de discretisation. = -5 = -4 = -3 = -2 = -1 = 1 calcul rapide avec precision moyenne. = 2 calcul rapide avec meilleure precision. = 3 calcul un peu plus lent avec bonne precision. = 4 calcul lent avec la meilleure precision possible. More...

static Standard_Integer	NivConstr (const GeomAbs_Shape ConstraintOrder)
	translates from GeomAbs_Shape to Integer More...

static GeomAbs_Shape	ConstraintOrder (const Standard_Integer NivConstr)
	translates from Integer to GeomAbs_Shape More...

static void	EvalLength (const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real &PolynomialCoeff, const Standard_Real U1, const Standard_Real U2, Standard_Real &Length)

static void	EvalLength (const Standard_Integer Degree, const Standard_Integer Dimension, Standard_Real &PolynomialCoeff, const Standard_Real U1, const Standard_Real U2, const Standard_Real Tol, Standard_Real &Length, Standard_Real &Error)

Detailed Description

PLib means Polynomial functions library. This pk provides basic computation functions for polynomial functions. Note: weight arrays can be passed by pointer for some functions so that NULL pointer is valid. That means no weights passed.

Member Function Documentation

static Standard_Real PLib::Bin	(	const Standard_Integer	N,
		const Standard_Integer	P
	)

static

Returns the Binomial Cnp. N should be <= BSplCLib::MaxDegree().

static void PLib::CoefficientsPoles	(	const TColgp_Array1OfPnt &	Coefs,
		const TColStd_Array1OfReal *	WCoefs,
		TColgp_Array1OfPnt &	Poles,
		TColStd_Array1OfReal *	WPoles
	)

static

static void PLib::CoefficientsPoles	(	const TColgp_Array1OfPnt2d &	Coefs,
		const TColStd_Array1OfReal *	WCoefs,
		TColgp_Array1OfPnt2d &	Poles,
		TColStd_Array1OfReal *	WPoles
	)

static

static void PLib::CoefficientsPoles	(	const TColStd_Array1OfReal &	Coefs,
		const TColStd_Array1OfReal *	WCoefs,
		TColStd_Array1OfReal &	Poles,
		TColStd_Array1OfReal *	WPoles
	)

static

static void PLib::CoefficientsPoles	(	const Standard_Integer	dim,
		const TColStd_Array1OfReal &	Coefs,
		const TColStd_Array1OfReal *	WCoefs,
		TColStd_Array1OfReal &	Poles,
		TColStd_Array1OfReal *	WPoles
	)

static

static void PLib::CoefficientsPoles	(	const TColgp_Array2OfPnt &	Coefs,
		const TColStd_Array2OfReal *	WCoefs,
		TColgp_Array2OfPnt &	Poles,
		TColStd_Array2OfReal *	WPoles
	)

static

static GeomAbs_Shape PLib::ConstraintOrder ( const Standard_Integer NivConstr )

static

translates from Integer to GeomAbs_Shape

static Standard_Integer PLib::EvalCubicHermite	(	const Standard_Real	U,
		const Standard_Integer	DerivativeOrder,
		const Standard_Integer	Dimension,
		Standard_Real &	ValueArray,
		Standard_Real &	DerivativeArray,
		Standard_Real &	ParameterArray,
		Standard_Real &	Results
	)

static

Performs the Cubic Hermite Interpolation of given series of points with given parameters with the requested derivative order. ValueArray stores the value at the first and last parameter. It has the following format : [0], [Dimension-1] : value at first param [Dimension], [Dimension + Dimension-1] : value at last param Derivative array stores the value of the derivatives at the first parameter and at the last parameter in the following format [0], [Dimension-1] : derivative at first param [Dimension], [Dimension + Dimension-1] : derivative at last param.

ParameterArray stores the first and last parameter in the following format : [0] : first parameter [1] : last parameter

Results will store things in the following format with d = DerivativeOrder

[0], [Dimension-1] : value [Dimension], [Dimension + Dimension-1] : first derivative

[d *Dimension], [d*Dimension + Dimension-1]: dth derivative

static Standard_Integer PLib::EvalLagrange	(	const Standard_Real	U,
		const Standard_Integer	DerivativeOrder,
		const Standard_Integer	Degree,
		const Standard_Integer	Dimension,
		Standard_Real &	ValueArray,
		Standard_Real &	ParameterArray,
		Standard_Real &	Results
	)

static

Performs the Lagrange Interpolation of given series of points with given parameters with the requested derivative order Results will store things in the following format with d = DerivativeOrder.

[0], [Dimension-1] : value [Dimension], [Dimension + Dimension-1] : first derivative

[d *Dimension], [d*Dimension + Dimension-1]: dth derivative

static void PLib::EvalLength	(	const Standard_Integer	Degree,
		const Standard_Integer	Dimension,
		Standard_Real &	PolynomialCoeff,
		const Standard_Real	U1,
		const Standard_Real	U2,
		Standard_Real &	Length
	)

static

static void PLib::EvalLength	(	const Standard_Integer	Degree,
		const Standard_Integer	Dimension,
		Standard_Real &	PolynomialCoeff,
		const Standard_Real	U1,
		const Standard_Real	U2,
		const Standard_Real	Tol,
		Standard_Real &	Length,
		Standard_Real &	Error
	)

static

static void PLib::EvalPoly2Var	(	const Standard_Real	U,
		const Standard_Real	V,
		const Standard_Integer	UDerivativeOrder,
		const Standard_Integer	VDerivativeOrder,
		const Standard_Integer	UDegree,
		const Standard_Integer	VDegree,
		const Standard_Integer	Dimension,
		Standard_Real &	PolynomialCoeff,
		Standard_Real &	Results
	)

static

Applies EvalPolynomial twice to evaluate the derivative of orders UDerivativeOrder in U, VDerivativeOrder in V at parameters U,V.

PolynomialCoeff are stored in the following fashion c00(1) .... c00(Dimension) c10(1) .... c10(Dimension) .... cm0(1) .... cm0(Dimension) .... c01(1) .... c01(Dimension) c11(1) .... c11(Dimension) .... cm1(1) .... cm1(Dimension) .... c0n(1) .... c0n(Dimension) c1n(1) .... c1n(Dimension) .... cmn(1) .... cmn(Dimension)

where the polynomial is defined as : 2 m c00 + c10 U + c20 U + .... + cm0 U 2 m

c01 V + c11 UV + c21 U V + .... + cm1 U V n m n
.... + c0n V + .... + cmn U V

with m = UDegree and n = VDegree

Results stores the result in the following format

f(1) f(2) .... f(Dimension)

Warning: <Results> and <PolynomialCoeff> must be dimensioned properly

static void PLib::EvalPolynomial	(	const Standard_Real	U,
		const Standard_Integer	DerivativeOrder,
		const Standard_Integer	Degree,
		const Standard_Integer	Dimension,
		Standard_Real &	PolynomialCoeff,
		Standard_Real &	Results
	)

static

Performs Horner method with synthethic division for derivatives parameter <U>, with <Degree> and <Dimension>. PolynomialCoeff are stored in the following fashion c0(1) c0(2) .... c0(Dimension) c1(1) c1(2) .... c1(Dimension)

cDegree(1) cDegree(2) .... cDegree(Dimension) where the polynomial is defined as :

2 Degree c0 + c1 X + c2 X + .... cDegree X

Results stores the result in the following format

f(1) f(2) .... f(Dimension) (1) (1) (1) f (1) f (2) .... f (Dimension)

(DerivativeRequest) (DerivativeRequest) f (1) f (Dimension)

this just evaluates the point at parameter U

Warning: <Results> and <PolynomialCoeff> must be dimensioned properly

static void PLib::GetPoles	(	const TColStd_Array1OfReal &	FP,
		TColgp_Array1OfPnt &	Poles
	)

static

Get from FP the coordinates of the poles.

static void PLib::GetPoles	(	const TColStd_Array1OfReal &	FP,
		TColgp_Array1OfPnt &	Poles,
		TColStd_Array1OfReal &	Weights
	)

static

Get from FP the coordinates of the poles.

static void PLib::GetPoles	(	const TColStd_Array1OfReal &	FP,
		TColgp_Array1OfPnt2d &	Poles
	)

static

Get from FP the coordinates of the poles.

static void PLib::GetPoles	(	const TColStd_Array1OfReal &	FP,
		TColgp_Array1OfPnt2d &	Poles,
		TColStd_Array1OfReal &	Weights
	)

static

Get from FP the coordinates of the poles.

static Standard_Boolean PLib::HermiteCoefficients	(	const Standard_Real	FirstParameter,
		const Standard_Real	LastParameter,
		const Standard_Integer	FirstOrder,
		const Standard_Integer	LastOrder,
		math_Matrix &	MatrixCoefs
	)

static

This build the coefficient of Hermite's polynomes on [FirstParameter, LastParameter].

if j <= FirstOrder+1 then

MatrixCoefs[i, j] = ith coefficient of the polynome H0,j-1

else

MatrixCoefs[i, j] = ith coefficient of the polynome H1,k with k = j - FirstOrder - 2

return false if

|FirstParameter| > 100
|LastParameter| > 100
|FirstParameter| +|LastParameter| < 1/100
|LastParameter - FirstParameter| / (|FirstParameter| +|LastParameter|) < 1/100

static Standard_Boolean PLib::HermiteInterpolate	(	const Standard_Integer	Dimension,
		const Standard_Real	FirstParameter,
		const Standard_Real	LastParameter,
		const Standard_Integer	FirstOrder,
		const Standard_Integer	LastOrder,
		const TColStd_Array2OfReal &	FirstConstr,
		const TColStd_Array2OfReal &	LastConstr,
		TColStd_Array1OfReal &	Coefficients
	)

static

Compute the coefficients in the canonical base of the polynomial satisfying the given constraints at the given parameters The array FirstContr(i,j) i=1,Dimension j=0,FirstOrder contains the values of the constraint at parameter FirstParameter idem for LastConstr.

static void PLib::JacobiParameters	(	const GeomAbs_Shape	ConstraintOrder,
		const Standard_Integer	MaxDegree,
		const Standard_Integer	Code,
		Standard_Integer &	NbGaussPoints,
		Standard_Integer &	WorkDegree
	)

static

Compute the number of points used for integral computations (NbGaussPoints) and the degree of Jacobi Polynomial (WorkDegree). ConstraintOrder has to be GeomAbs_C0, GeomAbs_C1 or GeomAbs_C2 Code: Code d' init. des parametres de discretisation. = -5 = -4 = -3 = -2 = -1 = 1 calcul rapide avec precision moyenne. = 2 calcul rapide avec meilleure precision. = 3 calcul un peu plus lent avec bonne precision. = 4 calcul lent avec la meilleure precision possible.

static Standard_Integer PLib::NivConstr ( const GeomAbs_Shape ConstraintOrder )

static

translates from GeomAbs_Shape to Integer

static void PLib::NoDerivativeEvalPolynomial	(	const Standard_Real	U,
		const Standard_Integer	Degree,
		const Standard_Integer	Dimension,
		const Standard_Integer	DegreeDimension,
		Standard_Real &	PolynomialCoeff,
		Standard_Real &	Results
	)

static

Same as above with DerivativeOrder = 0;.

static TColStd_Array1OfReal* PLib::NoWeights ( )

inlinestatic

Used as argument for a non rational functions.

static TColStd_Array2OfReal* PLib::NoWeights2 ( )

inlinestatic

Used as argument for a non rational functions.

static void PLib::RationalDerivative	(	const Standard_Integer	Degree,
		const Standard_Integer	N,
		const Standard_Integer	Dimension,
		Standard_Real &	Ders,
		Standard_Real &	RDers,
		const Standard_Boolean	All = `Standard_True`
	)

static

Computes the derivatives of a ratio at order <N> in dimension <Dimension>.

<Ders> is an array containing the values of the input derivatives from 0 to Min(<N>,<Degree>). For orders higher than <Degree> the inputcd /s2d1/BMDL/ derivatives are assumed to be 0.

Content of <Ders> :

x(1),x(2),...,x(Dimension),w x'(1),x'(2),...,x'(Dimension),w' x''(1),x''(2),...,x''(Dimension),w''

If <All> is false, only the derivative at order <N> is computed. <RDers> is an array of length Dimension which will contain the result :

x(1)/w , x(2)/w , ... derivated <N> times

If <All> is true all the derivatives up to order <N> are computed. <RDers> is an array of length Dimension * (N+1) which will contains :

x(1)/w , x(2)/w , ... x(1)/w , x(2)/w , ... derivated <1> times x(1)/w , x(2)/w , ... derivated <2> times ... x(1)/w , x(2)/w , ... derivated <N> times

Warning: <RDers> must be dimensionned properly.

static void PLib::RationalDerivatives	(	const Standard_Integer	DerivativesRequest,
		const Standard_Integer	Dimension,
		Standard_Real &	PolesDerivatives,
		Standard_Real &	WeightsDerivatives,
		Standard_Real &	RationalDerivates
	)

static

Computes DerivativesRequest derivatives of a ratio at of a BSpline function of degree <Degree> dimension <Dimension>.

<PolesDerivatives> is an array containing the values of the input derivatives from 0 to <DerivativeRequest> For orders higher than <Degree> the input derivatives are assumed to be 0.

Content of <PoleasDerivatives> :

x(1),x(2),...,x(Dimension) x'(1),x'(2),...,x'(Dimension) x''(1),x''(2),...,x''(Dimension)

WeightsDerivatives is an array that contains derivatives from 0 to <DerivativeRequest> After returning from the routine the array RationalDerivatives contains the following x(1)/w , x(2)/w , ... x(1)/w , x(2)/w , ... derivated once x(1)/w , x(2)/w , ... twice x(1)/w , x(2)/w , ... derivated <DerivativeRequest> times

The array RationalDerivatives and PolesDerivatives can be same since the overwrite is non destructive within the algorithm

Warning: <RationalDerivates> must be dimensionned properly.

static void PLib::SetPoles	(	const TColgp_Array1OfPnt &	Poles,
		TColStd_Array1OfReal &	FP
	)

static

Copy in FP the coordinates of the poles.

static void PLib::SetPoles	(	const TColgp_Array1OfPnt &	Poles,
		const TColStd_Array1OfReal &	Weights,
		TColStd_Array1OfReal &	FP
	)

static

Copy in FP the coordinates of the poles.

static void PLib::SetPoles	(	const TColgp_Array1OfPnt2d &	Poles,
		TColStd_Array1OfReal &	FP
	)

static

Copy in FP the coordinates of the poles.

static void PLib::SetPoles	(	const TColgp_Array1OfPnt2d &	Poles,
		const TColStd_Array1OfReal &	Weights,
		TColStd_Array1OfReal &	FP
	)

static

Copy in FP the coordinates of the poles.

static void PLib::Trimming	(	const Standard_Real	U1,
		const Standard_Real	U2,
		TColgp_Array1OfPnt &	Coeffs,
		TColStd_Array1OfReal *	WCoeffs
	)

static

static void PLib::Trimming	(	const Standard_Real	U1,
		const Standard_Real	U2,
		TColgp_Array1OfPnt2d &	Coeffs,
		TColStd_Array1OfReal *	WCoeffs
	)

static

static void PLib::Trimming	(	const Standard_Real	U1,
		const Standard_Real	U2,
		TColStd_Array1OfReal &	Coeffs,
		TColStd_Array1OfReal *	WCoeffs
	)

static

static void PLib::Trimming	(	const Standard_Real	U1,
		const Standard_Real	U2,
		const Standard_Integer	dim,
		TColStd_Array1OfReal &	Coeffs,
		TColStd_Array1OfReal *	WCoeffs
	)

static

static void PLib::UTrimming	(	const Standard_Real	U1,
		const Standard_Real	U2,
		TColgp_Array2OfPnt &	Coeffs,
		TColStd_Array2OfReal *	WCoeffs
	)

static

static void PLib::VTrimming	(	const Standard_Real	V1,
		const Standard_Real	V2,
		TColgp_Array2OfPnt &	Coeffs,
		TColStd_Array2OfReal *	WCoeffs
	)

static

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

PLib.hxx

Static Public Member Functions

Detailed Description

Member Function Documentation