FoundationClasses
TKMath
PLib

PLib Class Reference

PLib means Polynomial functions library. This pk
provides basic computation functions for
polynomial functions.

.

#include <PLib.hxx>

Public Member Functions

void * operator new (size_t, void *anAddress)

void * operator new (size_t size)

void operator delete (void *anAddress)

Static Public Member Functions

static TColStd_Array1OfReal & NoWeights ()

Used as argument for a non rational functions

.

static TColStd_Array2OfReal & NoWeights2 ()

Used as argument for a non rational functions

.

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

Copy in FP the coordinates of the poles.
.

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

Copy in FP the coordinates of the poles.
.

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

Get from FP the coordinates of the poles.
.

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

Get from FP the coordinates of the poles.
.

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

Copy in FP the coordinates of the poles.
.

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

Copy in FP the coordinates of the poles.
.

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

Get from FP the coordinates of the poles.
.

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

Get from FP the coordinates of the poles.
.

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

Returns the Binomial Cnp , without testing anything.
.

static void Binomial (const Standard_Integer N)

test on N > maxbinom and build the PASCAL triangle
on size N if necessary.

static Standard_EXPORT void InternalBinomial (const Standard_Integer N, Standard_Integer &maxbinom, Standard_Address &binom)

only called by Binomial(N,P)

static Standard_EXPORT 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>.

<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 Standard_EXPORT 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>.

<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 Standard_EXPORT 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)

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 Standard_EXPORT 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;
.

static Standard_EXPORT 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

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 Standard_EXPORT 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

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

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

static Standard_EXPORT 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

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_EXPORT Standard_Boolean HermiteCoefficients (const Standard_Real FirstParameter, const Standard_Real LastParameter, const Standard_Integer FirstOrder, const Standard_Integer LastOrder, math_Matrix &MatrixCoefs)

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

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

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

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

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

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

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

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

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

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

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

static Standard_EXPORT 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
.

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

static Standard_EXPORT Standard_Integer NivConstr (const GeomAbs_Shape ConstraintOrder)

static Standard_EXPORT GeomAbs_Shape ConstraintOrder (const Standard_Integer NivConstr)

static Standard_EXPORT 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 Standard_EXPORT 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)

Member Function Documentation

Standard_Real PLib::Bin ( const Standard_Integer N,

const Standard_Integer P

) [inline, static]

void PLib::Binomial ( const Standard_Integer N ) [inline, static]

static Standard_EXPORT void PLib::CoefficientsPoles ( const TColgp_Array2OfPnt & Coefs,

const TColStd_Array2OfReal & WCoefs,

TColgp_Array2OfPnt & Poles,

TColStd_Array2OfReal & WPoles

) [static]

static Standard_EXPORT void PLib::CoefficientsPoles ( const Standard_Integer dim,

const TColStd_Array1OfReal & Coefs,

const TColStd_Array1OfReal & WCoefs,

TColStd_Array1OfReal & Poles,

TColStd_Array1OfReal & WPoles

) [static]

static Standard_EXPORT void PLib::CoefficientsPoles ( const TColStd_Array1OfReal & Coefs,

const TColStd_Array1OfReal & WCoefs,

TColStd_Array1OfReal & Poles,

TColStd_Array1OfReal & WPoles

) [static]

static Standard_EXPORT void PLib::CoefficientsPoles ( const TColgp_Array1OfPnt2d & Coefs,

const TColStd_Array1OfReal & WCoefs,

TColgp_Array1OfPnt2d & Poles,

TColStd_Array1OfReal & WPoles

) [static]

static Standard_EXPORT void PLib::CoefficientsPoles ( const TColgp_Array1OfPnt & Coefs,

const TColStd_Array1OfReal & WCoefs,

TColgp_Array1OfPnt & Poles,

TColStd_Array1OfReal & WPoles

) [static]

static Standard_EXPORT GeomAbs_Shape PLib::ConstraintOrder ( const Standard_Integer NivConstr ) [static]

static Standard_EXPORT 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]

static Standard_EXPORT 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]

static Standard_EXPORT 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 Standard_EXPORT 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]

static Standard_EXPORT 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]

static Standard_EXPORT void PLib::GetPoles ( const TColStd_Array1OfReal & FP,

TColgp_Array1OfPnt2d & Poles,

TColStd_Array1OfReal & Weights

) [static]

static Standard_EXPORT void PLib::GetPoles ( const TColStd_Array1OfReal & FP,

TColgp_Array1OfPnt2d & Poles

) [static]

static Standard_EXPORT void PLib::GetPoles ( const TColStd_Array1OfReal & FP,

TColgp_Array1OfPnt & Poles,

TColStd_Array1OfReal & Weights

) [static]

static Standard_EXPORT void PLib::GetPoles ( const TColStd_Array1OfReal & FP,

TColgp_Array1OfPnt & Poles

) [static]

static Standard_EXPORT Standard_Boolean PLib::HermiteCoefficients ( const Standard_Real FirstParameter,

const Standard_Real LastParameter,

const Standard_Integer FirstOrder,

const Standard_Integer LastOrder,

math_Matrix & MatrixCoefs

) [static]

static Standard_EXPORT 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]

static Standard_EXPORT void PLib::InternalBinomial ( const Standard_Integer N,

Standard_Integer & maxbinom,

Standard_Address & binom

) [static]

static Standard_EXPORT void PLib::JacobiParameters ( const GeomAbs_Shape ConstraintOrder,

const Standard_Integer MaxDegree,

const Standard_Integer Code,

Standard_Integer & NbGaussPoints,

Standard_Integer & WorkDegree

) [static]

static Standard_EXPORT Standard_Integer PLib::NivConstr ( const GeomAbs_Shape ConstraintOrder ) [static]

static Standard_EXPORT 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]

TColStd_Array1OfReal & PLib::NoWeights ( ) [inline, static]

TColStd_Array2OfReal & PLib::NoWeights2 ( ) [inline, static]

void PLib::operator delete ( void * anAddress ) [inline]

void* PLib::operator new ( size_t size ) [inline]

void* PLib::operator new ( size_t ,

void * anAddress

) [inline]

static Standard_EXPORT 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]

static Standard_EXPORT void PLib::RationalDerivatives ( const Standard_Integer DerivativesRequest,

const Standard_Integer Dimension,

Standard_Real & PolesDerivatives,

Standard_Real & WeightsDerivatives,

Standard_Real & RationalDerivates

) [static]

static Standard_EXPORT void PLib::SetPoles ( const TColgp_Array1OfPnt2d & Poles,

const TColStd_Array1OfReal & Weights,

TColStd_Array1OfReal & FP

) [static]

static Standard_EXPORT void PLib::SetPoles ( const TColgp_Array1OfPnt2d & Poles,

TColStd_Array1OfReal & FP

) [static]

static Standard_EXPORT void PLib::SetPoles ( const TColgp_Array1OfPnt & Poles,

const TColStd_Array1OfReal & Weights,

TColStd_Array1OfReal & FP

) [static]

static Standard_EXPORT void PLib::SetPoles ( const TColgp_Array1OfPnt & Poles,

TColStd_Array1OfReal & FP

) [static]

static Standard_EXPORT void PLib::Trimming ( const Standard_Real U1,

const Standard_Real U2,

const Standard_Integer dim,

TColStd_Array1OfReal & Coeffs,

TColStd_Array1OfReal & WCoeffs

) [static]

static Standard_EXPORT void PLib::Trimming ( const Standard_Real U1,

const Standard_Real U2,

TColStd_Array1OfReal & Coeffs,

TColStd_Array1OfReal & WCoeffs

) [static]

static Standard_EXPORT void PLib::Trimming ( const Standard_Real U1,

const Standard_Real U2,

TColgp_Array1OfPnt2d & Coeffs,

TColStd_Array1OfReal & WCoeffs

) [static]

static Standard_EXPORT void PLib::Trimming ( const Standard_Real U1,

const Standard_Real U2,

TColgp_Array1OfPnt & Coeffs,

TColStd_Array1OfReal & WCoeffs

) [static]

static Standard_EXPORT void PLib::UTrimming ( const Standard_Real U1,

const Standard_Real U2,

TColgp_Array2OfPnt & Coeffs,

TColStd_Array2OfReal & WCoeffs

) [static]

static Standard_EXPORT 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 files:

Generated on Mon Aug 25 13:13:11 2008 for OpenCASCADE by

1.4.1


Public Member Functions
void *	operator new (size_t, void *anAddress)
void *	operator new (size_t size)
void	operator delete (void *anAddress)
Static Public Member Functions
static TColStd_Array1OfReal &	NoWeights ()
	Used as argument for a non rational functions .
static TColStd_Array2OfReal &	NoWeights2 ()
	Used as argument for a non rational functions .
static Standard_EXPORT void	SetPoles (const TColgp_Array1OfPnt &Poles, TColStd_Array1OfReal &FP)
	Copy in FP the coordinates of the poles. .
static Standard_EXPORT void	SetPoles (const TColgp_Array1OfPnt &Poles, const TColStd_Array1OfReal &Weights, TColStd_Array1OfReal &FP)
	Copy in FP the coordinates of the poles. .
static Standard_EXPORT void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array1OfPnt &Poles)
	Get from FP the coordinates of the poles. .
static Standard_EXPORT void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array1OfPnt &Poles, TColStd_Array1OfReal &Weights)
	Get from FP the coordinates of the poles. .
static Standard_EXPORT void	SetPoles (const TColgp_Array1OfPnt2d &Poles, TColStd_Array1OfReal &FP)
	Copy in FP the coordinates of the poles. .
static Standard_EXPORT void	SetPoles (const TColgp_Array1OfPnt2d &Poles, const TColStd_Array1OfReal &Weights, TColStd_Array1OfReal &FP)
	Copy in FP the coordinates of the poles. .
static Standard_EXPORT void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array1OfPnt2d &Poles)
	Get from FP the coordinates of the poles. .
static Standard_EXPORT void	GetPoles (const TColStd_Array1OfReal &FP, TColgp_Array1OfPnt2d &Poles, TColStd_Array1OfReal &Weights)
	Get from FP the coordinates of the poles. .
static Standard_Real	Bin (const Standard_Integer N, const Standard_Integer P)
	Returns the Binomial Cnp , without testing anything. .
static void	Binomial (const Standard_Integer N)
	test on N > maxbinom and build the PASCAL triangle on size N if necessary.
static Standard_EXPORT void	InternalBinomial (const Standard_Integer N, Standard_Integer &maxbinom, Standard_Address &binom)
	only called by Binomial(N,P)
static Standard_EXPORT 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>. <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 Standard_EXPORT 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>. <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 Standard_EXPORT 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) 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 Standard_EXPORT 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; .
static Standard_EXPORT 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 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 Standard_EXPORT 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 [0], [Dimension-1] : value [Dimension], [Dimension + Dimension-1] : first derivative [d Dimension], [dDimension + Dimension-1]: dth derivative .
static Standard_EXPORT 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 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], [dDimension + Dimension-1]: dth derivative .
static Standard_EXPORT Standard_Boolean	HermiteCoefficients (const Standard_Real FirstParameter, const Standard_Real LastParameter, const Standard_Integer FirstOrder, const Standard_Integer LastOrder, math_Matrix &MatrixCoefs)
static Standard_EXPORT void	CoefficientsPoles (const TColgp_Array1OfPnt &Coefs, const TColStd_Array1OfReal &WCoefs, TColgp_Array1OfPnt &Poles, TColStd_Array1OfReal &WPoles)
static Standard_EXPORT void	CoefficientsPoles (const TColgp_Array1OfPnt2d &Coefs, const TColStd_Array1OfReal &WCoefs, TColgp_Array1OfPnt2d &Poles, TColStd_Array1OfReal &WPoles)
static Standard_EXPORT void	CoefficientsPoles (const TColStd_Array1OfReal &Coefs, const TColStd_Array1OfReal &WCoefs, TColStd_Array1OfReal &Poles, TColStd_Array1OfReal &WPoles)
static Standard_EXPORT void	CoefficientsPoles (const Standard_Integer dim, const TColStd_Array1OfReal &Coefs, const TColStd_Array1OfReal &WCoefs, TColStd_Array1OfReal &Poles, TColStd_Array1OfReal &WPoles)
static Standard_EXPORT void	Trimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array1OfPnt &Coeffs, TColStd_Array1OfReal &WCoeffs)
static Standard_EXPORT void	Trimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array1OfPnt2d &Coeffs, TColStd_Array1OfReal &WCoeffs)
static Standard_EXPORT void	Trimming (const Standard_Real U1, const Standard_Real U2, TColStd_Array1OfReal &Coeffs, TColStd_Array1OfReal &WCoeffs)
static Standard_EXPORT void	Trimming (const Standard_Real U1, const Standard_Real U2, const Standard_Integer dim, TColStd_Array1OfReal &Coeffs, TColStd_Array1OfReal &WCoeffs)
static Standard_EXPORT void	CoefficientsPoles (const TColgp_Array2OfPnt &Coefs, const TColStd_Array2OfReal &WCoefs, TColgp_Array2OfPnt &Poles, TColStd_Array2OfReal &WPoles)
static Standard_EXPORT void	UTrimming (const Standard_Real U1, const Standard_Real U2, TColgp_Array2OfPnt &Coeffs, TColStd_Array2OfReal &WCoeffs)
static Standard_EXPORT void	VTrimming (const Standard_Real V1, const Standard_Real V2, TColgp_Array2OfPnt &Coeffs, TColStd_Array2OfReal &WCoeffs)
static Standard_EXPORT 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 .
static Standard_EXPORT void	JacobiParameters (const GeomAbs_Shape ConstraintOrder, const Standard_Integer MaxDegree, const Standard_Integer Code, Standard_Integer &NbGaussPoints, Standard_Integer &WorkDegree)
static Standard_EXPORT Standard_Integer	NivConstr (const GeomAbs_Shape ConstraintOrder)
static Standard_EXPORT GeomAbs_Shape	ConstraintOrder (const Standard_Integer NivConstr)
static Standard_EXPORT 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 Standard_EXPORT 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)

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