#include <ApproxSurface.h>

Public Member Functions
virtual void	AllBasisFunctions (double fParam, TColStd_Array1OfReal &vFuncVals)
	Calculates the function values of the basic functions that do not vanish at fParam. More...

virtual double	BasisFunction (int iIndex, double fParam)
	Calculates the function value Nik(t) at the point fParam (from: Piegl/Tiller 96 The NURBS-Book) More...

	BSplineBasis (int iSize)
	Constructor. More...

	BSplineBasis (TColStd_Array1OfReal &vKnots, int iOrder=1)
	Constructor. More...

	BSplineBasis (TColStd_Array1OfReal &vKnots, TColStd_Array1OfInteger &vMults, int iSize, int iOrder=1)
	Constructor. More...

virtual double	DerivativeOfBasisFunction (int iIndex, int k, double fParam)
	Calculates the kth derivative at the point fParam. More...

virtual void	DerivativesOfBasisFunction (int iIndex, int iMaxDer, double fParam, TColStd_Array1OfReal &Derivat)
	Calculates the function values of the first iMaxDer derivatives at the point fParam (from: Piegl/Tiller 96 The NURBS-Book) More...

virtual int	FindSpan (double fParam)
	Specifies the knot index for the parameter value (from: Piegl/Tiller 96 The NURBS-Book) More...

virtual double	GetIntegralOfProductOfBSplines (int i, int j, int r, int s)
	Calculates the integral of the product of two B-splines or their derivatives. More...

virtual ValueT	LocalSupport (int iIndex, double fParam)
	Specifies whether the function value Nik(t) at the position fParam results in 0, 1 or a value in between. More...

virtual	~BSplineBasis ()
	Destructor. More...

Public Member Functions inherited from Reen::SplineBasisfunction
virtual double	BasisFunction (int iIndex, double fParam)=0
	Calculates the function value Nik(t) at the point fParam (from: Piegl/Tiller 96 The NURBS-Book) More...

virtual double	DerivativeOfBasisFunction (int iIndex, int k, double fParam)=0
	Calculates the kth derivative at the point fParam. More...

virtual void	DerivativesOfBasisFunction (int iIndex, int iMaxDer, double fParam, TColStd_Array1OfReal &Derivat)=0
	Calculates the function values of the first iMaxDer derivatives on the fParam position (from: Piegl/Tiller 96 The NURBS-Book) More...

virtual ValueT	LocalSupport (int iIndex, double fParam)=0
	Indicates whether the function value Nik(t) at the point fParam results in 0, 1 or a value in between. More...

virtual void	SetKnots (TColStd_Array1OfReal &vKnots, int iOrder=1)
	Sets the knot vector and the order. More...

virtual void	SetKnots (TColStd_Array1OfReal &vKnots, TColStd_Array1OfInteger &vMults, int iOrder=1)
	Sets the knot vector and the order. More...

	SplineBasisfunction (int iSize)
	Constructor. More...

	SplineBasisfunction (TColStd_Array1OfReal &vKnots, int iOrder=1)
	Constructor. More...

	SplineBasisfunction (TColStd_Array1OfReal &vKnots, TColStd_Array1OfInteger &vMults, int iSize, int iOrder=1)
	Constructor. More...

virtual	~SplineBasisfunction ()

Protected Member Functions
int	CalcSize (int r, int s)
	Calculates the number of roots/weights of the Legendre-Polynomials to be used as a function of the degree. More...

virtual void	FindIntegrationArea (int iIdx1, int iIdx2, int &iBegin, int &iEnd)
	Calculates the limits of integration (Indexes of the knots) More...

virtual void	GenerateRootsAndWeights (TColStd_Array1OfReal &vAbscissas, TColStd_Array1OfReal &vWeights)
	Calculates the roots of the Legendre-Polynomials and the corresponding weights. More...

Additional Inherited Members
Public Types inherited from Reen::SplineBasisfunction
enum	ValueT { Zero = 0 , Full , Other }

Constructor & Destructor Documentation

◆ BSplineBasis() [1/3]

BSplineBasis::BSplineBasis ( int iSize )

Constructor.

Parameters

iSize Length of the knot vector

◆ BSplineBasis() [2/3]

BSplineBasis::BSplineBasis	(	TColStd_Array1OfReal &	vKnots,
		int	iOrder = `1`
	)

Constructor.

Parameters

vKnots	Knot vector
iOrder	Order (degree + 1) of the basic polynomial

◆ BSplineBasis() [3/3]

BSplineBasis::BSplineBasis	(	TColStd_Array1OfReal &	vKnots,
		TColStd_Array1OfInteger &	vMults,
		int	iSize,
		int	iOrder = `1`
	)

Constructor.

Parameters

vKnots	Knot vector of shape (value)
vMults	Knot vector of shape (multiplicity)
iSize	Length of the knot vector The arrays vKnots and vMults have to be of the same size and the sum of the values in vMults has to be identical to iSize.
iOrder	Order (degree + 1) of the basic polynomial

◆ ~BSplineBasis()

BSplineBasis::~BSplineBasis ( )

Destructor.

Member Function Documentation

◆ AllBasisFunctions()

void BSplineBasis::AllBasisFunctions	(	double	fParam,
		TColStd_Array1OfReal &	vFuncVals
	)

virtual

Calculates the function values of the basic functions that do not vanish at fParam.

It must be ensured that the list for d (= degree of the B-spline) elements (0, ..., d-1) is sufficient (from: Piegl/Tiller 96 The NURBS-Book)

Parameters

fParam	Parameter
vFuncVals	List of function values Index, Parameter value

References FindSpan().

◆ BasisFunction()

double BSplineBasis::BasisFunction	(	int	iIndex,
		double	fParam
	)

virtual

Calculates the function value Nik(t) at the point fParam (from: Piegl/Tiller 96 The NURBS-Book)

Parameters

iIndex	Index
fParam	Parameter value

Returns: Function value Nik(t)

Implements Reen::SplineBasisfunction.

Referenced by DerivativeOfBasisFunction().

◆ CalcSize()

int BSplineBasis::CalcSize	(	int	r,
		int	s
	)

protected

Calculates the number of roots/weights of the Legendre-Polynomials to be used as a function of the degree.

Referenced by GetIntegralOfProductOfBSplines().

◆ DerivativeOfBasisFunction()

double BSplineBasis::DerivativeOfBasisFunction	(	int	iIndex,
		int	k,
		double	fParam
	)

virtual

Calculates the kth derivative at the point fParam.

Implements Reen::SplineBasisfunction.

References BasisFunction().

Referenced by GetIntegralOfProductOfBSplines().

◆ DerivativesOfBasisFunction()

void BSplineBasis::DerivativesOfBasisFunction	(	int	iIndex,
		int	iMaxDer,
		double	fParam,
		TColStd_Array1OfReal &	Derivat
	)

virtual

Calculates the function values of the first iMaxDer derivatives at the point fParam (from: Piegl/Tiller 96 The NURBS-Book)

Parameters

iIndex	Index
iMaxDer	max. derivative
fParam	Parameter value
Derivat	The list must be sufficiently long for iMaxDer+1 elements.

Returns: List of function values

Implements Reen::SplineBasisfunction.

◆ FindIntegrationArea()

void BSplineBasis::FindIntegrationArea	(	int	iIdx1,
		int	iIdx2,
		int &	iBegin,
		int &	iEnd
	)

protectedvirtual

Calculates the limits of integration (Indexes of the knots)

Referenced by GetIntegralOfProductOfBSplines().

◆ FindSpan()

int BSplineBasis::FindSpan ( double fParam )

virtual

Specifies the knot index for the parameter value (from: Piegl/Tiller 96 The NURBS-Book)

Parameters

fParam Parameter value

Returns: Knot index

Referenced by AllBasisFunctions().

◆ GenerateRootsAndWeights()

void BSplineBasis::GenerateRootsAndWeights	(	TColStd_Array1OfReal &	vAbscissas,
		TColStd_Array1OfReal &	vWeights
	)

protectedvirtual

Calculates the roots of the Legendre-Polynomials and the corresponding weights.

Referenced by GetIntegralOfProductOfBSplines().

◆ GetIntegralOfProductOfBSplines()

double BSplineBasis::GetIntegralOfProductOfBSplines	(	int	i,
		int	j,
		int	r,
		int	s
	)

virtual

Calculates the integral of the product of two B-splines or their derivatives.

The integration area extends over the entire domain of definition. The integral is calculated by means of the Gaussian quadrature formulas.

References CalcSize(), DerivativeOfBasisFunction(), FindIntegrationArea(), and GenerateRootsAndWeights().

◆ LocalSupport()

BSplineBasis::ValueT BSplineBasis::LocalSupport	(	int	iIndex,
		double	fParam
	)

virtual

Specifies whether the function value Nik(t) at the position fParam results in 0, 1 or a value in between.

This serves to speed up the calculation under certain circumstances.

Parameters

iIndex	Index
fParam	Parameter value

Returns: ValueT

Implements Reen::SplineBasisfunction.

References Reen::SplineBasisfunction::Full, Reen::SplineBasisfunction::Other, and Reen::SplineBasisfunction::Zero.

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

FreeCAD/src/Mod/ReverseEngineering/App/ApproxSurface.h
FreeCAD/src/Mod/ReverseEngineering/App/ApproxSurface.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ BSplineBasis() [1/3]

◆ BSplineBasis() [2/3]

◆ BSplineBasis() [3/3]

◆ ~BSplineBasis()

Member Function Documentation

◆ AllBasisFunctions()

◆ BasisFunction()

◆ CalcSize()

◆ DerivativeOfBasisFunction()

◆ DerivativesOfBasisFunction()

◆ FindIntegrationArea()

◆ FindSpan()

◆ GenerateRootsAndWeights()

◆ GetIntegralOfProductOfBSplines()

◆ LocalSupport()