sablib::BSpline< Scalar > Class Template Reference

A class for B-Spline operations including basis function calculation and interpolation. More...

#include <bspline.h>

Public Member Functions
	BSpline (const int degree, const Eigen::VectorX< Scalar > &knots)
	Constructor that initializes a B-Spline with a given degree and knot vector.
	BSpline (const int degree, const Eigen::VectorX< Scalar > &knots, const Eigen::VectorX< Scalar > &x, const Eigen::VectorX< Scalar > &y)
	Constructor that initializes a B-Spline and fits it to the given data points.
	BSpline (const int degree, const Eigen::VectorX< Scalar > &knots, const Eigen::VectorX< Scalar > &coefficients)
	Constructor that initializes a B-Spline with a given degree, knot vector, and coefficients.
int	BasisSize () const
	Gets the number of basis functions.
const Eigen::VectorX< Scalar >	Knots () const
	Returns the knot vector.
const Eigen::VectorX< Scalar >	Coefficients () const
	Returns the internal B-Spline coefficients.
const Eigen::SparseMatrix< Scalar >	DesignMatrix (const Eigen::VectorX< Scalar > &x) const
	Constructs the design matrix (collocation matrix) for a given set of x-coordinates.
void	Fit (const Eigen::VectorX< Scalar > &x, const Eigen::VectorX< Scalar > &y)
	Fits the B-Spline to the given data points by calculating the coefficients.
const Scalar	Interpolate (const Scalar x, const Eigen::VectorX< Scalar > &coefficients) const
	Interpolates the value at a given x-coordinate using provided B-Spline coefficients.
const Scalar	Interpolate (const Scalar x) const
	Interpolates the value at a given x-coordinate using the internal coefficients.

Detailed Description

template<typename Scalar>
class sablib::BSpline< Scalar >

A class for B-Spline operations including basis function calculation and interpolation.

Template Parameters

Scalar

The scalar type for the spline (e.g., double, float).

Definition at line 23 of file bspline.h.

Constructor & Destructor Documentation

BSpline() [1/3]

template<typename Scalar>

sablib::BSpline< Scalar >::BSpline	(	const int	degree,
		const Eigen::VectorX< Scalar > &	knots )

Constructor that initializes a B-Spline with a given degree and knot vector.

Parameters

degree	The degree of the B-Spline.
knots	The knot vector.

Definition at line 144 of file bspline.h.

BSpline() [2/3]

template<typename Scalar>

sablib::BSpline< Scalar >::BSpline	(	const int	degree,
		const Eigen::VectorX< Scalar > &	knots,
		const Eigen::VectorX< Scalar > &	x,
		const Eigen::VectorX< Scalar > &	y )

Constructor that initializes a B-Spline and fits it to the given data points.

Parameters

degree	The degree of the B-Spline.
knots	The knot vector.
x	The x-coordinates of the data points.
y	The y-coordinates of the data points.

Definition at line 154 of file bspline.h.

References Fit().

BSpline() [3/3]

template<typename Scalar>

sablib::BSpline< Scalar >::BSpline	(	const int	degree,
		const Eigen::VectorX< Scalar > &	knots,
		const Eigen::VectorX< Scalar > &	coefficients )

Constructor that initializes a B-Spline with a given degree, knot vector, and coefficients.

Parameters

degree	The degree of the B-Spline.
knots	The knot vector.
coefficients	The B-Spline coefficients.

Definition at line 166 of file bspline.h.

Member Function Documentation

BasisSize()

template<typename Scalar>

int sablib::BSpline< Scalar >::BasisSize

(

)

const

Gets the number of basis functions.

Returns

The number of basis functions.

Definition at line 176 of file bspline.h.

Coefficients()

template<typename Scalar>

const Eigen::VectorX< Scalar > sablib::BSpline< Scalar >::Coefficients

(

)

const

Returns the internal B-Spline coefficients.

Returns

The B-Spline coefficients.

Definition at line 194 of file bspline.h.

DesignMatrix()

template<typename Scalar>

const Eigen::SparseMatrix< Scalar > sablib::BSpline< Scalar >::DesignMatrix

(

const Eigen::VectorX< Scalar > &

x

)

const

Constructs the design matrix (collocation matrix) for a given set of x-coordinates.

Parameters

x	The x-coordinates of the data points.

Returns

The sparse design matrix.

Definition at line 267 of file bspline.h.

Referenced by Fit(), and sablib::PSpline().

Fit()

template<typename Scalar>

void sablib::BSpline< Scalar >::Fit	(	const Eigen::VectorX< Scalar > &	x,
		const Eigen::VectorX< Scalar > &	y )

Fits the B-Spline to the given data points by calculating the coefficients.

Parameters

x	The x-coordinates of the data points.
y	The y-coordinates of the data points.

Definition at line 296 of file bspline.h.

References DesignMatrix().

Referenced by BSpline().

Interpolate() [1/2]

template<typename Scalar>

const Scalar sablib::BSpline< Scalar >::Interpolate ( const Scalar x ) const

inline

Interpolates the value at a given x-coordinate using the internal coefficients.

Parameters

x	The x-coordinate to interpolate.

Returns

The interpolated value at x.

Definition at line 337 of file bspline.h.

References Interpolate().

Interpolate() [2/2]

template<typename Scalar>

const Scalar sablib::BSpline< Scalar >::Interpolate	(	const Scalar	x,
		const Eigen::VectorX< Scalar > &	coefficients ) const

Interpolates the value at a given x-coordinate using provided B-Spline coefficients.

Parameters

x	The x-coordinate to interpolate.
coefficients	The B-Spline coefficients.

Returns

The interpolated value at x.

Definition at line 315 of file bspline.h.

Referenced by Interpolate(), and sablib::PSpline().

Knots()

template<typename Scalar>

const Eigen::VectorX< Scalar > sablib::BSpline< Scalar >::Knots

(

)

const

Returns the knot vector.

Returns

The knot vector.

Definition at line 185 of file bspline.h.

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

• misc/bspline.h