The central Spline class of the library. More...

#include <Spline.h>

Public Types
using	data_type = T
	The data type T of the spline.

Public Member Functions
	Spline (Support< T > support, std::vector< std::array< T, ARRAY_SIZE > > coefficients)
	Constructor setting the data. Performs sanity checks.

	Spline (Grid< T > grid)
	Constructs an empty spline on the global grid.

const Support< T > &	getSupport () const noexcept
	Returns the spline's support.

const std::vector< std::array< T, ARRAY_SIZE > > &	getCoefficients () const noexcept
	The spline's polynomial coefficients.

T	operator() (const T &x) const
	Evaluates the spline at point x.

const T &	front () const
	Returns the begin of the spline's support.

const T &	back () const
	Returns the end of the spline's support.

template<size_t order2>
bool	checkOverlap (const Spline< T, order2 > &m2) const
	Checks whether the supports of the two splines overlap.

bool	isZero () const
	Checks whether this spline is a zero over the whole number line.

Spline< T, order >	operator/ (const T &d) const
	Scalar-division operator.

Spline< T, order >	operator* (const T &d) const
	Scalar-multiplication operator.

Spline< T, order > &	operator*= (const T &d)
	In-place scalar-multiplication operator.

Spline< T, order > &	operator/= (const T &d)
	In-place scalar-division operator.

Spline< T, order >	operator- () const
	Unary minus operator.

template<size_t ordera>
Spline< T, order > &	operator= (const Spline< T, ordera > &a)
	Copy assign operator.

template<size_t ordera>
Spline< T, order+ordera >	operator* (const Spline< T, ordera > &a) const
	Spline-spline multiplication operator.

template<size_t ordera>
Spline< T, std::max(order, ordera)>	operator+ (const Spline< T, ordera > &a) const
	Spline addition operator.

template<size_t ordera>
Spline< T, order > &	operator+= (const Spline< T, ordera > &a)
	In-place addition operator.

template<size_t ordera>
Spline< T, order > &	operator-= (const Spline< T, ordera > &a)
	Binary in-place subtraction operator.

template<size_t ordera>
Spline< T, std::max(order, ordera)>	operator- (const Spline< T, ordera > &a) const
	Binary subtraction operator.

bool	operator== (const Spline &other) const
	Compares two splines for equality.

bool	operator!= (const Spline &other) const
	Compares two splines for inequality.

Static Public Attributes
static constexpr size_t	spline_order = order
	The order of the spline.

Detailed Description

template<typename T, size_t order>
class bspline::Spline< T, order >

The central Spline class of the library.

Spline class representing spline of datatype T and order order. The coefficients of the spline are defined with respect to the center point xm of each interval.

Template Parameters

T	Datatype of the spline.
order	Order of the spline.

Constructor & Destructor Documentation

◆ Spline() [1/2]

template<typename T , size_t order>

bspline::Spline< T, order >::Spline	(	Support< T >	support,
		std::vector< std::array< T, ARRAY_SIZE > >	coefficients
	)

inline

Constructor setting the data. Performs sanity checks.

Parameters

support	The spline's support.
coefficients	Polynomial coefficients of the spline on each interval.

◆ Spline() [2/2]

template<typename T , size_t order>

bspline::Spline< T, order >::Spline ( Grid< T > grid )

inlineexplicit

Constructs an empty spline on the global grid.

Parameters

grid	The global grid.

Member Function Documentation

◆ back()

template<typename T , size_t order>

const T & bspline::Spline< T, order >::back ( ) const

inline

Returns the end of the spline's support.

Returns the end of the support of this spline. If the spline is empty, an exception is thrown.

Exceptions

BSplineException If the spline's support is empty.

Returns: The end of the spline's support.

◆ checkOverlap()

template<typename T , size_t order>

template<size_t order2>

bool bspline::Spline< T, order >::checkOverlap ( const Spline< T, order2 > & m2 ) const

inline

Checks whether the supports of the two splines overlap.

Parameters

m2	Other spline against which to check.

Template Parameters

order2 Order of spline m2.

Returns: True if the intersection of the supports of the two splines is not empty or point-like.

◆ front()

template<typename T , size_t order>

const T & bspline::Spline< T, order >::front ( ) const

inline

Returns the begin of the spline's support.

Returns the beginning of the support of this spline. If the spline is empty, an exception is thrown.

Exceptions

BSplineException If the spline's support is empty.

Returns: The begin of the spline's support.

◆ getCoefficients()

template<typename T , size_t order>

const std::vector< std::array< T, ARRAY_SIZE > > & bspline::Spline< T, order >::getCoefficients ( ) const

inlinenoexcept

The spline's polynomial coefficients.

Returns the polynomial coefficients of the spline for each interval.

Returns: A refrence to a vector of arrays containing this spline's polynomial coefficients.

◆ getSupport()

template<typename T , size_t order>

const Support< T > & bspline::Spline< T, order >::getSupport ( ) const

inlinenoexcept

Returns the spline's support.

Returns: This spline's support.

◆ isZero()

template<typename T , size_t order>

bool bspline::Spline< T, order >::isZero ( ) const

inline

Checks whether this spline is a zero over the whole number line.

Checks whether this spline returns zero for all x. Can be the case, either if the support contains no intervals (i.e. the vector intervals is empty) or if all coefficients are zero.

Returns: True if the evaluation of the spline returns zero for all input values.

◆ operator!=()

template<typename T , size_t order>

bool bspline::Spline< T, order >::operator!= ( const Spline< T, order > & other ) const

inline

Compares two splines for inequality.

Parameters

other The spline to compare this spline to.

Returns: false if the splines are identical, true otherwise.

◆ operator()()

template<typename T , size_t order>

T bspline::Spline< T, order >::operator() ( const T & x ) const

inline

Evaluates the spline at point x.

Parameters

x	Point at which to evaluate the spline. If x is outside of the support of the spline, zero is returned.

Returns: The value of the spline at point x. If x is outside the spline's support, zero is returned.

◆ operator*() [1/2]

template<typename T , size_t order>

template<size_t ordera>

Spline< T, order+ordera > bspline::Spline< T, order >::operator* ( const Spline< T, ordera > & a ) const

inline

Spline-spline multiplication operator.

Spline-spline multiplication operator. Returns a spline of order order + ordera.

Parameters

a	Spline to be multiplied with this spline.

Template Parameters

ordera Order of spline a.

Exceptions

BSplineException If the two splines are defined on different grids.

Returns: A new spline representing the product of this spline and spline a.

◆ operator*() [2/2]

template<typename T , size_t order>

Spline< T, order > bspline::Spline< T, order >::operator* ( const T & d ) const

inline

Scalar-multiplication operator.

Scalar-multiplication operator. Multiplies this spline with the scalar d.

Parameters

d	Scalar by which to multiply this spline.

Returns: A new, scaled spline.

◆ operator*=()

template<typename T , size_t order>

Spline< T, order > & bspline::Spline< T, order >::operator*= ( const T & d )

inline

In-place scalar-multiplication operator.

In-place scalar-multiplication operator. Multiplies this spline with the scalar d in-place.

Parameters

d	Scalar by which to multiply this spline.

Returns: A reference to this spline.

◆ operator+()

template<typename T , size_t order>

template<size_t ordera>

Spline< T, std::max(order, ordera)> bspline::Spline< T, order >::operator+ ( const Spline< T, ordera > & a ) const

inline

Spline addition operator.

Addition operator. Adds spline a to this spline.

Parameters

a	Spline to be added.

Template Parameters

ordera Order of spline a.

Exceptions

BSplineException If the two splines are defined on different grids.

Returns: A new spline representing the sum of this spline and spline a.

◆ operator+=()

template<typename T , size_t order>

template<size_t ordera>

Spline< T, order > & bspline::Spline< T, order >::operator+= ( const Spline< T, ordera > & a )

inline

In-place addition operator.

In-place addition operator. Adds spline a to this spline. The operation is only well defined if the order of spline a is lower than or equal to the order of this spline object.

Parameters

a	Spline to be added.

Template Parameters

ordera Order of spline a.

Exceptions

BSplineException If the two splines are defined on different grids.

Returns: A reference to this spline.

◆ operator-() [1/2]

template<typename T , size_t order>

Spline< T, order > bspline::Spline< T, order >::operator- ( ) const

inline

Unary minus operator.

Returns: A new, scaled spline.

◆ operator-() [2/2]

template<typename T , size_t order>

template<size_t ordera>

Spline< T, std::max(order, ordera)> bspline::Spline< T, order >::operator- ( const Spline< T, ordera > & a ) const

inline

Binary subtraction operator.

Binary subtraction operator. Subtracts spline a from this spline.

Parameters

a	Spline to be subtracted.

Template Parameters

ordera Order of spline a.

Exceptions

BSplineException If the two splines are defined on different grids.

Returns: A new spline representing the difference of this spline and spline a.

◆ operator-=()

template<typename T , size_t order>

template<size_t ordera>

Spline< T, order > & bspline::Spline< T, order >::operator-= ( const Spline< T, ordera > & a )

inline

Binary in-place subtraction operator.

Binary in-place subtraction operator. Subtracts spline a from this spline. The operation is only well defined if the order of the spline to be subtracted is lower than or equal to the order of this spline object.

Parameters

a	Spline to be subtracted.

Template Parameters

ordera Order of spline a.

Exceptions

BSplineException If the two splines are defined on different grids.

Returns: A reference to this spline.

◆ operator/()

template<typename T , size_t order>

Spline< T, order > bspline::Spline< T, order >::operator/ ( const T & d ) const

inline

Scalar-division operator.

Scalar-division operator. Divides this spline by the scalar d.

Parameters

d	Scalar by which to divide this spline.

Returns: A new, scaled spline.

◆ operator/=()

template<typename T , size_t order>

Spline< T, order > & bspline::Spline< T, order >::operator/= ( const T & d )

inline

In-place scalar-division operator.

In-place scalar-division operator. Divides this spline by the scalar d in-place.

Parameters

d	Scalar by which to divide this spline.

Returns: A reference to this spline.

◆ operator=()

template<typename T , size_t order>

template<size_t ordera>

Spline< T, order > & bspline::Spline< T, order >::operator= ( const Spline< T, ordera > & a )

inline

Copy assign operator.

Copy assign of spline to this spline object. The operation is only well defined if the order of the spline to be assigned is lower than or equal to the order of this spline object.

Parameters

a	Spline to be assigned.

Template Parameters

ordera Order of spline a.

Returns: A reference to this spline.

◆ operator==()

template<typename T , size_t order>

bool bspline::Spline< T, order >::operator== ( const Spline< T, order > & other ) const

inline

Compares two splines for equality.

Parameters

other The spline to compare this spline to.

Returns: true if the splines are identical, false otherwise.

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

include/bspline/Spline.h

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Spline() [1/2]

◆ Spline() [2/2]

Member Function Documentation

◆ back()

◆ checkOverlap()

◆ front()

◆ getCoefficients()

◆ getSupport()

◆ isZero()

◆ operator!=()

◆ operator()()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator=()

◆ operator==()