The common code for all 3rd order polynomial splines with where the number of sampling points only known at run-time. More...

#include <dumux/common/variablelengthspline_.hh>

Inheritance diagram for Dumux::VariableLengthSpline_< ScalarT >:

Description

template<class ScalarT>
class Dumux::VariableLengthSpline_< ScalarT >

The common code for all 3rd order polynomial splines with where the number of sampling points only known at run-time.

Public Member Functions
int	numSamples () const
	Returns the number of sampling points. More...

template<class ScalarArrayX , class ScalarArrayY >
void	setXYArrays (int nSamples, const ScalarArrayX &x, const ScalarArrayY &y, Scalar m0, Scalar m1)
	Set the sampling points and the boundary slopes of a full spline using C-style arrays. More...

template<class ScalarContainerX , class ScalarContainerY >
void	setXYContainers (const ScalarContainerX &x, const ScalarContainerY &y, Scalar m0, Scalar m1)
	Set the sampling points and the boundary slopes of a full spline using STL-compatible containers. More...

template<class PointArray >
void	setArrayOfPoints (int nSamples, const PointArray &points, Scalar m0, Scalar m1)
	Set the sampling points and the boundary slopes of a full spline using a C-style array. More...

template<class XYContainer >
void	setContainerOfPoints (const XYContainer &points, Scalar m0, Scalar m1)
	Set the sampling points and the boundary slopes of a full spline using a STL-compatible container of array-like objects. More...

template<class XYContainer >
void	setContainerOfTuples (const XYContainer &points, Scalar m0, Scalar m1)
	Set the sampling points and the boundary slopes of a full spline using a STL-compatible container of tuple-like objects. More...

template<class ScalarArrayX , class ScalarArrayY >
void	setXYArrays (int nSamples, const ScalarArrayX &x, const ScalarArrayY &y)
	Set the sampling points natural spline using C-style arrays. More...

template<class ScalarContainerX , class ScalarContainerY >
void	setXYContainers (const ScalarContainerX &x, const ScalarContainerY &y)
	Set the sampling points of a natural spline using STL-compatible containers. More...

template<class PointArray >
void	setArrayOfPoints (int nSamples, const PointArray &points)
	Set the sampling points of a natural spline using a C-style array. More...

template<class XYContainer >
void	setContainerOfPoints (const XYContainer &points)
	Set the sampling points of a natural spline using a STL-compatible container of array-like objects. More...

template<class XYContainer >
void	setContainerOfTuples (const XYContainer &points)
	Set the sampling points of a natural spline using a STL-compatible container of tuple-like objects. More...

bool	applies (Scalar x) const
	Return true if the given x is in range [x1, xn]. More...

Scalar	xMin () const
	Return the x value of the leftmost sampling point. More...

Scalar	xMax () const
	Return the x value of the rightmost sampling point. More...

void	printCSV (Scalar xi0, Scalar xi1, int k) const
	Prints k tuples of the format (x, y, dx/dy, isMonotonic) to stdout. More...

Scalar	eval (Scalar x, bool extrapolate=false) const
	Evaluate the spline at a given position. More...

Scalar	evalDerivative (Scalar x, bool extrapolate=false) const
	Evaluate the spline's derivative at a given position. More...

Scalar	intersect (Scalar a, Scalar b, Scalar c, Scalar d) const
	Find the intersections of the spline with a cubic polynomial in the whole intervall, throws Dune::MathError exception if there is more or less than one solution. More...

Scalar	intersectInterval (Scalar x0, Scalar x1, Scalar a, Scalar b, Scalar c, Scalar d) const
	Find the intersections of the spline with a cubic polynomial in a sub-intervall of the spline, throws Dune::MathError exception if there is more or less than one solution. More...

int	monotonic (Scalar x0, Scalar x1) const
	Returns 1 if the spline is monotonically increasing, -1 if the spline is mononously decreasing and 0 if the spline is not monotonous in the interval (x0, x1). More...

int	monotonic () const
	Same as monotonic(x0, x1), but with the entire range of the spline as interval. More...

Protected Member Functions
void	setNumSamples_ (int nSamples)
	Resizes the internal vectors to store the sample points. More...

void	makeFullSpline_ (Scalar m0, Scalar m1)
	Create a natural spline from the already set sampling points. More...

void	makeNaturalSpline_ ()
	Create a natural spline from the already set sampling points. More...

Scalar	x_ (int i) const
	Returns the x coordinate of the i-th sampling point. More...

Scalar	y_ (int i) const
	Returns the y coordinate of the i-th sampling point. More...

Scalar	moment_ (int i) const
	Returns the moment (i.e. second derivative) of the spline at the i-th sampling point. More...

void	assignSamplingPoints_ (DestVector &destX, DestVector &destY, const SourceVector &srcX, const SourceVector &srcY, int numSamples)
	Set the sampling point vectors. More...

void	assignFromArrayList_ (DestVector &destX, DestVector &destY, const ListIterator &srcBegin, const ListIterator &srcEnd, int numSamples)

void	assignFromTupleList_ (DestVector &destX, DestVector &destY, ListIterator srcBegin, ListIterator srcEnd, int numSamples)
	Set the sampling points. More...

void	makePeriodicSystem_ (Matrix &M, Vector &d)
	Make the linear system of equations Mx = d which results in the moments of the periodic spline. More...

void	makeFullSystem_ (Matrix &M, Vector &d, Scalar m0, Scalar m1)
	Make the linear system of equations Mx = d which results in the moments of the full spline. More...

void	makeNaturalSystem_ (Matrix &M, Vector &d)
	Make the linear system of equations Mx = d which results in the moments of the natural spline. Stoer 2005: Numerische Mathematik 1, p. 111 [64]. More...

Scalar	eval_ (Scalar x, int i) const

Scalar	evalDerivative_ (Scalar x, int i) const

int	monotonic_ (int i, Scalar x0, Scalar x1) const

int	intersectSegment_ (Scalar *sol, int segIdx, Scalar a, Scalar b, Scalar c, Scalar d, Scalar x0=-1e100, Scalar x1=1e100) const
	Find all the intersections of a segment of the spline with a cubic polynomial within a specified interval. More...

int	segmentIdx_ (Scalar x) const

Scalar	h_ (int i) const
	Returns x[i] - x[i - 1]. More...

Scalar	a_ (int i) const

Scalar	b_ (int i) const

Scalar	c_ (int i) const

Scalar	d_ (int i) const

int	numSamples_ () const
	Returns the number of sampling points. More...

Protected Attributes
Vector	xPos_

Vector	yPos_

Vector	m_

Member Function Documentation

◆ a_()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::a_ ( int i ) const

inlineprotectedinherited

◆ applies()

bool Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::applies ( Scalar x ) const

inlineinherited

Return true if the given x is in range [x1, xn].

◆ assignFromArrayList_()

void Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::assignFromArrayList_	(	DestVector &	destX,
		DestVector &	destY,
		const ListIterator &	srcBegin,
		const ListIterator &	srcEnd,
		int	numSamples
	)

inlineprotectedinherited

◆ assignFromTupleList_()

void Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::assignFromTupleList_	(	DestVector &	destX,
		DestVector &	destY,
		ListIterator	srcBegin,
		ListIterator	srcEnd,
		int	numSamples
	)

inlineprotectedinherited

Set the sampling points.

Here we assume that the elements of the source vector have an [] operator where v[0] is the x value and v[1] is the y value if the sampling point.

◆ assignSamplingPoints_()

void Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::assignSamplingPoints_	(	DestVector &	destX,
		DestVector &	destY,
		const SourceVector &	srcX,
		const SourceVector &	srcY,
		int	numSamples
	)

inlineprotectedinherited

Set the sampling point vectors.

This takes care that the order of the x-values is ascending, although the input must be ordered already!

◆ b_()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::b_ ( int i ) const

inlineprotectedinherited

◆ c_()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::c_ ( int i ) const

inlineprotectedinherited

◆ d_()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::d_ ( int i ) const

inlineprotectedinherited

◆ eval()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::eval	(	Scalar	x,
		bool	extrapolate = `false`
	)		const

inlineinherited

Evaluate the spline at a given position.

Parameters

x	The value on the abscissa where the spline ought to be evaluated
extrapolate	If this parameter is set to true, the spline will be extended beyond its range by straight lines, if false calling extrapolate for \( x \not [x_{min}, x_{max}]\) will cause a failed assertation.

◆ eval_()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::eval_	(	Scalar	x,
		int	i
	)		const

inlineprotectedinherited

◆ evalDerivative()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::evalDerivative	(	Scalar	x,
		bool	extrapolate = `false`
	)		const

inlineinherited

Evaluate the spline's derivative at a given position.

Parameters

x	The value on the abscissa where the spline's derivative ought to be evaluated
extrapolate	If this parameter is set to true, the spline will be extended beyond its range by straight lines, if false calling extrapolate for \( x \not [x_{min}, x_{max}]\) will cause a failed assertation.

◆ evalDerivative_()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::evalDerivative_	(	Scalar	x,
		int	i
	)		const

inlineprotectedinherited

◆ h_()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::h_ ( int i ) const

inlineprotectedinherited

Returns x[i] - x[i - 1].

◆ intersect()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::intersect	(	Scalar	a,
		Scalar	b,
		Scalar	c,
		Scalar	d
	)		const

inlineinherited

Find the intersections of the spline with a cubic polynomial in the whole intervall, throws Dune::MathError exception if there is more or less than one solution.

◆ intersectInterval()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::intersectInterval	(	Scalar	x0,
		Scalar	x1,
		Scalar	a,
		Scalar	b,
		Scalar	c,
		Scalar	d
	)		const

inlineinherited

Find the intersections of the spline with a cubic polynomial in a sub-intervall of the spline, throws Dune::MathError exception if there is more or less than one solution.

◆ intersectSegment_()

int Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::intersectSegment_	(	Scalar *	sol,
		int	segIdx,
		Scalar	a,
		Scalar	b,
		Scalar	c,
		Scalar	d,
		Scalar	x0 = `-1e100`,
		Scalar	x1 = `1e100`
	)		const

inlineprotectedinherited

Find all the intersections of a segment of the spline with a cubic polynomial within a specified interval.

◆ makeFullSpline_()

template<class ScalarT >

void Dumux::VariableLengthSpline_< ScalarT >::makeFullSpline_	(	Scalar	m0,
		Scalar	m1
	)

inlineprotected

Create a natural spline from the already set sampling points.

Also creates temporary matrix and right hand side vector.

◆ makeFullSystem_()

void Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::makeFullSystem_	(	Matrix &	M,
		Vector &	d,
		Scalar	m0,
		Scalar	m1
	)

inlineprotectedinherited

Make the linear system of equations Mx = d which results in the moments of the full spline.

◆ makeNaturalSpline_()

template<class ScalarT >

void Dumux::VariableLengthSpline_< ScalarT >::makeNaturalSpline_ ( )

inlineprotected

Create a natural spline from the already set sampling points.

Also creates temporary matrix and right hand side vector.

◆ makeNaturalSystem_()

void Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::makeNaturalSystem_	(	Matrix &	M,
		Vector &	d
	)

inlineprotectedinherited

Make the linear system of equations Mx = d which results in the moments of the natural spline. Stoer 2005: Numerische Mathematik 1, p. 111 [64].

◆ makePeriodicSystem_()

void Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::makePeriodicSystem_	(	Matrix &	M,
		Vector &	d
	)

inlineprotectedinherited

Make the linear system of equations Mx = d which results in the moments of the periodic spline.

When solving Mx = d, it should be noted that x[0] is trash and needs to be set to x[n-1]

◆ moment_()

template<class ScalarT >

Scalar Dumux::VariableLengthSpline_< ScalarT >::moment_ ( int i ) const

inlineprotected

Returns the moment (i.e. second derivative) of the spline at the i-th sampling point.

◆ monotonic() [1/2]

int Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::monotonic ( ) const

inlineinherited

Same as monotonic(x0, x1), but with the entire range of the spline as interval.

◆ monotonic() [2/2]

int Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::monotonic	(	Scalar	x0,
		Scalar	x1
	)		const

inlineinherited

Returns 1 if the spline is monotonically increasing, -1 if the spline is mononously decreasing and 0 if the spline is not monotonous in the interval (x0, x1).

In the corner case where the whole spline is flat, it returns 2.

◆ monotonic_()

int Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::monotonic_	(	int	i,
		Scalar	x0,
		Scalar	x1
	)		const

inlineprotectedinherited

◆ numSamples()

template<class ScalarT >

int Dumux::VariableLengthSpline_< ScalarT >::numSamples ( ) const

inline

Returns the number of sampling points.

◆ numSamples_()

int Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::numSamples_ ( ) const

inlineprotectedinherited

Returns the number of sampling points.

◆ printCSV()

void Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::printCSV	(	Scalar	xi0,
		Scalar	xi1,
		int	k
	)		const

inlineinherited

Prints k tuples of the format (x, y, dx/dy, isMonotonic) to stdout.

If the spline does not apply for parts of [x0, x1] it is extrapolated using a straight line. The result can be inspected using the following commands:

--------— snip --------— ./yourProgramm > spline.csv gnuplot

gnuplot> plot "spline.csv" using 1:2 w l ti "Curve", \ "spline.csv" using 1:3 w l ti "Derivative", \ "spline.csv" using 1:4 w p ti "Monotonic" --------— snap --------—

◆ segmentIdx_()

int Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::segmentIdx_ ( Scalar x ) const

inlineprotectedinherited

◆ setArrayOfPoints() [1/2]

template<class ScalarT >

template<class PointArray >

void Dumux::VariableLengthSpline_< ScalarT >::setArrayOfPoints	(	int	nSamples,
		const PointArray &	points
	)

inline

Set the sampling points of a natural spline using a C-style array.

This method uses a single array of sampling points, which are seen as an array-like object which provides access to the X and Y coordinates. In this context 'array-like' means that an access to the members is provided via the [] operator. (e.g. C arrays, std::vector, std::array, etc.) The array containing the sampling points must be of size 'nSamples' at least. Also, the number of sampling points must be larger than 1.

◆ setArrayOfPoints() [2/2]

template<class ScalarT >

template<class PointArray >

void Dumux::VariableLengthSpline_< ScalarT >::setArrayOfPoints	(	int	nSamples,
		const PointArray &	points,
		Scalar	m0,
		Scalar	m1
	)

inline

Set the sampling points and the boundary slopes of a full spline using a C-style array.

This method uses a single array of sampling points, which are seen as an array-like object which provides access to the X and Y coordinates. In this context 'array-like' means that an access to the members is provided via the [] operator. (e.g. C arrays, std::vector, std::array, etc.) The array containing the sampling points must be of size 'nSamples' at least. Also, the number of sampling points must be larger than 1.

◆ setContainerOfPoints() [1/2]

template<class ScalarT >

template<class XYContainer >

void Dumux::VariableLengthSpline_< ScalarT >::setContainerOfPoints ( const XYContainer & points )

inline

Set the sampling points of a natural spline using a STL-compatible container of array-like objects.

This method uses a single STL-compatible container of sampling points, which are assumed to be array-like objects storing the X and Y coordinates. "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setContainerOfPoints() [2/2]

template<class ScalarT >

template<class XYContainer >

void Dumux::VariableLengthSpline_< ScalarT >::setContainerOfPoints	(	const XYContainer &	points,
		Scalar	m0,
		Scalar	m1
	)

inline

Set the sampling points and the boundary slopes of a full spline using a STL-compatible container of array-like objects.

This method uses a single STL-compatible container of sampling points, which are assumed to be array-like objects storing the X and Y coordinates. "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setContainerOfTuples() [1/2]

template<class ScalarT >

template<class XYContainer >

void Dumux::VariableLengthSpline_< ScalarT >::setContainerOfTuples ( const XYContainer & points )

inline

Set the sampling points of a natural spline using a STL-compatible container of tuple-like objects.

This method uses a single STL-compatible container of sampling points, which are assumed to be tuple-like objects storing the X and Y coordinates. "tuple-like" means that the objects provide access to the x values via std::get<0>(obj) and to the y value via std::get<1>(obj) (e.g. std::tuple or std::pair). "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setContainerOfTuples() [2/2]

template<class ScalarT >

template<class XYContainer >

void Dumux::VariableLengthSpline_< ScalarT >::setContainerOfTuples	(	const XYContainer &	points,
		Scalar	m0,
		Scalar	m1
	)

inline

Set the sampling points and the boundary slopes of a full spline using a STL-compatible container of tuple-like objects.

This method uses a single STL-compatible container of sampling points, which are assumed to be tuple-like objects storing the X and Y coordinates. "tuple-like" means that the objects provide access to the x values via std::get<0>(obj) and to the y value via std::get<1>(obj) (e.g. std::tuple or std::pair). "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setNumSamples_()

template<class ScalarT >

void Dumux::VariableLengthSpline_< ScalarT >::setNumSamples_ ( int nSamples )

inlineprotected

Resizes the internal vectors to store the sample points.

◆ setXYArrays() [1/2]

template<class ScalarT >

template<class ScalarArrayX , class ScalarArrayY >

void Dumux::VariableLengthSpline_< ScalarT >::setXYArrays	(	int	nSamples,
		const ScalarArrayX &	x,
		const ScalarArrayY &	y
	)

inline

Set the sampling points natural spline using C-style arrays.

This method uses separate array-like objects for the values of the X and Y coordinates. In this context 'array-like' means that an access to the members is provided via the [] operator. (e.g. C arrays, std::vector, std::array, etc.) Each array must be of size 'nSamples' at least. Also, the number of sampling points must be larger than 1.

◆ setXYArrays() [2/2]

template<class ScalarT >

template<class ScalarArrayX , class ScalarArrayY >

void Dumux::VariableLengthSpline_< ScalarT >::setXYArrays	(	int	nSamples,
		const ScalarArrayX &	x,
		const ScalarArrayY &	y,
		Scalar	m0,
		Scalar	m1
	)

inline

Set the sampling points and the boundary slopes of a full spline using C-style arrays.

This method uses separate array-like objects for the values of the X and Y coordinates. In this context 'array-like' means that an access to the members is provided via the [] operator. (e.g. C arrays, std::vector, std::array, etc.) Each array must be of size 'nSamples' at least. Also, the number of sampling points must be larger than 1.

◆ setXYContainers() [1/2]

template<class ScalarT >

template<class ScalarContainerX , class ScalarContainerY >

void Dumux::VariableLengthSpline_< ScalarT >::setXYContainers	(	const ScalarContainerX &	x,
		const ScalarContainerY &	y
	)

inline

Set the sampling points of a natural spline using STL-compatible containers.

This method uses separate STL-compatible containers for the values of the sampling points' X and Y coordinates. "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ setXYContainers() [2/2]

template<class ScalarT >

template<class ScalarContainerX , class ScalarContainerY >

void Dumux::VariableLengthSpline_< ScalarT >::setXYContainers	(	const ScalarContainerX &	x,
		const ScalarContainerY &	y,
		Scalar	m0,
		Scalar	m1
	)

inline

Set the sampling points and the boundary slopes of a full spline using STL-compatible containers.

This method uses separate STL-compatible containers for the values of the sampling points' X and Y coordinates. "STL-compatible" means that the container provides access to iterators using the begin(), end() methods and also provides a size() method. Also, the number of entries in the X and the Y containers must be equal and larger than 1.

◆ x_()

template<class ScalarT >

Scalar Dumux::VariableLengthSpline_< ScalarT >::x_ ( int i ) const

inlineprotected

Returns the x coordinate of the i-th sampling point.

◆ xMax()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::xMax ( ) const

inlineinherited

Return the x value of the rightmost sampling point.

◆ xMin()

Scalar Dumux::SplineCommon_< ScalarT, VariableLengthSpline_< ScalarT > >::xMin ( ) const

inlineinherited

Return the x value of the leftmost sampling point.

◆ y_()

template<class ScalarT >

Scalar Dumux::VariableLengthSpline_< ScalarT >::y_ ( int i ) const

inlineprotected

Returns the y coordinate of the i-th sampling point.

Member Data Documentation

◆ m_

template<class ScalarT >

Vector Dumux::VariableLengthSpline_< ScalarT >::m_

protected

◆ xPos_

template<class ScalarT >

Vector Dumux::VariableLengthSpline_< ScalarT >::xPos_

protected

◆ yPos_

template<class ScalarT >

Vector Dumux::VariableLengthSpline_< ScalarT >::yPos_

protected

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

variablelengthspline_.hh

Description

Public Member Functions

Protected Member Functions

Protected Attributes

Member Function Documentation

◆ a_()

◆ applies()

◆ assignFromArrayList_()

◆ assignFromTupleList_()

◆ assignSamplingPoints_()

◆ b_()

◆ c_()

◆ d_()

◆ eval()

◆ eval_()

◆ evalDerivative()

◆ evalDerivative_()

◆ h_()

◆ intersect()

◆ intersectInterval()

◆ intersectSegment_()

◆ makeFullSpline_()

◆ makeFullSystem_()

◆ makeNaturalSpline_()

◆ makeNaturalSystem_()

◆ makePeriodicSystem_()

◆ moment_()

◆ monotonic() [1/2]

◆ monotonic() [2/2]

◆ monotonic_()

◆ numSamples()

◆ numSamples_()

◆ printCSV()

◆ segmentIdx_()

◆ setArrayOfPoints() [1/2]

◆ setArrayOfPoints() [2/2]

◆ setContainerOfPoints() [1/2]

◆ setContainerOfPoints() [2/2]

◆ setContainerOfTuples() [1/2]

◆ setContainerOfTuples() [2/2]

◆ setNumSamples_()

◆ setXYArrays() [1/2]

◆ setXYArrays() [2/2]

◆ setXYContainers() [1/2]

◆ setXYContainers() [2/2]

◆ x_()

◆ xMax()

◆ xMin()

◆ y_()

Member Data Documentation

◆ m_

◆ xPos_

◆ yPos_