A cubic spline. More...

#include <qwt_spline_cubic.h>

Inheritance diagram for QwtSplineCubic:

Classes
class	PrivateData

Public Member Functions
	QwtSplineCubic ()
	Constructor.

	~QwtSplineCubic () override
	Destructor.

virtual uint	locality () const override
	Get locality (always 0 - non-local)

virtual QPainterPath	painterPath (const QPolygonF &) const override
	Get painter path from polygon.

virtual QVector< QLineF >	bezierControlLines (const QPolygonF &points) const override
	Get Bezier control lines.

virtual QVector< QwtSplinePolynomial >	polynomials (const QPolygonF &) const override
	Get polynomials from polygon.

virtual QVector< double >	slopes (const QPolygonF &) const override
	Get slopes at control points.

virtual QVector< double >	curvatures (const QPolygonF &) const override
	Get curvatures at control points.

Public Member Functions inherited from QwtSplineC2
	QwtSplineC2 ()
	Constructor.

	~QwtSplineC2 () override
	Destructor.

virtual QPolygonF	equidistantPolygon (const QPolygonF &, double distance, bool withNodes) const override
	Find an interpolated polygon with "equidistant" points.

Public Member Functions inherited from QwtSplineC1
	QwtSplineC1 ()
	Constructor.

	~QwtSplineC1 () override
	Destructor.

virtual double	slopeAtBeginning (const QPolygonF &, double slopeNext) const
	Calculate the slope at the beginning of the spline.

virtual double	slopeAtEnd (const QPolygonF &, double slopeBefore) const
	Calculate the slope at the end of the spline.

Public Member Functions inherited from QwtSplineG1
	QwtSplineG1 ()
	Constructor.

	~QwtSplineG1 () override
	Destructor.

Public Member Functions inherited from QwtSplineInterpolating
	QwtSplineInterpolating ()
	Constructor.

	~QwtSplineInterpolating () override
	Destructor.

virtual QPolygonF	polygon (const QPolygonF &, double tolerance) const override
	Interpolate a curve by a polygon.

Public Member Functions inherited from QwtSpline
	QwtSpline ()
	Constructor.

virtual	~QwtSpline ()
	Destructor.

void	setParametrization (int type)
	Set parametrization by type.

void	setParametrization (QwtSplineParametrization *)
	Set parametrization object.

const QwtSplineParametrization *	parametrization () const
	Get parametrization.

void	setBoundaryType (BoundaryType)
	Set boundary type.

BoundaryType	boundaryType () const
	Get boundary type.

void	setBoundaryValue (BoundaryPosition, double value)
	Set boundary value.

double	boundaryValue (BoundaryPosition) const
	Get boundary value.

void	setBoundaryCondition (BoundaryPosition, int condition)
	Set boundary condition.

int	boundaryCondition (BoundaryPosition) const
	Get boundary condition.

void	setBoundaryConditions (int condition, double valueBegin=0.0, double valueEnd=0.0)
	Set boundary conditions for both ends.

Additional Inherited Members
Public Types inherited from QwtSplineC2
enum	BoundaryConditionC2 { CubicRunout = LinearRunout + 1 , NotAKnot }
	Boundary condition that requires C2 continuity. More...

Public Types inherited from QwtSpline
enum	BoundaryType { ConditionalBoundaries , PeriodicPolygon , ClosedPolygon }
	Boundary type specifying the spline at its endpoints. More...

enum	BoundaryPosition { AtBeginning , AtEnd }
	position of a boundary condition More...

enum	BoundaryCondition { Clamped1 , Clamped2 , Clamped3 , LinearRunout }
	Boundary condition. More...

Detailed Description

A cubic spline.

A cubic spline is a spline with C2 continuity at all control points. It is a non local spline, where a modification of one control point affects the whole spline.

The implementation is based on the equation system of the second derivatives M(x) of the control points P(x).

QwtSplineCubic offers several algorithms for finding M(x), that are selected by setBoundaryType().

The default setting is a "natural spline" having M(x0) = M(xn) = 0.

See also: QwtSpline::BoundaryType

Constructor & Destructor Documentation

◆ QwtSplineCubic()

QwtSplineCubic::QwtSplineCubic ( )

Constructor.

The default setting is a non-closing natural spline with no parametrization.

Destructor

Member Function Documentation

◆ bezierControlLines()

QVector< QLineF > QwtSplineCubic::bezierControlLines ( const QPolygonF & points ) const

overridevirtual

Get Bezier control lines.

Interpolate a curve with Bezier curves.

Interpolates a polygon piecewise with cubic Bezier curves and returns the 2 control points of each curve as QLineF.

Parameters

[in] points Control points

Returns: Control points of the interpolating Bezier curves

Note: The implementation simply calls QwtSplineC1::bezierControlLines()

Reimplemented from QwtSplineC2.

◆ curvatures()

QVector< double > QwtSplineCubic::curvatures ( const QPolygonF & points ) const

overridevirtual

Get curvatures at control points.

Find the second derivative at the control points.

Parameters

[in] points Control nodes of the spline

Returns: Vector with the values of the second derivative at the control points

See also: slopes()

Note: The x coordinates need to be increasing or decreasing

Implements QwtSplineC2.

◆ locality()

uint QwtSplineCubic::locality ( ) const

overridevirtual

Get locality (always 0 - non-local)

Get locality.

A cubic spline is non-local, where changing one point has an effect on all polynomials.

Returns: 0

Reimplemented from QwtSpline.

◆ painterPath()

QPainterPath QwtSplineCubic::painterPath ( const QPolygonF & points ) const

overridevirtual

Get painter path from polygon.

Interpolate a curve with Bezier curves.

Interpolates a polygon piecewise with cubic Bezier curves and returns them as QPainterPath.

Parameters

[in] points Control points

Returns: Painter path that can be rendered by QPainter

Note: The implementation simply calls QwtSplineC1::painterPath()

Reimplemented from QwtSplineC2.

◆ polynomials()

QVector< QwtSplinePolynomial > QwtSplineCubic::polynomials ( const QPolygonF & points ) const

overridevirtual

Get polynomials from polygon.

Calculate the interpolating polynomials for a non-parametric spline.

Parameters

[in] points Control points

Returns: Interpolating polynomials

Note: The x coordinates need to be increasing or decreasing; The implementation simply calls QwtSplineC2::polynomials(), but is intended to be replaced by a one-pass calculation some day.

Reimplemented from QwtSplineC2.

◆ slopes()

QVector< double > QwtSplineCubic::slopes ( const QPolygonF & points ) const

overridevirtual

Get slopes at control points.

Find the first derivative at the control points.

In contrast to the QwtSplineC2::slopes implementation, the first derivatives are calculated directly, without calculating the second derivatives first.

Parameters

[in] points Control nodes of the spline

Returns: Vector with the values of the first derivative at the control points

See also: curvatures(), QwtSplinePolynomial::fromCurvatures()

Note: The x coordinates need to be increasing or decreasing

Reimplemented from QwtSplineC2.

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

/home/runner/work/QWT/QWT/src/plot/qwt_spline_cubic.h
/home/runner/work/QWT/QWT/src/plot/qwt_spline_cubic.cpp

Classes

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ QwtSplineCubic()

Member Function Documentation

◆ bezierControlLines()

◆ curvatures()

◆ locality()

◆ painterPath()

◆ polynomials()

◆ slopes()