A cubic spline. More...

#include <qwt_spline_cubic.h>

Inheritance diagram for QwtSplineCubic:

Public Member Functions
	QwtSplineCubic ()
	Constructor The default setting is a non closing natural spline with no parametrization.

virtual	~QwtSplineCubic ()
	Destructor.

virtual uint	locality () const override

virtual QPainterPath	painterPath (const QPolygonF &) const override
	Interpolate a curve with Bezier curves. More...

virtual QVector< QLineF >	bezierControlLines (const QPolygonF &points) const override
	Interpolate a curve with Bezier curves. More...

virtual QVector< QwtSplinePolynomial >	polynomials (const QPolygonF &) const override
	Calculate the interpolating polynomials for a non parametric spline. More...

virtual QVector< double >	slopes (const QPolygonF &) const override
	Find the first derivative at the control points. More...

virtual QVector< double >	curvatures (const QPolygonF &) const override
	Find the second derivative at the control points. More...

Public Member Functions inherited from QwtSplineC2
	QwtSplineC2 ()
	Constructor. More...

virtual	~QwtSplineC2 ()
	Destructor.

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

Public Member Functions inherited from QwtSplineC1
	QwtSplineC1 ()
	Constructor. More...

virtual	~QwtSplineC1 ()
	Destructor.

virtual double	slopeAtBeginning (const QPolygonF &, double slopeNext) const

virtual double	slopeAtEnd (const QPolygonF &, double slopeBefore) const

Public Member Functions inherited from QwtSplineG1
	QwtSplineG1 ()
	Constructor.

virtual	~QwtSplineG1 ()
	Destructor.

Public Member Functions inherited from QwtSplineInterpolating
	QwtSplineInterpolating ()
	Constructor.

virtual	~QwtSplineInterpolating ()
	Destructor.

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

Public Member Functions inherited from QwtSpline
	QwtSpline ()
	Constructor. More...

virtual	~QwtSpline ()
	Destructor.

void	setParametrization (int type)

void	setParametrization (QwtSplineParametrization *)

const QwtSplineParametrization *	parametrization () const

void	setBoundaryType (BoundaryType)

BoundaryType	boundaryType () const

void	setBoundaryValue (BoundaryPosition, double value)
	Define the boundary value. More...

double	boundaryValue (BoundaryPosition) const

void	setBoundaryCondition (BoundaryPosition, int condition)
	Define the condition for an endpoint of the spline. More...

int	boundaryCondition (BoundaryPosition) const

void	setBoundaryConditions (int condition, double valueBegin=0.0, double valueEnd=0.0)
	Define the condition at the endpoints of a spline. More...

Additional Inherited Members
Public Types inherited from QwtSplineC2
enum	BoundaryConditionC2 { CubicRunout = LinearRunout + 1 , NotAKnot }

Public Types inherited from QwtSpline
enum	BoundaryType { ConditionalBoundaries , PeriodicPolygon , ClosedPolygon }

enum	BoundaryPosition { AtBeginning , AtEnd }

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, what means that all polynomials are changing when one control point has changed.

The implementation is based on the fact, that the continuity condition means an equation with 3 unknowns for 3 adjacent points. The equation system can be resolved by defining start/end conditions, that allow substituting of one of the unknowns for the start/end equations.

Resolving the equation system is a 2 pass algorithm, requiring more CPU costs than all other implemented type of splines.

Definition at line 33 of file qwt_spline_cubic.h.

Member Function Documentation

◆ bezierControlLines()

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

overridevirtual

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

points Control points

Returns: Control points of the interpolating Bezier curves

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

Reimplemented from QwtSplineC2.

Definition at line 1149 of file qwt_spline_cubic.cpp.

◆ curvatures()

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

overridevirtual

Find the second derivative at the control points.

Parameters

points Control nodes of the spline

Returns: Vector with the values of the 2nd derivate at the control points

See also: slopes()

Note: The x coordinates need to be increasing or decreasing

Implements QwtSplineC2.

Definition at line 1078 of file qwt_spline_cubic.cpp.

◆ locality()

uint QwtSplineCubic::locality ( ) const

overridevirtual

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

Returns: 0

Reimplemented from QwtSpline.

Definition at line 989 of file qwt_spline_cubic.cpp.

◆ painterPath()

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

overridevirtual

Interpolate a curve with Bezier curves.

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

Parameters

points Control points

Returns: Painter path, that can be rendered by QPainter

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

Reimplemented from QwtSplineC2.

Definition at line 1130 of file qwt_spline_cubic.cpp.

◆ polynomials()

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

overridevirtual

Calculate the interpolating polynomials for a non parametric spline.

Parameters

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.

Definition at line 1167 of file qwt_spline_cubic.cpp.

◆ slopes()

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

overridevirtual

Find the first derivative at the control points.

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

Parameters

points Control nodes of the spline

Returns: Vector with the values of the 2nd derivate at the control points

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

Note: The x coordinates need to be increasing or decreasing

Reimplemented from QwtSplineC2.

Definition at line 1006 of file qwt_spline_cubic.cpp.

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ bezierControlLines()

◆ curvatures()

◆ locality()

◆ painterPath()

◆ polynomials()

◆ slopes()