A cubic spline. More...

#include <qwt_spline_cubic.h>

Inheritance diagram for QwtSplineCubic:

Classes
class	PrivateData

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

virtual	~QwtSplineCubic ()
	Destructor.

virtual uint	locality () const QWT_OVERRIDE
	A cubic spline is non local, where changing one point has em effect on all polynomials.

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

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

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

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

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

Public Member Functions inherited from QwtSplineC2
	QwtSplineC2 ()
	Constructor.

virtual	~QwtSplineC2 ()
	Destructor.

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

Public Member Functions inherited from QwtSplineC1
	QwtSplineC1 ()
	Constructor.

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 QWT_OVERRIDE
	Interpolate a curve by a polygon.

Public Member Functions inherited from QwtSpline
	QwtSpline ()
	Constructor.

virtual	~QwtSpline ()
	Destructor.

void	setParametrization (int type)
	Define the parametrization for a parametric spline approximation The default setting is a chordal parametrization.

void	setParametrization (QwtSplineParametrization *)
	Define the parametrization for a parametric spline approximation The default setting is a chordal parametrization.

const QwtSplineParametrization *	parametrization () const

void	setBoundaryType (BoundaryType)
	Define the boundary type for the endpoints of the approximating spline.

BoundaryType	boundaryType () const

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

double	boundaryValue (BoundaryPosition) const

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

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.

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, 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.

Todo:: The implementation is not numerical stable

Member Function Documentation

◆ bezierControlLines()

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

virtual

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.

◆ curvatures()

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

virtual

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.

◆ locality()

uint QwtSplineCubic::locality ( ) const

virtual

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

Returns: 0

Reimplemented from QwtSpline.

◆ painterPath()

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

virtual

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.

◆ polynomials()

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

virtual

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.

◆ slopes()

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

virtual

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.

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

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

Classes

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ bezierControlLines()

◆ curvatures()

◆ locality()

◆ painterPath()

◆ polynomials()

◆ slopes()