Base class for spline interpolations with C2 (second order parametric) continuity. More...

#include <qwt_spline.h>

Inheritance diagram for QwtSplineC2:

Public Types
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...

Public Member Functions
	QwtSplineC2 ()
	Constructor.

	~QwtSplineC2 () override
	Destructor.

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

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

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

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

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

virtual QVector< double >	curvatures (const QPolygonF &) const =0
	Find the second derivative at the control 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.

virtual uint	locality () const
	Get locality (number of points used for calculation)

Detailed Description

Base class for spline interpolations with C2 (second order parametric) continuity.

All interpolations with C2 continuity are based on rules for finding the second derivative at some control points.

For non-parametric splines those points are the curve points, while for parametric splines the calculation is done twice using a parameter value t.

See also: QwtSplineParametrization

Member Enumeration Documentation

◆ BoundaryConditionC2

enum QwtSplineC2::BoundaryConditionC2

Boundary condition that requires C2 continuity.

See also: QwtSpline::boundaryCondition, QwtSpline::BoundaryCondition

Enumerator

CubicRunout

The second derivate at the endpoint is related to the second derivatives at the 2 neighbours: cv[0] := 2.0 * cv[1] - cv[2].

Note: boundaryValue() is ignored

NotAKnot

The 3rd derivate at the endpoint matches the 3rd derivate at its neighbours.

Or in other words: the first/last curve segment extents the polynomial of its neighboured polynomial

Note: boundaryValue() is ignored

Constructor & Destructor Documentation

◆ QwtSplineC2()

QwtSplineC2::QwtSplineC2 ( )

Constructor.

The default setting is a non-closing spline with no parametrization (QwtSplineParametrization::ParameterX).

See also: QwtSpline::setParametrization(), QwtSpline::setBoundaryType()

Member Function Documentation

◆ bezierControlLines()

QVector< QLineF > QwtSplineC2::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

[in] points Control points

Returns: Control points of the interpolating Bezier curves

Note: The implementation simply calls QwtSplineC1::bezierControlLines(), but is intended to be replaced by a more efficient implementation that builds the polynomials by the curvatures some day.

Reimplemented from QwtSplineC1.

Reimplemented in QwtSplineCubic.

◆ curvatures()

QVector< double > QwtSplineC2::curvatures ( const QPolygonF & points ) const

pure 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

Implemented in QwtSplineCubic.

◆ equidistantPolygon()

QPolygonF QwtSplineC2::equidistantPolygon	(	const QPolygonF &	points,
		double	distance,
		bool	withNodes
	)		const

overridevirtual

Find an interpolated polygon with "equidistant" points.

The implementation is optimized for non-parametric curves (QwtSplineParametrization::ParameterX) and falls back to QwtSpline::equidistantPolygon() otherwise.

Parameters

[in]	points	Control nodes of the spline
[in]	distance	Distance between 2 points according to the parametrization
[in]	withNodes	When true, also add the control nodes (even if not being equidistant)

Returns: Interpolating polygon

See also: QwtSpline::equidistantPolygon()

Reimplemented from QwtSplineC1.

◆ painterPath()

QPainterPath QwtSplineC2::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

[in] points Control points

Returns: Painter path that can be rendered by QPainter

Note: The implementation simply calls QwtSplineC1::painterPath(), but is intended to be replaced by a one-pass calculation some day.

Reimplemented from QwtSplineC1.

Reimplemented in QwtSplineCubic.

◆ polynomials()

QVector< QwtSplinePolynomial > QwtSplineC2::polynomials ( const QPolygonF & points ) const

overridevirtual

Calculate the interpolating polynomials for a non-parametric spline.

C2 spline interpolations are based on finding values for the second derivatives of f at the control points. The interpolating polynomials can be calculated from the second derivatives using QwtSplinePolynomial::fromCurvatures.

The default implementation is a two-pass calculation. In derived classes it might be overloaded by a one-pass implementation.

Parameters

[in] points Control points

Returns: Interpolating polynomials

Note: The x coordinates need to be increasing or decreasing

Reimplemented from QwtSplineC1.

Reimplemented in QwtSplineCubic.

◆ slopes()

QVector< double > QwtSplineC2::slopes ( const QPolygonF & points ) const

overridevirtual

Find the first derivative at the control points.

An implementation calculating the second derivatives and then building the slopes in a second loop. QwtSplineCubic overloads it with a more performant implementation doing it in one loop.

Parameters

[in] points Control nodes of the spline

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

See also: curvatures()

Note: The x coordinates need to be increasing or decreasing

Implements QwtSplineC1.

Reimplemented in QwtSplineCubic.

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

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

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ BoundaryConditionC2

Constructor & Destructor Documentation

◆ QwtSplineC2()

Member Function Documentation

◆ bezierControlLines()

◆ curvatures()

◆ equidistantPolygon()

◆ painterPath()

◆ polynomials()

◆ slopes()