Base class for spline interpolations providing a second order parametric continuity ( C2 ) between adjoining curves. 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.

virtual	~QwtSplineC2 ()
	Destructor.

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

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

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

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 =0
	Find the second derivative at the control 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.

virtual uint	locality () const
	The locality of an spline interpolation identifies how many adjacent polynomials are affected, when changing the position of one point.

Detailed Description

Base class for spline interpolations providing a second order parametric continuity ( C2 ) between adjoining curves.

All interpolations with C2 continuity are based on rules for finding the 2. derivate at some control points.

In case of 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

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(), 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

virtual

Find an interpolated polygon with "equidistant" points.

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

Parameters

points	Control nodes of the spline
distance	Distance between 2 points according to the parametrization
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

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(), 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

virtual

Calculate the interpolating polynomials for a non parametric spline.

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

The default implementation is a 2 pass calculation. In derived classes it might be overloaded by a one pass implementation.

Parameters

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

virtual

Find the first derivative at the control points.

An implementation calculating the 2nd derivatives and then building the slopes in a 2nd loop. QwtSplineCubic overloads it with a more performant implementation doing it in one loop.

Parameters

points Control nodes of the spline

Returns: Vector with the values of the 1nd derivate 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/qwt_spline.h
/home/runner/work/QWT/QWT/src/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()