A spline with C1 continuity. More...

#include <qwt_spline_local.h>

Inheritance diagram for QwtSplineLocal:

Public Types
enum	Type { Cardinal , ParabolicBlending , Akima , PChip }
	Spline interpolation type. More...

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

enum	BoundaryPosition { AtBeginning , AtEnd }

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

Public Member Functions
	QwtSplineLocal (Type type)
	Constructor.

virtual	~QwtSplineLocal ()
	Destructor.

Type	type () const

virtual uint	locality () const override

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 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.

Public Member Functions inherited from QwtSplineC1
	QwtSplineC1 ()
	Constructor.

virtual	~QwtSplineC1 ()
	Destructor.

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

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.

Public Member Functions inherited from QwtSpline
	QwtSpline ()
	Constructor.

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.

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.

Detailed Description

A spline with C1 continuity.

QwtSplineLocal offers several standard algorithms for interpolating a curve with polynomials having C1 continuity at the control points. All algorithms are local in a sense, that changing one control point only few polynomials.

Definition at line 24 of file qwt_spline_local.h.

Member Enumeration Documentation

◆ Type

enum QwtSplineLocal::Type

Spline interpolation type.

All type of spline interpolations are lightweight algorithms calculating the slopes at a point by looking 1 or 2 points back and ahead.

Enumerator
Cardinal	A cardinal spline The cardinal spline interpolation is a very cheap calculation with a locality of 1.
ParabolicBlending	Parabolic blending is a cheap calculation with a locality of 1. Sometimes it is also called Cubic Bessel interpolation.
Akima	The algorithm of H.Akima is a calculation with a locality of 2.
PChip	Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) is an algorithm that is popular because of being offered by MATLAB. It preserves the shape of the data and respects monotonicity. It has a locality of 1.

Definition at line 34 of file qwt_spline_local.h.

Constructor & Destructor Documentation

◆ QwtSplineLocal()

QwtSplineLocal::QwtSplineLocal ( Type type )

Constructor.

Parameters

type	Spline type, specifying the type of interpolation

See also: type()

Definition at line 450 of file qwt_spline_local.cpp.

◆ ~QwtSplineLocal()

QwtSplineLocal::~QwtSplineLocal ( )

virtual

Destructor.

Definition at line 461 of file qwt_spline_local.cpp.

Member Function Documentation

◆ bezierControlLines()

QVector< QLineF > QwtSplineLocal::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

Reimplemented from QwtSplineC1.

Definition at line 502 of file qwt_spline_local.cpp.

◆ locality()

uint QwtSplineLocal::locality ( ) const

overridevirtual

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

The Cardinal, ParabolicBlending and PChip algorithms have a locality of 1, while the Akima interpolation has a locality of 2.

Returns: 1 or 2.

Reimplemented from QwtSpline.

Definition at line 552 of file qwt_spline_local.cpp.

◆ painterPath()

QPainterPath QwtSplineLocal::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

Reimplemented from QwtSplineC1.

Definition at line 482 of file qwt_spline_local.cpp.

◆ polynomials()

QVector< QwtSplinePolynomial > QwtSplineLocal::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 QwtSplineC1::polynomials(), but is intended to be replaced by a one pass calculation some day.

Reimplemented from QwtSplineC1.

Definition at line 537 of file qwt_spline_local.cpp.

◆ slopes()

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

overridevirtual

Find the first 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

Note: The x coordinates need to be increasing or decreasing

Implements QwtSplineC1.

Definition at line 521 of file qwt_spline_local.cpp.

◆ type()

QwtSplineLocal::Type QwtSplineLocal::type ( ) const

Returns: Spline type, specifying the type of interpolation

Definition at line 468 of file qwt_spline_local.cpp.

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ Type

Constructor & Destructor Documentation

◆ QwtSplineLocal()

◆ ~QwtSplineLocal()

Member Function Documentation

◆ bezierControlLines()

◆ locality()

◆ painterPath()

◆ polynomials()

◆ slopes()

◆ type()