A cubic spline. More...

#include <qwt_spline_cubic.h>

Inheritance diagram for QwtSplineCubic:

[legend]

Classes
class	PrivateData

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

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

virtual uint	locality () const

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

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

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

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

virtual	~QwtSplineCubic ()
	Destructor. More...

Public Member Functions inherited from QwtSplineC2
virtual QPolygonF	equidistantPolygon (const QPolygonF &, double distance, bool withNodes) const
	Find an interpolated polygon with "equidistant" points. More...

	QwtSplineC2 ()
	Constructor. More...

virtual	~QwtSplineC2 ()
	Destructor. More...

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

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

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

virtual	~QwtSplineC1 ()
	Destructor. More...

Public Member Functions inherited from QwtSplineG1
	QwtSplineG1 ()
	Constructor. More...

virtual	~QwtSplineG1 ()
	Destructor. More...

Public Member Functions inherited from QwtSplineInterpolating
virtual QPolygonF	polygon (const QPolygonF &, double tolerance) const
	Interpolate a curve by a polygon. More...

	QwtSplineInterpolating ()
	Constructor. More...

virtual	~QwtSplineInterpolating ()
	Destructor. More...

Public Member Functions inherited from QwtSpline
int	boundaryCondition (BoundaryPosition) const

BoundaryType	boundaryType () const

double	boundaryValue (BoundaryPosition) const

const QwtSplineParametrization *	parametrization () const

	QwtSpline ()
	Constructor. More...

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

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

void	setBoundaryType (BoundaryType)

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

void	setParametrization (int type)

void	setParametrization (QwtSplineParametrization *)

virtual	~QwtSpline ()
	Destructor. More...

Private Attributes
PrivateData *	d_data

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

Public Types inherited from QwtSpline
enum	BoundaryCondition { Clamped1, Clamped2, Clamped3, LinearRunout }
	Boundary condition. More...

enum	BoundaryPosition { AtBeginning, AtEnd }

enum	BoundaryType { ConditionalBoundaries, PeriodicPolygon, ClosedPolygon }

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

Definition at line 33 of file qwt_spline_cubic.h.

Constructor & Destructor Documentation

QwtSplineCubic::QwtSplineCubic ( )

Constructor The default setting is a non closing natural spline with no parametrization.

Definition at line 965 of file qwt_spline_cubic.cpp.

QwtSplineCubic::~QwtSplineCubic ( )

virtual

Destructor.

Definition at line 979 of file qwt_spline_cubic.cpp.

Member Function Documentation

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.

Definition at line 1150 of file qwt_spline_cubic.cpp.

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.

Definition at line 1079 of file qwt_spline_cubic.cpp.

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.

Definition at line 990 of file qwt_spline_cubic.cpp.

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.

Definition at line 1131 of file qwt_spline_cubic.cpp.

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.

Definition at line 1168 of file qwt_spline_cubic.cpp.

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.

Definition at line 1007 of file qwt_spline_cubic.cpp.

Member Data Documentation

PrivateData* QwtSplineCubic::d_data

private

Definition at line 50 of file qwt_spline_cubic.h.

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

Classes

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation