QwtSplineCubic - A cubic spline.

NAME SYNOPSIS Public Member Functions Additional Inherited Members Detailed Description Constructor & Destructor Documentation QwtSplineCubic::QwtSplineCubic () QwtSplineCubic::˜QwtSplineCubic () [virtual] Member Function Documentation QVector< QLineF > QwtSplineCubic::bezierControlLines (const QPolygonF &points) const [override], [virtual] QVector< double > QwtSplineCubic::curvatures (const QPolygonF & points)const [override], [virtual] uint QwtSplineCubic::locality () const [override], [virtual] QPainterPath QwtSplineCubic::painterPath (const QPolygonF & points) const[override], [virtual] QVector< QwtSplinePolynomial > QwtSplineCubic::polynomials (const QPolygonF& points) const [override], [virtual] QVector< double > QwtSplineCubic::slopes (const QPolygonF & points) const[override], [virtual] Author

SYNOPSIS

#include <qwt_spline_cubic.h>

Inherits QwtSplineC2.

Public Member Functions

QwtSplineCubic ()
Constructor The default setting is a non closing natural spline with no parametrization.
virtual ˜QwtSplineCubic ()
Destructor.
virtual uint locality () const override
virtual QPainterPath painterPath (const QPolygonF &) const override
Interpolate a curve with Bezier curves.
virtual QVector< QLineF > bezierControlLines (const QPolygonF &points) 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.
virtual QVector< double > curvatures (const QPolygonF &) const 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 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 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.

Additional Inherited Members

Public Types inherited from QwtSplineC2

enum BoundaryConditionC2 { CubicRunout = LinearRunout + 1, NotAKnot }

Public Types inherited from QwtSpline

enum BoundaryType { ConditionalBoundaries, PeriodicPolygon, ClosedPolygon }
enum BoundaryPosition { AtBeginning, AtEnd }
enum BoundaryCondition { Clamped1, Clamped2, Clamped3, LinearRunout }
Boundary condition.

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.

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 966 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 [override], [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 1149 of file qwt_spline_cubic.cpp.

QVector< double > QwtSplineCubic::curvatures (const QPolygonF & points)const [override], [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 1078 of file qwt_spline_cubic.cpp.

uint QwtSplineCubic::locality () const [override], [virtual]

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

Returns

Reimplemented from QwtSpline.

Definition at line 989 of file qwt_spline_cubic.cpp.

QPainterPath QwtSplineCubic::painterPath (const QPolygonF & points) const[override], [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 1130 of file qwt_spline_cubic.cpp.

QVector< QwtSplinePolynomial > QwtSplineCubic::polynomials (const QPolygonF& points) const [override], [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 1167 of file qwt_spline_cubic.cpp.

QVector< double > QwtSplineCubic::slopes (const QPolygonF & points) const[override], [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 1006 of file qwt_spline_cubic.cpp.

Author

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Updated 2026-06-01 - jenkler.se | uex.se