# QwtSplineCubic - Man Page

A cubic spline.

## 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.

### Additional Inherited Members

## 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.

## 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**

0

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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