# QwtSplineC2 - Man Page

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

## Synopsis

`#include <qwt_spline.h>`

Inherits **QwtSplineC1**.

Inherited by **QwtSplineCubic**.

### Public Types

enum **BoundaryConditionC2** { **CubicRunout** = LinearRunout + 1, **NotAKnot** }

### Public Member Functions

**QwtSplineC2** ()

Constructor.

virtual **~QwtSplineC2** ()

Destructor.

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 QPolygonF **equidistantPolygon** (const QPolygonF &, double distance, bool withNodes) const override

Find an interpolated polygon with 'equidistant' points.

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 =0

Find the second derivative at the control points.

## 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**

Definition at line 267 of file qwt_spline.h.

## Member Enumeration Documentation

### 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

Definition at line 275 of file qwt_spline.h.

## Constructor & Destructor Documentation

### QwtSplineC2::QwtSplineC2 ()

Constructor. The default setting is a non closing spline with no parametrization ( **QwtSplineParametrization::ParameterX** ).

**See also****QwtSpline::setParametrization()**,**QwtSpline::setBoundaryType()**

Definition at line 1228 of file qwt_spline.cpp.

## Member Function Documentation

### QVector< QLineF > QwtSplineC2::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()**, 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**.

Definition at line 1270 of file qwt_spline.cpp.

### 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**.

### QPolygonF QwtSplineC2::equidistantPolygon (const QPolygonF & points, double distance, bool withNodes) const [override], [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**.

Definition at line 1295 of file qwt_spline.cpp.

### QPainterPath QwtSplineC2::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()**, but is intended to be replaced by a one pass calculation some day.

Reimplemented from **QwtSplineC1**.

Reimplemented in **QwtSplineCubic**.

Definition at line 1249 of file qwt_spline.cpp.

### QVector< QwtSplinePolynomial > QwtSplineC2::polynomials (const QPolygonF & points) const [override], [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**.

Definition at line 1381 of file qwt_spline.cpp.

### QVector< double > QwtSplineC2::slopes (const QPolygonF & points) const [override], [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**.

Definition at line 1339 of file qwt_spline.cpp.

## Author

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