# QwtSplineC1 - Man Page

Base class for spline interpolations providing a first order parametric continuity ( C1 ) between adjoining curves.

## Synopsis

`#include <qwt_spline.h>`

Inherits **QwtSplineG1**.

Inherited by **QwtSplineC2**, and **QwtSplineLocal**.

### Public Member Functions

**QwtSplineC1** ()

Constructor.

virtual **~QwtSplineC1** ()

Destructor.

virtual QPainterPath **painterPath** (const QPolygonF &) const override

Calculate an interpolated painter path.

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

Calculate the interpolating polynomials for a non parametric spline.

virtual **QVector**< double > **slopes** (const QPolygonF &) const =0

Find the first derivative at the control points.

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

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

### Additional Inherited Members

## Detailed Description

Base class for spline interpolations providing a first order parametric continuity ( C1 ) between adjoining curves.

All interpolations with C1 continuity are based on rules for finding the 1. 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 235 of file qwt_spline.h.

## Constructor & Destructor Documentation

### QwtSplineC1::QwtSplineC1 ()

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

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

Definition at line 962 of file qwt_spline.cpp.

## Member Function Documentation

### QVector< QLineF > QwtSplineC1::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

Implements **QwtSplineInterpolating**.

Reimplemented in **QwtSplineCubic**, **QwtSplineLocal**, and **QwtSplineC2**.

Definition at line 1101 of file qwt_spline.cpp.

### QPolygonF QwtSplineC1::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 **QwtSplineInterpolating**.

Reimplemented in **QwtSplineC2**.

Definition at line 1167 of file qwt_spline.cpp.

### QPainterPath QwtSplineC1::painterPath (const QPolygonF & points) const [override], [virtual]

Calculate an interpolated painter path. Interpolates a polygon piecewise into cubic Bezier curves and returns them as QPainterPath.

The implementation calculates the slopes at the control points and converts them into painter path elements in an additional loop.

**Parameters***points*Control points**Returns**QPainterPath Painter path, that can be rendered by QPainter

**Note**Derived spline classes might overload

**painterPath()**to avoid the extra loops for converting results into a QPainterPath

Reimplemented from **QwtSplineInterpolating**.

Reimplemented in **QwtSplineLocal**, **QwtSplineCubic**, and **QwtSplineC2**.

Definition at line 1043 of file qwt_spline.cpp.

### QVector< QwtSplinePolynomial > QwtSplineC1::polynomials (const QPolygonF & points) const [virtual]

Calculate the interpolating polynomials for a non parametric spline. C1 spline interpolations are based on finding values for the first derivates at the control points. The interpolating polynomials can be calculated from the the first derivates using **QwtSplinePolynomial::fromSlopes()**.

The default implementation is a two 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 in **QwtSplineLocal**, **QwtSplineCubic**, and **QwtSplineC2**.

Definition at line 1201 of file qwt_spline.cpp.

### double QwtSplineC1::slopeAtBeginning (const QPolygonF & points, double slopeNext) const [virtual]

**Parameters***points*Control points*slopeNext*Value of the first derivative at the second point**Returns**value of the first derivative at the first point

**See also****slopeAtEnd()**,**QwtSpline::boundaryCondition()**,**QwtSpline::boundaryValue()**

Definition at line 979 of file qwt_spline.cpp.

### double QwtSplineC1::slopeAtEnd (const QPolygonF & points, double slopeBefore) const [virtual]

**Parameters***points*Control points*slopeBefore*Value of the first derivative at the point before the last one**Returns**value of the first derivative at the last point

**See also****slopeAtBeginning()**,**QwtSpline::boundaryCondition()**,**QwtSpline::boundaryValue()**

Definition at line 997 of file qwt_spline.cpp.

### QVector< double > QwtSplineC1::slopes (const QPolygonF & points) const [pure virtual]

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

Implemented in **QwtSplineLocal**, **QwtSplineCubic**, and **QwtSplineC2**.

## Author

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