QwtSplineC2(3) Qwt User's Guide QwtSplineC2(3)

# NAME

QwtSplineC2 - 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.

QwtSplineParametrization

Definition at line 267 of file qwt_spline.h.

# Member Enumeration Documentation

## enum QwtSplineC2::BoundaryConditionC2

Boundary condition that requires C2 continuity

QwtSpline::boundaryCondition, QwtSpline::BoundaryCondition

Enumerator

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
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 ).

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

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

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

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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