# QwtSplineLocal - Man Page

A spline with C1 continuity.

## Synopsis

`#include <qwt_spline_local.h>`

Inherits QwtSplineC1.

### Public Types

enum Type { Cardinal, ParabolicBlending, Akima, PChip }
Spline interpolation type.

### Public Member Functions

QwtSplineLocal (Type type)
Constructor.
virtual ~QwtSplineLocal ()
Destructor.
Type type () const
virtual uint locality () const override
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 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.

## Detailed Description

A spline with C1 continuity.

QwtSplineLocal offers several standard algorithms for interpolating a curve with polynomials having C1 continuity at the control points. All algorithms are local in a sense, that changing one control point only few polynomials.

Definition at line 24 of file qwt_spline_local.h.

## Member Enumeration Documentation

### enum QwtSplineLocal::Type

Spline interpolation type. All type of spline interpolations are lightweight algorithms calculating the slopes at a point by looking 1 or 2 points back and ahead.

Enumerator

Cardinal

A cardinal spline

The cardinal spline interpolation is a very cheap calculation with a locality of 1.

ParabolicBlending

Parabolic blending is a cheap calculation with a locality of 1. Sometimes it is also called Cubic Bessel interpolation.

Akima

The algorithm of H.Akima is a calculation with a locality of 2.

PChip

Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) is an algorithm that is popular because of being offered by MATLAB.

It preserves the shape of the data and respects monotonicity. It has a locality of 1.

Definition at line 34 of file qwt_spline_local.h.

## Constructor & Destructor Documentation

### QwtSplineLocal::QwtSplineLocal (Type type)

Constructor.

Parameters

type Spline type, specifying the type of interpolation

type()

Definition at line 450 of file qwt_spline_local.cpp.

## Member Function Documentation

### QVector< QLineF > QwtSplineLocal::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

Reimplemented from QwtSplineC1.

Definition at line 502 of file qwt_spline_local.cpp.

### uint QwtSplineLocal::locality () const [override], [virtual]

The locality of an spline interpolation identifies how many adjacent polynomials are affected, when changing the position of one point.

The Cardinal, ParabolicBlending and PChip algorithms have a locality of 1, while the Akima interpolation has a locality of 2.

Returns

1 or 2.

Reimplemented from QwtSpline.

Definition at line 552 of file qwt_spline_local.cpp.

### QPainterPath QwtSplineLocal::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

Reimplemented from QwtSplineC1.

Definition at line 482 of file qwt_spline_local.cpp.

### QVector< QwtSplinePolynomial > QwtSplineLocal::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 QwtSplineC1::polynomials(), but is intended to be replaced by a one pass calculation some day.

Reimplemented from QwtSplineC1.

Definition at line 537 of file qwt_spline_local.cpp.

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

Implements QwtSplineC1.

Definition at line 521 of file qwt_spline_local.cpp.

### QwtSplineLocal::Type QwtSplineLocal::type () const

Returns

Spline type, specifying the type of interpolation

Definition at line 468 of file qwt_spline_local.cpp.

## Author

Generated automatically by Doxygen for Qwt User's Guide from the source code.

## Info

Sun Jul 18 2021 Version 6.2.0 Qwt User's Guide