Qwt User's Guide  6.2.0
QwtSplineLocal Class Reference

A spline with C1 continuity. More...

#include <qwt_spline_local.h>

Inheritance diagram for QwtSplineLocal:

Public Types

enum  Type { Cardinal , ParabolicBlending , Akima , PChip }
 Spline interpolation type. More...
 
- Public Types inherited from QwtSpline
enum  BoundaryType { ConditionalBoundaries , PeriodicPolygon , ClosedPolygon }
 
enum  BoundaryPosition { AtBeginning , AtEnd }
 
enum  BoundaryCondition { Clamped1 , Clamped2 , Clamped3 , LinearRunout }
 Boundary condition. More...
 

Public Member Functions

 QwtSplineLocal (Type type)
 Constructor. More...
 
virtual ~QwtSplineLocal ()
 Destructor.
 
Type type () const
 
virtual uint locality () const override
 
virtual QPainterPath painterPath (const QPolygonF &) const override
 Interpolate a curve with Bezier curves. More...
 
virtual QVector< QLineF > bezierControlLines (const QPolygonF &) const override
 Interpolate a curve with Bezier curves. More...
 
virtual QVector< QwtSplinePolynomialpolynomials (const QPolygonF &) const override
 Calculate the interpolating polynomials for a non parametric spline. More...
 
virtual QVector< double > slopes (const QPolygonF &) const override
 Find the first derivative at the control points. More...
 
- Public Member Functions inherited from QwtSplineC1
 QwtSplineC1 ()
 Constructor. More...
 
virtual ~QwtSplineC1 ()
 Destructor.
 
virtual QPolygonF equidistantPolygon (const QPolygonF &, double distance, bool withNodes) const override
 Find an interpolated polygon with "equidistant" points. More...
 
virtual double slopeAtBeginning (const QPolygonF &, double slopeNext) const
 
virtual double slopeAtEnd (const QPolygonF &, double slopeBefore) const
 
- Public Member Functions inherited from QwtSplineG1
 QwtSplineG1 ()
 Constructor.
 
virtual ~QwtSplineG1 ()
 Destructor.
 
- Public Member Functions inherited from QwtSplineInterpolating
 QwtSplineInterpolating ()
 Constructor.
 
virtual ~QwtSplineInterpolating ()
 Destructor.
 
virtual QPolygonF polygon (const QPolygonF &, double tolerance) const override
 Interpolate a curve by a polygon. More...
 
- Public Member Functions inherited from QwtSpline
 QwtSpline ()
 Constructor. More...
 
virtual ~QwtSpline ()
 Destructor.
 
void setParametrization (int type)
 
void setParametrization (QwtSplineParametrization *)
 
const QwtSplineParametrizationparametrization () const
 
void setBoundaryType (BoundaryType)
 
BoundaryType boundaryType () const
 
void setBoundaryValue (BoundaryPosition, double value)
 Define the boundary value. More...
 
double boundaryValue (BoundaryPosition) const
 
void setBoundaryCondition (BoundaryPosition, int condition)
 Define the condition for an endpoint of the spline. More...
 
int boundaryCondition (BoundaryPosition) const
 
void setBoundaryConditions (int condition, double valueBegin=0.0, double valueEnd=0.0)
 Define the condition at the endpoints of a spline. More...
 

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

◆ 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::QwtSplineLocal ( Type  type)

Constructor.

Parameters
typeSpline type, specifying the type of interpolation
See also
type()

Definition at line 450 of file qwt_spline_local.cpp.

Member Function Documentation

◆ bezierControlLines()

QVector< QLineF > QwtSplineLocal::bezierControlLines ( const QPolygonF &  points) const
overridevirtual

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
pointsControl points
Returns
Control points of the interpolating Bezier curves

Reimplemented from QwtSplineC1.

Definition at line 502 of file qwt_spline_local.cpp.

◆ locality()

uint QwtSplineLocal::locality ( ) const
overridevirtual

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.

◆ painterPath()

QPainterPath QwtSplineLocal::painterPath ( const QPolygonF &  points) const
overridevirtual

Interpolate a curve with Bezier curves.

Interpolates a polygon piecewise with cubic Bezier curves and returns them as QPainterPath.

Parameters
pointsControl points
Returns
Painter path, that can be rendered by QPainter

Reimplemented from QwtSplineC1.

Definition at line 482 of file qwt_spline_local.cpp.

◆ polynomials()

QVector< QwtSplinePolynomial > QwtSplineLocal::polynomials ( const QPolygonF &  points) const
overridevirtual

Calculate the interpolating polynomials for a non parametric spline.

Parameters
pointsControl 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.

◆ slopes()

QVector< double > QwtSplineLocal::slopes ( const QPolygonF &  points) const
overridevirtual

Find the first derivative at the control points.

Parameters
pointsControl 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.

◆ type()

QwtSplineLocal::Type QwtSplineLocal::type ( ) const
Returns
Spline type, specifying the type of interpolation

Definition at line 468 of file qwt_spline_local.cpp.