Base class for all splines. More...

#include <qwt_spline.h>

Inheritance diagram for QwtSpline:

Classes
class	PrivateData

Public Types
enum	BoundaryType { ConditionalBoundaries , PeriodicPolygon , ClosedPolygon }
	Boundary type specifying the spline at its endpoints. More...

enum	BoundaryPosition { AtBeginning , AtEnd }
	position of a boundary condition More...

enum	BoundaryCondition { Clamped1 , Clamped2 , Clamped3 , LinearRunout }
	Boundary condition. More...

Public Member Functions
	QwtSpline ()
	Constructor.

virtual	~QwtSpline ()
	Destructor.

void	setParametrization (int type)
	Set parametrization by type.

void	setParametrization (QwtSplineParametrization *)
	Set parametrization object.

const QwtSplineParametrization *	parametrization () const
	Get parametrization.

void	setBoundaryType (BoundaryType)
	Set boundary type.

BoundaryType	boundaryType () const
	Get boundary type.

void	setBoundaryValue (BoundaryPosition, double value)
	Set boundary value.

double	boundaryValue (BoundaryPosition) const
	Get boundary value.

void	setBoundaryCondition (BoundaryPosition, int condition)
	Set boundary condition.

int	boundaryCondition (BoundaryPosition) const
	Get boundary condition.

void	setBoundaryConditions (int condition, double valueBegin=0.0, double valueEnd=0.0)
	Set boundary conditions for both ends.

virtual QPolygonF	polygon (const QPolygonF &, double tolerance) const
	Get polygon approximation with tolerance.

virtual QPainterPath	painterPath (const QPolygonF &) const =0
	Get painter path from polygon (pure virtual)

virtual uint	locality () const
	Get locality (number of points used for calculation)

Detailed Description

Base class for all splines.

A spline is a curve represented by a sequence of polynomials. Spline approximation is the process of finding polynomials for a given set of points. When the algorithm preserves the initial points it is called interpolating.

Splines can be classified according to conditions of the polynomials that are met at the start/endpoints of the pieces:

Geometric Continuity
- G0: polynomials are joined
- G1: first derivatives are proportional at the join point The curve tangents thus have the same direction, but not necessarily the same magnitude. i.e., C1'(1) = (a,b,c) and C2'(0) = (k*a, k*b, k*c).
- G2: first and second derivatives are proportional at join point
Parametric Continuity
- C0: curves are joined
- C1: first derivatives equal
- C2: first and second derivatives are equal

Geometric continuity requires the geometry to be continuous, while parametric continuity requires that the underlying parameterization be continuous as well. Parametric continuity of order n implies geometric continuity of order n, but not vice-versa.

QwtSpline is the base class for spline approximations of any continuity.

Member Enumeration Documentation

◆ BoundaryCondition

enum QwtSpline::BoundaryCondition

Boundary condition.

A spline algorithm calculates polynomials by looking a couple of points back/ahead ( locality() ). At the ends additional rules are necessary to compensate the missing points.

See also: boundaryCondition(), boundaryValue(); QwtSplineC2::BoundaryConditionC2

Enumerator
Clamped1	The first derivative at the end point is given See also boundaryValue()
Clamped2	The second derivative at the end point is given See also boundaryValue() Note a condition having a second derivative of 0 is also called "natural".
Clamped3	The third derivative at the end point is given See also boundaryValue() Note a condition having a third derivative of 0 is also called "parabolic runout".
LinearRunout	The first derivate at the endpoint is related to the first derivative at its neighbour by the boundary value. F,e when the boundary value at the end is 1.0 then the slope at the last 2 points is the same. See also boundaryValue().

◆ BoundaryPosition

enum QwtSpline::BoundaryPosition

position of a boundary condition

See also: boundaryCondition(), boundaryValue()

Enumerator
AtBeginning	the condition is at the beginning of the polynomial
AtEnd	the condition is at the end of the polynomial

◆ BoundaryType

enum QwtSpline::BoundaryType

Boundary type specifying the spline at its endpoints.

See also: setBoundaryType(), boundaryType()

Enumerator

ConditionalBoundaries

The polynomials at the start/endpoint depend on specific conditions

See also: QwtSpline::BoundaryCondition

PeriodicPolygon

The polynomials at the start/endpoint are found by using imaginary additional points. Additional points at the end are found by translating points from the beginning or v.v.

ClosedPolygon

ClosedPolygon is similar to PeriodicPolygon beside, that the interpolation includes the connection between the last and the first control point.

Note: Only works for parametrizations, where the parameter increment for the the final closing line is positive. This excludes QwtSplineParametrization::ParameterX and QwtSplineParametrization::ParameterY

Constructor & Destructor Documentation

◆ QwtSpline()

QwtSpline::QwtSpline ( )

Constructor.

The default setting is a non-closing spline with chordal parametrization.

See also: setParametrization(), setBoundaryType()

Destructor

Member Function Documentation

◆ boundaryCondition()

int QwtSpline::boundaryCondition ( BoundaryPosition position ) const

Get boundary condition.

Parameters

[in] position At the beginning or the end of the spline

Returns: Condition for an endpoint of the spline

See also: setBoundaryCondition(), boundaryValue(), setBoundaryConditions()

◆ boundaryType()

QwtSpline::BoundaryType QwtSpline::boundaryType ( ) const

Get boundary type.

Returns: Boundary type

See also: setBoundaryType()

◆ boundaryValue()

double QwtSpline::boundaryValue ( BoundaryPosition position ) const

Get boundary value.

Parameters

[in] position At the beginning or the end of the spline

Returns: Boundary value

See also: setBoundaryValue(), boundaryCondition()

◆ locality()

uint QwtSpline::locality ( ) const

virtual

Get locality (number of points used for calculation)

Get the locality of the spline interpolation.

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

A locality of 'n' means that changing the coordinates of a point has an effect on 'n' leading and 'n' following polynomials. Those polynomials can be calculated from a local subpolygon.

A value of 0 means the interpolation is not local and any modification of the polygon requires recalculating all polynomials (e.g., cubic splines).

Returns: Order of locality

Reimplemented in QwtSplineBasis, QwtSplineCubic, QwtSplineLocal, and QwtSplinePleasing.

◆ painterPath()

QPainterPath QwtSpline::painterPath ( const QPolygonF & points ) const

pure virtual

Get painter path from polygon (pure virtual)

Approximates 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

See also: polygon(), QwtBezier

Implemented in QwtSplineInterpolating, QwtSplineC1, QwtSplineC2, QwtSplineBasis, QwtSplineCubic, QwtSplineLocal, and QwtSplinePleasing.

◆ parametrization()

const QwtSplineParametrization * QwtSpline::parametrization ( ) const

Get parametrization.

Returns: Parametrization object

See also: setParametrization()

◆ polygon()

QPolygonF QwtSpline::polygon	(	const QPolygonF &	points,
		double	tolerance
	)		const

virtual

Get polygon approximation with tolerance.

Interpolate a curve by a polygon.

Interpolates a polygon piecewise with Bezier curves interpolating them in a 2nd pass by polygons.

The interpolation is based on "Piecewise Linear Approximation of Bezier Curves" by Roger Willcocks ( http://www.rops.org )

Parameters

[in]	points	Control points
[in]	tolerance	Maximum for the accepted error of the approximation

Returns: Polygon approximating the interpolating polynomials

See also: bezierControlLines(), QwtBezier

Reimplemented in QwtSplineInterpolating.

◆ setBoundaryCondition()

void QwtSpline::setBoundaryCondition	(	BoundaryPosition	position,
		int	condition
	)

Set boundary condition.

Define the condition for an endpoint of the spline.

Parameters

[in]	position	At the beginning or the end of the spline
[in]	condition	Condition

See also: BoundaryCondition, QwtSplineC2::BoundaryCondition, boundaryCondition()

◆ setBoundaryConditions()

void QwtSpline::setBoundaryConditions	(	int	condition,
		double	valueBegin = `0.0`,
		double	valueEnd = `0.0`
	)

Set boundary conditions for both ends.

Define the condition at the endpoints of a spline.

Parameters

[in]	condition	Condition
[in]	valueBegin	Used for the condition at the beginning of the spline
[in]	valueEnd	Used for the condition at the end of the spline

See also: BoundaryCondition, QwtSplineC2::BoundaryCondition, testBoundaryCondition(), setBoundaryValue()

◆ setBoundaryType()

void QwtSpline::setBoundaryType ( BoundaryType boundaryType )

Set boundary type.

Define the boundary type for the endpoints of the approximating spline.

Parameters

[in] boundaryType Boundary type

See also: boundaryType()

◆ setBoundaryValue()

void QwtSpline::setBoundaryValue	(	BoundaryPosition	position,
		double	value
	)

Set boundary value.

The boundary value is a parameter used in combination with the boundary condition. Its meaning depends on the condition.

Parameters

[in]	position	At the beginning or the end of the spline
[in]	value	Value used for the condition at the endpoint

See also: boundaryValue(), setBoundaryCondition()

◆ setParametrization() [1/2]

void QwtSpline::setParametrization ( int type )

Set parametrization by type.

Define the parametrization for a parametric spline approximation. The default setting is a chordal parametrization.

Parameters

[in] type Type of parametrization, usually one of QwtSplineParametrization::Type

See also: parametrization()

◆ setParametrization() [2/2]

void QwtSpline::setParametrization ( QwtSplineParametrization * parametrization )

Set parametrization object.

Define the parametrization for a parametric spline approximation. The default setting is a chordal parametrization.

Parameters

[in] parametrization Parametrization object

See also: parametrization()

The documentation for this class was generated from the following files:

/home/runner/work/QWT/QWT/src/plot/qwt_spline.h
/home/runner/work/QWT/QWT/src/plot/qwt_spline.cpp

Classes

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ BoundaryCondition

◆ BoundaryPosition

◆ BoundaryType

Constructor & Destructor Documentation

◆ QwtSpline()

Member Function Documentation

◆ boundaryCondition()

◆ boundaryType()

◆ boundaryValue()

◆ locality()

◆ painterPath()

◆ parametrization()

◆ polygon()

◆ setBoundaryCondition()

◆ setBoundaryConditions()

◆ setBoundaryType()

◆ setBoundaryValue()

◆ setParametrization() [1/2]

◆ setParametrization() [2/2]