Base class for all splines. More...

#include <qwt_spline.h>

Inheritance diagram for QwtSpline:

Public Types
enum	BoundaryType { ConditionalBoundaries , PeriodicPolygon , ClosedPolygon }

enum	BoundaryPosition { AtBeginning , AtEnd }

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

Public Member Functions
	QwtSpline ()
	Constructor.

virtual	~QwtSpline ()
	Destructor.

void	setParametrization (int type)

void	setParametrization (QwtSplineParametrization *)

const QwtSplineParametrization *	parametrization () const

void	setBoundaryType (BoundaryType)

BoundaryType	boundaryType () const

void	setBoundaryValue (BoundaryPosition, double value)
	Define the boundary value.

double	boundaryValue (BoundaryPosition) const

void	setBoundaryCondition (BoundaryPosition, int condition)
	Define the condition for an endpoint of the spline.

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.

virtual QPolygonF	polygon (const QPolygonF &, double tolerance) const
	Interpolate a curve by a polygon.

virtual QPainterPath	painterPath (const QPolygonF &) const =0

virtual uint	locality () const

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.

Definition at line 57 of file qwt_spline.h.

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().

Definition at line 119 of file qwt_spline.h.

◆ 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

Definition at line 99 of file qwt_spline.h.

◆ 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

Definition at line 65 of file qwt_spline.h.

Constructor & Destructor Documentation

◆ QwtSpline()

QwtSpline::QwtSpline ( )

Constructor.

The default setting is a non closing spline with chordal parametrization

See also: setParametrization(), setBoundaryType()

Definition at line 540 of file qwt_spline.cpp.

◆ ~QwtSpline()

QwtSpline::~QwtSpline ( )

virtual

Destructor.

Definition at line 546 of file qwt_spline.cpp.

Member Function Documentation

◆ boundaryCondition()

int QwtSpline::boundaryCondition ( BoundaryPosition position ) const

Returns: Condition for an endpoint of the spline

Parameters

position At the beginning or the end of the spline

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

Definition at line 651 of file qwt_spline.cpp.

◆ boundaryType()

QwtSpline::BoundaryType QwtSpline::boundaryType ( ) const

Returns: Boundary type

See also: setBoundaryType()

Definition at line 626 of file qwt_spline.cpp.

◆ boundaryValue()

double QwtSpline::boundaryValue ( BoundaryPosition position ) const

Returns: Boundary value

Parameters

position At the beginning or the end of the spline

See also: setBoundaryValue(), boundaryCondition()

Definition at line 682 of file qwt_spline.cpp.

◆ locality()

uint QwtSpline::locality ( ) const

virtual

The locality of an 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, that the interpolation is not local and any modification of the polygon requires to recalculate all polynomials ( f.e cubic splines ).

Returns: Order of locality

Reimplemented in QwtSplineBasis, QwtSplineCubic, QwtSplineLocal, and QwtSplinePleasing.

Definition at line 564 of file qwt_spline.cpp.

◆ painterPath()

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

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

Returns: parametrization

See also: setParametrization()

Definition at line 605 of file qwt_spline.cpp.

◆ polygon()

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

virtual

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 Bézier Curves" by Roger Willcocks ( http://www.rops.org )

Parameters

points	Control points
tolerance	Maximum for the accepted error of the approximation

Returns: polygon approximating the interpolating polynomials

See also: bezierControlLines(), QwtBezier

Reimplemented in QwtSplineInterpolating.

Definition at line 496 of file qwt_spline.cpp.

◆ setBoundaryCondition()

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

Define the condition for an endpoint of the spline.

Parameters

position	At the beginning or the end of the spline
condition	Condition

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

Definition at line 639 of file qwt_spline.cpp.

◆ setBoundaryConditions()

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

Define the condition at the endpoints of a spline.

Parameters

condition	Condition
valueBegin	Used for the condition at the beginning of te spline
valueEnd	Used for the condition at the end of te spline

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

Definition at line 700 of file qwt_spline.cpp.

◆ setBoundaryType()

void QwtSpline::setBoundaryType ( BoundaryType boundaryType )

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

Parameters

boundaryType Boundary type

See also: boundaryType()

Definition at line 617 of file qwt_spline.cpp.

◆ setBoundaryValue()

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

Define the boundary value.

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

Parameters

position	At the beginning or the end of the spline
value	Value used for the condition at the end point

See also: boundaryValue(), setBoundaryCondition()

Definition at line 670 of file qwt_spline.cpp.

◆ setParametrization() [1/2]

void QwtSpline::setParametrization ( int type )

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

Parameters

type	Type of parametrization, usually one of QwtSplineParametrization::Type

See also: parametrization()

Definition at line 576 of file qwt_spline.cpp.

◆ setParametrization() [2/2]

void QwtSpline::setParametrization ( QwtSplineParametrization * parametrization )

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

Parameters

parametrization Parametrization

See also: parametrization()

Definition at line 592 of file qwt_spline.cpp.

Public Types

Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ BoundaryCondition

◆ BoundaryPosition

◆ BoundaryType

Constructor & Destructor Documentation

◆ QwtSpline()

◆ ~QwtSpline()

Member Function Documentation

◆ boundaryCondition()

◆ boundaryType()

◆ boundaryValue()

◆ locality()

◆ painterPath()

◆ parametrization()

◆ polygon()

◆ setBoundaryCondition()

◆ setBoundaryConditions()

◆ setBoundaryType()

◆ setBoundaryValue()

◆ setParametrization() [1/2]

◆ setParametrization() [2/2]