Base class for all splines 更多...

#include <qwt_spline.h>

类 QwtSpline 继承关系图:

类
class	PrivateData

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

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

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

Public 成员函数
	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)

详细描述

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.

成员枚举类型说明

◆ 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.

参见: boundaryCondition(), boundaryValue(); QwtSplineC2::BoundaryConditionC2

枚举值
Clamped1	The first derivative at the end point is given 参见 boundaryValue()
Clamped2	The second derivative at the end point is given 参见 boundaryValue() 注解 a condition having a second derivative of 0 is also called "natural".
Clamped3	The third derivative at the end point is given 参见 boundaryValue() 注解 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. 参见 boundaryValue().

◆ BoundaryPosition

enum QwtSpline::BoundaryPosition

position of a boundary condition

参见: boundaryCondition(), boundaryValue()

枚举值
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

参见: setBoundaryType(), boundaryType()

枚举值

ConditionalBoundaries

The polynomials at the start/endpoint depend on specific conditions

参见: 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.

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

构造及析构函数说明

◆ QwtSpline()

QwtSpline::QwtSpline ( )

Constructor

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

参见: setParametrization(), setBoundaryType()

Destructor

成员函数说明

◆ boundaryCondition()

int QwtSpline::boundaryCondition ( BoundaryPosition position ) const

Get boundary condition

参数

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

返回: Condition for an endpoint of the spline

参见: setBoundaryCondition(), boundaryValue(), setBoundaryConditions()

◆ boundaryType()

QwtSpline::BoundaryType QwtSpline::boundaryType ( ) const

Get boundary type

返回: Boundary type

参见: setBoundaryType()

◆ boundaryValue()

double QwtSpline::boundaryValue ( BoundaryPosition position ) const

Get boundary value

参数

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

返回: Boundary value

参见: 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).

返回: Order of locality

被 QwtSplineBasis, QwtSplineCubic, QwtSplineLocal , 以及 QwtSplinePleasing 重载.

◆ 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.

参数

points Control points

返回: Painter path, that can be rendered by QPainter

参见: polygon(), QwtBezier

在 QwtSplineInterpolating, QwtSplineC1, QwtSplineC2, QwtSplineBasis, QwtSplineCubic, QwtSplineLocal , 以及 QwtSplinePleasing 内被实现.

◆ parametrization()

const QwtSplineParametrization * QwtSpline::parametrization ( ) const

Get parametrization

返回: Parametrization object

参见: 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 )

参数

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

返回: Polygon approximating the interpolating polynomials

参见: bezierControlLines(), QwtBezier

被 QwtSplineInterpolating 重载.

◆ setBoundaryCondition()

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

Set boundary condition

Define the condition for an endpoint of the spline.

参数

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

参见: 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.

参数

[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

参见: 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.

参数

[in] boundaryType Boundary type

参见: 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.

参数

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

参见: 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.

参数

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

参见: 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.

参数

[in] parametrization Parametrization object

参见: parametrization()

该类的文档由以下文件生成:

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

类

Public 类型

Public 成员函数

详细描述

成员枚举类型说明

◆ BoundaryCondition

◆ BoundaryPosition

◆ BoundaryType

构造及析构函数说明

◆ QwtSpline()

成员函数说明

◆ boundaryCondition()

◆ boundaryType()

◆ boundaryValue()

◆ locality()

◆ painterPath()

◆ parametrization()

◆ polygon()

◆ setBoundaryCondition()

◆ setBoundaryConditions()

◆ setBoundaryType()

◆ setBoundaryValue()

◆ setParametrization() [1/2]

◆ setParametrization() [2/2]