An implementation of the de Casteljau’s Algorithm for interpolating Bézier curves. More...

#include <qwt_bezier.h>

Public Member Functions
void	appendToPolygon (const QPointF &p1, const QPointF &cp1, const QPointF &cp2, const QPointF &p2, QPolygonF &polygon) const
	Interpolate a Bézier curve by a polygon. More...

	QwtBezier (double tolerance=0.5)
	Constructor. More...

void	setTolerance (double tolerance)

double	tolerance () const

QPolygonF	toPolygon (const QPointF &p1, const QPointF &cp1, const QPointF &cp2, const QPointF &p2) const
	Interpolate a Bézier curve by a polygon. More...

	~QwtBezier ()
	Destructor. More...

Static Public Member Functions
static QPointF	pointAt (const QPointF &p1, const QPointF &cp1, const QPointF &cp2, const QPointF &p2, double t)

Private Attributes
double	m_flatness

double	m_tolerance

Detailed Description

An implementation of the de Casteljau’s Algorithm for interpolating Bézier curves.

The flatness criterion for terminating the subdivision is based on "Piecewise Linear Approximation of Bézier Curves" by Roger Willcocks ( http://www.rops.org )

This article explains the maths behind in a very nice way: https://jeremykun.com/2013/05/11/bezier-curves-and-picasso

Definition at line 29 of file qwt_bezier.h.

Constructor & Destructor Documentation

◆ QwtBezier()

QwtBezier::QwtBezier ( double tolerance = 0.5 )

Constructor.

Parameters

tolerance Termination criterion for the subdivision

See also: setTolerance()

Definition at line 116 of file qwt_bezier.cpp.

◆ ~QwtBezier()

QwtBezier::~QwtBezier ( )

Destructor.

Definition at line 123 of file qwt_bezier.cpp.

Member Function Documentation

◆ appendToPolygon()

void QwtBezier::appendToPolygon	(	const QPointF &	p1,
		const QPointF &	cp1,
		const QPointF &	cp2,
		const QPointF &	p2,
		QPolygonF &	polygon
	)		const

Interpolate a Bézier curve by a polygon.

appendToPolygon() is tailored for cumulating points from a sequence of bezier curves like being created by a spline interpolation.

Parameters

p1	Start point
cp1	First control point
cp2	Second control point
p2	End point
polygon	Polygon, where the interpolating points are added

Note: If the last point of the incoming polygon matches p1 it won't be inserted a second time.

Definition at line 186 of file qwt_bezier.cpp.

◆ pointAt()

QPointF QwtBezier::pointAt	(	const QPointF &	p1,
		const QPointF &	cp1,
		const QPointF &	cp2,
		const QPointF &	p2,
		double	t
	)

static

Find a point on a Bézier Curve

Parameters

p1	Start point
cp1	First control point
cp2	Second control point
p2	End point
t	Parameter value, something between [0,1]

Returns: Point on the curve

Definition at line 239 of file qwt_bezier.cpp.

◆ setTolerance()

void QwtBezier::setTolerance ( double tolerance )

Set the tolerance

The tolerance is a measurement for the flatness of a curve. A curve with a flatness below the tolerance is considered as being flat terminating the subdivision algorithm.

When interpolating a Bezier curve to render it as a sequence of lines to some sort of raster ( f.e to screen ) a value of 0.5 of the pixel size is a good value for the tolerance.

Parameters

tolerance Termination criterion for the subdivision

See also: tolerance()

Definition at line 141 of file qwt_bezier.cpp.

◆ tolerance()

double QwtBezier::tolerance ( ) const

inline

Returns: Tolerance, that is used as criterion for the subdivision

See also: setTolerance()

Definition at line 56 of file qwt_bezier.h.

◆ toPolygon()

QPolygonF QwtBezier::toPolygon	(	const QPointF &	p1,
		const QPointF &	cp1,
		const QPointF &	cp2,
		const QPointF &	p2
	)		const

Interpolate a Bézier curve by a polygon.

Parameters

p1	Start point
cp1	First control point
cp2	Second control point
p2	End point

Returns: Interpolating polygon

Definition at line 157 of file qwt_bezier.cpp.

Member Data Documentation

◆ m_flatness

double QwtBezier::m_flatness

private

Definition at line 49 of file qwt_bezier.h.

◆ m_tolerance

double QwtBezier::m_tolerance

private

Definition at line 48 of file qwt_bezier.h.

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

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ QwtBezier()

◆ ~QwtBezier()

Member Function Documentation

◆ appendToPolygon()

◆ pointAt()

◆ setTolerance()

◆ tolerance()

◆ toPolygon()

Member Data Documentation

◆ m_flatness

◆ m_tolerance