QwtBezier(3) Qwt User's Guide QwtBezier(3)

# NAME

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

# SYNOPSIS

#include <qwt_bezier.h>

## Public Member Functions

QwtBezier (double tolerance=0.5)
Constructor. ~QwtBezier ()
Destructor. 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. void appendToPolygon (const QPointF &p1, const QPointF &cp1, const QPointF &cp2, const QPointF &p2, QPolygonF &polygon) const
Interpolate a Bézier curve by a polygon.

## Static Public Member Functions

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

# 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 (double tolerance = 0.5)

Constructor.

Parameters

tolerance Termination criterion for the subdivision

setTolerance()

Definition at line 116 of file qwt_bezier.cpp.

# Member Function Documentation

## 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.

## 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.

## 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

tolerance()

Definition at line 141 of file qwt_bezier.cpp.

## double QwtBezier::tolerance () const [inline]

Returns

Tolerance, that is used as criterion for the subdivision

setTolerance()

Definition at line 56 of file qwt_bezier.h.

## 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.

# Author

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 Sun Jul 18 2021 Version 6.2.0