Clothoid2 Class Reference

Clothoid curves. More...

#include <clothoid.h>

Public Member Functions
	Clothoid2 ()
	Empty constructor. More...
	Clothoid2 (const double &)
	Create a clothoid given a slope multiplier parameter. More...
	Clothoid2 (const double &, const double &)
	Create a clothoid with one pair of parameters. More...
	Clothoid2 (const double &, const double &, const double &, const double &)
	Create a clothoid given two pairs of parameters. More...
	~Clothoid2 ()
	Empty.
Vector2	Vertex (const double &) const
	Compute the point of the clothoid curve at parameter curvilinear abscissa t. More...
double	Curvature (const double &) const
	Compute the curvature of the clothoid at curvilinear abscissa t. More...
Vector2	Tangent (const double &) const
	Compute the tangent to the clothoid at curvilinear abscissa t. More...
double	GetSlope () const
	Return the slope of the clothoid.
void	Draw (QGraphicsScene &, const QPen &, const QBrush &) const
	Draw the clothoid arc. More...

Protected Attributes
double	B
	Slope parameter.

Detailed Description

Clothoid curves.

An clothoid, also referred to as Euler spiral, is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius).

See Sketching piecewise clothoid curves, Sketch-Based Interfaces and Modeling, 2008.

Author

Eric Guérin

Constructor & Destructor Documentation

Clothoid2() [1/4]

Clothoid2::Clothoid2

(

)

Empty constructor.

Set slope to 1.0/Pi.

Clothoid2() [2/4]

Clothoid2::Clothoid2 ( const double &  slope )

explicit

Create a clothoid given a slope multiplier parameter.

Parameters

slope

Slope.

Clothoid2() [3/4]

Clothoid2::Clothoid2 ( const double &  a, const double &  ca  )

explicit

Create a clothoid with one pair of parameters.

Parameters

a	Curvilinear abscissa of the point.
ca	Curvature.

Clothoid2() [4/4]

Clothoid2::Clothoid2 ( const double &  a, const double &  ca, const double &  b, const double &  cb  )

explicit

Create a clothoid given two pairs of parameters.

Parameters

a,b	Curvilinear abscissa of the two points.
ca,cb	Curvature of the two points.

Member Function Documentation

Curvature()

double Clothoid2::Curvature ( const double &  t ) const

inline

Compute the curvature of the clothoid at curvilinear abscissa t.

By definition the curvature of the clothoid is a linear function of t defined as c(t)=t/B.

Parameters

t	Curvilinear abscissa.

Draw()

void Clothoid2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen,
		const QBrush &	brush
	)		const

Draw the clothoid arc.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush.

Tangent()

Vector2 Clothoid2::Tangent

(

const double &

t

)

const

Compute the tangent to the clothoid at curvilinear abscissa t.

It is defined as Pi*B*(cos(Pi/2*t^2),sin(Pi/2*t^2))

Parameters

t

parameter

Vertex()

Vector2 Clothoid2::Vertex

(

const double &

t

)

const

Compute the point of the clothoid curve at parameter curvilinear abscissa t.

The implementation relies on a rational approximation.

M. Heald. Rational approximations for the fresnel integrals. Mathematics of Computation, 44 (170), 459–461, 1985.

Parameters

t	Parameter.