Lens2 Class Reference

Lenses in the plane with uniform radius. More...

#include <lens.h>

Public Member Functions
	Lens2 (const Vector2 &, const Vector2 &, const double &)
	Create a lens.
	Lens2 (const Vector2 &, const double &, const double &)
	Create a lens.
bool	Inside (const Vector2 &) const
	Test if a point is inside the lens.
double	R (const Vector2 &) const
	Compute the squared Euclidean distance to the lens.
double	Signed (const Vector2 &) const
	Compute the Euclidean distance to the lens.
double	Height () const
	Compute the height of the lens.
double	Thickness () const
	Compute the thickness of the lens.
Vector2	Center () const
	Compute the center of the lens.
double	Alpha () const
	Compute the internal half opening angle of the lens.
double	Area () const
	Compute the area of the lens.
Box2	GetBox () const
	Compute the (tight) bounding box.
Frame2	GetFrame () const
	Compute the local frame of the lens.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw the lens.

Protected Attributes
Vector2	b = -Vector::X
	Centers.
double	r = 3.0
	Radius.

Friends
std::ostream &	operator<< (std::ostream &s, const Lens2 &l)
	Overloaded.

Detailed Description

Lenses in the plane with uniform radius.

A lens is defined as the intersection of two circles. Lenses are used in beta-skeletons geometric graphs.

Constructor & Destructor Documentation

Lens2() [1/2]

Lens2::Lens2	(	const Vector2 &	a,
		const Vector2 &	b,
		const double &	r )

Create a lens.

Parameters

a,b	Centers of the circles.
r	Radius.

Lens2() [2/2]

Lens2::Lens2	(	const Vector2 &	c,
		const double &	t,
		const double &	h )

Create a lens.

Parameters

c	Centers of the lens.
t	Thickness.
h	Height.

Member Function Documentation

Alpha()

double Lens2::Alpha ( ) const

inline

Compute the internal half opening angle of the lens.

This is an inlined and optimized version of:

Lens2 lens;
double a = acos(lens.Height()/(0.5*lens.Thickness()));

Area()

double Lens2::Area

(

)

const

Compute the area of the lens.

This is a simplified version of the equation of the area of two intersecting circles with different radii.

See also

Circle2::Area(const Circle2&) const

Draw()

void Lens2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush() ) const

Draw the lens.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush, should the circle be filled.

Inside()

bool Lens2::Inside

(

const Vector2 &

p

)

const

Test if a point is inside the lens.

Parameters

p

Point.

R()

double Lens2::R

(

const Vector2 &

p

)

const

Compute the squared Euclidean distance to the lens.

Parameters

p

Point.

Signed()

double Lens2::Signed

(

const Vector2 &

p

)

const

Compute the Euclidean distance to the lens.

Parameters

p

Point.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Lens2 & l )

friend

Overloaded.

Parameters

s	Stream.
l	Lens.