Ellipse2 Class Reference

Axis aligned ellipses. More...

#include <ellipse.h>

Public Member Functions
	Ellipse2 ()
	Empty.
	Ellipse2 (const Vector2 &, const double &, const double &)
	Create an ellipse. More...
	~Ellipse2 ()
	Empty.
Vector2	Center () const
	Gets the center.
double	A () const
	Major radius of the ellipse.
double	B () const
	Minor radius of the ellipse.
Vector2	Vertex (const double &) const
	Compute a vertex on the ellipse. More...
double	Curvature (const double &) const
	Compute the curvature at a vertex on the ellipse. More...
bool	Inside (const Vector2 &) const
	Check if a point is inside the circle. More...
double	R (const Vector2 &) const
	Compute the squared distance between a point and the ellipse. More...
double	Signed (const Vector2 &) const
	Compute the signed distance between a point and the ellipse. More...
Ellipse2	Translated (const Vector2 &) const
	Translate an ellipse. More...
Ellipse2	Scaled (const double &) const
	Scales an ellipse. More...
Ellipse2	Scaled (const Vector2 &) const
	Scales an ellipse. More...
double	Eccentricity () const
	Eccentricity.
double	Focus () const
	Area of an ellipse.
Box2	GetBox () const
	Compute the bounding box.
double	Area () const
	Area of an ellipse.
double	Perimeter () const
	Perimeter of an ellipse. More...
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the circle. More...
void	Draw (QGraphicsScene &, const QPen &, const QBrush &) const
	Draw a circle. More...
double	Value (const Vector2 &) const
	Compute the field function value of an ellipse. More...
Vector2	Gradient (const Vector2 &) const
	Compute the gradient of the field function. More...

Protected Attributes
Vector2	c
	Center of the ellipse.
double	b = 1.0
	Axes lengths.

Friends
std::ostream &	operator<< (std::ostream &, const Ellipse2 &)
	Overloaded. More...

Detailed Description

Axis aligned ellipses.

See also

Circle2

Constructor & Destructor Documentation

Ellipse2()

Ellipse2::Ellipse2 ( const Vector2 &  c, const double &  a, const double &  b  )

explicit

Create an ellipse.

Parameters

c	Center.
a,b	Axes lengths.

Member Function Documentation

Curvature()

double Ellipse2::Curvature

(

const double &

t

)

const

Compute the curvature at a vertex on the ellipse.

Parameters

t

Angle.

Draw()

void Ellipse2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen,
		const QBrush &	brush
	)		const

Draw a circle.

Parameters

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

Gradient()

Vector2 Ellipse2::Gradient

(

const Vector2 &

p

)

const

Compute the gradient of the field function.

Parameters

p

Point.

Inside()

bool Ellipse2::Inside

(

const Vector2 &

p

)

const

Check if a point is inside the circle.

Parameters

p

Point.

Perimeter()

double Ellipse2::Perimeter

(

)

const

Perimeter of an ellipse.

The exact perimeter of an ellipse is 4 a E(e) where e is the eccentricity, and the function E is the complete elliptic integral of the second kind.

Here we use an approximation of Srinivasa Ramanujan, Modular Equations and Approximations to pi, that gives close approximations.

R()

double Ellipse2::R

(

const Vector2 &

p

)

const

Compute the squared distance between a point and the ellipse.

Parameters

p

Point.

RandomInside()

Vector2 Ellipse2::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the circle.

Parameters

random

Random number generator.

Scaled() [1/2]

Ellipse2 Ellipse2::Scaled

(

const double &

s

)

const

Scales an ellipse.

Parameters

s	Scaling factor.

Scaled() [2/2]

Ellipse2 Ellipse2::Scaled

(

const Vector2 &

s

)

const

Scales an ellipse.

Parameters

s	Scaling vector.

Signed()

double Ellipse2::Signed

(

const Vector2 &

p

)

const

Compute the signed distance between a point and the ellipse.

Parameters

p

Point.

Translated()

Ellipse2 Ellipse2::Translated

(

const Vector2 &

t

)

const

Translate an ellipse.

Parameters

t	Translation vector.

Value()

double Ellipse2::Value

(

const Vector2 &

p

)

const

Compute the field function value of an ellipse.

Parameters

p

Point.

Vertex()

Vector2 Ellipse2::Vertex

(

const double &

t

)

const

Compute a vertex on the ellipse.

Parameters

t

Angle.

Friends And Related Function Documentation

operator<<

std::ostream & operator<< ( std::ostream &  s, const Ellipse2 &  ellipse  )

friend

Overloaded.

Parameters

s	Stream.
ellipse	The ellipse.