Ellipse2 Class Reference

Axis aligned ellipses. More...

#include <ellipse.h>

Inheritance diagram for Ellipse2:

Public Member Functions
	Ellipse2 ()
	Empty.
	Ellipse2 (const Vector2 &, const double &, const double &, const Vector2 &=Vector2::X)
	Create an ellipse.
	Ellipse2 (const double &, const double &)
	Create an ellipse.
	Ellipse2 (const Matrix2 &A, const Vector2 &center)
	Create an ellipse : (p - center)^T . A . (p - center)
	~Ellipse2 ()
	Empty.
Vector2	Center () const
	Gets the center.
double	C () const
	Return the half distance between the focus points of the ellipse.
double	P () const
	Return the parameter of the ellipse.
Vector2	Axis () const
	Return the major axis.
Vector2	Focus (bool) const
	Return the focus points of the ellipse.
double	A () const
	Return the major axis length.
double	B () const
	Return the minor axis length.
Vector2	Vertex (const double &) const
	Compute a vertex on the ellipse.
double	Curvature (const double &) const
	Compute the curvature at a vertex on the ellipse.
bool	Inside (const Vector2 &) const
	Check if a point is inside the ellipse.
double	R (const Vector2 &) const
	Compute the squared distance between a point and the ellipse.
double	Signed (const Vector2 &) const
	Compute the signed distance between a point and the ellipse.
Ellipse2	Translated (const Vector2 &) const
	Translate an ellipse.
Ellipse2	Scaled (const double &) const
	Scales an ellipse.
Ellipse2	Scaled (const Vector2 &, bool=true) const
	Scales an ellipse.
Ellipse2	Rotated (const double &) const
	Rotates an ellipse.
Ellipse2	Rotated (const Matrix2 &) const
	Rotates an ellipse.
Ellipse2	Transformed (const Frame2 &) const
	Return a ellipse transformed by a frame.
double	Eccentricity () const
	Eccentricity.
double	Focus () const
	Focus of an ellipse.
Box2	GetBox () const
	Compute the bounding box.
Circle2	GetCircle () const
	Compute the bounding circle.
double	Area () const
	Area of an ellipse.
double	Perimeter () const
	Perimeter of an ellipse.
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the circle.
QVector< Vector2 >	Poisson (const double &, int, Random &=Random::R239) const
	Compute a Poisson disc distribution inside the irregular octogon.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a circle.
double	Value (const Vector2 &) const
	Compute the field function value of an ellipse.
Vector2	Gradient (const Vector2 &) const
	Compute the gradient of the field function.

Static Public Member Functions
static Ellipse2	Lerp (const double &, const Ellipse2 &, const Ellipse2 &)
	Linear interpolation between two ellipses.
static Ellipse2	FromPoints (const std::vector< Vector2 > &points, double tolerance=0.05)
	Builds a ellipse around a point cloud, using a Minium Volume Ellipsoid algorithm.

Protected Member Functions
Matrix2	MatrixForm () const
	Compute the matrix form of the ellipse.

Protected Attributes
Vector2	c = Vector2::Null
	Center of the ellipse.
Vector2	u = Vector2::X
	Major axis.
double	b = 1.0
	Axes lengths.

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

Detailed Description

Axis aligned ellipses.

See also

Circle2

Constructor & Destructor Documentation

Ellipse2() [1/3]

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

explicit

Create an ellipse.

Parameters

c	Center.
a,b	Axes lengths.
u	Major axis direction.

Ellipse2() [2/3]

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

explicit

Create an ellipse.

Parameters

a,b	Axes lengths.

Ellipse2() [3/3]

Ellipse2::Ellipse2 ( const Matrix2 & A, const Vector2 & center )

explicit

Create an ellipse : (p - center)^T . A . (p - center)

Parameters

A	Ellipse matrix (symmetric positive-definite).
center	Ellipse center.

Member Function Documentation

C()

double Ellipse2::C

(

)

const

Return the half distance between the focus points of the ellipse.

The focus points can be derived as:

Ellipse e;
Vector2 f=e.Center()+e.C()*Vector2::X; // And e.Center()-e.C()*Vector2::X;

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 = QPen(),
		const QBrush &	brush = QBrush() ) const

Draw a circle.

Parameters

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

Focus()

Vector2 Ellipse2::Focus

(

bool

i

)

const

Return the focus points of the ellipse.

Parameters

i	Index of the focus point, true for focus in the direction of the axis, false for the point in the opposite direction.

See also

Ellipse2::C()

FromPoints()

Ellipse2 Ellipse2::FromPoints ( const std::vector< Vector2 > & p, double t = 0.05 )

static

Builds a ellipse around a point cloud, using a Minium Volume Ellipsoid algorithm.

Parameters

p	Points.
t	Tolerance

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 ellipse.

Parameters

p

Point.

Lerp()

Ellipse2 Ellipse2::Lerp ( const double & t, const Ellipse2 & ea, const Ellipse2 & eb )

static

Linear interpolation between two ellipses.

Linear interpolation of centers, radii, and main axis.

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 proposed by Srinivasa Ramanujan, Modular Equations and Approximations to Pi.

Poisson()

QVector< Vector2 > Ellipse2::Poisson	(	const double &	r,
		int	n,
		Random &	random = Random::R239 ) const

Compute a Poisson disc distribution inside the irregular octogon.

This function uses a simple dart throwing algorithm.

Parameters

r	Radius of the discs.
n	Number of candidate points.
random	Random number generator.

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.

Rotated() [1/2]

Ellipse2 Ellipse2::Rotated

(

const double &

a

)

const

Rotates an ellipse.

Parameters

a	Rotation angle.

Rotated() [2/2]

Ellipse2 Ellipse2::Rotated

(

const Matrix2 &

r

)

const

Rotates an ellipse.

Parameters

r	Rotation matrix.

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,
		bool	local = true ) const

Scales an ellipse.

See also

Ellipse2::Scaled(const Vector2&) const

Parameters

s	Scaling vector.
local	Boolean, set to true if scaling occurs in the local frame of the ellipse (default), otherwise computations are performed in the world coordinate system.

Signed()

double Ellipse2::Signed

(

const Vector2 &

p

)

const

Compute the signed distance between a point and the ellipse.

Parameters

p

Point.

Transformed()

Ellipse2 Ellipse2::Transformed

(

const Frame2 &

f

)

const

Return a ellipse transformed by a frame.

Parameters

f	Transformation.

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 Symbol Documentation

operator<<

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

friend

Overloaded.

Parameters

s	Stream.
ellipse	The ellipse.