Circle2 Class Reference

Circles in the plane. More...

#include <circle.h>

Inheritance diagram for Circle2:

Public Member Functions
	Circle2 ()
	Empty.
	Circle2 (const double &)
	Create a circle centered at origin.
	Circle2 (const Vector2 &, const double &)
	Create a circle.
	Circle2 (const Vector2 &, const Vector2 &, const Vector2 &)
	Create the circle passing through 3 points.
	Circle2 (Vector2 *, int)
	Creates a circle enclosing a set of points.
bool	Inside (const Vector2 &) const
	Check if a point is inside the circle.
bool	Inside (const Circle2 &) const
	Test if a circle is entirely embedded in another one.
bool	Inside (const Box2 &) const
	Test if a box is inside the circle.
bool	InsideRange (const Vector2 &, const double &) const
	Check if a point is within a given range of the circle.
Vector2	Center () const
	Center of the circle.
Vector2	Vertex (const double &) const
	Vertex on the circle.
Vector2	Tangent (const double &) const
	Tangent to the circle.
double	Radius () const
	Radius of the circle.
void	Extend (const Vector2 &)
	Extend the circle so that the argument point should be embedded in the new circle.
Circle2	Extended (const double &) const
	Extend the radius of the circle.
bool	Intersect (const Box2 &) const
	Check intersection with a box.
bool	Intersect (const Circle2 &) const
	Check if two circles intersect each other.
bool	Intersect (const Ray2 &, double &, double &) const
	Check the intersection between a circle and a ray.
bool	Intersect (const Ray2 &) const
	Check the intersection between a circle and a ray.
bool	Intersect (const Segment2 &) const
	Check the intersection between a circle and a segment.
Vector2	Normal (const Vector2 &) const
	Compute the distance vector between a ciecle.
double	R (const Vector2 &) const
	Compute the squared distance between a point and the circle.
Box2	GetBox () const
	Compute the axis aligned bounding box of a circle.
Circle2	Translated (const Vector &) const
	Translate a circle.
Circle2	Rotated (const Matrix2 &) const
	Rotates a circle.
Circle2	Transformed (const Frame2 &) const
	Return a circle transformed by a frame.
void	Translate (const Vector2 &)
	Translate a circle.
void	Rotate (const Matrix2 &)
	Rotates a circle.
void	Scale (const double &)
	Scales a circle.
double	Area () const
	Area of the circle.
double	Length () const
	Perimeter of the circle.
double	Area (const Circle2 &) const
	Compute the area of the surface between two circles.
Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the circle.
Vector2	RandomOn (Random &=Random::R239) const
	Generate a random vector on the circle.
Vector2	Vogel (int, int) const
	Generate a spiraling vector in the disc.
QVector< Vector2 >	Poisson (const double &, int, bool=false, Random &=Random::R239) const
	Compute a Poisson sphere distribution inside a circle.
QuadricCurve2	QuadricBezierArc (const double &) const
	Compute the quadratic Bézier approximation of a circle arc.
CubicCurve2	CubicBezierArc (const double &) const
	Compute the cubic Bézier approximation of a circle arc.
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a circle.

Static Public Member Functions
static Vector2	RandomUnit (Random &=Random::R239)
	Compute a random vertex inside a unit disc.

Static Public Attributes
static const Circle2	Unit
	Unit circle.
static const Circle2	Infinite
	Infinite circle.

Protected Attributes
Vector2	c = Vector2::Null
	Center.
double	r = 1.0
	Radius.

Static Protected Attributes
static constexpr const double	Epsilon = 1.e-6
	Epslion for intersection tests

Friends
std::ostream &	operator<< (std::ostream &s, const Circle2 &circle)
	Overloaded.

Detailed Description

Circles in the plane.

See also

Circle

Constructor & Destructor Documentation

Circle2() [1/4]

Circle2::Circle2 ( const double & r )

explicit

Create a circle centered at origin.

Parameters

r

Radius.

Circle2() [2/4]

Circle2::Circle2 ( const Vector2 & c, const double & r )

explicit

Create a circle.

Parameters

c	Center.
r	Radius.

Circle2() [3/4]

Circle2::Circle2 ( const Vector2 & a, const Vector2 & b, const Vector2 & c )

explicit

Create the circle passing through 3 points.

This is the circumscribed circle of the triangle.

Parameters

a,b,c

Points.

Circle2() [4/4]

Circle2::Circle2 ( Vector2 * p, int n )

explicit

Creates a circle enclosing a set of points.

The algorithm computes a fast approximation of the bounding ball for a point set based on the algorithm given by [Jack Ritter, 1990].

Parameters

p	Array of vertices.
n	Number of vertices.

Member Function Documentation

Area()

double Circle2::Area

(

const Circle2 &

circle

)

const

Compute the area of the surface between two circles.

If the circles do not intersect, the function returns 0; if the smallest is included in the largest, the function returns the area of the smallest, otherwise complex computations are performed.

Parameters

circle

The other circle.

CubicBezierArc()

CubicCurve2 Circle2::CubicBezierArc

(

const double &

t

)

const

Compute the cubic Bézier approximation of a circle arc.

Parameters

t

Angle.

Draw()

void Circle2::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 circle be filled.

Extend()

void Circle2::Extend

(

const Vector2 &

p

)

Extend the circle so that the argument point should be embedded in the new circle.

This is the same as computing the smallest enclosing circle of a circle and a point.

Parameters

p

Point.

Extended()

Circle2 Circle2::Extended

(

const double &

re

)

const

Extend the radius of the circle.

Parameters

re	Radius extension.

Inside() [1/3]

bool Circle2::Inside

(

const Box2 &

box

)

const

Test if a box is inside the circle.

Parameters

box

The box.

Inside() [2/3]

bool Circle2::Inside

(

const Circle2 &

circle

)

const

Test if a circle is entirely embedded in another one.

Parameters

circle

The other circle.

Inside() [3/3]

bool Circle2::Inside

(

const Vector2 &

p

)

const

Check if a point is inside the circle.

Parameters

p

Point.

InsideRange()

bool Circle2::InsideRange	(	const Vector2 &	p,
		const double &	e ) const

Check if a point is within a given range of the circle.

Parameters

p	Point.
e	Range.

Intersect() [1/5]

bool Circle2::Intersect

(

const Box2 &

box

)

const

Check intersection with a box.

Simply compute the distance between the center of the circle and the box and compare to radius of the circle.

See also

Box::R(const Vector&) const

Parameters

box

The box.

Intersect() [2/5]

bool Circle2::Intersect

(

const Circle2 &

circle

)

const

Check if two circles intersect each other.

Parameters

circle

The other circle.

Intersect() [3/5]

bool Circle2::Intersect

(

const Ray2 &

ray

)

const

Check the intersection between a circle and a ray.

Parameters

ray	The (normalized) ray.

Intersect() [4/5]

bool Circle2::Intersect	(	const Ray2 &	ray,
		double &	ta,
		double &	tb ) const

Check the intersection between a circle and a ray.

Note that intersections are sorted.

This function assumes that the ray is normalized, i.e. has a unit direction vector.

Parameters

ray	The (normalized) ray.
ta,tb	Intersection depths.

Intersect() [5/5]

bool Circle2::Intersect

(

const Segment2 &

segment

)

const

Check the intersection between a circle and a segment.

Parameters

segment

The segment.

Normal()

Vector2 Circle2::Normal

(

const Vector2 &

p

)

const

Compute the distance vector between a ciecle.

Parameters

p

Point.

Poisson()

QVector< Vector2 > Circle2::Poisson	(	const double &	ra,
		int	n,
		bool	border = false,
		Random &	random = Random::R239 ) const

Compute a Poisson sphere distribution inside a circle.

This function uses a simple O(n³) dart throwing algorithm.

See also

Box2::Poisson

Parameters

ra	Radius of the sphere.
n	Number of candidate points.
border	True to sample the border
random	Random number generator.

QuadricBezierArc()

QuadricCurve2 Circle2::QuadricBezierArc

(

const double &

t

)

const

Compute the quadratic Bézier approximation of a circle arc.

Approximation yields best results for 0 ≤ t ≤ π;/4.

Parameters

t

Angle.

R()

double Circle2::R

(

const Vector2 &

p

)

const

Compute the squared distance between a point and the circle.

Parameters

p

Point.

RandomInside()

Vector2 Circle2::RandomInside

(

Random &

random = Random::R239

)

const

Generate a random vector inside the circle.

Parameters

random

Random number generator.

RandomOn()

Vector2 Circle2::RandomOn

(

Random &

random = Random::R239

)

const

Generate a random vector on the circle.

Parameters

random

Random number generator.

RandomUnit()

Vector2 Circle2::RandomUnit ( Random & random = Random::R239 )

static

Compute a random vertex inside a unit disc.

Parameters

random

Random number generator.

Rotate()

void Circle2::Rotate ( const Matrix2 & m )

inline

Rotates a circle.

Parameters

m	Rotation matrix.

Rotated()

Circle2 Circle2::Rotated ( const Matrix2 & r ) const

inline

Rotates a circle.

Parameters

r	Rotation matrix.

Scale()

void Circle2::Scale ( const double & s )

inline

Scales a circle.

Parameters

s	Scaling factor.

Tangent()

Vector2 Circle2::Tangent

(

const double &

a

)

const

Tangent to the circle.

Parameters

a

Angle.

Transformed()

Circle2 Circle2::Transformed ( const Frame2 & f ) const

inline

Return a circle transformed by a frame.

Parameters

f	Transformation.

Translate()

void Circle2::Translate ( const Vector2 & t )

inline

Translate a circle.

Parameters

t	Translation vector.

Translated()

Circle2 Circle2::Translated ( const Vector & t ) const

inline

Translate a circle.

Parameters

t	Translation vector.

Vertex()

Vector2 Circle2::Vertex

(

const double &

a

)

const

Vertex on the circle.

Parameters

a

Angle.

Vogel()

Vector2 Circle2::Vogel	(	int	i,
		int	n ) const

Generate a spiraling vector in the disc.

Parameters

i	Integer, should be <n.
n	Number of points.

Friends And Related Symbol Documentation

operator<<

std::ostream & operator<< ( std::ostream & s, const Circle2 & circle )

friend

Overloaded.

Parameters

s	Stream.
circle	The circle.