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. More...

	Circle2 (const Vector2 &, const double &)
	Create a circle. More...

	Circle2 (const Vector2 &, const Vector2 &, const Vector2 &)
	Create the circle passing through 3 points. More...

	Circle2 (Vector2 *, int)
	Creates a circle enclosing a set of points. More...

bool	Inside (const Vector2 &) const
	Check if a point is inside the circle. More...

bool	Inside (const Circle2 &) const
	Test if a circle is entirely embedded in another one. More...

bool	Inside (const Box2 &) const
	Test if a box is inside the circle. More...

bool	InsideRange (const Vector2 &, const double &) const
	Check if a point is within a given range of the circle. More...

Vector2	Center () const
	Center of the circle.

Vector2	Vertex (const double &) const
	Vertex on the circle. More...

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. More...

Circle2	Extended (const double &) const
	Extend the radius of the circle. More...

bool	Intersect (const Box2 &) const
	Check intersection with a box. More...

bool	Intersect (const Circle2 &) const
	Check if two circles intersect each other. More...

bool	Intersect (const Ray2 &, double &, double &) const
	Check the intersection between a circle and a ray. More...

bool	Intersect (const Ray2 &) const
	Check the intersection between a circle and a ray. More...

bool	Intersect (const Segment2 &) const
	Check the intersection between a circle and a segment. More...

Vector2	Normal (const Vector2 &) const
	Compute the distance vector between a ciecle. More...

double	R (const Vector2 &) const
	Compute the squared distance between a point and the circle. More...

Box2	GetBox () const
	Compute the axis aligned bounding box of a circle.

Circle2	Translated (const Vector &) const
	Translate a circle. More...

Circle2	Rotated (const Matrix2 &) const
	Rotates a circle. More...

void	Translate (const Vector2 &)
	Translate a circle. More...

void	Rotate (const Matrix2 &)
	Rotates a circle. More...

void	Scale (const double &)
	Scales a circle. More...

double	Area () const
	Area of the circle.

double	Area (const Circle2 &) const
	Compute the area of the surface between two circles. More...

Vector2	RandomInside (Random &=Random::R239) const
	Generate a random vector inside the circle. More...

Vector2	RandomOn (Random &=Random::R239) const
	Generate a random vector on the circle. More...

QVector< Vector2 >	Poisson (const double &, int, bool=false, Random &=Random::R239) const
	Compute a Poisson sphere distribution inside a circle. More...

QuadricCurve2	QuadricBezierArc (const double &) const
	Compute the quadratic B�zier approximation of a circle arc. More...

CubicCurve2	CubicBezierArc (const double &) const
	Compute the cubic B�zier approximation of a circle arc. More...

void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a circle. More...

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

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 &, const Circle2 &)
	Overloaded. More...

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 B�zier 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: Box::Poisson, Box2::Poisson

Parameters

r	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 B�zier 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.

◆ 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.

Friends And Related Function Documentation

◆ operator<<

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

friend

Overloaded.

Parameters

s	Stream.
circle	The circle.

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Static Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Circle2() [1/4]

◆ Circle2() [2/4]

◆ Circle2() [3/4]

◆ Circle2() [4/4]

Member Function Documentation

◆ Area()

◆ CubicBezierArc()

◆ Draw()

◆ Extend()

◆ Extended()

◆ Inside() [1/3]

◆ Inside() [2/3]

◆ Inside() [3/3]

◆ InsideRange()

◆ Intersect() [1/5]

◆ Intersect() [2/5]

◆ Intersect() [3/5]

◆ Intersect() [4/5]

◆ Intersect() [5/5]

◆ Normal()

◆ Poisson()

◆ QuadricBezierArc()

◆ R()

◆ RandomInside()

◆ RandomOn()

◆ RandomUnit()

◆ Rotate()

◆ Rotated()

◆ Scale()

◆ Translate()

◆ Translated()

◆ Vertex()

Friends And Related Function Documentation

◆ operator<<