CircleArc2 Class Reference

Circle arcs in the plane. More...

#include <circlearc.h>

Inheritance diagram for CircleArc2:

Public Member Functions
	CircleArc2 ()
	Empty.
	CircleArc2 (const Vector2 &, const double &, const Vector2 &, const Vector2 &)
	Creates a circle arc. More...
	CircleArc2 (const Vector2 &, const Vector2 &, const Vector2 &)
	Creates a circle arc given three vertices. More...
void	Rotate (const Matrix2 &)
	Rotates the arc. More...
void	Translate (const Vector2 &)
	Translates the arc. More...
void	Scale (const double &)
	Uniformly scales a circle. More...
Box2	GetBox () const
	Compute the axis aligned bounding box of the arc. More...
Vector2	Normal (const Vector2 &) const
	Compute the distance vector between a circular arc and a given point. More...
double	R (const Vector2 &) const
	Compute the squared distance between a point and the circle arc. More...
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw the circle arc. More...

Protected Attributes
Vector2	b
	End points of arc.
Protected Attributes inherited from Circle2
Vector2	c = Vector2::Null
	Center.
double	r = 1.0
	Radius.

Additional Inherited Members
Protected Member Functions inherited from Circle2
	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 Bézier approximation of a circle arc. More...
CubicCurve2	CubicBezierArc (const double &) const
	Compute the cubic Bézier approximation of a circle arc. More...
void	Draw (QGraphicsScene &, const QPen &=QPen(), const QBrush &=QBrush()) const
	Draw a circle. More...
Static Protected Member Functions inherited from Circle2
static Vector2	RandomUnit (Random &=Random::R239)
	Compute a random vertex inside a unit disc. More...
Static Protected Attributes inherited from Circle2
static constexpr const double	Epsilon = 1.e-6
	Epslion for intersection tests
static const Circle2	Unit
	Unit circle.
static const Circle2	Infinite
	Infinite circle.

Detailed Description

Circle arcs in the plane.

Constructor & Destructor Documentation

CircleArc2() [1/2]

CircleArc2::CircleArc2 ( const Vector2 &  c, const double &  r, const Vector2 &  a, const Vector2 &  b  )

explicit

Creates a circle arc.

Parameters

c	Center.
r	Radius.
a,b	End points, should be in trigonometric order (counter-clockwise).

CircleArc2() [2/2]

CircleArc2::CircleArc2 ( const Vector2 &  c, const Vector2 &  a, const Vector2 &  b  )

explicit

Creates a circle arc given three vertices.

Parameters

c	Center.
a,b	End points.

Member Function Documentation

Draw()

void CircleArc2::Draw	(	QGraphicsScene &	scene,
		const QPen &	pen = QPen(),
		const QBrush &	brush = QBrush()
	)		const

Draw the circle arc.

The arc is approximated by line segments, with an π/64 angle accuracy.

Parameters

scene	Graphics scene.
pen	The pen.
brush	The brush.

GetBox()

Box2 CircleArc2::GetBox

(

)

const

Compute the axis aligned bounding box of the arc.

This function analyzes 16 different configurations.

Normal()

Vector2 CircleArc2::Normal

(

const Vector2 &

p

)

const

Compute the distance vector between a circular arc and a given point.

Parameters

p

Point.

R()

double CircleArc2::R

(

const Vector2 &

p

)

const

Compute the squared distance between a point and the circle arc.

Parameters

p

Point.

Rotate()

void CircleArc2::Rotate

(

const Matrix2 &

m

)

Rotates the arc.

Parameters

m	Rotation matrix.

Scale()

void CircleArc2::Scale

(

const double &

s

)

Uniformly scales a circle.

Parameters

s	Scaling factor.

Translate()

void CircleArc2::Translate

(

const Vector2 &

t

)

Translates the arc.

Parameters

t	Translation vector.