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

Protected Attributes
Vector2	b = Vector2(Math::Sqrt12, Math::Sqrt12)
	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.
	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.
	Circle2 (const Circle2 &, const Circle2 &)
	Create a circle embedding two circles.
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 Vector2 &) const
	Translate a circle.
Circle2	Rotated (const Matrix2 &) const
	Rotates a circle.
Circle2	Transformed (const Frame2 &) const
	Return a circle transformed by a frame.
Circle2	Scaled (const double &) const
	Return a uniformly scaled circle.
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 disc distribution inside a circle.
QVector< Vector2 >	PoissonNorder (const double &, int, Random &=Random::R239) const
	Compute a Poisson disc distribution on the boundary of a circle.
QVector< Vector2 >	Border (const double &, Random &=Random::R239) const
	Compute a Poisson disc distribution on the boundary of the circle.
QuadricCurve2	QuadricBezierArc (const double &) const
	Compute the quadratic Bézier approximation of a circle arc.
QuadricCurve2	QuadricBezierArc (const double &, 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 Protected Member Functions inherited from Circle2
static Vector2	RandomUnit (Random &=Random::R239)
	Compute a random vertex inside a unit disc.
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	Point on the arc.
a,b	End points of the arc.

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.