CGAL::Circular_arc_2< CircularKernel > Class Template Reference

#include <CGAL/Circular_arc_2.h>

Definition

Is Model Of:

CircularKernel::CircularArc_2

See Also

CGAL::Circular_arc_point_2<CircularKernel>

CGAL::Line_arc_2<CircularKernel>

Examples:

Circular_kernel_2/functor_has_on_2.cpp, and Circular_kernel_2/intersecting_arcs.cpp.

Related Functions
(Note that these are not member functions.)
bool	operator== (const Circular_arc_2< CircularKernel > &ca1, const Circular_arc_2< CircularKernel > &ca2)
	Test for equality. More...
bool	operator!= (const Circular_arc_2< CircularKernel > &ca1, const Circular_arc_2< CircularKernel > &ca2)
	Test for non-equality. More...
istream &	operator>> (std::istream &is, Circular_arc_2 &ca)
ostream &	operator<< (std::ostream &os, const Circular_arc_2 &ca)

Creation
	Circular_arc_2 (const Circle_2< CircularKernel > &c)
	Constructs an arc from a full circle. More...
	Circular_arc_2 (const Circle_2< CircularKernel > &c, const Circular_arc_point_2< CircularKernel > &p, const Circular_arc_point_2< CircularKernel > &q)
	Constructs the circular arc supported by c, whose source is p and whose target is q when traversing the circle in counterclockwise direction. More...
	Circular_arc_2 (const Point_2< CircularKernel > &p, const Point_2< CircularKernel > &q, const Point_2< CircularKernel > &r)
	Constructs an arc that is supported by the circle of type Circle_2<CircularKernel> passing through the points p, q and r. More...

Access Functions
Circle_2< CircularKernel >	supporting_circle ()
Point_2< CircularKernel > const &	center () const
	returns the center of the supporting circle. More...
CircularKernel::FT const &	squared_radius () const
	returns the squared radius of the supporting circle. More...
A circular arc is not oriented. Still, its source and target endpoints can be defined, supposing that its supporting circle in traversed the counterclockwise direction from source to target.
Circular_arc_point_2 < CircularKernel >	source ()
Circular_arc_point_2 < CircularKernel >	target ()
When the methods source and target return the same point, then the arc is in fact a full circle. When an arc is x-monotone, its left and right points can be accessed directly:
Circular_arc_point_2 < CircularKernel >	left ()
Circular_arc_point_2 < CircularKernel >	right ()
Bbox_2	bbox () const
	Returns a bounding box containing the arc. More...

Query Functions
bool	is_x_monotone ()
	Tests whether the arc is x-monotone. More...
bool	is_y_monotone ()
	Tests whether the arc is y-monotone. More...

Constructor & Destructor Documentation

template<typename CircularKernel >

CGAL::Circular_arc_2< CircularKernel >::Circular_arc_2

(

const Circle_2< CircularKernel > &

c

)

Constructs an arc from a full circle.

template<typename CircularKernel >

CGAL::Circular_arc_2< CircularKernel >::Circular_arc_2	(	const Circle_2< CircularKernel > &	c,
		const Circular_arc_point_2< CircularKernel > &	p,
		const Circular_arc_point_2< CircularKernel > &	q
	)

Constructs the circular arc supported by c, whose source is p and whose target is q when traversing the circle in counterclockwise direction.

Precondition

p and q lie on c.

template<typename CircularKernel >

CGAL::Circular_arc_2< CircularKernel >::Circular_arc_2	(	const Point_2< CircularKernel > &	p,
		const Point_2< CircularKernel > &	q,
		const Point_2< CircularKernel > &	r
	)

Constructs an arc that is supported by the circle of type Circle_2<CircularKernel> passing through the points p, q and r.

The source and target are respectively p and r, when traversing the supporting circle in the counterclockwise direction. Note that, depending on the orientation of the point triple (p,q,r), q may not lie on the arc.

Precondition

p, q, and r are not collinear.

Member Function Documentation

template<typename CircularKernel >

Bbox_2 CGAL::Circular_arc_2< CircularKernel >::bbox

(

)

const

Returns a bounding box containing the arc.

template<typename CircularKernel >

Point_2<CircularKernel> const& CGAL::Circular_arc_2< CircularKernel >::center

(

)

const

returns the center of the supporting circle.

template<typename CircularKernel >

bool CGAL::Circular_arc_2< CircularKernel >::is_x_monotone

(

)

Tests whether the arc is x-monotone.

template<typename CircularKernel >

bool CGAL::Circular_arc_2< CircularKernel >::is_y_monotone

(

)

Tests whether the arc is y-monotone.

template<typename CircularKernel >

Circular_arc_point_2<CircularKernel> CGAL::Circular_arc_2< CircularKernel >::left

(

)

Precondition

ca.is_x_monotone().

template<typename CircularKernel >

Circular_arc_point_2<CircularKernel> CGAL::Circular_arc_2< CircularKernel >::right

(

)

Precondition

ca.is_x_monotone().

template<typename CircularKernel >

Circular_arc_point_2<CircularKernel> CGAL::Circular_arc_2< CircularKernel >::source

(

)

template<typename CircularKernel >

CircularKernel::FT const& CGAL::Circular_arc_2< CircularKernel >::squared_radius

(

)

const

returns the squared radius of the supporting circle.

template<typename CircularKernel >

Circle_2<CircularKernel> CGAL::Circular_arc_2< CircularKernel >::supporting_circle

(

)

template<typename CircularKernel >

Circular_arc_point_2<CircularKernel> CGAL::Circular_arc_2< CircularKernel >::target

(

)

Friends And Related Function Documentation

template<typename CircularKernel >

bool operator!= ( const Circular_arc_2< CircularKernel > &  ca1, const Circular_arc_2< CircularKernel > &  ca2  )

related

Test for non-equality.

template<typename CircularKernel >

ostream & operator<< ( std::ostream &  os, const Circular_arc_2< CircularKernel > &  ca  )

related

template<typename CircularKernel >

bool operator== ( const Circular_arc_2< CircularKernel > &  ca1, const Circular_arc_2< CircularKernel > &  ca2  )

related

Test for equality.

Two arcs are equal, iff their non-oriented supporting circles are equal (i.e. they have same center and same squared radius) and their endpoints are equal.

template<typename CircularKernel >

istream & operator>> ( std::istream &  is, Circular_arc_2< CircularKernel > &  ca  )

related