#include <CGAL/Circle_2.h>

Definition

template<typename Kernel>
class CGAL::Circle_2< Kernel >

An object c of type Circle_2 is a circle in the two-dimensional Euclidean plane \( \E^2\). The circle is oriented, i.e. its boundary has clockwise or counterclockwise orientation. The boundary splits \( \E^2\) into a positive and a negative side, where the positive side is to the left of the boundary. The boundary also splits \( \E^2\) into a bounded and an unbounded side. Note that the circle can be degenerated, i.e. the squared radius may be zero.

Is Model Of:

Kernel::Circle_2

Hashable if Kernel is a cartesian kernel and if Kernel::FT is Hashable

Creation
	Circle_2 (const Point_2< Kernel > &center, const Kernel::FT &squared_radius, const Orientation &ori=COUNTERCLOCKWISE)
	introduces a variable `c` of type `Circle_2`. More...

	Circle_2 (const Point_2< Kernel > &p, const Point_2< Kernel > &q, const Point_2< Kernel > &r)
	introduces a variable `c` of type `Circle_2`. More...

	Circle_2 (const Point_2< Kernel > &p, const Point_2< Kernel > &q, const Orientation &ori=COUNTERCLOCKWISE)
	introduces a variable `c` of type `Circle_2`. More...

	Circle_2 (const Point_2< Kernel > &center, const Orientation &ori=COUNTERCLOCKWISE)
	introduces a variable `c` of type `Circle_2`. More...

Access Functions
const Point_2< Kernel > &	center () const
	returns the center of `c`. More...

const Kernel::FT &	squared_radius () const
	returns the squared radius of `c`. More...

Orientation	orientation () const
	returns the orientation of `c`. More...

bool	operator== (const Circle_2< Kernel > &circle2) const
	returns `true`, iff `c` and `circle2` are equal, i.e. if they have the same center, same squared radius and same orientation. More...

bool	operator!= (const Circle_2< Kernel > &circle2) const
	returns `true`, iff `c` and `circle2` are not equal. More...

Predicates
bool	is_degenerate () const
	returns `true`, iff `c` is degenerate, i.e. if `c` has squared radius zero. More...

Oriented_side	oriented_side (const Point_2< Kernel > &p) const
	returns either the constant ON_ORIENTED_BOUNDARY, ON_POSITIVE_SIDE, or ON_NEGATIVE_SIDE, iff `p` lies on the boundary, properly on the positive side, or properly on the negative side of `c`, resp. More...

Bounded_side	bounded_side (const Point_2< Kernel > &p) const
	returns ON_BOUNDED_SIDE, ON_BOUNDARY, or ON_UNBOUNDED_SIDE iff `p` lies properly inside, on the boundary, or properly outside of `c`, resp. More...

bool	has_on_positive_side (const Point_2< Kernel > &p) const

bool	has_on_negative_side (const Point_2< Kernel > &p) const

bool	has_on_boundary (const Point_2< Kernel > &p) const

bool	has_on_bounded_side (const Point_2< Kernel > &p) const

bool	has_on_unbounded_side (const Point_2< Kernel > &p) const

Miscellaneous
Circle_2< Kernel >	opposite () const
	returns the circle with the same center and squared radius as `c` but with opposite orientation. More...

Circle_2< Kernel >	orthogonal_transform (Aff_transformation_2< Kernel > const &at) const
	returns the circle obtained by applying \( at\) on `c`. More...

Bbox_2	bbox () const
	returns a bounding box containing `c`. More...

Constructor & Destructor Documentation

◆ Circle_2() [1/4]

template<typename Kernel >

CGAL::Circle_2< Kernel >::Circle_2	(	const Point_2< Kernel > &	center,
		const Kernel::FT &	squared_radius,
		const Orientation &	ori = `COUNTERCLOCKWISE`
	)

introduces a variable c of type Circle_2.

It is initialized to the circle with center center, squared radius squared_radius and orientation ori.

Precondition: ori \( \neq\) COLLINEAR, and further, squared_radius \( \geq\) 0.

◆ Circle_2() [2/4]

template<typename Kernel >

CGAL::Circle_2< Kernel >::Circle_2	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q,
		const Point_2< Kernel > &	r
	)

introduces a variable c of type Circle_2.

It is initialized to the unique circle which passes through the points p, q and r. The orientation of the circle is the orientation of the point triple p, q, r.

Precondition: p, q, and r are not collinear.

◆ Circle_2() [3/4]

template<typename Kernel >

CGAL::Circle_2< Kernel >::Circle_2	(	const Point_2< Kernel > &	p,
		const Point_2< Kernel > &	q,
		const Orientation &	ori = `COUNTERCLOCKWISE`
	)

introduces a variable c of type Circle_2.

It is initialized to the circle with diameter \( \overline{pq}\) and orientation ori.

Precondition: ori \( \neq\) COLLINEAR.

◆ Circle_2() [4/4]

template<typename Kernel >

CGAL::Circle_2< Kernel >::Circle_2	(	const Point_2< Kernel > &	center,
		const Orientation &	ori = `COUNTERCLOCKWISE`
	)

introduces a variable c of type Circle_2.

It is initialized to the circle with center center, squared radius zero and orientation ori.

Precondition: ori \( \neq\) COLLINEAR.

Postcondition: c.is_degenerate() = true.

Member Function Documentation

◆ bbox()

template<typename Kernel >

Bbox_2 CGAL::Circle_2< Kernel >::bbox ( ) const

returns a bounding box containing c.

◆ bounded_side()

template<typename Kernel >

Bounded_side CGAL::Circle_2< Kernel >::bounded_side ( const Point_2< Kernel > & p ) const

returns ON_BOUNDED_SIDE, ON_BOUNDARY, or ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of c, resp.

◆ center()

template<typename Kernel >

const Point_2<Kernel>& CGAL::Circle_2< Kernel >::center ( ) const

returns the center of c.

◆ has_on_boundary()

template<typename Kernel >

bool CGAL::Circle_2< Kernel >::has_on_boundary ( const Point_2< Kernel > & p ) const

◆ has_on_bounded_side()

template<typename Kernel >

bool CGAL::Circle_2< Kernel >::has_on_bounded_side ( const Point_2< Kernel > & p ) const

◆ has_on_negative_side()

template<typename Kernel >

bool CGAL::Circle_2< Kernel >::has_on_negative_side ( const Point_2< Kernel > & p ) const

◆ has_on_positive_side()

template<typename Kernel >

bool CGAL::Circle_2< Kernel >::has_on_positive_side ( const Point_2< Kernel > & p ) const

◆ has_on_unbounded_side()

template<typename Kernel >

bool CGAL::Circle_2< Kernel >::has_on_unbounded_side ( const Point_2< Kernel > & p ) const

◆ is_degenerate()

template<typename Kernel >

bool CGAL::Circle_2< Kernel >::is_degenerate ( ) const

returns true, iff c is degenerate, i.e. if c has squared radius zero.

◆ operator!=()

template<typename Kernel >

bool CGAL::Circle_2< Kernel >::operator!= ( const Circle_2< Kernel > & circle2 ) const

returns true, iff c and circle2 are not equal.

◆ operator==()

template<typename Kernel >

bool CGAL::Circle_2< Kernel >::operator== ( const Circle_2< Kernel > & circle2 ) const

returns true, iff c and circle2 are equal, i.e. if they have the same center, same squared radius and same orientation.

◆ opposite()

template<typename Kernel >

Circle_2<Kernel> CGAL::Circle_2< Kernel >::opposite ( ) const

returns the circle with the same center and squared radius as c but with opposite orientation.

◆ orientation()

template<typename Kernel >

Orientation CGAL::Circle_2< Kernel >::orientation ( ) const

returns the orientation of c.

◆ oriented_side()

template<typename Kernel >

Oriented_side CGAL::Circle_2< Kernel >::oriented_side ( const Point_2< Kernel > & p ) const

returns either the constant ON_ORIENTED_BOUNDARY, ON_POSITIVE_SIDE, or ON_NEGATIVE_SIDE, iff p lies on the boundary, properly on the positive side, or properly on the negative side of c, resp.

◆ orthogonal_transform()

template<typename Kernel >

Circle_2<Kernel> CGAL::Circle_2< Kernel >::orthogonal_transform ( Aff_transformation_2< Kernel > const & at ) const

returns the circle obtained by applying \( at\) on c.

Precondition: at is an orthogonal transformation.

◆ squared_radius()

template<typename Kernel >

const Kernel::FT& CGAL::Circle_2< Kernel >::squared_radius ( ) const

returns the squared radius of c.

Definition

template<typename Kernel> class CGAL::Circle_2< Kernel >

Creation

Access Functions

Predicates

Miscellaneous

Constructor & Destructor Documentation

◆ Circle_2() [1/4]

◆ Circle_2() [2/4]

◆ Circle_2() [3/4]

◆ Circle_2() [4/4]

Member Function Documentation

◆ bbox()

◆ bounded_side()

◆ center()

◆ has_on_boundary()

◆ has_on_bounded_side()

◆ has_on_negative_side()

◆ has_on_positive_side()

◆ has_on_unbounded_side()

◆ is_degenerate()

◆ operator!=()

◆ operator==()

◆ opposite()

◆ orientation()

◆ oriented_side()

◆ orthogonal_transform()

◆ squared_radius()

template<typename Kernel>
class CGAL::Circle_2< Kernel >