Circle Concept Reference

Definition

An object of the class Circle is a circle in two-dimensional Euclidean plane \( \E^2\). Its boundary splits the plane into a bounded and an unbounded side. By definition, an empty Circle has no boundary and no bounded side, i.e. its unbounded side equals the whole plane \( \E^2\). A Circle containing exactly one point \( p\) has no bounded side, its boundary is \( \{p\}\), and its unbounded side equals \( \E^2 \setminus \{p\}\).

Types
typedef unspecified_type	Point
	Point type.
typedef unspecified_type	Distance
	Distance type. More...

Creation
void	set ()
	sets circle to the empty circle.
void	set (const Point &p)
	sets circle to the circle containing exactly \( \{\mbox{`p` }\}\).
void	set (const Point &p, const Point &q)
	sets circle to the circle with diameter equal to the segment connecting p and q. More...
void	set (const Point &p, const Point &q, const Point &r)
	sets circle to the circle through p,q,r. More...

Predicates
bool	has_on_unbounded_side (const Point &p) const
	returns true, iff p lies properly outside of circle.
CGAL::Bounded_side	bounded_side (const Point &p) const
	returns CGAL::ON_BOUNDED_SIDE, CGAL::ON_BOUNDARY, or CGAL::ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of circle, resp. More...
bool	has_on_bounded_side (const Point &p) const
	returns true, iff p lies properly inside circle. More...
bool	has_on_boundary (const Point &p) const
	returns true, iff p lies on the boundary of circle. More...
bool	is_empty () const
	returns true, iff circle is empty (this implies degeneracy). More...
bool	is_degenerate () const
	returns true, iff circle is degenerate, i.e. if circle is empty or equal to a single point. More...

Additional Operations for Checking
bool	operator== (const Circle &circle2) const
	returns true, iff circle and circle2 are equal. More...
Point	center () const
	returns the center of circle. More...
Distance	squared_radius () const
	returns the squared radius of circle. More...

I/O
std::ostream &	operator<< (std::ostream &os, const Circle &circle)
	writes circle to output stream os.

Member Typedef Documentation

typedef unspecified_type Circle::Distance

Distance type.

The function squared_radius() (see below) returns an object of this type.

Note

Only needed, if the member function is_valid() of Min_circle_2 is used.

Member Function Documentation

CGAL::Bounded_side Circle::bounded_side

(

const Point &

p)

const

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

Note

Only needed, if the corresponding predicate of Min_circle_2 is used.

Point Circle::center

(

)

const

returns the center of circle.

Note

Only needed, if the member function is_valid() of Min_circle_2 is used.

bool Circle::has_on_boundary

(

const Point &

p)

const

returns true, iff p lies on the boundary of circle.

Note

Only needed, if the corresponding predicate of Min_circle_2 is used.

bool Circle::has_on_bounded_side

(

const Point &

p)

const

returns true, iff p lies properly inside circle.

Note

Only needed, if the corresponding predicate of Min_circle_2 is used.

bool Circle::is_degenerate

(

)

const

returns true, iff circle is degenerate, i.e. if circle is empty or equal to a single point.

Note

Only needed, if the corresponding predicate of Min_circle_2 is used.

bool Circle::is_empty

(

)

const

returns true, iff circle is empty (this implies degeneracy).

Note

Only needed, if the corresponding predicate of Min_circle_2 is used.

bool Circle::operator==

(

const Circle &

circle2)

const

returns true, iff circle and circle2 are equal.

Note

Only needed, if the member function is_valid() of Min_circle_2 is used.

void Circle::set	(	const Point &	p,
		const Point &	q
	)

sets circle to the circle with diameter equal to the segment connecting p and q.

The algorithm guarantees that set is never called with two equal points.

void Circle::set	(	const Point &	p,
		const Point &	q,
		const Point &	r
	)

sets circle to the circle through p,q,r.

The algorithm guarantees that set is never called with three collinear points.

Distance Circle::squared_radius

(

)

const

returns the squared radius of circle.

Note

Only needed, if the member function is_valid() of Min_circle_2 is used.