Ellipse Concept Reference

Definition

An object ellipse of the class Ellipse is an ellipse in two-dimensional Euclidean plane \( \E^2\). Its boundary splits the plane into a bounded and an unbounded side. By definition, an empty ellipse has no boundary and no bounded side, i.e. its unbounded side equals the whole plane \( \E^2\).

Types
typedef unspecified_type	Point
	Point type.

Creation
void	set ()
	sets ellipse to the empty ellipse.
void	set (const Point &p)
	sets ellipse to the ellipse containing exactly p.
void	set (const Point &p, const Point &q)
	sets ellipse to the ellipse containing exactly the segment connecting p and q. More...
void	set (const Point &p, const Point &q, const Point &r)
	sets ellipse to the smallest ellipse through p,q,r. More...
void	set (const Point &p, const Point &q, const Point &r, const Point &s)
	sets ellipse to the smallest ellipse through p,q,r,s. More...
void	set (const Point &p, const Point &q, const Point &r, const Point &s, const Point &t)
	sets ellipse to the unique conic through p,q,r,s,t. More...

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

I/O
The following I/O operator is only needed, if the corresponding I/O operator of CGAL::Min_ellipse_2 is used.
ostream &	operator<< (ostream &os, const Ellipse &ellipse)
	writes ellipse to output stream os. More...

Member Function Documentation

CGAL::Bounded_side Ellipse::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 ellipse, resp.

Note

Only needed, if the corresponding predicate of CGAL::Min_ellipse_2 is used.

bool Ellipse::has_on_boundary

(

const Point &

p)

const

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

Note

Only needed, if the corresponding predicate of CGAL::Min_ellipse_2 is used.

bool Ellipse::has_on_bounded_side

(

const Point &

p)

const

returns true, iff p lies properly inside ellipse.

Note

Only needed, if the corresponding predicate of CGAL::Min_ellipse_2 is used.

bool Ellipse::is_degenerate

(

)

const

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

Note

Only needed, if the corresponding predicate of CGAL::Min_ellipse_2 is used.

bool Ellipse::is_empty

(

)

const

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

Note

Only needed, if the corresponding predicate of CGAL::Min_ellipse_2 is used.

ostream& Ellipse::operator<<	(	ostream &	os,
		const Ellipse &	ellipse
	)

writes ellipse to output stream os.

Note

Only needed, if the corresponding I/O operator of CGAL::Min_ellipse_2 is used.

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

sets ellipse to the ellipse containing exactly the segment connecting p and q.

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

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

sets ellipse to the smallest ellipse through p,q,r.

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

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

sets ellipse to the smallest ellipse through p,q,r,s.

The algorithm guarantees that this ellipse exists.

void Ellipse::set	(	const Point &	p,
		const Point &	q,
		const Point &	r,
		const Point &	s,
		const Point &	t
	)

sets ellipse to the unique conic through p,q,r,s,t.

The algorithm guarantees that this conic is an ellipse.