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

◆ bounded_side()

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.

◆ has_on_boundary()

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.

◆ has_on_bounded_side()

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.

◆ is_degenerate()

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.

◆ is_empty()

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.

◆ operator

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.

◆ set() [1/4]

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.

◆ set() [2/4]

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.

◆ set() [3/4]

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.

◆ set() [4/4]

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.

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