2D Optimisation Ellipse (Optimisation_ellipse_2)

Definition

An object of the class Optimisation_ellipse_2<R> is an ellipse in the two-dimensional Euclidean plane $$ ₂. Its boundary splits $$ ₂ into a bounded and an unbounded side. Note that the ellipse can be degenerate, i.e. it can be empty, equal to a single point or equal to a segment. By definition, an empty Optimisation_ellipse_2<R> has no boundary and no bounded side, i.e. its unbounded side equals the whole plane $$ ₂. A Optimisation_ellipse_2<R> equal to a single point $$p or equal to a segment $$s, resp., has no bounded side, its boundary is $${p} or $$s, resp., and its unbounded side equals $$ ₂-$${p} or $$ ₂-$$s, resp.

#include <CGAL/Optimisation_ellipse_2.h>

Types

typedef Point_2<R>

Point;

Point type.

Creation

void	ellipse.set ()	sets ellipse to the empty ellipse.
void	ellipse.set ( Point_2<R> p)
		sets ellipse to the ellipse equal to the single point p.
void	ellipse.set ( Point_2<R> p, Point_2<R> q)
		sets ellipse to the ellipse equal to the segment connecting p and q. Precondition: p and q are distinct.
void	ellipse.set ( Point_2<R> p1, Point_2<R> p2, Point_2<R> p3)
		sets ellipse to the ellipse of smallest area through p1, p2 and p3. Precondition: p1,p2,p3 are not collinear.
void	ellipse.set ( Point_2<R> p1, Point_2<R> p2, Point_2<R> p3, Point_2<R> p4)
		sets ellipse to the ellipse of smallest area through p1, p2, p3 and p4. Precondition: p1,p2,p3,p4 are in convex position.
void	ellipse.set ( Point_2<R> p1, Point_2<R> p2, Point_2<R> p3, Point_2<R> p4, Point_2<R> p5)
		sets ellipse to the unique ellipse through p1, p2, p3, p4 and p5. Precondition: There exists an ellipse through p1,p2,p3,p4,p5.

Access Functions

int	ellipse.number_of_boundary_points ()
		returns the number of boundary points defining ellipse.

Equality Tests

bool	ellipse == ellipse2
		returns true, iff ellipse and ellipse2 are equal, i.e. if both ellipses were constructed from the same set of points.
bool	ellipse != ellipse2
		returns true, iff ellipse and ellipse2 are not equal.

Predicates

Bounded_side	ellipse.bounded_side ( Point_2<R> p)
		returns ON_BOUNDED_SIDE, ON_BOUNDARY, or ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary of, or properly outside of ellipse, resp.
bool	ellipse.has_on_bounded_side ( Point_2<R> p)
		returns true, iff p lies properly inside ellipse.
bool	ellipse.has_on_boundary ( Point_2<R> p)
		returns true, iff p lies on the boundary of ellipse.
bool	ellipse.has_on_unbounded_side ( Point_2<R> p)
		returns true, iff p lies properly outside of ellipse.
bool	ellipse.is_empty ()
		returns true, iff ellipse is empty (this implies degeneracy).
bool	ellipse.is_degenerate ()
		returns true, iff ellipse is degenerate, i.e. if ellipse is empty, equal to a single point or equal to a segment.

I/O

ostream&	ostream& os << ellipse
		writes ellipse to output stream os.
istream&	istream& is >> & ellipse
		reads ellipse from input stream is.

#include <CGAL/IO/Window_stream.h>

Window_stream&	Window_stream& ws << ellipse
		writes ellipse to window stream ws.