2D Optimisation Circle (Optimisation_circle_2)

Definition

An object of the class Optimisation_circle_2<R> is a circle in the two-dimensional Euclidean plane $$ ₂. Its boundary splits $$ ₂ into a bounded and an unbounded side. Note that the circle can be degenerate, i.e. it can be empty or contain only a single point. By definition, an empty Optimisation_circle_2<R> has no boundary and no bounded side, i.e. its unbounded side equals the whole plane $$ ₂. An Optimisation_circle_2<R> containing exactly one point $$p has no bounded side, its boundary is $${p}, and its unbounded side equals $$ ₂-$${p}.

#include <CGAL/Optimisation_circle_2.h>

Types

typedef Point_2<R>	Point;	Point type.
typedef R::FT	Distance;	Distance type.

Creation

void	circle.set ()	sets circle to the empty circle.
void	circle.set ( Point_2<R> p)
		sets circle to the circle equal to the single point p.
void	circle.set ( Point_2<R> p, Point_2<R> q)
		sets circle to the circle with diameter equal to the segment connecting p and q. Precondition: p and q are distinct.
void	circle.set ( Point_2<R> p, Point_2<R> q, Point_2<R> r)
		sets circle to the unique circle through p,q,r. Precondition: p,q,r are not collinear.
void	circle.set ( Point_2<R> center, R::FT squared_radius)
		sets circle to the circle with center center and squared radius squared_radius.

Access Functions

Point_2<R>	circle.center ()	returns the center of circle.
R::FT	circle.squared_radius ()
		returns the squared radius of circle.

Equality Tests

bool	circle == circle2	returns true, iff circle and circle2 are equal, i.e. if they have the same center and same squared radius.
bool	circle != circle2	returns true, iff circle and circle2 are not equal.

Predicates

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

I/O

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

#include <CGAL/IO/Window_stream.h>

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