Circle Type (Circle)

Definition

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

Types

Circle::Point
	Point type.

The following type is only needed, if the member function is_valid of Min_circle_2 is used.

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

Creation

void	circle.set ()	sets circle to the empty circle.
void	circle.set ( Point p)
		sets circle to the circle containing exactly $${p$$}.
void	circle.set ( Point p, 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 ( Point p, Point q, Point r)
		sets circle to the circle through p,q,r. The algorithm guarantees that set is never called with three collinear points.

Predicates

bool	circle.has_on_unbounded_side ( Point p)
		returns true, iff p lies properly outside of circle.

Each of the following predicates is only needed, if the corresponding predicate of Min_circle_2 is used.

CGAL::Bounded_side	circle.bounded_side ( Point p)
		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.
bool	circle.has_on_bounded_side ( Point p)
		returns true, iff p lies properly inside circle.
bool	circle.has_on_boundary ( Point p)
		returns true, iff p lies on the boundary 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.

Additional Operations for Checking

The following operations are only needed, if the member function is_valid of Min_circle_2 is used.

bool	circle == circle2	returns true, iff circle and circle2 are equal.
Point	circle.center ()	returns the center of circle.
Distance	circle.squared_radius ()
		returns the squared radius of circle.

I/O

The following I/O operators are only needed, if the corresponding I/O operators of Min_circle_2 are used.

std::ostream&	std::ostream& os << circle
		writes circle to output stream os.
CGAL::Window_stream&
	CGAL::Window_stream& ws << circle
		writes circle to window stream ws.