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### 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.

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The CGAL Project . Tue, December 21, 2004 .