 ## CGAL::Circle_2<Kernel>

### Definition

An object of type Circle_2<Kernel> is a circle in the two-dimensional Euclidean plane 2. The circle is oriented, i.e. its boundary has clockwise or counterclockwise orientation . The boundary splits 2 into a positive and a negative side, where the positive side is to the left of the boundary. The boundary also splits 2 into a bounded and an unbounded side. Note that the circle can be degenerated, i.e. the squared radius may be zero.

### Creation

Circle_2<Kernel> c ( Point_2<Kernel> center, Kernel::FT squared_radius, Orientation ori = COUNTERCLOCKWISE);
introduces a variable c of type Circle_2<Kernel>. It is initialized to the circle with center center, squared radius squared_radius and orientation ori.
 Precondition: ori COLLINEAR, and further, squared_radius 0.

Circle_2<Kernel> c ( Point_2<Kernel> p, Point_2<Kernel> q, Point_2<Kernel> r);
introduces a variable c of type Circle_2<Kernel>. It is initialized to the unique circle which passes through the points p, q and r. The orientation of the circle is the orientation of the point triple p, q, r.
 Precondition: p, q, and r are not collinear.

Circle_2<Kernel> c ( Point_2<Kernel> p, Point_2<Kernel> q, Orientation ori = COUNTERCLOCKWISE);
introduces a variable c of type Circle_2<Kernel>. It is initialized to the circle with diameter pq and orientation ori.
 Precondition: ori COLLINEAR.

Circle_2<Kernel> c ( Point_2<Kernel> center, Orientation ori = COUNTERCLOCKWISE);
introduces a variable c of type Circle_2<Kernel>. It is initialized to the circle with center center, squared radius zero and orientation ori.
 Precondition: ori COLLINEAR.
 Postcondition: c.is_degenerate() = true.

### Access Functions

 Point_2 c.center () returns the center of c. Kernel::FT c.squared_radius () returns the squared radius of c. Orientation c.orientation () returns the orientation of c. bool c.operator == ( circle2) returns true, iff c and circle2 are equal, i.e. if they have the same center, same squared radius and same orientation . bool c.operator != ( circle2) returns true, iff c and circle2 are not equal.

### Predicates

 bool c.is_degenerate () returns true, iff c is degenerate, i.e. if c has squared radius zero. Oriented_side c.oriented_side ( Point_2 p) returns either the constant ON_ORIENTED_BOUNDARY, ON_POSITIVE_SIDE, or ON_NEGATIVE_SIDE, iff p lies on the boundary, properly on the positive side, or properly on the negative side of c, resp. Bounded_side c.bounded_side ( Point_2 p) returns ON_BOUNDED_SIDE, ON_BOUNDARY, or ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of c, resp. bool c.has_on_positive_side ( Point_2 p) bool c.has_on_negative_side ( Point_2 p) bool c.has_on_boundary ( Point_2 p) bool c.has_on_bounded_side ( Point_2 p) bool c.has_on_unbounded_side ( Point_2 p)

### Miscellaneous

Circle_2<Kernel> c.opposite () returns the circle with the same center and squared radius as c but with opposite orientation .

Circle_2<Kernel> c.orthogonal_transform ( Aff_transformation_2<Kernel> at)
returns the circle obtained by applying at on c.
 Precondition: at is an orthogonal transformation.

Bbox_2 c.bbox () returns a bounding box containing c.