An object of type Circle_2<Kernel> is a circle in the twodimensional 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.
 
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.
 
 
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.
 
 
introduces a variable c of type Circle_2<Kernel>.
It is initialized to the circle with diameter
$$pq
and
orientation
ori. Precondition: ori $$ COLLINEAR.
 
 
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.


 returns the center of c. 

 
returns the squared radius of c.  

 returns the orientation of c. 

 
returns true, iff c and circle2 are equal, i.e. if they have the same center, same squared radius and same orientation .  

 
returns true, iff c and circle2 are not equal. 

 returns true, iff c is degenerate, i.e. if c has squared radius zero. 

 
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.  

 
returns ON_BOUNDED_SIDE, ON_BOUNDARY, or ON_UNBOUNDED_SIDE iff p lies properly inside, on the boundary, or properly outside of c, resp.  

 

 

 

 



 returns the circle with the same center and squared radius as c but with opposite orientation .  

 
returns the circle obtained by applying $$at on c. Precondition: at is an orthogonal transformation.  

 returns a bounding box containing c. 