An object of type Sphere_3<Kernel> is a sphere in the threedimensional Euclidean space $$ ^{3}. The sphere is oriented, i.e. its boundary has clockwise or counterclockwise orientation. The boundary splits $$ ^{3} into a positive and a negative side, where the positive side is to the left of the boundary. The boundary also splits $$ ^{3} into a bounded and an unbounded side. Note that the sphere can be degenerated, i.e. the squared radius may be zero.
 
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the sphere with center center,
squared radius squared_radius and orientation
orientation.
 
 
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the unique sphere which passes through
the points p, q, r and s. The orientation of
the sphere is the orientation of the point quadruple p,
q, r, s.
 
 
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the smallest sphere which passes through
the points p, q, and r. The orientation of
the sphere is o.
 
 
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the smallest sphere which passes through
the points p and q. The orientation of
the sphere is o.
 
 
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the sphere with center center, squared
radius zero and orientation orientation.


 returns the center of c. 

 returns the squared radius of c. 

 returns the orientation of c. 

 returns true, iff c and sphere2 are equal, i.e. if they have the same center, same squared radius and same orientation. 

 returns true, iff c and sphere2 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 sphere with the same center and squared radius as c but with opposite orientation.  

 
returns the sphere obtained by applying $$at on c.
 

 returns a bounding box containing c. 