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. Precondition: orientation $$ COPLANAR, and furthermore, squared_radius $$ 0.
 
 
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. Precondition: p, q, r, and s are not collinear.
 
 
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. Precondition: o is not COPLANAR.
 
 
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. Precondition: o is not COPLANAR.
 
 
introduces a variable c of type Sphere_3<Kernel>.
It is initialized to the sphere with center center, squared
radius zero and orientation orientation. Precondition: orientation $$ COPLANAR. 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 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. Precondition: at is an orthogonal transformation.  

 returns a bounding box containing c. 