An object c of type Sphere_circle is an oriented great circle on the surface of a unit sphere. Such circles correspond to the intersection of an oriented plane (that contains the origin) and the surface of $$S_{2}. The orientation of the great circle is that of a counterclockwise walk along the circle as seen from the positive halfspace of the oriented plane.
 
ring type.
 
 
plane a Sphere_circle lies in.

 
creates some great circle.
 
 
If $$p and $$q are
opposite of each other, then we create the unique great circle on $$S_{2}
which contains p and q. This circle is oriented such
that a walk along c meets $$p just before the shorter segment
between $$p and $$q. If $$p and $$q are opposite of each other then
we create any great circle that contains $$p and $$q.
 
 
creates the
circle corresponding to the plane h. Precondition: h contains the origin.
 
 
creates the circle orthogonal to the vector $$(x,y,z).
 
 
creates a great circle orthogonal to $$c that contains $$p. Precondition: $$p is not part of $$c.


 Returns a sphere circle in the oppostie direction of c. 

 
returns true iff c contains p.  

 returns the plane supporting c. 

 
returns the point that is the pole of the hemisphere left of c. 

 
returns true iff c1 and c2 are equal as unoriented circles. 