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## CGAL::Nef_polyhedron_S2<Traits>::Sphere_circle

### Definition

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 S2. 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.

### Types

Nef_polyhedron_S2<Traits>::Sphere_circle::RT
| ring type.
Nef_polyhedron_S2<Traits>::Sphere_circle::Plane_3
| plane a Sphere_circle lies in.

### Creation

Nef_polyhedron_S2<Traits>::Sphere_circle c;
| creates some great circle.
Nef_polyhedron_S2<Traits>::Sphere_circle c ( | Sphere_point p, Sphere_point q);
| If p and q are opposite of each other, then we create the unique great circle on S2 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.
Nef_polyhedron_S2<Traits>::Sphere_circle c ( Plane_3 h);
| creates the circle corresponding to the plane h. Precondition: h contains the origin.
Nef_polyhedron_S2<Traits>::Sphere_circle c ( RT x, RT y, RT z);
| creates the circle orthogonal to the vector (x,y,z).
Nef_polyhedron_S2<Traits>::Sphere_circle c ( | Sphere_circle c, Sphere_point p);
| creates a great circle orthogonal to c that contains p. Precondition: p is not part of c.

### Operations

Sphere_circle | c.opposite () | Returns a sphere circle in the oppostie direction of c.
bool | c.has_on ( Sphere_point p)
|  | returns true iff c contains p.
Plane_3 | c.plane () | returns the plane supporting c.
Sphere_point | c.orthogonal_pole ()
|  | returns the point that is the pole of the hemisphere left of c.

### Global functions

bool | equal_as_sets ( const c1, const c2)
|  | returns true iff c1 and c2 are equal as unoriented circles.

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The CGAL Project . Tue, December 21, 2004 .