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.