CGAL 4.7 - 2D Boolean Operations on Nef Polygons Embedded on the Sphere
CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle Class Reference

#include <CGAL/Nef_polyhedron_S2.h>

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 $$S_2$$. 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.

Related Functions

(Note that these are not member functions.)

bool equal_as_sets (const Nef_polyhedron_S2< Traits >::Sphere_circle c1, const Nef_polyhedron_S2< Traits >::Sphere_circle c2)
returns true iff c1 and c2 are equal as unoriented circles.

Types

typedef unspecified_type RT
ring type.

typedef unspecified_type Plane_3
plane a Sphere_circle lies in.

Creation

Sphere_circle ()
creates some great circle.

Sphere_circle (const Sphere_point &p, const Sphere_point &q)
If $$p$$ and $$q$$ are opposite of each other, then we create the unique great circle on $$S_2$$ which contains p and q. More...

Sphere_circle (const Plane_3 &h)
creates the circle corresponding to the plane h. More...

Sphere_circle (const RT &x, const RT &y, const RT &z)
creates the circle orthogonal to the vector $$(x,y,z)$$.

Sphere_circle (Sphere_circle c, const Sphere_point &p)
creates a great circle orthogonal to $$c$$ that contains $$p$$. More...

Operations

Sphere_circle opposite ()
Returns a sphere circle in the opposite direction of c.

bool has_on (const Sphere_point &p)
returns true iff c contains p.

Plane_3 plane ()
returns the plane supporting c.

Sphere_point orthogonal_pole ()
returns the point that is the pole of the hemisphere left of c.

Constructor & Destructor Documentation

template<typename Traits >
 CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle::Sphere_circle ( const Sphere_point & p, const Sphere_point & q )

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 $$q$$.

template<typename Traits >
 CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle::Sphere_circle ( const Plane_3 & h)

creates the circle corresponding to the plane h.

Precondition
h contains the origin.
template<typename Traits >
 CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle::Sphere_circle ( Sphere_circle c, const Sphere_point & p )

creates a great circle orthogonal to $$c$$ that contains $$p$$.

Precondition
$$p$$ is not part of $$c$$.