CGAL 4.9 - 2D Boolean Operations on Nef Polygons Embedded on the Sphere
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CGAL::Nef_polyhedron_S2< Traits >::Sphere_circle Class Reference
2D Boolean Operations on Nef Polygons Embedded on the Sphere 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 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.

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 S2 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 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.

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.