CGAL 5.1 - 2D Boolean Operations on Nef Polygons Embedded on the Sphere
CGAL::Nef_polyhedron_S2< Traits >::Sphere_point Class Reference

#include <CGAL/Nef_polyhedron_S2.h>

Definition

template<typename Traits>
class CGAL::Nef_polyhedron_S2< Traits >::Sphere_point

An object p of type Sphere_point<R> is a point on the surface of a unit sphere. Such points correspond to the nontrivial directions in space and similarly to the equivalence classes of all nontrivial vectors under normalization.

Operations

Access to the coordinates is provided by the following operations. Note that the vector \( (x,y,z)\) is not normalized.

Types

typedef unspecified_type RT
 ring number type. More...
 

Creation

 Sphere_point ()
 creates some sphere point. More...
 
 Sphere_point (RT x, RT y, RT z)
 creates a sphere point corresponding to the point of intersection of the ray starting at the origin in direction \( (x,y,z)\) and the surface of \( S_2\). More...
 

Operations

RT x ()
 the \( x\)-coordinate. More...
 
RT y ()
 the \( y\)-coordinate. More...
 
RT z ()
 the \( z\)-coordinate. More...
 
bool operator== (const Nef_polyhedron_S2< Traits >::Sphere_point &q)
 Equality. More...
 
bool operator!= (const Nef_polyhedron_S2< Traits >::Sphere_point &q)
 Inequality. More...
 
Sphere_point antipode ()
 returns the antipode of p. More...
 

Member Typedef Documentation

◆ RT

template<typename Traits >
typedef unspecified_type CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::RT

ring number type.

Constructor & Destructor Documentation

◆ Sphere_point() [1/2]

template<typename Traits >
CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::Sphere_point ( )

creates some sphere point.

◆ Sphere_point() [2/2]

template<typename Traits >
CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::Sphere_point ( RT  x,
RT  y,
RT  z 
)

creates a sphere point corresponding to the point of intersection of the ray starting at the origin in direction \( (x,y,z)\) and the surface of \( S_2\).

Member Function Documentation

◆ antipode()

template<typename Traits >
Sphere_point CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::antipode ( )

returns the antipode of p.

◆ operator!=()

template<typename Traits >
bool CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::operator!= ( const Nef_polyhedron_S2< Traits >::Sphere_point q)

Inequality.

◆ operator==()

template<typename Traits >
bool CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::operator== ( const Nef_polyhedron_S2< Traits >::Sphere_point q)

Equality.

◆ x()

template<typename Traits >
RT CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::x ( )

the \( x\)-coordinate.

◆ y()

template<typename Traits >
RT CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::y ( )

the \( y\)-coordinate.

◆ z()

template<typename Traits >
RT CGAL::Nef_polyhedron_S2< Traits >::Sphere_point::z ( )

the \( z\)-coordinate.