\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.7 - 2D Boolean Operations on Nef Polygons Embedded on the Sphere
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CGAL::Nef_polyhedron_S2< Traits >::SHalfloop Class Reference
2D Boolean Operations on Nef Polygons Embedded on the Sphere Reference

#include <CGAL/Nef_polyhedron_S2.h>

Definition

A sloop is a great circle on a sphere.

A shalfloop is an oriented sloop. It is always paired with a shalfloop whose supporting Sphere_circle is pointing in the opposite direction. The twin() member function returns this shalfloop of opposite orientation. Each Nef_polyhedron_S2 can only have one sloop (resp. two shalfloops).

The figure below depicts the relationship between a shalfloop and sfaces on a sphere map.

shalfloopB.png
Incidences of an SHalfloop
Creation

There is no need for a user to create a SHalfloop explicitly. The class Nef_polyhedron_S2<Traits> manages the needed shalfloops internally.

See also
CGAL::Nef_polyhedron_S2::SFace
CGAL::Nef_polyhedron_S2::Sphere_circle

Types

The following types are the same as in Nef_polyhedron_S2<Traits>.

typedef unspecified_type Mark
 type of mark. More...
 
typedef unspecified_type Sphere_circle
 sphere circle type stored in SHalfloop. More...
 
typedef unspecified_type SHalfloop_const_handle
 const handle to SHalfloop. More...
 
typedef unspecified_type SFace_const_handle
 const handle to SFace. More...
 

Operations

const Mark & mark () const
 the mark of the halfloop. More...
 
const Sphere_circle & circle () const
 the sphere circle of the halfloop. More...
 
SHalfloop_const_handle twin () const
 the twin of the halfloop. More...
 
SFace_const_handle incident_sface () const
 the incident sface of the halfloop. More...
 

Member Typedef Documentation

template<typename Traits >
typedef unspecified_type CGAL::Nef_polyhedron_S2< Traits >::SHalfloop::Mark

type of mark.

template<typename Traits >
typedef unspecified_type CGAL::Nef_polyhedron_S2< Traits >::SHalfloop::SFace_const_handle

const handle to SFace.

template<typename Traits >
typedef unspecified_type CGAL::Nef_polyhedron_S2< Traits >::SHalfloop::SHalfloop_const_handle

const handle to SHalfloop.

template<typename Traits >
typedef unspecified_type CGAL::Nef_polyhedron_S2< Traits >::SHalfloop::Sphere_circle

sphere circle type stored in SHalfloop.

Member Function Documentation

template<typename Traits >
const Sphere_circle& CGAL::Nef_polyhedron_S2< Traits >::SHalfloop::circle ( ) const

the sphere circle of the halfloop.

template<typename Traits >
SFace_const_handle CGAL::Nef_polyhedron_S2< Traits >::SHalfloop::incident_sface ( ) const

the incident sface of the halfloop.

template<typename Traits >
const Mark& CGAL::Nef_polyhedron_S2< Traits >::SHalfloop::mark ( ) const

the mark of the halfloop.

template<typename Traits >
SHalfloop_const_handle CGAL::Nef_polyhedron_S2< Traits >::SHalfloop::twin ( ) const

the twin of the halfloop.