\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 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.

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.
typedef unspecified_type | Sphere_circle
| sphere circle type stored in SHalfloop.
typedef unspecified_type | SHalfloop_const_handle
| const handle to SHalfloop.
typedef unspecified_type | SFace_const_handle
| const handle to SFace.

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