\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.7 - 3D Boolean Operations on Nef Polyhedra
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop Class Reference
3D Boolean Operations on Nef Polyhedra Reference

#include <CGAL/Nef_polyhedron_3.h>

Definition

template<class Nef_polyhedronTraits_3, class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
class CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop

A shalfloop is a great circle on a sphere map.

Figure figureNef3HalfloopIncidences depicts the relationship between a shalfloop and its incident shalfloops, and sfaces on a sphere map. 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.

shalfloopB.png

A sphere map having a shalfloop models the neighborhood of a vertex which is isolated on a facet. That facet is returned by the member function facet.

Creation

There is no need for a user to create a SHalfloop explicitly. The class Nef_polyhedron_3<Traits> manages the needed shalfloops internally.

See also
CGAL::Nef_polyhedron_3::Halffacet
CGAL::Nef_polyhedron_3::SFace
CGAL::Nef_polyhedron_S2::Sphere_point

Types

The following types are the same as in Nef_polyhedron_3<Traits>.

typedef unspecified_type Mark
 type of mark. More...
 
typedef unspecified_type Sphere_circle
 sphere circle type stored in SHalfloop. More...
 
typedef unspecified_type Halffacet_const_handle
 const handle to Halffacet. 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 se . More...
 
const Sphere_circle & circle () const
 the sphere circle of se . More...
 
SHalfloop_const_handle twin () const
 the twin of se . More...
 
Halffacet_const_handle facet () const
 the facet that corresponds to se in the 3D incidence structure. More...
 
SFace_const_handle incident_sface () const
 the incident sface of se . More...
 

Member Typedef Documentation

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::Halffacet_const_handle

const handle to Halffacet.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::Mark

type of mark.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::SFace_const_handle

const handle to SFace.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::SHalfloop_const_handle

const handle to SHalfloop.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
typedef unspecified_type CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::Sphere_circle

sphere circle type stored in SHalfloop.

Member Function Documentation

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
const Sphere_circle& CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::circle ( ) const

the sphere circle of se .

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
Halffacet_const_handle CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::facet ( ) const

the facet that corresponds to se in the 3D incidence structure.

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
SFace_const_handle CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::incident_sface ( ) const

the incident sface of se .

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
const Mark& CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::mark ( ) const

the mark of se .

template<class Nef_polyhedronTraits_3 , class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
SHalfloop_const_handle CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfloop::twin ( ) const

the twin of se .