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

CGAL 4.8 - 3D Triangulations

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CGAL::Triangulation_simplex_3< Triangulation_3 > Class Template Reference
Vertex and Cell Classes

`#include <CGAL/Triangulation_simplex_3.h>`

## Definition

The class `Triangulation_simplex_3` stores a simplex of any dimension defined by the `Triangulation_3` class.

It also defines the operator less such that simplices can be stored in a `map` or a `set` of simplices. The simplex is invalidated by any change in the triangulation.

Parameters

It is parameterized by the triangulation it derives the simplices from.

See Also
  `CGAL::Triangulation_3<TriangulationTraits_3,TriangulationDataStructure_3>`

## Types
typedef Triangulation_simplex_3 < Triangulation_3 > | Simplex
| The simplex class itself.
typedef Triangulation_3::Vertex_handle | Vertex_handle
typedef Triangulation_3::Edge | Edge
typedef Triangulation_3::Facet | Facet
typedef Triangulation_3::Cell_handle | Cell_handle
typedef Triangulation_3::Cell_circulator | Cell_circulator
typedef Triangulation_3::Facet_circulator | Facet_circulator
typedef Triangulation_3::Edge_iterator | Edge_iterator
typedef Triangulation_3::Facet_iterator | Facet_iterator
typedef Triangulation_3::Finite_vertices_iterator | Finite_vertices_iterator
typedef Triangulation_3::Finite_edges_iterator | Finite_edges_iterator
typedef Triangulation_3::Finite_facets_iterator | Finite_facets_iterator
typedef Triangulation_3::Finite_cells_iterator | Finite_cells_iterator

## Creation
| Triangulation_simplex_3 ()
| Initializes the simplex to an invalid simplex.
| Triangulation_simplex_3 (Vertex_handle vh)
| Triangulation_simplex_3 (Edge e)
| Triangulation_simplex_3 (Facet f)
| Triangulation_simplex_3 (Cell_handle ch)
| Triangulation_simplex_3 (Cell_circulator ccir)
| Triangulation_simplex_3 (Facet_circulator fcir)
| Triangulation_simplex_3 (Edge_iterator eit)
| Triangulation_simplex_3 (Facet_iterator fit)

## Operations
int | dimension () const
| returns the dimension of the simplex.
| operator Vertex_handle () const
| Returns the `Vertex_handle` stored in the simplex. More...
| operator Edge () const
| Returns the `Edge` stored in the simplex. More...
| operator Facet () const
| Returns the `Facet` stored in the simplex. More...
| operator Cell_handle () const
| Returns the `Cell_handle` stored in the simplex. More...
Cell_handle | incident_cell () const
| Returns a cell incident to the simplex.
bool | operator== (const Triangulation_simplex_3< Triangulation_3 > &s1)
| Test whether two simplices are equal.
bool | operator< (const Triangulation_simplex_3< Triangulation_3 > &s1)
| Defines a ordering on the simplices. More...

## Member Function Documentation

template<typename Triangulation_3 >

CGAL::Triangulation_simplex_3< Triangulation_3 >::operator Cell_handle | ( | ) |  | const

Returns the `Cell_handle` stored in the simplex.

Precondition
  dimension() == 3

template<typename Triangulation_3 >

CGAL::Triangulation_simplex_3< Triangulation_3 >::operator Edge | ( | ) |  | const

Returns the `Edge` stored in the simplex.

Precondition
  dimension() == 1

template<typename Triangulation_3 >

CGAL::Triangulation_simplex_3< Triangulation_3 >::operator Facet | ( | ) |  | const

Returns the `Facet` stored in the simplex.

Precondition
  dimension() == 2

template<typename Triangulation_3 >

CGAL::Triangulation_simplex_3< Triangulation_3 >::operator Vertex_handle | ( | ) |  | const

Returns the `Vertex_handle` stored in the simplex.

Precondition
  dimension() == 0

template<typename Triangulation_3 >

bool CGAL::Triangulation_simplex_3< Triangulation_3 >::operator< | ( | const Triangulation_simplex_3< Triangulation_3 > & | s1) |  |

Defines a ordering on the simplices.

This ordering depends on the memory layout and is independent of the geometry. Therefore, the ordering is not intrinsic