CGAL 6.1 - 2D Periodic Hyperbolic Triangulations

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Periodic_4HyperbolicTriangulationFaceBase_2 Concept Reference
Reference Manual » Concepts

## Definition

Refines
  `TriangulationFaceBase_2`

A refinement of the concept `TriangulationFaceBase_2` that adds an interface for hyperbolic translations.

At the base level, a face stores handles to its incident vertices and to its neighboring faces. Compare with Section Software Design of the 2D Triangulations package. The vertices and neighbors are indexed counterclockwise 0, 1, and 2. Neighbor `i` lies opposite to vertex `i`.

For periodic hyperbolic triangulations, the face base class needs to store three hyperbolic translations, one for each vertex. Applying each translation to the point stored in the corresponding vertex produces the canonical representative of the face in the hyperbolic plane. Hyperbolic translations are represented by a nested type which is provided by the concept `Periodic_4HyperbolicDelaunayTriangulationTraits_2`.

Has models
  `CGAL::Periodic_4_hyperbolic_triangulation_face_base_2`

See also
  `TriangulationDataStructure_2`
  `Periodic_4HyperbolicTriangulationVertexBase_2`

## Types
typedef Periodic_4HyperbolicDelaunayTriangulationTraits_2 | Geometric_traits
typedef Geometric_traits::Hyperbolic_translation | Hyperbolic_translation

## Creation
| Periodic_4HyperbolicTriangulationFaceBase_2 ()
| Default constructor.
| Periodic_4HyperbolicTriangulationFaceBase_2 (const Vertex_handle &v0, const Vertex_handle &v1, const Vertex_handle &v2)
| Creates a face with vertices `v0, v1` and `v1`.
| Periodic_4HyperbolicTriangulationFaceBase_2 (const Vertex_handle &v0, const Vertex_handle &v1, const Vertex_handle &v2, const Face_handle &n0, const Face_handle &n1, const Face_handle &n2)
| Creates a face with vertices `v0, v1` and `v1`, setting also neighborhood relations with `n0, n1` and `n2`.

## Access functions
Hyperbolic_translation | translation (int i) const
| Returns the translation corresponding to the vertex `i`.
void | set_translation (const int &i, const Hyperbolic_translation &new_tr)
| Sets the `i`-th translation to `new_tr`.
void | reorient ()
| Changes the orientation of the face by exchanging `vertex(0)` with `vertex(1)`, `neighbor(0)` with `neighbor(1)`, and `translation(0)` with `translation(1)`.

## Member Function Documentation

## ◆ reorient()

void Periodic_4HyperbolicTriangulationFaceBase_2::reorient | ( |  | ) |

Changes the orientation of the face by exchanging `vertex(0)` with `vertex(1)`, `neighbor(0)` with `neighbor(1)`, and `translation(0)` with `translation(1)`.

See also
  TriangulationFaceBase_2::reorient()

## ◆ set_translation()

void Periodic_4HyperbolicTriangulationFaceBase_2::set_translation | ( | const int & | i,
|  | const Hyperbolic_translation & | new_tr
| ) |  |

Sets the `i`-th translation to `new_tr`.

Precondition
  \( 0 \leq i \leq 2\).

## ◆ translation()

Hyperbolic_translation Periodic_4HyperbolicTriangulationFaceBase_2::translation | ( | int | i | ) | const

Returns the translation corresponding to the vertex `i`.

Precondition
  \( 0 \leq i \leq 2\).