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

CGAL 4.8 - 2D Triangulation Data Structure

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2D Triangulation Data Structure Reference

##

Sylvain Pion and Mariette Yvinec
This package provides a data structure to store a two-dimensional triangulation that has the topology of a two-dimensional sphere. The package acts as a container for the vertices and faces of the triangulation and provides basic combinatorial operation on the triangulation.

Introduced in: CGAL 2.2
BibTeX: cgal:py-tds2-16a
License: GPL

The triangulation data structure can be seen as a container for the faces and vertices of a triangulation. This class also takes care of all the combinatorial operations performed on the triangulation.

The class `CGAL::Triangulation_data_structure_2<Vb,Fb>` is a model of the concept `TriangulationDataStructure_2`. which includes the sub-concepts `TriangulationDataStructure_2::Face` and `TriangulationDataStructure_2::Vertex`.

To ensure all the flexibility of the triangulation classes, described and in Section Flexibility of Chapter 2D Triangulations, the model `CGAL::Triangulation_data_structure_2<Vb,Fb>` has two template parameters. The class `CGAL::Triangulation_data_structure_2<Vb,Fb>` derives its `Vertex` and `Face` types from the two template parameters `Vb` and `Fb` respectively.

If the triangulation data structure is used alone, these parameters have to be instantiated by models of the concepts `TriangulationDSFaceBase_2` and `TriangulationDSVertexBase_2`. These concepts are described in this chapter together with their default models `CGAL::Triangulation_ds_face_base_2<Tds>` and `CGAL::Triangulation_ds_vertex_base_2<Tds>`.

If the triangulation data structure is plugged into a triangulation class, the parameters have to be instantiated by models of different refining concepts according to the actual type of the triangulation. These refining concepts and their models are described in Chapter 2D Triangulations.

## Classified Reference Pages

## Concepts

- `TriangulationDataStructure_2`
- `TriangulationDataStructure_2::Face`
- `TriangulationDataStructure_2::Vertex`
- `TriangulationDSFaceBase_2`
- `TriangulationDSVertexBase_2`

## Classes

- `CGAL::Triangulation_data_structure_2<Vb,Fb>`
- `CGAL::Triangulation_ds_face_base_2<Tds>`
- `CGAL::Triangulation_ds_vertex_base_2<Tds>`
- `CGAL::Triangulation_cw_ccw_2`

## Modules
| Concepts

## Classes
class | CGAL::Triangulation_data_structure_2< Vb, Fb >
| The class `Triangulation_data_structure_2` is a model for the `TriangulationDataStructure_2` concept. More...
class | CGAL::Triangulation_ds_face_base_2< Tds >
| The class `Triangulation_ds_face_base_2` is a model for the concept `TriangulationDSFaceBase_2` to be used by `Triangulation_data_structure_2`. More...
class | CGAL::Triangulation_ds_vertex_base_2< Tds >
| The class `Triangulation_ds_vertex_base_2` can be used as the base vertex for a `Triangulation_data_structure_2`, it is a model of the concept `TriangulationDSVertexBase_2`. More...