CGAL 4.7 - dD Triangulations: Concepts

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CGAL 4.7 - dD Triangulations

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dD Triangulations

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## Concepts

concept | DelaunayTriangulationTraits

This concept describes the geometric types and predicates required to build a Delaunay triangulation. It corresponds to the first template parameter of the class `CGAL::Delaunay_triangulation<DelaunayTriangulationTraits, TriangulationDataStructure>`. More...

concept | FullCellData
| The concept `FullCellData` describes the requirements on the type which is used to mark some full cells, during modifications of the triangulation data structure. More...
concept | TriangulationDataStructure

The `TriangulationDataStructure` concept describes objects responsible for storing and maintaining the combinatorial part of a \( d\)-dimensional pure simplicial complex that has the topology of the \( d\)-dimensional sphere \( \mathbb{S}^d\) with \( d\in[-2,D]\). Since the simplicial \( d\)-complex is pure, all faces are sub-faces of some \( d\)-simplex. And since it has the topology of the sphere \( \mathbb{S}^d\), it is manifold, thus any \( d-1\)-face belongs to exactly two \( d\)-dimensional full cells. More...

concept | TriangulationDataStructure::Vertex
| The concept `TriangulationDataStructure::Vertex` describes the type used by a `TriangulationDataStructure` to store the vertices. More...
concept | TriangulationDataStructure::FullCell
| The concept `TriangulationDataStructure::FullCell` describes the type used by a `TriangulationDataStructure` to store the full cells. More...
concept | TriangulationDSFace

A `TriangulationDSFace` describes a face `f` with dimension `k` (a `k`-face) in a triangulation. It gives access to a handle to a full cell `c` containing the face `f` in its boundary, as well as the indices of the vertices of `f` in `c`. It must hold that `f` is a proper face of full cell `c`, i.e., the dimension of `f` is strictly less than the dimension of `c`. The dimension of a face is implicitely set when `TriangulationDSFace::set_index` is called. For example, if `TriangulationDSFace::set_index` is called two times to set the first two vertices (`i = 0` and `i = 1`), then the dimension is 1. More...

concept | TriangulationDSFullCell
| The concept `TriangulationDSFullCell` describes the requirements for the full cell class of a `CGAL::Triangulation_data_structure`. It refines the concept `TriangulationDataStructure::FullCell`. More...
concept | TriangulationDSVertex
| The concept `TriangulationDSVertex` describes the requirements for the vertex base class of a `CGAL::Triangulation_data_structure`. It refines the concept `TriangulationDataStructure::Vertex`. More...
concept | TriangulationFullCell
| The concept `TriangulationFullCell` describes the requirements on the type used by the class `Triangulation<TriangulationTraits, TriangulationDataStructure>`, and its derived classes, to represent a full cell. More...
concept | TriangulationTraits
| This concept describes the geometric types and predicates required to build a triangulation. It corresponds to the first template parameter of the class `CGAL::Triangulation<TriangulationTraits, TriangulationDataStructure>`. More...
concept | TriangulationVertex
| The concept `TriangulationVertex` describes the requirements on the type used by the class `Triangulation<TriangulationTraits, TriangulationDataStructure>`, and its derived classes, to represent a vertex. More...