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CGAL 4.8 - 3D Mesh Generation

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MeshComplex_3InTriangulation_3 Concept Reference
Main Concepts

## Definition

The concept `MeshComplex_3InTriangulation_3` describes a data structure to represent and maintain a 3D complex embedded in a 3D triangulation. More precisely, the concept `MeshComplex_3InTriangulation_3` is a minimal version designed to represent 3D complexes that have only faces with dimension \( 2\) and \( 3\). Embedded 3D complexes with faces of dimension \( 0\), \( 1\), \( 2\) and \( 3\), are more conveniently represented by the refined concept `MeshComplexWithFeatures_3InTriangulation_3`.

The data structure includes a 3D triangulation which is itself a 3D complex. To distinguish the faces of the embedded 3D complex from the faces of the triangulation, we call the faces of the embedded complex respectively subdomains, for 3D faces and surface patches, for 2D faces, while the triangulations faces are called respectively cells, facets, edges and vertices.

Each subdomain of the embedded 3D complex is a union of triangulation cells. Cells that belong to some subdomain are said to belong to the embedded complex. Each surface patch is a union of triangulation facets. Triangulation facets that belong to some surface patch are called surface facets. The concept `MeshComplex_3InTriangulation_3` handles the marking and retrieval of the cells of the triangulation belonging to the subdomains and of the facets of the triangulation belonging to the surface patches. The concept `MeshComplex_3InTriangulation_3` also includes an index type for vertices of the triangulation and attaches an integer, called the dimension to each vertex. When used by the meshing algorithm, the index and the dimension of each vertex are used to store respectively the lowest dimensional face of the input complex including the vertex and the dimension of this face.

In the 3D mesh generator, the concept `MeshComplex_3InTriangulation_3` is used when the domain to be meshed has no feature with dimension \( 0\) and \( 1\). Such a data structure is used internally by the mesh generator to maintain the current approximation of each subdomain and each boundary surface patch. The data structure encodes the final mesh at the end of the meshing process.

Has Models:
  `CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveSegmentIndex>`

See Also
  `MeshDomain_3`
  `MeshComplexWithFeatures_3InTriangulation_3`
  `CGAL::make_mesh_3()`

## Types
typedef unspecified_type | Triangulation
| The type of the embedding 3D triangulation. More...
typedef Triangulation::Vertex_handle | Vertex_handle
| Type `Vertex_handle` type of the triangulation.
typedef Triangulation::Cell_handle | Cell_handle
| The `Cell_handle` type of the triangulation.
typedef Triangulation::Facet | Facet
| The `Facet` type of the triangulation.
typedef Triangulation::Edge | Edge
| The `Edge` type of the triangulation.
typedef Triangulation::size_type | size_type
| Size type (unsigned integral type).
typedef unspecified_type | Subdomain_index
| A type for indices of subdomains. More...
typedef unspecified_type | Surface_patch_index
| A type for indices of surface patches. More...
typedef unspecified_type | Index
| A type for indexing vertices that belong to some surface patches or subdomains. More...
typedef unspecified_type | Cells_in_complex_iterator
| An iterator type to visit the cells of the triangulation belonging to the 3D complex.
typedef unspecified_type | Facets_in_complex_iterator
| An iterator type to visit the surface facets.

## Creation
| MeshComplex_3InTriangulation_3 ()
| Builds an empty 3D complex.
| MeshComplex_3InTriangulation_3 (const MeshComplex_3InTriangulation_3 &rhs)
| Copy constructor. More...
MeshComplex_3InTriangulation_3 & | operator= (const MeshComplex_3InTriangulation_3 &rhs)
| Assignment operator. More...
void | swap (MeshComplex_3InTriangulation_3 &rhs)
| Swaps the 3D complex and `rhs`.

## Access Functions
const Triangulation & | triangulation () const
| Returns a const reference to the triangulation.

## Non const access
Attention The responsibility of keeping a valid C3T3 belongs to the user when using advanced operations allowing a direct manipulation of the triangulation.
Triangulation & | triangulation ()
| Returns a reference to the triangulation.

## Modifiers
void | add_to_complex (Cell_handle c, Subdomain_index index)
| Sets the cell `c` as a cell of the subdomain `index`.
void | add_to_complex (Facet f, Surface_patch_index index)
| Adds the facet `f` as a facet of the surface patch `index`.
void | add_to_complex (Cell_handle c, int i, Surface_patch_index index)
| Same as above with `f=(c,i)`.
void | remove_from_complex (Cell_handle c)
| Removes cell `c` from the embedded complex.
void | remove_from_complex (Facet f)
| Removes facet `f` from the embedded complex.
void | remove_from_complex (Cell_handle c, int i)
| Same as above with `f=(c,i)`.
void | set_dimension (Vertex_handle v, int dimension)
| Sets the `dimension` of vertex `v`. More...
void | set_index (Vertex_handle v, Index index)
| Sets the index of a vertex.

## Queries on the faces of the embedded complex
size_type | number_of_cells ()
| Returns the number of cells that belong to the embedded complex.
size_type | number_of_cells (Subdomain_index index)
| Returns the number of cells that belong to the subdomain of the embedded complex with index `index`.
size_type | number_of_facets ()
| Returns the number of facets that are surface facets, i. More...
size_type | number_of_facets (Surface_patch_index index)
| Returns the number of facets that belong to the surface patch of the embedded complex with index `index`.
bool | is_in_complex (Cell_handle c)
| Returns `true` iff the cell `c` belongs to the 3D complex.
bool | is_in_complex (Facet f)
| Returns `true` iff the facet `f` belongs to the boundary 2D complex.
bool | is_in_complex (Cell_handle c, int i)
| Same as above with `f=(c,i)`.

## Queries on the identifier of the face complex including triangulation cells, facets and vertices.
Subdomain_index | subdomain_index (Cell_handle c)
| Returns the index of the subdomain containing the cell `c`. More...
Surface_patch_index | surface_patch_index (Facet f)
| For a surface facet, returns the index of the surface patch containing the facet. More...
Surface_patch_index | surface_patch_index (Cell_handle c, int i)
| Same as above with `f=(c,i)`.
int | in_dimension (Vertex_handle v) const
| Returns the dimension of the vertex `v`.
Index | index (Vertex_handle v) const
| Returns the index of the vertex `v`.

## Traversal of the complex
The data structure provides iterators to visit the cells and facets of the complex. All those iterators are bidirectional and non mutable.
Cells_in_complex_iterator | cells_in_complex_begin ()
| Returns a `Cell_in_complex_iterator` to visit the cells of the triangulation contained in the embedded complex.
Cells_in_complex_iterator | cells_in_complex_end ()
| Returns the past-the-end iterator for the above iterator.
Cells_in_complex_iterator | cells_in_complex_begin (Subdomain_index index)
| Returns a `Cell_in_complex_iterator` to visit the cells of the triangulation which belong to the approximation of subdomain of index `index`.
Cells_in_complex_iterator | cells_in_complex_end (Subdomain_index index)
| Returns the past-the-end iterator for the above iterator.
Facets_in_complex_iterator | facets_in_complex_begin ()
| Returns a `Facet_in_complex_iterator` to visit the facets in the surface patches of the embedded complexes.
Facets_in_complex_iterator | facets_in_complex_end ()
| Returns the past-the-end iterator for the above iterator.
Facets_in_complex_iterator | facets_in_complex_begin (Surface_patch_index index)
| Returns a `Facet_in_complex_iterator` to visit the facets of the triangulation which which belong to the approximation of surface patch of index `index`.
Facets_in_complex_iterator | facets_in_complex_end (Surface_patch_index index)
| Returns the past-the-end iterator for the above iterator.

## Member Typedef Documentation

typedef unspecified_type MeshComplex_3InTriangulation_3::Index

A type for indexing vertices that belong to some surface patches or subdomains.

This type must match the type `MeshDomain_3::Index` when the concept is used for mesh generation.

typedef unspecified_type MeshComplex_3InTriangulation_3::Subdomain_index

A type for indices of subdomains.

This type must match the type `MeshDomain_3::Subdomain_index` when the concept is used for mesh generation.

typedef unspecified_type MeshComplex_3InTriangulation_3::Surface_patch_index

A type for indices of surface patches.

This type must match the type `MeshDomain_3::Surface_patch_index` when the concept is used for mesh generation.

typedef unspecified_type MeshComplex_3InTriangulation_3::Triangulation

The type of the embedding 3D triangulation.

It is required to be the nested type `CGAL::Mesh_triangulation_3::type`, provided by the meta functor `CGAL::Mesh_triangulation_3<MD, GT, Concurrency_tag, Vertex_base, Cell_base>` where the Vertex_base and Cell_base template parameters are respectively instantiated with models of the concepts `MeshVertexBase_3` and `MeshCellBase_3`. The provided triangulation type is then a `CGAL::Regular_triangulation_3` with Vertex_base and Cell_base for respectively vertex and cell base types.

## Constructor & Destructor Documentation

MeshComplex_3InTriangulation_3::MeshComplex_3InTriangulation_3 | ( | const MeshComplex_3InTriangulation_3 & | rhs) |  |

Copy constructor.

Embedded triangulation is duplicated.

## Member Function Documentation

size_type MeshComplex_3InTriangulation_3::number_of_facets | ( | ) |  |

Returns the number of facets that are surface facets, i.

e. belong to some surface patch of the embedded complex.

MeshComplex_3InTriangulation_3& MeshComplex_3InTriangulation_3::operator= | ( | const MeshComplex_3InTriangulation_3 & | rhs) |  |

Assignment operator.

Embedded triangulation is duplicated, and the former triangulation of the 3D complex is deleted.

void MeshComplex_3InTriangulation_3::set_dimension | ( | Vertex_handle | v,
|  | int | dimension
| ) |  |

Sets the `dimension` of vertex `v`.

The dimension is an integer attached to the vertex. When the concept `MeshComplex_3InTriangulation_3` is used for mesh generation this integer is used to store the dimension of the lowest dimensional face of the input complex including the vertex.

Subdomain_index MeshComplex_3InTriangulation_3::subdomain_index | ( | Cell_handle | c) |  |

Returns the index of the subdomain containing the cell `c`.

The default subdomain index is returned if the cell `c` does not belong to the embedded complex.

Surface_patch_index MeshComplex_3InTriangulation_3::surface_patch_index | ( | Facet | f) |  |

For a surface facet, returns the index of the surface patch containing the facet.

The default `Surface_patch_index` value is returned if the facet is not a surface facet.