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,CurveIndex>

See also: MeshDomain_3; MeshComplexWithFeatures_3InTriangulation_3; CGAL::make_mesh_3()

Types
typedef unspecified_type	Triangulation
	The type of the embedding 3D triangulation.

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.

typedef unspecified_type	Surface_patch_index
	A type for indices of surface patches.

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

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.

MeshComplex_3InTriangulation_3 &	operator= (const MeshComplex_3InTriangulation_3 &rhs)
	Assignment operator.

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`.

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.

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`.

Surface_patch_index	surface_patch_index (Facet f)
	For a surface facet, returns the index of the surface patch containing the facet.

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

◆ Index

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.

◆ Subdomain_index

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.

◆ Surface_patch_index

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.

◆ Triangulation

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 class 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::MeshComplex_3InTriangulation_3 ( const MeshComplex_3InTriangulation_3 & rhs )

Copy constructor.

Embedded triangulation is duplicated.

Member Function Documentation

◆ number_of_facets()

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.

◆ operator=()

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.

◆ set_dimension()

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()

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()

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.

Definition

Types

Creation

Access Functions

Non const access

Modifiers

Queries on the faces of the embedded complex

Queries on the identifier of the face complex including triangulation cells, facets and vertices.

Traversal of the complex