CGAL 5.1.3  3D Mesh Generation

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.
CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>
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  
 
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 pasttheend 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 pasttheend 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 pasttheend 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 pasttheend iterator for the above iterator.  
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.
A type for indices of subdomains.
This type must match the type MeshDomain_3::Subdomain_index
when the concept is used for mesh generation.
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.
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.
MeshComplex_3InTriangulation_3::MeshComplex_3InTriangulation_3  (  const MeshComplex_3InTriangulation_3 &  rhs  ) 
Copy constructor.
Embedded triangulation is duplicated.
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.