CGAL 5.5.1  3D Mesh Generation

The concept MeshComplexWithFeatures_3InTriangulation_3
describes a data structure to represent and maintain a 3D complex embedded in a 3D triangulation. The concept MeshComplexWithFeatures_3InTriangulation_3
refines the minimal concept MeshComplex_3InTriangulation_3
, designed to represent 3D complexes having only faces with dimension 2 and 3. Therefore, the concept MeshComplexWithFeatures_3InTriangulation_3
may represent embedded complexes including features, i.e. faces with dimension \( 0\) and \( 1\).
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 respectively subdomains, surface patches curves and corners the faces of the complex with respective dimensions \( 3\), \( 2\), \( 1\) and \( 0\). The triangulations faces are called respectively cells, facets, edges and vertices.
Each subdomain of the embedded 3D complex is a union of triangulation cells. Likewise, each surface patch is a union of triangulation facets and each curve is a union of triangulation edges. The corners form a subset of the triangulation vertices. Note that subdomains, and surface patches are not necessarily connected. Likewise each corner may be related to several mesh vertices. Triangulation facets that belong to some surface patch are called surface facets.
The concept MeshComplexWithFeatures_3InTriangulation_3
allows us to mark and retrieve the cells of the triangulation belonging to the subdomains, the facets of the triangulation belonging to surface patches, the edges belonging to curves and the vertices that are corners of the embedded complex.
Within the mesh generation functions, the concept MeshComplexWithFeatures_3InTriangulation_3
is the concept describing the data structure used to maintain the current approximation of the input domain. At the end of the meshing process, the data structure encodes the resulting mesh. In particular, each subdomain (resp. surface patch) of the input domain is then approximated by a subdomain (resp. a surface patch) of the embedded complex while the curves and corners represent the \( 1\) and \( 0\)dimensional features of the input complex.
CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveIndex>
Types  
typedef unspecified_type  Curve_index 
A type for indexes of curve. More...  
typedef unspecified_type  Corner_index 
A type for indexes of corners. More...  
typedef unspecified_type  Edges_in_complex_iterator 
An iterator type to visit the edges of the triangulation belonging to curves.  
typedef unspecified_type  Vertices_in_complex_iterator 
An iterator type to visit the vertices of the triangulation that are corners of the embedded complex.  
Modifiers  
void  add_to_complex (Edge e, const Curve_index &index) 
Adds edge e as an element of the curve with index index .  
void  add_to_complex (const Vertex_handle &v1, const Vertex_handle &v2, const Curve_index &index) 
Same as above with e=(v1,v2) .  
void  add_to_complex (const Vertex_handle &v, const Corner_index &index) 
Marks vertex v as a corner with index index .  
void  remove_from_complex (const Edge &e) 
Removes edge e from the embedded complex.  
void  remove_from_complex (const Vertex_handle &v1, const Vertex_handle &v2) 
Same as above with e=(v1,v2) .  
void  remove_from_complex (const Vertex_handle &v) 
Removes vertex v from the embedded complex.  
Queries  
size_type  number_of_edges () const 
Returns the number of edges which belong to curves.  
size_type  number_of_corners () const 
Returns the number of vertices which are corners of the complex.  
bool  is_in_complex (const Edge &e) const 
Returns true iff edge e belongs to some curve.  
bool  is_in_complex (const Vertex_handle &v1, const Vertex_handle &v2) const 
Same as above with e=(v1,v2) .  
bool  is_in_complex (const Vertex_handle &v) const 
Returns true if vertex v is a corner.  
Curve_index  curve_index (const Edge &e) 
Returns Curve_index of edge e . More...  
Curve_index  curve_index (const Vertex_handle &v1, const Vertex_handle &v2) 
Same as above with e=(v1,v2) .  
Corner_index  corner_index (const Vertex_handle &v) 
Returns Corner_index of vertex v . More...  
Traversal of the complex  
Edges_in_complex_iterator  edges_in_complex_begin () const 
Returns an Edges_in_complex_iterator to visit the edges of the triangulation belonging to curves.  
Edges_in_complex_iterator  edges_in_complex_end () const 
Returns the pasttheend iterator for the above iterator.  
Edges_in_complex_iterator  edges_in_complex_begin (Curve_index index) const 
Returns an Edges_in_complex_iterator to visit the edges of the triangulation belonging to curves of index index .  
Edges_in_complex_iterator  edges_in_complex_end (Curve_index index) const 
Returns the pasttheend iterator for the above iterator.  
template<typename OutputIterator >  
OutputIterator  adjacent_vertices_in_complex (const Vertex_handle &v, OutputIterator out) const 
Fills out with the vertices of the triangulation that are adjacent to vertex v through an edge belonging to some curve. More...  
Vertices_in_complex_iterator  vertices_in_complex_begin () const 
Returns a Vertices_in_complex_iterator to visit the vertices of the triangulation that are corners.  
Vertices_in_complex_iterator  vertices_in_complex_end () const 
Returns the pasttheend iterator for the above iterator.  
Vertices_in_complex_iterator  vertices_in_complex_begin (Corner_index index) const 
Returns a Vertices_in_complex_iterator to visit the vertices of the triangulation that are corners of index index .  
Vertices_in_complex_iterator  vertices_in_complex_end (Corner_index index) const 
Returns the pasttheend iterator for the above iterator.  
A type for indexes of corners.
The type must match the type MeshDomainWithFeatures_3::Corner_index
when the concept is used for mesh generation.
A type for indexes of curve.
The type must match the type MeshDomainWithFeatures_3::Curve_index
when the concept is used for mesh generation.
OutputIterator MeshComplexWithFeatures_3InTriangulation_3::adjacent_vertices_in_complex  (  const Vertex_handle &  v, 
OutputIterator  out  
)  const 
Fills out
with the vertices of the triangulation that are adjacent to vertex v
through an edge belonging to some curve.
The value type of out
must be std::pair<Vertex_handle,Curve_index>
.
c3t3.in_dimension(v) < 2
Corner_index MeshComplexWithFeatures_3InTriangulation_3::corner_index  (  const Vertex_handle &  v  ) 
Returns Corner_index
of vertex v
.
The default Corner_index
value is returned if vertex v
is not a corner of the complex.
Curve_index MeshComplexWithFeatures_3InTriangulation_3::curve_index  (  const Edge &  e  ) 
Returns Curve_index
of edge e
.
The default Curve_index
value is returned if edge e
does not belong to any curve.