CGAL 4.7 - 3D Mesh Generation
MeshComplexWithFeatures_3InTriangulation_3 Concept Reference

## Definition

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 curve segments 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 segment is a union of triangulation edges. The corners form a subset of the triangulation vertices. Note that subdomains, surface patches and and curved segments 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 curve segments 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 curve segments and corners represent the $$1$$ and $$0$$-dimensional features of the input complex.

Refines:
MeshComplex_3InTriangulation_3
Has Models:
CGAL::Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveSegmentIndex>
MeshComplex_3InTriangulation_3
MeshDomainWithFeatures_3

## Types

typedef unspecified_type Curve_segment_index
A type for indexes of curve segment. 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 curve segments.

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_segment_index &index)
Adds edge e as an element of the curve segment with index index.

void add_to_complex (const Vertex_handle &v1, const Vertex_handle &v2, const Curve_segment_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

Queries on the 1D complex and 0D complex.

size_type number_of_edges () const
Returns the number of edges which belong to curve segments.

size_type number_of_edges (Curve_segment_index index) const
Returns the number of edges which belong to curve segment with index index.

size_type number_of_corners () const
Returns the number of vertices which are corners of the complex.

size_type number_of_corners (Corner_index index) const
Returns the number of vertices which are corners of the complex with index index.

bool is_in_complex (const Edge &e) const
Returns true iff edge e belongs to some curve segment.

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_segment_index curve_segment_index (const Edge &e)
Returns Curve_segment_index of edge e. More...

Curve_segment_index curve_segment_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 curve segments.

Edge_in_complex_iterator edges_in_complex_end () const
Returns the past-the-end iterator for the above iterator.

Edges_in_complex_iterator edges_in_complex_begin (Curve_segment_index index) const
Returns an Edges_in_complex_iterator to visit the edges of the triangulation belonging to curve segments of index index.

Edge_in_complex_iterator edges_in_complex_end (Curve_segment_index index) const
Returns the past-the-end 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 segment. 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 past-the-end 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 past-the-end iterator for the above iterator.

## Member Typedef Documentation

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 segment.

The type must match the type MeshDomainWithFeatures_3::Curve_segment_index when the concept is used for mesh generation.

## Member Function Documentation

template<typename OutputIterator >
 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 segment.

The value type of out must be std::pair<Vertex_handle,Curve_segment_index>.

Precondition
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_segment_index MeshComplexWithFeatures_3InTriangulation_3::curve_segment_index ( const Edge & e)

Returns Curve_segment_index of edge e.

The default Curve_segment_index value is returned if edge e does not belong to any curve segment.