Definition

The concept TriangulationDSFaceBase_2 describes the requirements for the face base class of a CGAL::Triangulation_data_structure_2<Vb,Fb>.

Note that if the CGAL::Triangulation_data_structure_2 is plugged into a triangulation class, the face base class may have additional geometric requirements depending on the triangulation class.

At the base level, (see Sections Software Design and The Default Triangulation Data Structure ), a face stores handles on its three vertices and on the three neighboring faces. The vertices and neighbors are indexed 0,1 and 2. Neighbor i lies opposite to vertex i.

Since the CGAL::Triangulation_data_structure_2 is the class which defines the handle types, the face base class has to be somehow parameterized by the triangulation data structure. But since the CGAL::Triangulation_data_structure_2 itself is parameterized by the face and vertex base classes, there is a cycle in the definition of these classes. In order to break the cycle, the base classes for faces and vertices which are plugged in to instantiate a CGAL::Triangulation_data_structure_2 use void as triangulation data structure parameter. Then, the CGAL::Triangulation_data_structure_2 uses a rebind mechanism (similar to the one specified in std::allocator) in order to plug itself as parameter in the face and vertex base classes. This mechanism requires that the base class provides a templated nested class Rebind_TDS that itself provides the subtype Rebind_TDS::Other which is the rebound version of the base class. This rebound base class is the class that the CGAL::Triangulation_data_structure_2 actually uses as a base class for the class CGAL::Triangulation_data_structure_2::Face.

Refines:: TriangulationDataStructure_2::Face

Has Models:

CGAL::Triangulation_ds_face_base_2<Tds>

CGAL::Triangulation_face_base_2<Traits,Fb>

CGAL::Regular_triangulation_face_base_2<Traits,Fb>

CGAL::Constrained_triangulation_face_base_2<Traits,Fb>

CGAL::Triangulation_face_base_with_info_2<Info,Traits,Fb>

See also: TriangulationDSVertexBase_2; TriangulationDataStructure_2::Face; TriangulationFaceBase_2; CGAL::Triangulation_data_structure_2<Vb,Fb>

Types
The concept `TriangulationDSFaceBase_2` has to provide the following types.
template<typename TDS2 >
using	Rebind_TDS = unspecified_type
	This template class has to define a type `Rebind_TDS<TDS_2>::Other` which is the rebound face base, where the `CGAL::Triangulation_data_structure_2` is actually plugged in. More...

typedef TriangulationDataStructure_2	Triangulation_data_structure

typedef TriangulationDataStructure_2::Vertex_handle	Vertex_handle

typedef TriangulationDataStructure_2::Face_handle	Face_handle

Creation
	TriangulationDSFaceBase_2 ()
	default constructor.

	TriangulationDSFaceBase_2 (Vertex_handle v0, Vertex_handle v1, Vertex_handle v2)
	Initializes the vertices with `v0, v1, v2` and the neighbors with `Face_handle()`.

	TriangulationDSFaceBase_2 (Vertex_handle v0, Vertex_handle v1, Vertex_handle v2, Face_handle n0, Face_handle n1, Face_handle n2)
	initializes the vertices with `v0,v1, v2` and the neighbors with `n0, n1, n2`.

Access Functions
int	dimension ()
	returns the dimension.

Vertex_handle	vertex (int i) const
	returns the vertex `i` of the face. More...

bool	has_vertex (Vertex_handle v)
	returns `true` if `v` is a vertex of the face.

bool	has_vertex (Vertex_handle v, int &i) const
	as above, and sets `i` to the index of `v` in the face.

int	index (Vertex_handle v) const
	returns the index of `v` in the face.

Face_handle	neighbor (int i) const
	returns the neighbor `i` of the face. More...

bool	has_neighbor (Face_handle n)
	returns `true` if `n` is a neighbor of the face.

bool	has_neigbor (Face_handle n, int &i) const
	as above, and sets i to the index of `n` in the face.

int	index (const Face_handle n) const
	returns the index of neighbor `n` in the face.

Setting
void	set_vertex (int i, Vertex_handle v)
	sets vertex `i` to `v`. More...

void	set_vertices ()
	sets the vertices to `Vertex_handle()`.

void	set_vertices (Vertex_handle v0, Vertex_handle v1, Vertex_handle v2)
	sets the vertices.

void	set_neighbor (int i, Face_handle n)
	sets neighbor `i` to `n`. More...

void	set_neighbors ()
	sets the neighbors to `Face_handle()`.

void	set_neighbors (Face_handle n0, Face_handle n1, Face_handle n2)
	sets the neighbors.

Orientation
void	reorient ()
	Changes the orientation of the face by exchanging `vertex(0)` with `vertex(1)` and `neighbor(0)` with `neighbor(1)`.

void	ccw_permute ()
	performs a counterclockwise permutation of the vertices and neighbors of the face.

void	cw_permute ()
	performs a clockwise permutation of the vertices and neighbors of the face.

Checking
bool	is_valid (bool verbose=false) const
	performs any required test on a face. More...

Various
These member functions are required by `CGAL::Triangulation_data_structure_2` because it uses `CGAL::Compact_container` to store its faces. See the documentation of `CGAL::Compact_container` for the exact requirements.
void *	for_compact_container () const

void *&	for_compact_container ()

Member Typedef Documentation

◆ Rebind_TDS

template<typename TDS2 >

using TriangulationDSFaceBase_2::Rebind_TDS = unspecified_type

This template class has to define a type Rebind_TDS<TDS_2>::Other which is the rebound face base, where the CGAL::Triangulation_data_structure_2 is actually plugged in.

This type Other will be the actual base of the class CGAL::Triangulation_data_structure_2::Face.

Note: It can be implemented using a nested template class.

Member Function Documentation

◆ is_valid()

bool TriangulationDSFaceBase_2::is_valid ( bool verbose = false ) const

performs any required test on a face.

If verbose is set to true, messages are printed to give a precise indication of the kind of invalidity encountered.

◆ neighbor()

Face_handle TriangulationDSFaceBase_2::neighbor ( int i ) const

returns the neighbor i of the face.

Precondition: \( 0\leq i \leq2\).

◆ set_neighbor()

void TriangulationDSFaceBase_2::set_neighbor	(	int	i,
		Face_handle	n
	)

sets neighbor i to n.

Precondition: \( 0\leq i \leq2\).

◆ set_vertex()

void TriangulationDSFaceBase_2::set_vertex	(	int	i,
		Vertex_handle	v
	)

sets vertex i to v.

Precondition: \( 0\leq i \leq2\).

◆ vertex()

Vertex_handle TriangulationDSFaceBase_2::vertex ( int i ) const

returns the vertex i of the face.

Precondition: \( 0\leq i \leq2\).

Definition

Types

Creation

Access Functions

Setting

Orientation

Checking

Various