Definition

The concept TriangulationDataStructure_2::Face describes the types used to store the faces face class of a TriangulationDataStructure_2. A TriangulationDataStructure_2::Face stores three handles to its three vertices and three handles to its three neighbors. The vertices are indexed 0,1, and 2 in counterclockwise order. The neighbor indexed i lies opposite to vertex i.

In degenerate cases, when the triangulation data structure stores a simplicial complex of dimension 0 and 1, the type TriangulationDataStructure_2::Face is used to store the faces of maximal dimension of the complex, i.e., a vertex in dimension 0, an edge in dimension 1. Only vertices and neighbors with index 0 are set in the first case, only vertices and neighbors with index 0 or 1 are set in the second case.

Types

The class TriangulationDataStructure_2::Face defines the same types as the triangulation data structure except the iterators and the circulators.

Creation

The methods create_face() and delete_face() have to be used to define new faces and to delete no longer used faces.

Has Models:: CGAL::Triangulation_ds_face_base_2<Tds>

See also: TriangulationDSFaceBase_2; TriangulationDataStructure_2; TriangulationDataStructure_2::Vertex

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

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

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

bool	has_vertex (Vertex_handle v, int &i) const
	returns `true` if `v` is a vertex of the face, and computes the index `i` of `v` in the face.

Neighbor Access Functions
The neighbor with index `i` is the neighbor which is opposite to the vertex with index `i`.
Face_handle	neighbor (int i) const
	returns the neighbor `i` of the face. More...

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

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

bool	has_neighbor (Face_handle n, int &i) const
	returns `true` if `n` is a neighbor of the face, and compute the index `i` of `n`.

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

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

void	set_vertices ()
	sets the vertex handles to `Vertex_handle()`.

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

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

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

Checking
bool	is_valid () const
	returns `true` if the function `is_valid()` of the base class returns `true` and if, for each index \( i\), \( 0 \le i < 3\), the face is a neighbor of its neighboring face `neighbor(i)` and shares with this neighbor the vertices `cw(i)` and `ccw(i)` in correct reverse order.

Miscellaneous
int	ccw (int i) const
	Returns \( i+1\) modulo 3, with \( 0\leq i \leq2\).

int	cw (int i) const
	Returns \( i+2\) modulo 3, with \( 0\leq i \leq2\).

std::istream &	operator>> (std::istream &is, TriangulationDataStructure_2::Face &f)
	Inputs any non combinatorial information possibly stored in the face.

std::ostream &	operator<< (std::ostream &os, const TriangulationDataStructure_2::Face &f)
	Outputs any non combinatorial information possibly stored in the face.

Member Function Documentation

◆ index() [1/2]

int TriangulationDataStructure_2::Face::index ( Vertex_handle v ) const

returns the index of vertex v in the face.

Precondition: v is a vertex of the face.

◆ index() [2/2]

int TriangulationDataStructure_2::Face::index ( Face_handle n ) const

returns the index of face n.

Precondition: n is a neighbor of the face.

◆ neighbor()

Face_handle TriangulationDataStructure_2::Face::neighbor ( int i ) const

returns the neighbor i of the face.

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

◆ set_neighbor()

void TriangulationDataStructure_2::Face::set_neighbor	(	int	i,
		Face_handle	n
	)

sets neighbor i to be n.

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

◆ set_vertex()

void TriangulationDataStructure_2::Face::set_vertex	(	int	i,
		Vertex_handle	v
	)

sets vertex i to be v.

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

◆ vertex()

Vertex_handle TriangulationDataStructure_2::Face::vertex ( int i ) const

returns the vertex i of the face.

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

Definition

Vertex Access Functions

Neighbor Access Functions

Setting

Checking