TriangulationDataStructure_2::Face

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 pointers to its three vertices and three pointers 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

Creation

The methods create_face and delete_face() have to be used to define new faces and to delete non longer used faces.

Vertex Access Functions

Vertex_handle	f.vertex ( int i)	returns the vertex i of f. Precondition: $$0 i 2.
int	f.index ( Vertex_handle v)
		returns the index of vertex v in f. Precondition: v is a vertex of f
bool	f.has_vertex ( Vertex_handle v)
		returns true if v is a vertex of f.
bool	f.has_vertex ( Vertex_handle v, int& i)
		returns true if v is a vertex of f, and computes the index i of v in f.

Neighbor Access Functions

The neighbor with index i is the neighbor which is opposite to the vertex with index i.

Face_handle	f.neighbor ( int i)
		returns the neighbor i of f. Precondition: $$0 i 2.
int	f.index ( Face_handle n)
		returns the index of face n. Precondition: n is a neighbor of f.
bool	f.has_neighbor ( Face_handle n)
		returns true if n is a neighbor of f.
bool	f.has_neighbor ( Face_handle n, int& i)
		returns true if n is a neighbor of f, and compute the index i of n.

Other Access Functions

advanced

Setting

void	f.set_vertex ( int i, Vertex_handle v)
		sets vertex i to be v. Precondition: $$0 i 2.
void	f.set_neighbor ( int i, Face_handle n)
		sets neighbor i to be n. Precondition: $$0 i 2.
void	f.set_vertices ()	sets the vertices pointers to NULL.
void	f.set_vertices ( Vertex_handle v0, Vertex_handle v1, Vertex_handle v2)
		sets the vertices pointers.
void	f.set_neighbors ()	sets the neighbors pointers to NULL.
void	f.set_neighbors ( Face_handle n0, Face_handle n1, Face_handle n2)
		sets the neighbors pointers.

Checking

bool

f.is_valid ()

returns true if the function is_valid() of the base class returns true and if, for each index $$i, $$0 i < 3, face $$f 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.

advanced

Miscellaneous

int	f.ccw ( int i)	Returns $$i+1 modulo 3. Precondition: $$0 i 2.
int	f.cw ( int i)	Returns $$i+2 modulo 3. Precondition: $$0 i 2.

See Also