A class Tds<Vb,Fb> that satisfies the requirements for a triangulation traits class must provide the following types and operations.

Tds<Vb,Fb>::Vertex
	Requirement for this type are described in section .
Tds<Vb,Fb>::Face
	Requirements for this type are described in described .

The following iterators allow to visit all the vertices, edges and faces of the triangulation data structure. They are all bidirectional, non mutable iterators.

Tds<Vb,Fb>::Face_iterator

Tds<Vb,Fb>::Edge_iterator

Tds<Vb,Fb>::Vertex_iterator

The following circulators allow to visit all the vertices, edges and faces incident to a given vertex. They are all bidirectional and non mutable.

Tds<Vb,Fb>::Face_circulator

Tds<Vb,Fb>::Edge_circulator

Tds<Vb,Fb>::Vertex_circulator

Creation

Tds<Vb,Fb> tds;
	A default constructor.
Tds<Vb,Fb> tds ( Vertex* v);
	Introduces a triangulation data structure tds that is initialized with a set of vertices and faces that are linked to vertex v. If v has no incident face the triangulation consists only of v. Otherwise v must be the vertex at infinity.
Tds<Vb,Fb> tds ( Tds tds1);
	Copy constructor. All the vertices and faces are duplicated.

Tds	tds = Tds tds1	Assignation. All the vertices and faces are duplicated.
void	tds.swap ( Tds &tds1)
		Swap tds and tds1. Should be preferred to tds= tds1 or tds(tds1) when tds1 is deleted after that.
void \ccTilde{	tds.\ccVar} ()	Destructor. All vertices and faces are deleted.

Access Functions

int	tds.dimension ()	The dimension of the convex hull.
int	tds.number_of_vertices ()
		The number of finite vertices.

Finite and Infinite Vertices and Faces

bool	tds.is_infinite ( Vertex* v)
		true, iff vertex *v is the infinite_vertex.
bool	tds.is_infinite ( Face* f)
		true, iff one of the vertices of *f is the infinite_vertex.
bool	tds.is_infinite ( Face* f, int i)
		true, iff one of the vertices cw(i) or ccw(i) of face *f is the infinite_vertex.
bool	tds.is_infinite ( Edge e)
		true, iff one of the vertices of edge e is the infinite_vertex.
bool	tds.is_infinite ( Edge_circulator& ec)
		true, iff one of the vertices of edge e is the infinite_vertex.
bool	tds.is_infinite ( Edge_iterator& ei e)
		true, iff one of the vertices of edge *ei is the infinite_vertex.
Face*	tds.infinite_face ()
		A face incident to the infinite_vertex.
Vertex*	tds.infinite_vertex ()
		The infinite vertex.
Vertex*	tds.finite_vertex ()
		A vertex different from the infinite_vertex.

Setting

void	tds.set_number_of_vertices ( int n)
void	tds.set_finite_vertex ( Vertex* v)
void	tds.set_infinite_vertex ( Vertex* v)

Modifiers

The following modifier member functions guarantee the combinatorial validity of the resulting triangulation.

void	tds.flip ( Face* f, int i)
		Exchange the edge incident to *f and f->neighbor(i) with the other diagonal of the quadrilateral formed by f and f->neighbor(i).

void	tds.insert_first ( Vertex* v)
		Insert the first finite vertex .
void	tds.insert_second ( Vertex* v)
		Insert the second finite vertex .
void	tds.insert_in_face ( Vertex* v, Face* f)
		Insert vertex v in face f. Face f is modified, two new faces are created

void	tds.insert_on_edge ( Vertex* v, Face* f, int i)
		Insert vertex v in edge i of f*
void	tds.insert_collinear_outside ( Vertex * v, Face * loc, int li)
		insert in a 1 dimensional triangulation a vertex which is collinear to the triangulation and outside the convex hull. loc->vertex(li) is the vertex of the triangulation closest to v.
void	tds.remove_degree_3 ( Vertex* v, Face *f=NULL)
		remove a vertex of degree 3. Two of the incident faces are destroyed, the third one is modified. If parameter f is specified, it has to be a face incident to v and will be the modified face. Precondition: Vertex v is a finite vertex with degree 3 and, if specified, face f is incident to v.
void	tds.remove_second ( Vertex* v)
		remove the before last finite vertex.
void	tds.remove_first ( Vertex* v)
		remove the last finite vertex.
void	tds.clear ()	Delete all faces and all finite vertices.

Traversing the triangulation

Face_iterator	tds.faces_begin ()
Face_iterator	tds.faces_end ()
Vertex_iterator	tds.vertices_begin ()
Vertex_iterator	tds.vertices_end ()
Edge_iterator	tds.edges_begin ()
Edge_iterator	tds.edges_end ()

Miscelleanous

int	tds.ccw ( int i)	Returns $i+1$ modulo 3. Precondition: .
int	tds.cw ( int i)	Returns $i+2$ modulo 3. Precondition: .
int	tds.number_of_faces ()
		Returns the number of finite faces.
bool	tds.is_valid ()	Check the combinatorial validity of the triangulation.