Triangulation Classes

Classes
class	CGAL::Constrained_Delaunay_triangulation_2< Traits, Tds, Itag >
	A constrained Delaunay triangulation is a triangulation with constrained edges which tries to be as much Delaunay as possible. More...
struct	CGAL::No_intersection_tag
	Intersection tag for constrained triangulations, when input constraints do not intersect. More...
struct	CGAL::Exact_intersections_tag
	Intersection tag for constrained triangulations, if exact predicates and exact constructions are provided. More...
struct	CGAL::Exact_predicates_tag
	Intersection tag for constrained triangulations, if the geometric traits provides exact predicates but approximate constructions. More...
class	CGAL::Constrained_triangulation_2< Traits, Tds, Itag >
	A constrained triangulation is a triangulation of a set of points which has to include among its edges a given set of polylines joining the points. More...
class	CGAL::Constrained_triangulation_plus_2< Tr >
	The class Constrained_triangulation_plus_2<Tr> provides a constrained triangulation with an additional data structure that keeps track of the input constraints and of their refinement in the triangulation. More...
class	CGAL::Constrained_triangulation_plus_2< Tr >::Context
	A context enables the access to the vertices of a constraint that pass through a subconstraint. More...
class	CGAL::Delaunay_triangulation_2< Traits, Tds >
	The class Delaunay_triangulation_2 is designed to represent the Delaunay triangulation of a set of points in a plane. More...
class	CGAL::Regular_triangulation_2< Traits, Tds >
	The class Regular_triangulation_2 is designed to maintain the regular triangulation of a set of weighted points. More...
class	CGAL::Triangulation_2< Traits, Tds >
	The class Triangulation_2 is the basic class designed to handle triangulations of set of points \( { A}\) in the plane. More...
class	CGAL::Triangulation_hierarchy_2< Tr >
	The class Triangulation_hierarchy_2 implements a triangulation augmented with a data structure which allows fast point location queries. More...

Handles, Iterators, and Circulators
The vertices and faces of the triangulations are accessed through handles, iterators and circulators. The handles are models of the concept Handle which basically offers the two dereference operators and ->. The iterators and circulators are all bidirectional and non-mutable. The circulators and iterators are convertible to handles with the same value type, so that whenever a handle appear in the parameter list of a function, an appropriate iterator or circulator can be passed as well. The edges of the triangulation can also be visited through iterators and circulators, the edge circulators and iterators are also bidirectional and non mutable. In the following, we called infinite any face or edge incident to the infinite vertex and the infinite vertex itself. Any other feature (face, edge or vertex) of the triangulation is said to be finite. Some iterators (the All iterators ) allows to visit finite or infinite feature while others (the Finite iterators) visit only finite features. Circulators visit infinite features as well as finite ones. The triangulation class also defines the following enum type to specify which case occurs when locating a point in the triangulation.
enum	CGAL::Triangulation_2< Traits, Tds >::Locate_type {   CGAL::Triangulation_2< Traits, Tds >::VERTEX =0, CGAL::Triangulation_2< Traits, Tds >::EDGE, CGAL::Triangulation_2< Traits, Tds >::FACE, CGAL::Triangulation_2< Traits, Tds >::OUTSIDE_CONVEX_HULL,   CGAL::Triangulation_2< Traits, Tds >::OUTSIDE_AFFINE_HULL }
	specifies which case occurs when locating a point in the triangulation. More...
typedef Tds::Vertex_handle	CGAL::Triangulation_2< Traits, Tds >::Vertex_handle
	handle to a vertex. More...
typedef Tds::Face_handle	CGAL::Triangulation_2< Traits, Tds >::Face_handle
	handle to a face. More...
typedef Tds::Face_iterator	CGAL::Triangulation_2< Traits, Tds >::All_faces_iterator
	iterator over all faces. More...
typedef Tds::Edge_iterator	CGAL::Triangulation_2< Traits, Tds >::All_edges_iterator
	iterator over all edges. More...
typedef Tds::Vertex_iterator	CGAL::Triangulation_2< Traits, Tds >::All_vertices_iterator
	iterator over all vertices. More...
typedef unspecified_type	CGAL::Triangulation_2< Traits, Tds >::Finite_faces_iterator
	iterator over finite faces. More...
typedef unspecified_type	CGAL::Triangulation_2< Traits, Tds >::Finite_edges_iterator
	iterator over finite edges. More...
typedef unspecified_type	CGAL::Triangulation_2< Traits, Tds >::Finite_vertices_iterator
	iterator over finite vertices. More...
typedef unspecified_type	CGAL::Triangulation_2< Traits, Tds >::Point_iterator
	iterator over the points corresponding the finite vertices of the triangulation. More...
typedef unspecified_type	CGAL::Triangulation_2< Traits, Tds >::Line_face_circulator
	circulator over all faces intersected by a line. More...
typedef unspecified_type	CGAL::Triangulation_2< Traits, Tds >::Face_circulator
	circulator over all faces incident to a given vertex. More...
typedef unspecified_type	CGAL::Triangulation_2< Traits, Tds >::Edge_circulator
	circulator over all edges incident to a given vertex. More...
typedef unspecified_type	CGAL::Triangulation_2< Traits, Tds >::Vertex_circulator
	circulator over all vertices incident to a given vertex. More...

Typedef Documentation

template<typename Traits, typename Tds>

typedef Tds::Edge_iterator CGAL::Triangulation_2< Traits, Tds >::All_edges_iterator

iterator over all edges.

template<typename Traits, typename Tds>

typedef Tds::Face_iterator CGAL::Triangulation_2< Traits, Tds >::All_faces_iterator

iterator over all faces.

template<typename Traits, typename Tds>

typedef Tds::Vertex_iterator CGAL::Triangulation_2< Traits, Tds >::All_vertices_iterator

iterator over all vertices.

template<typename Traits, typename Tds>

typedef unspecified_type CGAL::Triangulation_2< Traits, Tds >::Edge_circulator

circulator over all edges incident to a given vertex.

template<typename Traits, typename Tds>

typedef unspecified_type CGAL::Triangulation_2< Traits, Tds >::Face_circulator

circulator over all faces incident to a given vertex.

template<typename Traits, typename Tds>

typedef Tds::Face_handle CGAL::Triangulation_2< Traits, Tds >::Face_handle

handle to a face.

template<typename Traits, typename Tds>

typedef unspecified_type CGAL::Triangulation_2< Traits, Tds >::Finite_edges_iterator

iterator over finite edges.

template<typename Traits, typename Tds>

typedef unspecified_type CGAL::Triangulation_2< Traits, Tds >::Finite_faces_iterator

iterator over finite faces.

template<typename Traits, typename Tds>

typedef unspecified_type CGAL::Triangulation_2< Traits, Tds >::Finite_vertices_iterator

iterator over finite vertices.

template<typename Traits, typename Tds>

typedef unspecified_type CGAL::Triangulation_2< Traits, Tds >::Line_face_circulator

circulator over all faces intersected by a line.

template<typename Traits, typename Tds>

typedef unspecified_type CGAL::Triangulation_2< Traits, Tds >::Point_iterator

iterator over the points corresponding the finite vertices of the triangulation.

template<typename Traits, typename Tds>

typedef unspecified_type CGAL::Triangulation_2< Traits, Tds >::Vertex_circulator

circulator over all vertices incident to a given vertex.

template<typename Traits, typename Tds>

typedef Tds::Vertex_handle CGAL::Triangulation_2< Traits, Tds >::Vertex_handle

handle to a vertex.

Enumeration Type Documentation

template<typename Traits, typename Tds>

enum CGAL::Triangulation_2::Locate_type

specifies which case occurs when locating a point in the triangulation.

See also

CGAL::Triangulation_2<Traits,Tds>

Enumerator
VERTEX	when the located point coincides with a vertex of the triangulation
EDGE	when the point is in the relative interior of an edge
FACE	when the point is in the interior of a facet
OUTSIDE_CONVEX_HULL	when the point is outside the convex hull but in the affine hull of the current triangulation
OUTSIDE_AFFINE_HULL	when the point is outside the affine hull of the current triangulation.