Definition

template<typename Traits, typename Dcel>
class CGAL::Arrangement_2< Traits, Dcel >

An object arr of the class Arrangement_2 represents the planar subdivision induced by a set of \(x\)-monotone curves and isolated points into maximally connected cells. The arrangement is represented as a doubly-connected edge-list (DCEL) such that each DCEL vertex is associated with a point of the plane and each edge is associated with an \( x\)-monotone curve whose interior is disjoint from all other edges and vertices. Recall that an arrangement edge is always comprised of a pair of twin Dcel halfedges.

The Arrangement_2 template has two parameters:

The Traits template-parameter should be instantiated with a model of the AosBasicTraits_2 concept. The traits class defines the types of \(x\)-monotone curves and two-dimensional points, namely AosBasicTraits_2::X_monotone_curve_2 and AosBasicTraits_2::Point_2, respectively, and supports basic geometric predicates on them.
The Dcel template-parameter should be instantiated with a class that is a model of the AosDcel concept. The value of this parameter is by default Arr_default_dcel<Traits>.

The available traits classes and DCEL classes are described below.

See also: AosDcel; Arr_default_dcel<Traits>; AosBasicTraits_2; CGAL::overlay(); CGAL::is_valid()

Insertion Functions

See also: CGAL::insert(); CGAL::insert_non_intersecting_curve(); CGAL::insert_non_intersecting_curves(); CGAL::insert_point()

Removal functions

See also: CGAL::remove_edge(); CGAL::remove_vertex()

Input/output functions

See also: CGAL::IO::read(); CGAL::IO::write()

Examples: Arrangement_on_surface_2/algebraic_curves.cpp, Arrangement_on_surface_2/algebraic_segments.cpp, Arrangement_on_surface_2/bgl_dual_adapter.cpp, Arrangement_on_surface_2/consolidated_curve_data.cpp, Arrangement_on_surface_2/count_and_trace.cpp, Arrangement_on_surface_2/dcel_extension.cpp, Arrangement_on_surface_2/dcel_extension_io.cpp, Arrangement_on_surface_2/dual_with_data.cpp, and Arrangement_on_surface_2/face_extension.cpp.

Types
typedef Traits	Geometry_traits
	the geometry traits class.

typedef Default_planar_topology< Geometry_traits, Dcel >::Traits	Topology_traits
	The topology traits.

typedef Arrangement_on_surface_2< Geometry_traits, Topology_traits >	Base
	The base arrangement on surface type.

Types inherited from the base Arrangement_on_surface_2
typedef Base::Point_2	Point_2

typedef Base::X_monotone_curve_2	X_monotone_curve_2

typedef Base::Curve_2	Curve_2

typedef Base::Size	Size

typedef Base::Vertex	Vertex

typedef Base::Halfedge	Halfedge

typedef Base::Face	Face

typedef Base::Vertex_handle	Vertex_handle

typedef Base::Halfedge_handle	Halfedge_handle

typedef Base::Face_handle	Face_handle

typedef Base::Vertex_iterator	Vertex_iterator

typedef Base::Halfedge_iterator	Halfedge_iterator

typedef Base::Edge_iterator	Edge_iterator

typedef Base::Face_iterator	Face_iterator

typedef Base::Unbounded_face_iterator	Unbounded_face_iterator

typedef Base::Halfedge_around_vertex_circulator	Halfedge_around_vertex_circulator

typedef Base::Ccb_halfedge_circulator	Ccb_halfedge_circulator

typedef Base::Hole_iterator	Hole_iterator

typedef Base::Isolated_vertex_iterator	Isolated_vertex_iterator

typedef Base::Vertex_handle	Vertex_const_handle

typedef Base::Halfedge_handle	Halfedge_const_handle

typedef Base::Face_handle	Face_const_handle

typedef Base::Vertex_iterator	Vertex_const_iterator

typedef Base::Halfedge_iterator	Halfedge_const_iterator

typedef Base::Edge_iterator	Edge_const_iterator

typedef Base::Face_iterator	Face_const_iterator

typedef Base::Unbounded_face_iterator	Unbounded_face_const_iterator

typedef Base::Halfedge_around_vertex_circulator	Halfedge_around_const_vertex_circulator

typedef Base::Ccb_halfedge_circulator	Ccb_halfedge_const_circulator

typedef Base::Hole_iterator	Hole_const_iterator

typedef Base::Isolated_vertex_iterator	Isolated_vertex_const_iterator

Creation
	Arrangement_2 ()
	constructs an empty arrangement containing one unbounded face, which corresponds to the entire plane.

	Arrangement_2 (const Arrangement_2< Traits, Dcel > &other)
	copy constructor.

	Arrangement_2 (const Traits *traits)
	constructs an empty arrangement that uses the given `traits` instance for performing the geometric predicates.

Assignment Methods
Arrangement_2< Traits, Dcel > &	operator= (other)
	assignment operator.

void	assign (const Arrangement_2< Traits, Dcel > &other)
	assigns the contents of another arrangement.

void	clear ()
	clears the arrangement.