CGAL::Arrangement_2< Traits, Dcel > Class Template Reference

#include <CGAL/Arrangement_2.h>

Inherits from

CGAL::Arrangement_on_surface_2< Traits, Default_planar_topology< Traits, Dcel >::Traits >.

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 ArrangementBasicTraits_2 concept. The traits class defines the types of \( x\)-monotone curves and two-dimensional points, namely ArrangementBasicTraits_2::X_monotone_curve_2 and ArrangementBasicTraits_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 ArrangementDcel 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

ArrangementDcel

Arr_default_dcel<Traits>

ArrangementBasicTraits_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/draw_arr.cpp, Arrangement_on_surface_2/dual_with_data.cpp, Arrangement_on_surface_2/face_extension.cpp, Arrangement_on_surface_2/face_extension_overlay.cpp, Arrangement_on_surface_2/generic_curve_data.cpp, Arrangement_on_surface_2/overlay_color.cpp, Arrangement_on_surface_2/overlay_unbounded.cpp, and Arrangement_on_surface_2/predefined_kernel_non_intersecting.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.

Access Functions
Traits *	traits ()
	obtains the traits object used by the arrangement instance.

Member Function Documentation

traits()

template<typename Traits , typename Dcel >

Traits * CGAL::Arrangement_2< Traits, Dcel >::traits

(

)

obtains the traits object used by the arrangement instance.

A const version is also available.