CGAL::Arrangement_with_history_2< Traits, Dcel > Class Template Reference

#include <CGAL/Arrangement_with_history_2.h>

Inherits from

CGAL::Arrangement_on_surface_with_history_2< Traits, Default_planar_topology< Traits, Dcel >::Traits >.

Definition

template<typename Traits, typename Dcel>
class CGAL::Arrangement_with_history_2< Traits, Dcel >

An object arr of the class Arrangement_with_history_2 represents the planar subdivision induced by a set of input curves \(\cal C\). The arrangement is represented as a doubly-connected edge-list (DCEL). As is the case for the Arrangement_2<Traits,Dcel>, each DCEL vertex is associated with a point and each edge is associated with an \(x\)-monotone curve whose interior is disjoint from all other curves and points. Each such \(x\)-monotone curve is a subcurve of some \(C \in \cal C\), or may represent an overlap among several curves in \(\cal C\).

The Arrangement_with_history_2 class-template extends the Arrangement_2 class-template by keeping an additional container of input curves representing \(\cal C\), and by maintaining a cross-mapping between these curves and the arrangement edges they induce. This way it is possible to determine the inducing curve(s) of each arrangement edge. This mapping also allows the traversal of input curves, and the traversal of edges induced by each curve.

The Arrangement_with_history_2 template has two parameters:

• The Traits template-parameter should be substituted by a model of the AosTraits_2 concept. The traits class defines the Curve_2 type, which represents an input curve. It also defines the types of \(x\)-monotone curves and two-dimensional points, namely AosTraits_2::X_monotone_curve_2 and AosTraits_2::Point_2, respectively, and supports basic geometric predicates on them.
• The Dcel template-parameter should be substituted by a class that is a model of the AosDcelWithRebind concept. The value of this parameter is by default Arr_default_dcel<Traits>.

See also

AosDcel

Arr_default_dcel<Traits>

AosTraits_2

Arrangement_2<Traits,Dcel>

insertion functions

removal functions

overlaying arrangements

Examples

Arrangement_on_surface_2/curve_history.cpp, Arrangement_on_surface_2/edge_manipulation_curve_history.cpp, and Arrangement_on_surface_2/io_curve_history.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_with_history_2< Geometry_traits, Topology_traits >	Base
	The base arrangement on surface type.

Types inherited from the base Arrangement_on_surface_2_with_history_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::Curve_handle	Curve_handle
typedef Base::Curve_iterator	Curve_iterator
typedef Base::Induced_edge_iterator	Induced_edge_iterator
typedef Base::Originating_curve_iterator	Originating_curve_iterator

Creation
	Arrangement_with_history_2 ()
	constructs an empty arrangement containing one unbounded face, which corresponds to the whole plane.
	Arrangement_with_history_2 (const Arrangement_with_history_2< Traits, Dcel > &other)
	copy constructor.
	Arrangement_with_history_2 (const Traits *traits)
	constructs an empty arrangement that uses the given traits instance for performing the geometric predicates.

Assignment Methods
Arrangement_with_history_2< Traits, Dcel > &	operator= (other)
	assignment operator.
void	assign (const Arrangement_with_history_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_with_history_2< Traits, Dcel >::traits

(

)

obtains the traits object used by the arrangement instance.

A const version is also available.