#include <CGAL/Arrangement_with_history_2.h>

Inherits from

Definition

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 edges and vertices. 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 instantiated with a model of the ArrangementTraits_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 ArrangementTraits_2::X_monotone_curve_2 and ArrangementTraits_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 ArrangementDcelWithRebind concept. The value of this parameter is by default Arr_default_dcel<Traits>.

See Also: ArrangementDcel; Arr_default_dcel<Traits>; ArrangementTraits_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 Arrangement_with_history_2 < Traits_2, Dcel >	Self
	a private type used as an abbreviation of the `Arrangement_with_history_2` type hereafter. More...

typedef unspecified_type	Traits_2
	the traits class in use. More...

typedef Traits_2::Point_2	Point_2
	the point type, as defined by the traits class. More...

typedef Traits_2::X_monotone_curve_2	X_monotone_curve_2
	the \( x\)-monotone curve type, as defined by the traits class. More...

typedef Traits_2::Curve_2	Curve_2
	the curve type, as defined by the traits class. More...

In addition, the nested types `Vertex`, `Halfedge` and `Face` are defined, as well as all handle, iterator and circulator types, as defined by the `Arrangement_2` class-template.
typedef unspecified_type	Curve_handle
	a handle for an input curve. More...

typedef unspecified_type	Curve_iterator
	a bidirectional iterator over the curves that induce the arrangement. More...

typedef unspecified_type	Induced_edge_iterator
	an iterator over the edges induced by an input curve. More...

typedef unspecified_type	Originating_curve_iterator
	an iterator for the curves that originate a given arrangement edge. More...

Creation
	Arrangement_with_history_2 ()
	constructs an empty arrangement containing one unbounded face, which corresponds to the whole plane. More...

	Arrangement_with_history_2 (const Self &other)
	copy constructor. More...

	Arrangement_with_history_2 (Traits_2 *traits)
	constructs an empty arrangement that uses the given `traits` instance for performing the geometric predicates. More...

Assignment Methods
Self &	operator= (other)
	assignment operator. More...

void	assign (const Self &other)
	assigns the contents of another arrangement. More...

void	clear ()
	clears the arrangement. More...

Access Functions for Input Curves
See the `Arrangement_2` reference pages for the full list.
Size	number_of_curves () const
	returns the number of input curves that induce the arrangement. More...

Curve_iterator	curves_begin ()
	returns the begin-iterator of the curves inducing the arrangement. More...

Curve_iterator	curves_end ()
	returns the past-the-end iterator of the curves inducing the arrangement. More...

Size	number_of_induced_edges (Curve_handle ch) const
	returns the number of arrangement edges induced by the curve `ch`. More...

Induced_edge_iterator	induced_edges_begin (Curve_handle ch) const
	returns the begin-iterator of the edges induced by the curve `ch`. More...

Induced_edge_iterator	induced_edges_end (Curve_handle ch) const
	returns the past-the-end iterator of the edges induced by the curve `ch`. More...

Size	number_of_originating_curves (Halfedge_handle e) const
	returns the number of input curves that originate the edge `e`. More...

Originating_curve_iterator	originating_curves_begin (Halfedge_handle e) const
	returns the begin-iterator of the curves originating the edge `e`. More...

Originating_curve_iterator	originating_curves_end (Halfedge_handle e) const
	returns the past-the-end iterator of the curves originating the edge `e`. More...

Modifying Arrangement Edges
The following functions override their counterparts in the `Arrangement_2` class, as they also maintain the cross-relationships between the input curves and the edges they induce. See the `Arrangement_2` reference pages for the full list of functions for modifying arrangement vertices
Halfedge_handle	split_edge (Halfedge_handle e, const Point_2 &p)
	splits the edge `e` into two edges (more precisely, into two halfedge pairs), at a given split point `p`. More...

Halfedge_handle	merge_edge (Halfedge_handle e1, Halfedge_handle e2)
	merges the edges represented by `e1` and `e2` into a single edge. More...

Face_handle	remove_edge (Halfedge_handle e, bool remove_source=true, bool remove_target=true)
	removes the edge `e` from the arrangement. More...