Namespaces
namespace	IO

Classes
class	Aos_observer
	More...

class	Arr_accessor
	More...

class	Arr_algebraic_segment_traits_2
	The traits class `Arr_algebraic_segment_traits_2` is a model of the `ArrangementTraits_2` concept that handles planar algebraic curves of arbitrary degree, and \( x\)-monotone of such curves. More...

class	Arr_Bezier_curve_traits_2
	The traits class `Arr_Bezier_curve_traits_2` is a model of the `ArrangementTraits_2` concept that handles planar Bézier curves. More...

class	Arr_bounded_planar_topology_traits_2
	More...

class	Arr_circle_segment_traits_2
	The class `Arr_circle_segment_traits_2` is a model of the `ArrangementTraits_2` concept and can be used to construct and maintain arrangements of circular arcs and line segments. More...

class	Arr_circular_arc_traits_2
	This class is a traits class for CGAL arrangements, built on top of a model of concept `CircularKernel`. More...

class	Arr_circular_line_arc_traits_2
	This class is a traits class for CGAL arrangements, built on top of a model of concept `CircularKernel`. More...

struct	Arr_closed_side_tag
	This type tag is used to indicate that a side of the parameter space, either left, right, bottom, or top, is closed, and curves that reach this side might be inserted into the arrangement. More...

class	Arr_conic_traits_2
	The class `Arr_conic_traits_2` is a model of the `ArrangementTraits_2` concept and can be used to construct and maintain arrangements of bounded segments of algebraic curves of degree \(2\) at most, also known as conic curves. More...

class	Arr_consolidated_curve_data_traits_2
	The class `Arr_consolidated_curve_data_traits_2` is a model of the concept `ArrangementTraits_2`, and serves as a decorator class that enables the extension of the curve type defined by the `Traits` parameter. More...

struct	Arr_contracted_side_tag
	This type tag is used to indicate that a side of the parameter space, either left, right, bottom, or top, is contracted, and curves that approach this side might be inserted into the arrangement. More...

class	Arr_curve_data_traits_2
	The class `Arr_curve_data_traits_2` is a model of the `ArrangementTraits_2` concept and serves as a decorator class that allows the extension of the curves defined by the base traits-class (the `Tr` parameter), which serves as a geometric traits-class (a model of the `ArrangementTraits_2` concept), with extraneous (non-geometric) data fields. More...

class	Arr_dcel
	The DCEL class used by the `Arrangement_2`, `Arr_bounded_planar_topology_traits_2`, `Arr_unb_planar_topology_traits_2` class templates and other templates. More...

class	Arr_dcel_base
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class	Arr_default_overlay_traits
	An instance of `Arr_default_overlay_traits` should be used for overlaying two arrangements of type `Arrangement` that store no auxiliary data with their DCEL records, where the resulting overlaid arrangement stores no auxiliary DCEL data as well. More...

class	Arr_extended_dcel
	The `Arr_extended_dcel` class-template extends the topological-features of the DCEL namely the vertex, halfedge, and face types. More...

class	Arr_extended_dcel_text_formatter
	`Arr_extended_dcel_text_formatter` defines the format of an arrangement in an input or output stream (typically a file stream), thus enabling reading and writing an `Arrangement` instance using a simple text format. More...

class	Arr_extended_face
	The `Arr_extended_face` class-template extends the face topological-features of the DCEL. More...

class	Arr_extended_halfedge
	The `Arr_extended_halfedge` class-template extends the halfedge topological-features of the DCEL. More...

class	Arr_extended_vertex
	The `Arr_extended_vertex` class-template extends the vertex topological-features of the DCEL. More...

class	Arr_face_extended_dcel
	The `Arr_face_extended_dcel` class-template extends the DCEL face-records, making it possible to store extra (non-geometric) data with the arrangement faces. More...

class	Arr_face_extended_text_formatter
	`Arr_face_extended_text_formatter` defines the format of an arrangement in an input or output stream (typically a file stream), thus enabling reading and writing an `Arrangement` instance using a simple text format. More...

class	Arr_face_index_map
	`Arr_face_index_map` maintains a mapping of face handles of an attached arrangement object to indices (of type `unsigned int`). More...

class	Arr_face_overlay_traits
	An instance of `Arr_face_overlay_traits` should be used for overlaying two arrangements of types `Arr_A` and `Arr_B`, which are instantiated using the same geometric traits-class and with the DCEL classes `Dcel_A` and `Dcel_B` respectively, in order to store their overlay in an arrangement of type `Arr_R`, which is instantiated using a third DCEL class `Dcel_R`. More...

class	Arr_geodesic_arc_on_sphere_traits_2
	The traits class `Arr_geodesic_arc_on_sphere_traits_2` is a model of the `ArrangementTraits_2` concept. More...

struct	Arr_identified_side_tag
	This type tag is used to indicate that a side of the parameter space, either left, right, bottom, or top, is identified, and curves that approach this side might be inserted into the arrangement. More...

class	Arr_landmarks_point_location
	More...

class	Arr_line_arc_traits_2
	This class is a traits class for CGAL arrangements, built on top of a model of concept `CircularKernel`. More...

class	Arr_linear_traits_2
	The traits class `Arr_linear_traits_2` is a model of the `ArrangementTraits_2` concept, which enables the construction and maintenance of arrangements of linear objects. More...

class	Arr_naive_point_location
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class	Arr_non_caching_segment_basic_traits_2
	The traits class `Arr_non_caching_segment_basic_traits_2` is a model of the `ArrangementTraits_2` concept that allow the construction and maintenance of arrangements of sets of pairwise interior-disjoint line segments. More...

class	Arr_non_caching_segment_traits_2
	The traits class `Arr_non_caching_segment_traits_2` is a model of the `ArrangementTraits_2` concept that allows the construction and maintenance of arrangements of line segments. More...

struct	Arr_oblivious_side_tag
	This type tag is used to indicate that the condition of a boundary side of the parameter space is irrelevant. More...

struct	Arr_open_side_tag
	This type tag is used to indicate that a side of the parameter space, either left, right, bottom, or top, is open, and curves that approach this side might be inserted into the arrangement. More...

struct	Arr_point_location_result
	A unary metafunction to determine the return type of a point-location or vertical ray-shoot query. More...

class	Arr_polycurve_traits_2
	Note: The `SubcurveTraits_2` can comprise of Line_segments, Conic_arcs, Circular_arc, Bezier_curves, or Linear_curves. More...

class	Arr_polyline_traits_2
	The traits class `Arr_polyline_traits_2` handles piecewise linear curves, commonly referred to as polylines. More...

class	Arr_rational_function_traits_2
	The traits class `Arr_rational_function_traits_2` is a model of the `ArrangementTraits_2` concept. More...

class	Arr_segment_traits_2
	The traits class `Arr_segment_traits_2` is a model of the `ArrangementTraits_2` concept, which allows the construction and maintenance of arrangements of line segments. More...

class	Arr_spherical_topology_traits_2
	More...

class	Arr_text_formatter
	`Arr_text_formatter` defines the format of an arrangement in an input or output stream (typically a file stream), thus enabling reading and writing an `Arrangement` instance using a simple text format. More...

class	Arr_trapezoid_ric_point_location
	More...

class	Arr_triangulation_point_location
	More...

class	Arr_unb_planar_topology_traits_2
	More...

class	Arr_vertex_index_map
	`Arr_vertex_index_map` maintains a mapping of vertex handles of an attached arrangement object to indices (of type `unsigned int`). More...

class	Arr_walk_along_line_point_location
	More...

class	Arr_with_history_text_formatter
	`Arr_with_history_text_formatter` defines the format of an arrangement in an input or output stream (typically a file stream), thus enabling reading and writing an arrangement-with-history instance using a simple text format. More...

class	Arrangement_2
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class	Arrangement_on_surface_2
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class	Arrangement_on_surface_with_history_2
	More...

class	Arrangement_with_history_2
	More...

class	CORE_algebraic_number_traits
	`CORE_algebraic_number_traits` is a traits class for CORE's algebraic number types. More...

Typedefs
template<typename Traits >
using	Arr_default_dcel = Arr_dcel< Traits >
	The default DCEL class used by the `Arrangement_2`, `Arr_bounded_planar_topology_traits_2`, `Arr_unb_planar_topology_traits_2` class templates and other templates.

typedef Box_parameter_space_2	Arr_parameter_space

template<typename Arrangement_ >
using	Arr_observer = typename Arrangement_::Observer
	`Arr_observer<Arrangement_2>` is an alias for Aos_observer<Arrangement_on_surface_2>`, where`Arrangement_2`derives from`Arrangement_on_surface_2` and the latter is an instance of the template `CGAL::Arrangement_on_surface_2<GeometryTraits, TopologyTraits>`.

Enumerations
enum	Arr_curve_end { ARR_MIN_END , ARR_MAX_END }
	The enumeration `Arr_curve_end` is used to indicate one of the two ends of an \(x\)-monotone curve. More...

enum	Arr_halfedge_direction { ARR_LEFT_TO_RIGHT , ARR_RIGHT_TO_LEFT }
	The enumeration `Arr_halfedge_direction` is defined by `CGAL::Arrangement_2::Halfedge` to specify the direction of the halfedge. More...

Functions
template<typename Traits , typename Dcel , typename InputIterator , typename OutputIterator >
OutputIterator	locate (const Arrangement_2< Traits, Dcel > &arr, InputIterator begin, InputIterator end, OutputIterator oi)
	performs a batched point-location operation on a given arrangement.

template<class GeomTraitsA , class GeomTraitsB , class GeomTraitsRes , class TopTraitsA , class TopTraitsB , class TopTraitsRes , class OverlayTraits >
void	overlay (const Arrangement_2< GeomTraitsA, TopTraitsA > &arr1, const Arrangement_2< GeomTraitsB, TopTraitsB > &arr2, Arrangement_2< GeomTraitsRes, TopTraitsRes > &arr_res, OverlayTraits &ovl_tr)
	Computes the overlay of two arrangements `arr1` and `arr2`, and sets the output arrangement `res` to represent the overlaid arrangement.

template<typename Traits , typename Dcel1 , typename Dcel2 , typename ResDcel , typename OverlayTraits >
void	overlay (const Arrangement_with_history_2< Traits, Dcel1 > &arr1, const Arrangement_with_history_2< Traits, Dcel2 > &arr2, Arrangement_with_history_2< Traits, ResDcel > &res, OverlayTraits &ovl_tr)
	Computes the overlay of two arrangements with history `arr1` and `arr2`, and sets the output arrangement with history `res` to represent the overlaid arrangement.

template<typename Traits , typename TopologyTraits , typename OutputIterator >
OutputIterator	decompose (const Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, OutputIterator oi)
	produces the symbolic vertical decomposition of a given arrangement.

template<typename Traits , typename Dcel , typename PointLocation >
Arrangement_2< Traits, Dcel >::Halfedge_handle	insert_non_intersecting_curve (Arrangement_2< Traits, Dcel > &arr, const typename Traits::X_monotone_curve_2 &xc, const PointLocation &pl=walk_pl)
	Inserts a given \( x\)-monotone curve into a given arrangement, where the interior of the given curve is disjoint from all existing arrangement vertices and edges.

template<typename Traits , typename Dcel , InputIterator >
void	insert_non_intersecting_curves (Arrangement_2< Traits, Dcel > &arr, InputIterator first, InputIterator last)
	Inserts a set of \( x\)-monotone curves in a given range into a given arrangement.

template<typename Traits , typename Dcel , typename PointLocation >
Arrangement_2< Traits, Dcel >::Vertex_handle	insert_point (Arrangement_2< Traits, Dcel > &arr, const typename Traits::Point_2 &p, const PointLocation &pl=walk_pl)
	Inserts a given point into a given arrangement.

template<typename Traits , typename Dcel >
bool	is_valid (const Arrangement_2< Traits, Dcel > &arr)
	Checks the validity of a given arrangement.

template<typename Traits , typename Dcel >
Arrangement_2< Traits, Dcel >::Face_handle	remove_edge (Arrangement_2< Traits, Dcel > &arr, typename Arrangement_2< Traits, Dcel >::Halfedge_handle e)
	Removes an edge given by one of the twin halfedges that forms it, from a given arrangement.

template<typename Traits , typename Dcel >
bool	remove_vertex (Arrangement_2< Traits, Dcel > &arr, typename Arrangement_2< Traits, Dcel >::Vertex_handle v)
	Attempts to removed a given vertex from a given arrangement.

template<typename GeometryTraits , typename TopologyTraits , typename Curve , typename PointLocation >
bool	do_intersect (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, const Curve &c, const PointLocation &pl)
	Checks if a given curve or \(x\)-monotone curve intersects an existing arrangement's edges or vertices.

template<typename GeometryTraits , typename TopologyTraits , typename PointLocation >
Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Halfedge_handle	insert_non_intersecting_curve (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, const typename Traits::X_monotone_curve_2 &xc, const PointLocation &pl=walk_pl)
	Inserts a given \( x\)-monotone curve into a given arrangement, where the given curve and the existing arrangement edges (more precisely, the curves geometric mappings of the edges) must be pairwise disjoint in their interiors, and the interior of the input curve must not contain existing arrangement vertices (more precisely, the points geometric mappings of the vertices).

template<typename GeometryTraits , typename TopologyTraits , typename InputIterator >
void	insert_non_intersecting_curves (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, InputIterator first, InputIterator last)
	Inserts a set of \( x\)-monotone curves in a given range into a given arrangement.

template<typename GeometryTraits , typename TopologyTraits , typename PointLocation >
Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex_handle	insert_point (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, const typename Traits::Point_2 &p, const PointLocation &pl=walk_pl)
	Inserts a given point into a given arrangement.

template<typename GeometryTraits , typename TopologyTraits >
bool	is_valid (const Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr)
	Checks the validity of a given arrangement.

template<typename GeometryTraits , typename TopologyTraits >
Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Face_handle	remove_edge (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, typename Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Halfedge_handle e)
	Removes an edge given by one of the twin halfedges that forms it, from a given arrangement.

template<typename GeometryTraits , typename TopologyTraits >
bool	remove_vertex (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, typename Arrangement_on_surface_2< GeometryTraits, TopologyTraits >::Vertex_handle v)
	Attempts to removed a given vertex from a given arrangement.

template<typename GeometryTraits , typename TopologyTraits , typename OutputIterator , typename PointLocation >
OutputIterator	zone (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, const typename GeometryTraits::X_monotone_curve_2 &c, OutputIterator oi, const PointLocation &pl)
	computes the zone of the given \(x\)-monotone curve in a given arrangement.

template<typename GeometryTraits , typename TopologyTraits , typename PointLocation >
Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits >::Curve_handle	insert (Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits > &arr, const typename Traits::Curve_2 &c, const PointLocation &pl=walk_pl)
	Inserts the given curve `c` into the arrangement with history `arr`, and returns a handle to the inserted curve.

template<typename GeometryTraits , typename TopologyTraits , typename InputIterator >
void	insert (Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits > &arr, InputIterator first, InputIterator last)
	Aggregately inserts the curves in the range `[first,last)` into the arrangement with history `arr` using the sweep-line framework.

template<typename GeometryTraits , typename TopologyTraits >
Size	remove_curve (Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits > &arr, typename Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits >::Curve_handle ch)
	Removes a given curve from a given arrangement.

template<typename GeometryTraits , typename TopologyTraits1 , typename TopologyTraits12 , typename ResTopologyTraits , typename OverlayTraits >
void	overlay (const Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits1 > &arr1, const Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits12 > &arr2, Arrangement_on_surface_with_history_2< GeometryTraits, ResTopologyTraits > &res, OverlayTraits &ovl_tr)

template<typename GeometryTraits , typename TopologyTraits1 , typename TopologyTraits2 , typename ResTopologyTraits >
void	overlay (const Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits1 > &arr1, const Arrangement_on_surface_with_history_2< GeometryTraits, TopologyTraits2 > &arr2, Arrangement_on_surface_with_history_2< GeometryTraits, ResTopologyTraits > &res)

template<typename Traits , typename Dcel , typename PointLocation >
Arrangement_with_history_2< Traits, Dcel >::Curve_handle	insert (Arrangement_with_history_2< Traits, Dcel > &arr, const typename Traits::Curve_2 &c, const PointLocation &pl=walk_pl)
	Inserts the given curve `c` into the arrangement with history `arr`, and returns a handle to the inserted curve.

template<typename Traits , typename Dcel , typename InputIterator >
void	insert (Arrangement_with_history_2< Traits, Dcel > &arr, InputIterator first, InputIterator last)
	Aggregately inserts the curves in the range `[first,last)` into the arrangement with history `arr` using the sweep-line framework.

template<typename Traits , typename Dcel >
Size	remove_curve (Arrangement_with_history_2< Traits, Dcel > &arr, typename Arrangement_with_history_2< Traits, Dcel >::Curve_handle ch)
	Removes a given curvespecified by its handle `ch`, from a given arrangement `arr`, deleting all the edges it induces.

template<typename Traits , typename Dcel1 , typename Dcel2 , typename ResDcel >
void	overlay (const Arrangement_with_history_2< Traits, Dcel1 > &arr1, const Arrangement_with_history_2< Traits, Dcel2 > &arr2, Arrangement_with_history_2< Traits, ResDcel > &res)

template<typename GeometryTraits_2 , typename Dcel , typename GSOptions >
void	draw (const Arrangement_2< GeometryTraits_2, Dcel > &arr, const GSOptions &gso)
	opens a new window and draws `arr`, an instance of the `CGAL::Arrangement_2` class template.

template<typename GeometryTraits_2 , typename Dcel >
void	draw (const Arrangement_2< GeometryTraits_2, Dcel > &arr)
	A shortcut to `CGAL::draw(arr, Graphics_scene_options{})`.

template<typename GeometryTraits_2 , typename Dcel , typename GSOptions >
void	add_to_graphics_scene (const Arrangement_2< GeometryTraits_2, Dcel > &arr, CGAL::Graphics_scene &gs, const GSOptions &gso)
	adds the vertices, edges and faces of `arr` into the given graphic scene `gs`.

template<typename GeometryTraits_2 , typename Dcel >
void	add_to_graphics_scene (const Arrangement_2< GeometryTraits_2, Dcel > &arr, CGAL::Graphics_scene &gs)
	A shortcut to `CGAL::add_to_graphics_scene(arr, gs, Graphics_scene_options{})`.

template<typename Traits , typename Dcel >
std::ostream &	operator<< (std::ostream &os, const Arrangement_2< Traits, Dcel > &arr)
	Inserts the arrangement object `arr` into the output stream `os` using the output format defined by the `Arr_text_formatter` class.

template<class Traits , class Dcel >
std::istream &	operator>> (std::istream &is, Arrangement_2< Traits, Dcel > &arr)
	Extracts an arrangement from a given input stream using the input format defined by the `Arr_text_formatter` class - that is, only the basic geometric and topological features of the arrangement are read and no auxiliary data is attached to the Dcel features.

template<typename Traits , typename Dcel >
std::ostream &	operator<< (std::ostream &os, const Arrangement_with_history_2< Traits, Dcel > &arr)
	Inserts the arrangement-with-history object `arr` into the output stream `os` using the output format defined by the `Arr_with_history_text_formatter` class.

template<class Traits , class Dcel >
std::istream &	operator>> (std::istream &is, Arrangement_with_history_2< Traits, Dcel > &arr)
	Extracts an arrangement-with-history from a given input stream using the default input format.

Variables
const Arr_parameter_space	ARR_LEFT_BOUNDARY = LEFT_BOUNDARY

const Arr_parameter_space	ARR_RIGHT_BOUNDARY = RIGHT_BOUNDARY

const Arr_parameter_space	ARR_BOTTOM_BOUNDARY = BOTTOM_BOUNDARY

const Arr_parameter_space	ARR_TOP_BOUNDARY = TOP_BOUNDARY

const Arr_parameter_space	ARR_INTERIOR = INTERIOR

template<typename Traits , typename Dcel , typename Curve , typename PointLocation >
void	insert (Arrangement_2< Traits, Dcel > &arr, const Curve &c, const PointLocation &pl=walk_pl)
	The function `insert` inserts one or more curves or \( x\)-monotone curves into a given arrangement, where no restrictions are imposed on the inserted curves.

template<typename Traits , typename Dcel >
void	insert (Arrangement_2< Traits, Dcel > &arr, const typename Traits::X_monotone_curve_2 &xc, typename Arr_point_location_result< Arrangement_2< Traits, Dcel > >::type obj)
	Inserts the \( x\)-monotone (only) curve `xc` into the arrangement `arr`.

template<typename Traits , typename Dcel , class InputIterator >
void	insert (Arrangement_2< Traits, Dcel > &arr, InputIterator first, InputIterator last)
	Aggregately inserts the curves or \( x\)-monotone curves in the range `[first,last)` into the arrangement `arr` using the sweep-line framework.

template<typename GeometryTraits , typename TopologyTraits , typename Curve , typename PointLocation >
void	insert (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, const Curve &c, const PointLocation &pl=walk_pl)
	The function `insert` inserts one or more curves or \( x\)-monotone curves into a given arrangement, where no restrictions are imposed on the inserted curves.

template<typename GeometryTraits , typename TopologyTraits >
void	insert (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, const typename Traits::X_monotone_curve_2 &xc, typename Arr_point_location_result< Arrangement_on_surface_2< GeometryTraits, TopologyTraits > >::type obj)
	Inserts the \( x\)-monotone (only) curve `xc` into the arrangement `arr`.

template<typename GeometryTraits , typename TopologyTraits , typename InputIterator >
void	insert (Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr, InputIterator first, InputIterator last)
	Aggregately inserts the curves or \( x\)-monotone curves in the range `[first,last)` into the arrangement `arr` using the sweep-line framework.

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables