CGAL Namespace Reference

Namespaces
	cpp11
	IO
	Scale_space_reconstruction_3
	Shape_detection_3
	Surface_mesh_parameterization

Classes
class	Aff_transformation_2
class	Aff_transformation_3
class	Identity_transformation
class	Reflection
class	Rotation
class	Scaling
class	Translation
class	Bbox_2
class	Bbox_3
class	Cartesian
class	Cartesian_converter
class	Circle_2
class	Circle_3
class	Ambient_dimension
class	Dimension_tag
class	Dynamic_dimension_tag
class	Feature_dimension
class	Direction_2
class	Direction_3
class	Exact_predicates_exact_constructions_kernel
class	Exact_predicates_exact_constructions_kernel_with_kth_root
class	Exact_predicates_exact_constructions_kernel_with_root_of
class	Exact_predicates_exact_constructions_kernel_with_sqrt
class	Exact_predicates_inexact_constructions_kernel
class	Filtered_kernel_adaptor
class	Filtered_kernel
class	Filtered_predicate
class	Homogeneous
class	Homogeneous_converter
class	Iso_cuboid_3
class	Iso_rectangle_2
class	Kernel_traits
class	Line_2
class	Line_3
class	Null_vector
class	Origin
class	Plane_3
class	Point_2
class	Point_3
class	Projection_traits_xy_3
class	Projection_traits_xz_3
class	Projection_traits_yz_3
class	Ray_2
class	Ray_3
class	Segment_2
class	Segment_3
class	Simple_cartesian
class	Simple_homogeneous
class	Sphere_3
class	Tetrahedron_3
class	Triangle_2
class	Triangle_3
class	Vector_2
class	Vector_3
class	Weighted_point_2
class	Weighted_point_3
struct	Construct_array
class	CC_safe_handle
class	Compact_container_base
class	Compact_container
class	Compact_container_traits
class	Compact
class	Fast
class	Concurrent_compact_container_traits
class	Concurrent_compact_container
class	Default
class	Fourtuple
class	Cast_function_object
class	Compare_to_less
class	Creator_1
class	Creator_2
class	Creator_3
class	Creator_4
class	Creator_5
class	Creator_uniform_2
class	Creator_uniform_3
class	Creator_uniform_4
class	Creator_uniform_5
class	Creator_uniform_6
class	Creator_uniform_7
class	Creator_uniform_8
class	Creator_uniform_9
class	Creator_uniform_d
class	Dereference
class	Get_address
class	Identity
class	Project_facet
class	Project_next
class	Project_next_opposite
class	Project_normal
class	Project_opposite_prev
class	Project_plane
class	Project_point
class	Project_prev
class	Project_vertex
class	In_place_list_base
class	In_place_list
class	Const_oneset_iterator
class	Counting_iterator
class	Dispatch_or_drop_output_iterator
class	Dispatch_output_iterator
class	Emptyset_iterator
class	Filter_iterator
class	Insert_iterator
class	Inverse_index
class	Join_input_iterator_1
class	Join_input_iterator_2
class	Join_input_iterator_3
class	N_step_adaptor
class	Oneset_iterator
class	Random_access_adaptor
class	Random_access_value_adaptor
class	Iterator_range
class	Location_policy
class	Multiset
class	Object
class	Sixtuple
class	Spatial_lock_grid_3
class	Boolean_tag
struct	Null_functor
struct	Sequential_tag
struct	Parallel_tag
class	Null_tag
class	Threetuple
class	Twotuple
class	Uncertain
class	Quadruple
class	Triple
struct	value_type_traits
struct	value_type_traits< std::back_insert_iterator< Container > >
struct	value_type_traits< std::insert_iterator< Container > >
struct	value_type_traits< std::front_insert_iterator< Container > >
class	Algebraic_structure_traits
class	Euclidean_ring_tag
class	Field_tag
class	Field_with_kth_root_tag
class	Field_with_root_of_tag
class	Field_with_sqrt_tag
class	Integral_domain_tag
class	Integral_domain_without_division_tag
class	Unique_factorization_domain_tag
class	Coercion_traits
class	Fraction_traits
class	Real_embeddable_traits
class	Circulator_from_container
class	Circulator_from_iterator
class	Circulator_traits
class	Container_from_circulator
struct	Circulator_tag
struct	Iterator_tag
struct	Forward_circulator_tag
struct	Bidirectional_circulator_tag
struct	Random_access_circulator_tag
struct	Circulator_base
struct	Forward_circulator_base
struct	Bidirectional_circulator_base
struct	Random_access_circulator_base
class	Forward_circulator_ptrbase
class	Bidirectional_circulator_ptrbase
class	Random_access_circulator_ptrbase
class	Color
class	Input_rep
class	Output_rep
class	Istream_iterator
class	Ostream_iterator
class	Verbose_ostream
class	Gps_face_base
class	Gps_halfedge_base
class	Gps_default_dcel
class	General_polygon_2
class	General_polygon_set_2
class	Gps_circle_segment_traits_2
class	Gps_segment_traits_2
class	Gps_traits_2
class	Polygon_set_2
class	Protect_FPU_rounding
class	Set_ieee_double_precision
class	Gmpfi
class	Gmpfr
class	Gmpq
class	Gmpz
class	Gmpzf
class	Interval_nt
class	Lazy_exact_nt
class	MP_Float
class	Mpzf
class	NT_converter
class	Number_type_checker
class	Quotient
class	Rational_traits
class	Root_of_traits
class	Sqrt_extension
class	Is_valid
class	Max
class	Min
class	Algebraic_kernel_for_circles_2_2
class	Circular_arc_2
class	Circular_arc_point_2
class	Circular_kernel_2
class	Exact_circular_kernel_2
class	Line_arc_2
class	Polynomial_1_2
class	Polynomial_for_circles_2_2
class	Root_for_circles_2_2
class	Algebraic_kernel_d_1
class	Algebraic_kernel_d_2
class	Algebraic_kernel_rs_gmpq_d_1
class	Algebraic_kernel_rs_gmpz_d_1
class	HalfedgeDS_face_max_base_with_id
class	HalfedgeDS_halfedge_max_base_with_id
class	HalfedgeDS_vertex_max_base_with_id
class	Linear_cell_complex_bgl_min_items
class	Linear_cell_complex_for_bgl_combinatorial_map_helper
class	Polyhedron_items_with_id_3
class	Triangulation_vertex_base_with_id_2
class	Halfedge_around_source_iterator
class	Halfedge_around_target_iterator
class	Halfedge_around_face_iterator
class	Halfedge_around_target_circulator
class	Halfedge_around_source_circulator
class	Face_around_target_circulator
class	Halfedge_around_face_circulator
class	Face_around_face_iterator
class	Face_around_face_circulator
class	Face_around_target_iterator
class	Vertex_around_face_iterator
class	Vertex_around_target_circulator
class	Vertex_around_target_iterator
struct	Graph_with_descriptor_with_graph
struct	Graph_with_descriptor_with_graph_property_map
struct	Face_filtered_graph
class	Dual
class	Seam_mesh
class	Arr_accessor
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_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...
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...
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_base
class	Arr_default_dcel
	The default Dcel class used by the Arrangement_2 class-template is parameterized by a traits class, which is a model of the ArrangementBasicTraits_2 concept. More...
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_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_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_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_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_landmarks_point_location
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
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...
class	Arr_observer
class	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_oblivious_side_tag
	The categories Left_side_category, Right_side_category, Bottom_side_category, and Top_side_category, nested in any model of the ArrangementBasicTraits_2, must be convertible to Arr_oblivious_side_tag. More...
class	Arr_open_side_tag
	All the four types Left_side_category, Right_side_category, Bottom_side_category, and Top_side_category nested in any model of the concept ArrangementOpenBoundaryTraits must be convertible to Arr_open_side_tag, which derives from Arr_oblivious_side_tag. More...
class	Arr_trapezoid_ric_point_location
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
class	Arrangement_2
class	Arrangement_with_history_2
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_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_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_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...

Typedefs
typedef Box_parameter_space_2	Arr_parameter_space

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 points_begin, InputIterator points_end, OutputIterator oi)
	Performs a batched point-location operation on a given arrangement. More...
template<typename Traits , typename Dcel , typename Formatter >
std::istream &	read (Arrangement_2< Traits, Dcel > &arr, std::istream &is, Formatter &formatter)
	Reads the arrangement object arr from the given input stream is using a specific input format defined by "formatter".
template<typename Traits , typename Dcel , typename Formatter >
std::ostream &	write (const Arrangement_2< Traits, Dcel > &arr, std::ostream &os, Formatter &formatter)
	Writes the arrangement object arr into the given output stream os using a specific output format defined by formatter.
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. More...
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<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. More...
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. More...
template<typename Traits , typename Dcel , typename OutputIterator >
OutputIterator	decompose (const Arrangement_2< Traits, Dcel > &arr, OutputIterator oi)
	Produces the symbolic vertical decomposition of a given arrangement, performing a batched vertical ray-shooting query from all arrangement vertices, such that every vertex is associated with a pair of objects, one corresponds to the arrangement feature that lies below it, and the other corresponds to the feature that lies above it. More...
template<typename Traits , typename Dcel , typename WithHistoryFormatter >
std::istream &	read (Arrangement_with_history_2< Traits, Dcel > &arr, std::istream &is, WithHistoryFormatter &formatter)
	Reads the arrangement-with-history object arr from the given input stream is using a specific input format defined by "formatter".
template<typename Traits , typename Dcel , typename WithHistoryFormatter >
std::ostream &	write (const Arrangement_with_history_2< Traits, Dcel > &arr, std::ostream &os, WithHistoryFormatter &formatter)
	Writes the arrangement-with-history object arr into the given output stream os using a specific output format defined by formatter.
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. More...
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.
template<class GeomTraits , class TopTraits , class Curve , class PointLocation >
bool	do_intersect (Arrangement_on_surface_2< GeomTraits, TopTraits > &arr, const Curve &c, const PointLocation &pl)
	Checks if a given curve or \( x\)-monotone curve intersects an existing arrangement's edges or vertices. More...
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. More...
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. More...
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. More...
template<typename Traits , typename Dcel >
bool	is_valid (const Arrangement_2< Traits, Dcel > &arr)
	Checks the validity of a given arrangement. More...
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. More...
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. More...
template<class GeomTraits , class TopTraits , class OutputIterator , class PointLocation >
OutputIterator	zone (Arrangement_on_surface_2< GeomTraits, TopTraits > &arr, const typename GeomTraits::X_monotone_curve_2 &c, OutputIterator oi, const PointLocation &pl)
	Compute the zone of the given \( x\)-monotone curve in the existing arrangement. More...
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. More...
template<class Traits , class Dcel , 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<class Traits , class Dcel >
Size	remove_curve (Arrangement_with_history_2< Traits, Dcel > &arr, typename Arrangement_with_history_2< Traits, Dcel >::Curve_handle ch)
	Removes a given curve from a given arrangement. More...
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)

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