CGAL 5.4 - 2D Arrangements
Namespaces | Classes | Typedefs | Enumerations | Functions | Variables
CGAL Namespace Reference

Namespaces

 cpp11
 
 cpp98
 
 IO
 
 Regularized_boolean_set_operations_2
 

Classes

class  Aff_transformation_2
 
class  Aff_transformation_3
 
class  Algebraic_kernel_d_1
 
class  Algebraic_kernel_d_2
 
struct  Algebraic_kernel_for_circles_2_2
 
class  Algebraic_kernel_rs_gmpq_d_1
 
class  Algebraic_kernel_rs_gmpz_d_1
 
class  Algebraic_structure_traits
 
struct  Ambient_dimension
 
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_bounded_planar_topology_traits_2
 
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_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_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
 
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...
 
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...
 
class  Arr_observer
 
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
 
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
 
class  Arr_triangulation_point_location
 
class  Arr_unb_planar_topology_traits_2
 
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  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
 
class  Arrangement_on_surface_2
 
class  Arrangement_on_surface_with_history_2
 
class  Arrangement_with_history_2
 
class  Bbox_2
 
class  Bbox_3
 
struct  Bidirectional_circulator_base
 
class  Bidirectional_circulator_ptrbase
 
struct  Bidirectional_circulator_tag
 
struct  Boolean_tag
 
struct  Cartesian
 
class  Cartesian_converter
 
struct  Cast_function_object
 
class  CC_safe_handle
 
class  Circle_2
 
class  Circle_3
 
class  Circular_arc_2
 
class  Circular_arc_point_2
 
struct  Circular_kernel_2
 
struct  Circulator_base
 
class  Circulator_from_container
 
class  Circulator_from_iterator
 
struct  Circulator_tag
 
struct  Circulator_traits
 
struct  Coercion_traits
 
struct  Compact
 
class  Compact_container
 
class  Compact_container_base
 
struct  Compact_container_traits
 
class  Compare_to_less
 
class  Concurrent_compact_container
 
struct  Concurrent_compact_container_traits
 
class  Const_oneset_iterator
 
struct  Construct_array
 
class  Container_from_circulator
 
class  Counting_iterator
 
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
 
struct  Default
 
struct  Dereference
 
struct  Dimension_tag
 
class  Direction_2
 
class  Direction_3
 
class  Dispatch_or_drop_output_iterator
 
class  Dispatch_output_iterator
 
class  Dual
 
struct  Dynamic_dimension_tag
 
struct  dynamic_edge_property_t
 
struct  dynamic_face_property_t
 
struct  dynamic_halfedge_property_t
 
struct  dynamic_vertex_property_t
 
struct  Emptyset_iterator
 
struct  Euclidean_ring_tag
 
class  Exact_circular_kernel_2
 
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  Face_around_face_circulator
 
class  Face_around_face_iterator
 
class  Face_around_target_circulator
 
class  Face_around_target_iterator
 
struct  Face_filtered_graph
 
struct  Fast
 
struct  Feature_dimension
 
struct  Field_tag
 
struct  Field_with_kth_root_tag
 
struct  Field_with_root_of_tag
 
struct  Field_with_sqrt_tag
 
struct  Filter_iterator
 
struct  Filtered_kernel
 
struct  Filtered_kernel_adaptor
 
class  Filtered_predicate
 
struct  Forward_circulator_base
 
class  Forward_circulator_ptrbase
 
struct  Forward_circulator_tag
 
class  Fourtuple
 
class  Fraction_traits
 
class  General_polygon_2
 
class  General_polygon_set_2
 
struct  Get_address
 
class  Gmpfi
 
class  Gmpfr
 
class  Gmpq
 
class  Gmpz
 
class  Gmpzf
 
class  Gps_circle_segment_traits_2
 
class  Gps_default_dcel
 
class  Gps_face_base
 
class  Gps_halfedge_base
 
class  Gps_segment_traits_2
 
class  Gps_traits_2
 
struct  graph_has_property
 
struct  Graph_with_descriptor_with_graph
 
struct  Graph_with_descriptor_with_graph_property_map
 
class  Halfedge_around_face_circulator
 
class  Halfedge_around_face_iterator
 
class  Halfedge_around_source_circulator
 
class  Halfedge_around_source_iterator
 
class  Halfedge_around_target_circulator
 
class  Halfedge_around_target_iterator
 
class  HalfedgeDS_face_max_base_with_id
 
class  HalfedgeDS_halfedge_max_base_with_id
 
class  HalfedgeDS_vertex_max_base_with_id
 
struct  Hilbert_policy
 
class  Hilbert_sort_2
 
class  Hilbert_sort_3
 
class  Hilbert_sort_d
 
class  Hilbert_sort_on_sphere_3
 
struct  Homogeneous
 
class  Homogeneous_converter
 
struct  Identity
 
class  Identity_transformation
 
class  In_place_list
 
class  In_place_list_base
 
class  Input_rep
 
class  Insert_iterator
 
struct  Integral_domain_tag
 
struct  Integral_domain_without_division_tag
 
class  Interval_nt
 
class  Inverse_index
 
class  Is_valid
 
class  Iso_cuboid_3
 
class  Iso_rectangle_2
 
class  Istream_iterator
 
class  Iterator_range
 
struct  Iterator_tag
 
class  Join_input_iterator_1
 
class  Join_input_iterator_2
 
class  Join_input_iterator_3
 
struct  Kernel_traits
 
class  Lazy_exact_nt
 
class  Line_2
 
class  Line_3
 
class  Line_arc_2
 
struct  Linear_cell_complex_bgl_min_items
 
struct  Linear_cell_complex_for_bgl_combinatorial_map_helper
 
struct  Location_policy
 
struct  Max
 
struct  Median
 
struct  Middle
 
struct  Min
 
class  MP_Float
 
struct  Mpzf
 
class  Multiscale_sort
 
class  Multiset
 
class  N_step_adaptor
 
struct  NT_converter
 
struct  Null_functor
 
struct  Null_tag
 
class  Null_vector
 
class  Number_type_checker
 
class  Object
 
class  Oneset_iterator
 
class  Origin
 
class  Ostream_iterator
 
class  Output_rep
 
struct  Parallel_if_available_tag
 
struct  Parallel_tag
 
class  Plane_3
 
class  Point_2
 
class  Point_3
 
class  Polygon_set_2
 
class  Polyhedron_3
 
class  Polyhedron_incremental_builder_3
 
class  Polyhedron_items_3
 
class  Polyhedron_items_with_id_3
 
class  Polyhedron_min_items_3
 
class  Polyhedron_traits_3
 
class  Polyhedron_traits_with_normals_3
 
class  Polynomial_1_2
 
class  Polynomial_for_circles_2_2
 
struct  Project_facet
 
struct  Project_next
 
struct  Project_next_opposite
 
struct  Project_normal
 
struct  Project_opposite_prev
 
struct  Project_plane
 
struct  Project_point
 
struct  Project_prev
 
struct  Project_vertex
 
class  Projection_traits_3
 
class  Projection_traits_xy_3
 
class  Projection_traits_xz_3
 
class  Projection_traits_yz_3
 
struct  Protect_FPU_rounding
 
class  Quadruple
 
class  Quotient
 
class  Random_access_adaptor
 
struct  Random_access_circulator_base
 
class  Random_access_circulator_ptrbase
 
struct  Random_access_circulator_tag
 
class  Random_access_value_adaptor
 
class  Rational_traits
 
class  Ray_2
 
class  Ray_3
 
class  Real_embeddable_traits
 
class  Reflection
 
class  Root_for_circles_2_2
 
struct  Root_of_traits
 
class  Rotation
 
class  Scaling
 
class  Seam_mesh
 
class  Segment_2
 
class  Segment_3
 
struct  Sequential_tag
 
class  Set_ieee_double_precision
 
struct  Simple_cartesian
 
struct  Simple_homogeneous
 
class  Sixtuple
 
class  Spatial_lock_grid_3
 
class  Spatial_sort_traits_adapter_2
 
class  Spatial_sort_traits_adapter_3
 
class  Spatial_sort_traits_adapter_d
 
class  Sphere_3
 
class  Sqrt_extension
 
class  Tetrahedron_3
 
class  Threetuple
 
class  Translation
 
class  Triangle_2
 
class  Triangle_3
 
class  Triangulation_data_structure_2
 
class  Triangulation_ds_face_base_2
 
class  Triangulation_ds_vertex_base_2
 
class  Triangulation_face_base_with_id_2
 
class  Triangulation_vertex_base_with_id_2
 
class  Triple
 
class  Twotuple
 
class  Uncertain
 
struct  Unique_factorization_domain_tag
 
struct  value_type_traits
 
struct  value_type_traits< std::back_insert_iterator< Container > >
 
struct  value_type_traits< std::front_insert_iterator< Container > >
 
struct  value_type_traits< std::insert_iterator< Container > >
 
class  Vector_2
 
class  Vector_3
 
class  Verbose_ostream
 
class  Vertex_around_face_iterator
 
class  Vertex_around_target_circulator
 
class  Vertex_around_target_iterator
 
class  Weighted_point_2
 
class  Weighted_point_3
 

Typedefs

typedef Sign Orientation
 
typedef Location_policy< Compact > Compact_location
 
typedef Location_policy< Fast > Fast_location
 
typedef CGAL::Boolean_tag< false > Tag_false
 
typedef CGAL::Boolean_tag< true > Tag_true
 
typedef void(* Failure_function) (const char *type, const char *expression, const char *file, int line, const char *explanation)
 
typedef Interval_nt< false > Interval_nt_advanced
 
typedef unspecified_type Exact_integer
 
typedef unspecified_type Exact_rational
 
typedef Hilbert_policy< Median > Hilbert_sort_median_policy
 
typedef Hilbert_policy< Middle > Hilbert_sort_middle_policy
 
typedef Box_parameter_space_2 Arr_parameter_space
 

Enumerations

enum  Angle
 
enum  Bounded_side
 
enum  Comparison_result
 
enum  Sign
 
enum  Oriented_side
 
enum  Box_parameter_space_2
 
enum  Failure_behaviour
 
enum  vertex_index_t
 
enum  halfedge_index_t
 
enum  edge_index_t
 
enum  face_index_t
 
enum  vertex_point_t
 
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

std::string data_file_path (const std::string &filename)
 
bool do_intersect (const Polygon1 &p1, const Polygon2 &p2)
 
T enum_cast (const U &u)
 
Oriented_side opposite (const Oriented_side &o)
 
Bounded_side opposite (const Bounded_side &o)
 
bool do_intersect (Type1< Kernel > obj1, Type2< Kernel > obj2)
 
bool do_intersect (Plane_3< Kernel > obj1, Plane_3< Kernel > obj2, Plane_3< Kernel > obj3)
 
decltype(auto) intersection (Type1< Kernel > obj1, Type2< Kernel > obj2)
 
decltype(auto) intersection (const Plane_3< Kernel > &pl1, const Plane_3< Kernel > &pl2, const Plane_3< Kernel > &pl3)
 
Angle angle (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v)
 
Angle angle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
Angle angle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
 
Angle angle (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v)
 
Angle angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
Angle angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
Angle angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Vector_3< Kernel > &v)
 
Kernel::FT approximate_angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
Kernel::FT approximate_angle (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v)
 
Kernel::FT approximate_dihedral_angle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
Kernel::FT area (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool are_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool are_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
bool are_strictly_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool are_strictly_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
CGAL::Point_2< Kernel > barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2)
 
CGAL::Point_2< Kernel > barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2)
 
CGAL::Point_2< Kernel > barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3)
 
CGAL::Point_2< Kernel > barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3)
 
CGAL::Point_2< Kernel > barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_2< Kernel > &p4)
 
CGAL::Point_2< Kernel > barycenter (const CGAL::Point_2< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_2< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_2< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_2< Kernel > &p4, const Kernel::FT &w4)
 
CGAL::Point_3< Kernel > barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2)
 
CGAL::Point_3< Kernel > barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2)
 
CGAL::Point_3< Kernel > barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3)
 
CGAL::Point_3< Kernel > barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3)
 
CGAL::Point_3< Kernel > barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_3< Kernel > &p4)
 
CGAL::Point_3< Kernel > barycenter (const CGAL::Point_3< Kernel > &p1, const Kernel::FT &w1, const CGAL::Point_3< Kernel > &p2, const Kernel::FT &w2, const CGAL::Point_3< Kernel > &p3, const Kernel::FT &w3, const CGAL::Point_3< Kernel > &p4, const Kernel::FT &w4)
 
CGAL::Line_2< Kernel > bisector (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
CGAL::Line_2< Kernel > bisector (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
 
CGAL::Plane_3< Kernel > bisector (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
CGAL::Plane_3< Kernel > bisector (const CGAL::Plane_3< Kernel > &h1, const CGAL::Plane_3< Kernel > &h2)
 
CGAL::Point_2< Kernel > centroid (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
CGAL::Point_2< Kernel > centroid (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
 
CGAL::Point_2< Kernel > centroid (const CGAL::Triangle_2< Kernel > &t)
 
CGAL::Point_3< Kernel > centroid (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
CGAL::Point_3< Kernel > centroid (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
CGAL::Point_3< Kernel > centroid (const CGAL::Triangle_3< Kernel > &t)
 
CGAL::Point_3< Kernel > centroid (const CGAL::Tetrahedron_3< Kernel > &t)
 
CGAL::Point_2< Kernel > circumcenter (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
CGAL::Point_2< Kernel > circumcenter (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
CGAL::Point_2< Kernel > circumcenter (const CGAL::Triangle_2< Kernel > &t)
 
CGAL::Point_3< Kernel > circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
CGAL::Point_3< Kernel > circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
CGAL::Point_3< Kernel > circumcenter (const CGAL::Triangle_3< Kernel > &t)
 
CGAL::Point_3< Kernel > circumcenter (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
CGAL::Point_3< Kernel > circumcenter (const CGAL::Tetrahedron_3< Kernel > &t)
 
bool collinear_are_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool collinear_are_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
bool collinear_are_strictly_ordered_along_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool collinear_are_strictly_ordered_along_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
bool collinear (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool collinear (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
Comparison_result compare_dihedral_angle (const CGAL::Point_3< Kernel > &a1, const CGAL::Point_3< Kernel > &b1, const CGAL::Point_3< Kernel > &c1, const CGAL::Point_3< Kernel > &d1, const Kernel::FT &cosine)
 
Comparison_result compare_dihedral_angle (const CGAL::Point_3< Kernel > &a1, const CGAL::Point_3< Kernel > &b1, const CGAL::Point_3< Kernel > &c1, const CGAL::Point_3< Kernel > &d1, const CGAL::Point_3< Kernel > &a2, const CGAL::Point_3< Kernel > &b2, const CGAL::Point_3< Kernel > &c2, const CGAL::Point_3< Kernel > &d2)
 
Comparison_result compare_dihedral_angle (const CGAL::Vector_3< Kernel > &u1, const CGAL::Vector_3< Kernel > &v1, const CGAL::Vector_3< Kernel > &w1, const Kernel::FT &cosine)
 
Comparison_result compare_dihedral_angle (const CGAL::Vector_3< Kernel > &u1, const CGAL::Vector_3< Kernel > &v1, const CGAL::Vector_3< Kernel > &w1, const CGAL::Vector_3< Kernel > &u2, const CGAL::Vector_3< Kernel > &v2, const CGAL::Vector_3< Kernel > &w2)
 
Comparison_result compare_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
Comparison_result compare_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
Comparison_result compare_lexicographically (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
Comparison_result compare_lexicographically (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
Comparison_result compare_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
Comparison_result compare_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
 
Comparison_result compare_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
Comparison_result compare_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t)
 
Comparison_result compare_slope (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
 
Comparison_result compare_slope (const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2)
 
Comparison_result compare_slope (const CGAL::Point_2< Kernel > &s1s, const CGAL::Point_2< Kernel > &s1t, const CGAL::Point_2< Kernel > &s2s, const CGAL::Point_2< Kernel > &s2t)
 
Comparison_result compare_slope (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
Comparison_result compare_squared_distance (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const typename Kernel::FT &d2)
 
Comparison_result compare_squared_distance (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const typename Kernel::FT &d2)
 
Comparison_result compare_squared_radius (const CGAL::Point_3< Kernel > &p, const typename Kernel::FT &sr)
 
Comparison_result compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const typename Kernel::FT &sr)
 
Comparison_result compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const typename Kernel::FT &sr)
 
Comparison_result compare_squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const typename Kernel::FT &sr)
 
Comparison_result compare_x (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
Comparison_result compare_x (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
Comparison_result compare_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
 
Comparison_result compare_x (const CGAL::Line_2< Kernel > &l, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
 
Comparison_result compare_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
 
Comparison_result compare_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q)
 
Comparison_result compare_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q)
 
Comparison_result compare_x (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
 
Comparison_result compare_x (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
 
Comparison_result compare_xy (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
Comparison_result compare_xy (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
Comparison_result compare_xy (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q)
 
Comparison_result compare_xy (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q)
 
Comparison_result compare_xy (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
 
Comparison_result compare_xy (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
 
Comparison_result compare_x_at_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h)
 
Comparison_result compare_x_at_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
 
Comparison_result compare_x_at_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h)
 
Comparison_result compare_x_at_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
 
Comparison_result compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h)
 
Comparison_result compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
 
Comparison_result compare_y_at_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h)
 
Comparison_result compare_y_at_x (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
 
Comparison_result compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Segment_2< Kernel > &s)
 
Comparison_result compare_y_at_x (const CGAL::Point_2< Kernel > &p, const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2)
 
Comparison_result compare_y (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
Comparison_result compare_y (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
Comparison_result compare_y (const CGAL::Point_2< Kernel > &p, const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
 
Comparison_result compare_y (const CGAL::Line_2< Kernel > &l, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
 
Comparison_result compare_y (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2, const CGAL::Line_2< Kernel > &h1, const CGAL::Line_2< Kernel > &h2)
 
Comparison_result compare_y (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_point_2< CircularKernel > &q)
 
Comparison_result compare_y (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Point_2< CircularKernel > &q)
 
Comparison_result compare_y (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
 
Comparison_result compare_y (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
 
Comparison_result compare_xyz (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
Comparison_result compare_xyz (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
 
Comparison_result compare_xyz (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
 
Comparison_result compare_z (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
Comparison_result compare_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Circular_arc_point_3< SphericalKernel > &q)
 
Comparison_result compare_z (const CGAL::Circular_arc_point_3< SphericalKernel > &p, const CGAL::Point_3< SphericalKernel > &q)
 
Comparison_result compare_yx (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool coplanar (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
Orientation coplanar_orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
Orientation coplanar_orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
Bounded_side coplanar_side_of_bounded_circle (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
CGAL::Vector_3< Kernel > cross_product (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v)
 
Kernel::FT determinant (const CGAL::Vector_2< Kernel > &v, const CGAL::Vector_2< Kernel > &w)
 
Kernel::FT determinant (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v, const CGAL::Vector_3< Kernel > &w)
 
CGAL::Line_3< Kernel > equidistant_line (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
bool has_larger_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool has_larger_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
bool has_larger_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool has_larger_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
 
bool has_larger_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
bool has_larger_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t)
 
bool has_smaller_distance_to_point (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool has_smaller_distance_to_point (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
bool has_smaller_signed_distance_to_line (const CGAL::Line_2< Kernel > &l, const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool has_smaller_signed_distance_to_line (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &s)
 
bool has_smaller_signed_distance_to_plane (const CGAL::Plane_3< Kernel > &h, const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
bool has_smaller_signed_distance_to_plane (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t)
 
Kernel::FT l_infinity_distance (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
Kernel::FT l_infinity_distance (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
bool left_turn (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
bool lexicographically_xy_larger (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool lexicographically_xy_larger_or_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool lexicographically_xy_smaller (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool lexicographically_xy_smaller_or_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool lexicographically_xyz_smaller (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
bool lexicographically_xyz_smaller_or_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
CGAL::Point_2< Kernel > max_vertex (const CGAL::Iso_rectangle_2< Kernel > &ir)
 
CGAL::Point_3< Kernel > max_vertex (const CGAL::Iso_cuboid_3< Kernel > &ic)
 
CGAL::Point_2< Kernel > midpoint (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
CGAL::Point_2< Kernel > midpoint (const CGAL::Segment_2< Kernel > &s)
 
CGAL::Point_3< Kernel > midpoint (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
CGAL::Point_3< Kernel > midpoint (const CGAL::Segment_3< Kernel > &s)
 
CGAL::Point_2< Kernel > min_vertex (const CGAL::Iso_rectangle_2< Kernel > &ir)
 
CGAL::Point_3< Kernel > min_vertex (const CGAL::Iso_cuboid_3< Kernel > &ic)
 
CGAL::Vector_3< Kernel > normal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
Orientation orientation (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
Orientation orientation (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v)
 
Orientation orientation (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
Orientation orientation (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v, const CGAL::Vector_3< Kernel > &w)
 
CGAL::Vector_3< Kernel > orthogonal_vector (const CGAL::Plane_3< Kernel > &p)
 
CGAL::Vector_3< Kernel > orthogonal_vector (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
bool parallel (const CGAL::Line_2< Kernel > &l1, const CGAL::Line_2< Kernel > &l2)
 
bool parallel (const CGAL::Ray_2< Kernel > &r1, const CGAL::Ray_2< Kernel > &r2)
 
bool parallel (const CGAL::Segment_2< Kernel > &s1, const CGAL::Segment_2< Kernel > &s2)
 
bool parallel (const CGAL::Line_3< Kernel > &l1, const CGAL::Line_3< Kernel > &l2)
 
bool parallel (const CGAL::Plane_3< Kernel > &h1, const CGAL::Plane_3< Kernel > &h2)
 
bool parallel (const CGAL::Ray_3< Kernel > &r1, const CGAL::Ray_3< Kernel > &r2)
 
bool parallel (const CGAL::Segment_3< Kernel > &s1, const CGAL::Segment_3< Kernel > &s2)
 
CGAL::Plane_3< Kernel > radical_plane (const CGAL::Sphere_3< Kernel > &s1, const CGAL::Sphere_3< Kernel > &s2)
 
CGAL::Line_2< Kernel > radical_line (const CGAL::Circle_2< Kernel > &c1, const CGAL::Circle_2< Kernel > &c2)
 
bool right_turn (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
Kernel::FT scalar_product (const CGAL::Vector_2< Kernel > &u, const CGAL::Vector_2< Kernel > &v)
 
Kernel::FT scalar_product (const CGAL::Vector_3< Kernel > &u, const CGAL::Vector_3< Kernel > &v)
 
Bounded_side side_of_bounded_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &t)
 
Bounded_side side_of_bounded_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &t)
 
Bounded_side side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &t)
 
Bounded_side side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &t)
 
Bounded_side side_of_bounded_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &t)
 
Oriented_side side_of_oriented_circle (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r, const CGAL::Point_2< Kernel > &test)
 
Oriented_side side_of_oriented_sphere (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s, const CGAL::Point_3< Kernel > &test)
 
Kernel::FT squared_area (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
FT squared_radius (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q, const CGAL::Point_2< Kernel > &r)
 
FT squared_radius (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
FT squared_radius (const CGAL::Point_2< Kernel > &p)
 
FT squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r, const CGAL::Point_3< Kernel > &s)
 
FT squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
FT squared_radius (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
FT squared_radius (const CGAL::Point_3< Kernel > &p)
 
CGAL::Vector_3< Kernel > unit_normal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q, const CGAL::Point_3< Kernel > &r)
 
Kernel::FT volume (const CGAL::Point_3< Kernel > &p0, const CGAL::Point_3< Kernel > &p1, const CGAL::Point_3< Kernel > &p2, const CGAL::Point_3< Kernel > &p3)
 
bool x_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool x_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
bool y_equal (const CGAL::Point_2< Kernel > &p, const CGAL::Point_2< Kernel > &q)
 
bool y_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
bool z_equal (const CGAL::Point_3< Kernel > &p, const CGAL::Point_3< Kernel > &q)
 
void rational_rotation_approximation (const RingNumberType &dirx, const RingNumberType &diry, RingNumberType &sin_num, RingNumberType &cos_num, RingNumberType &denom, const RingNumberType &eps_num, const RingNumberType &eps_den)
 
Kernel::FT squared_distance (Type1< Kernel > obj1, Type2< Kernel > obj2)
 
Point_2< Homogeneous< RT > > cartesian_to_homogeneous (const Point_2< Cartesian< RT > > &cp)
 
Point_3< Homogeneous< RT > > cartesian_to_homogeneous (const Point_3< Cartesian< RT > > &cp)
 
Point_2< Cartesian< FT > > homogeneous_to_cartesian (const Point_2< Homogeneous< FT > > &hp)
 
Point_3< Cartesian< FT > > homogeneous_to_cartesian (const Point_3< Homogeneous< FT > > &hp)
 
Point_2< Cartesian< Quotient< RT > > > homogeneous_to_quotient_cartesian (const Point_2< Homogeneous< RT > > &hp)
 
Point_3< Cartesian< Quotient< RT > > > homogeneous_to_quotient_cartesian (const Point_3< Homogeneous< RT > > &hp)
 
Point_2< Homogeneous< RT > > quotient_cartesian_to_homogeneous (const Point_2< Cartesian< Quotient< RT > > > &cp)
 
Point_3< Homogeneous< RT > > quotient_cartesian_to_homogeneous (const Point_3< Cartesian< Quotient< RT > > > &cp)
 
bool do_intersect (Type1< CircularKernel > obj1, Type2< CircularKernel > obj2)
 
OutputIterator intersection (const Type1 &obj1, const Type2 &obj2, OutputIterator intersections)
 
Comparison_result compare_y_at_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Circular_arc_2< CircularKernel > &a)
 
Comparison_result compare_y_at_x (const CGAL::Circular_arc_point_2< CircularKernel > &p, const CGAL::Line_arc_2< CircularKernel > &a)
 
bool do_intersect (Type1< SphericalKernel > obj1, Type2< SphericalKernel > obj2)
 
bool do_intersect (Type1< SphericalKernel > obj1, Type2< SphericalKernel > obj2, Type3< SphericalKernel > obj3)
 
OutputIterator intersection (const SphericalType1 &obj1, const SphericalType2 &obj2, OutputIterator intersections)
 
OutputIterator intersection (const Type1 &obj1, const Type2 &obj2, const Type3 &obj3, OutputIterator intersections)
 
OutputIterator copy_n (InputIterator first, Size n, OutputIterator result)
 
std::pair< ForwardIterator, ForwardIterator > min_max_element (ForwardIterator first, ForwardIterator last)
 
std::pair< ForwardIterator, ForwardIterator > min_max_element (ForwardIterator first, ForwardIterator last, CompareMin comp_min, CompareMax comp_max)
 
BidirectionalIterator predecessor (BidirectionalIterator it)
 
ForwardIterator successor (ForwardIterator it)
 
std::array< T, N > make_array (const T &...)
 
CC_safe_handle< CC_iterator > make_cc_safe_handle (CC_iterator iterator)
 
Compare_to_less< F > compare_to_less (const F &f)
 
Iterator_range< T > make_range (const T &b, const T &e)
 
T range_begin (Iterator_range< T > &x)
 
T range_end (Iterator_range< T > &x)
 
T range_begin (const Iterator_range< T > &x)
 
T range_end (const Iterator_range< T > &x)
 
Failure_function set_error_handler (Failure_function handler)
 
Failure_function set_warning_handler (Failure_function handler)
 
Failure_behaviour set_error_behaviour (Failure_behaviour eb)
 
Failure_behaviour set_warning_behaviour (Failure_behaviour eb)
 
NT abs (const NT &x)
 
result_type compare (const NT &x, const NT &y)
 
result_type div (const NT1 &x, const NT2 &y)
 
void div_mod (const NT1 &x, const NT2 &y, result_type &q, result_type &r)
 
result_type gcd (const NT1 &x, const NT2 &y)
 
result_type integral_division (const NT1 &x, const NT2 &y)
 
NT inverse (const NT &x)
 
result_type is_negative (const NT &x)
 
result_type is_one (const NT &x)
 
result_type is_positive (const NT &x)
 
result_type is_square (const NT &x)
 
result_type is_square (const NT &x, NT &y)
 
result_type is_zero (const NT &x)
 
NT kth_root (int k, const NT &x)
 
result_type mod (const NT1 &x, const NT2 &y)
 
NT root_of (int k, InputIterator begin, InputIterator end)
 
result_type sign (const NT &x)
 
void simplify (const NT &x)
 
NT sqrt (const NT &x)
 
NT square (const NT &x)
 
double to_double (const NT &x)
 
std::pair< double, double > to_interval (const NT &x)
 
NT unit_part (const NT &x)
 
void Assert_circulator (const C &c)
 
void Assert_iterator (const I &i)
 
void Assert_circulator_or_iterator (const IC &i)
 
void Assert_input_category (const I &i)
 
void Assert_output_category (const I &i)
 
void Assert_forward_category (const IC &ic)
 
void Assert_bidirectional_category (const IC &ic)
 
void Assert_random_access_category (const IC &ic)
 
C::difference_type circulator_distance (C c, C d)
 
C::size_type circulator_size (C c)
 
bool is_empty_range (const IC &i, const IC &j)
 
iterator_traits< IC >::difference_type iterator_distance (IC ic1, IC ic2)
 
Iterator_tag query_circulator_or_iterator (const I &i)
 
Circulator_tag query_circulator_or_iterator (const C &c)
 
OutputIterator connect_holes (const Polygon_with_holes_2< Kernel, Container > &pwh, OutputIterator oi)
 
void draw (const PS &aps)
 
bool is_finite (double x)
 
bool is_finite (float x)
 
bool is_finite (long double x)
 
OutputIterator compute_roots_of_2 (const RT &a, const RT &b, const RT &c, OutputIterator oit)
 
Root_of_traits< RT >::Root_of_2 make_root_of_2 (const RT &a, const RT &b, const RT &c, bool s)
 
Root_of_traits< RT >::Root_of_2 make_root_of_2 (RT alpha, RT beta, RT gamma)
 
Root_of_traits< RT >::Root_of_2 make_sqrt (const RT &x)
 
Rational simplest_rational_in_interval (double d1, double d2)
 
Rational to_rational (double d)
 
bool is_valid (const T &x)
 
T max (const T &x, const T &y)
 
T min (const T &x, const T &y)
 
bool has_in_x_range (const Circular_arc_2< CircularKernel > &ca, const Circular_arc_point_2< CircularKernel > &p)
 
bool has_in_x_range (const Line_arc_2< CircularKernel > &ca, const Circular_arc_point_2< CircularKernel > &p)
 
bool has_on (const Circle_2< CircularKernel > &c, const Circular_arc_point_2< CircularKernel > &p)
 
OutputIterator make_x_monotone (const Circular_arc_2< CircularKernel > &ca, OutputIterator res)
 
OutputIterator make_xy_monotone (const Circular_arc_2< CircularKernel > &ca, OutputIterator res)
 
Circular_arc_point_2< CircularKernel > x_extremal_point (const Circle_2< CircularKernel > &c, bool b)
 
OutputIterator x_extremal_points (const Circle_2< CircularKernel > &c, OutputIterator res)
 
Circular_arc_point_2< CircularKernel > y_extremal_point (const Circle_2< CircularKernel > &c, bool b)
 
OutputIterator y_extremal_points (const Circle_2< CircularKernel > &c, OutputIterator res)
 
CGAL::Comparison_result compare_y_to_right (const Circular_arc_2< CircularKernel > &ca1, const Circular_arc_2< CircularKernel > &ca2, Circular_arc_point_2< CircularKernel > &p)
 
void set_halfedgeds_items_id (Polyhedron_with_id &P)
 
void set_triangulation_ids (Triangulation &tr)
 
Iterator_range< Halfedge_around_source_iterator< Graph > > halfedges_around_source (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
 
Iterator_range< Halfedge_around_source_iterator< Graph > > halfedges_around_source (typename boost::graph_traits< Graph >::vertex_descriptor v, const Graph &g)
 
Iterator_range< Halfedge_around_target_iterator< Graph > > halfedges_around_target (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
 
Iterator_range< Halfedge_around_target_iterator< Graph > > halfedges_around_target (typename boost::graph_traits< Graph >::vertex_descriptor v, const Graph &g)
 
Iterator_range< Halfedge_around_face_iterator< Graph > > halfedges_around_face (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
 
Iterator_range< Face_around_target_iterator< Graph > > faces_around_target (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
 
Iterator_range< Face_around_face_iterator< Graph > > faces_around_face (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
 
Iterator_range< Vertex_around_target_iterator< Graph > > vertices_around_target (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
 
Iterator_range< Vertex_around_face_iterator< Graph > > vertices_around_face (typename boost::graph_traits< Graph >::halfedge_descriptor h, const Graph &g)
 
bool is_border (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_border_edge (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_border (typename boost::graph_traits< FaceGraph >::edge_descriptor ed, const FaceGraph &g)
 
boost::optional< typename boost::graph_traits< FaceGraph >::halfedge_descriptor > is_border (typename boost::graph_traits< FaceGraph >::vertex_descriptor vd, const FaceGraph &g)
 
bool is_closed (const FaceGraph &g)
 
bool is_bivalent (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_bivalent_mesh (const FaceGraph &g)
 
bool is_trivalent (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_trivalent_mesh (const FaceGraph &g)
 
bool is_isolated_triangle (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_triangle (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_triangle_mesh (const FaceGraph &g)
 
bool is_isolated_quad (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_quad (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_quad_mesh (const FaceGraph &g)
 
bool is_tetrahedron (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
bool is_valid_halfedge_graph (const Graph &g, bool verb=false)
 
bool is_valid_face_graph (const Graph &g, bool verb=false)
 
bool is_valid_polygon_mesh (const Mesh &g, bool verb=false)
 
bool is_hexahedron (typename boost::graph_traits< FaceGraph >::halfedge_descriptor hd, const FaceGraph &g)
 
void clear (FaceGraph &g)
 
bool is_empty (const FaceGraph &g)
 
int vertex_index_in_face (const typename boost::graph_traits< Graph >::vertex_descriptor vd, const typename boost::graph_traits< Graph >::face_descriptor fd, const Graph &g)
 
int halfedge_index_in_face (typename boost::graph_traits< Graph >::halfedge_descriptor he, const Graph &g)
 
boost::graph_traits< Graph >::halfedge_descriptor make_triangle (const P &p0, const P &p1, const P &p2, Graph &g)
 
boost::graph_traits< Graph >::halfedge_descriptor make_quad (const P &p0, const P &p1, const P &p2, const P &p3, Graph &g)
 
boost::graph_traits< Graph >::halfedge_descriptor make_hexahedron (const P &p0, const P &p1, const P &p2, const P &p3, const P &p4, const P &p5, const P &p6, const P &p7, Graph &g)
 
boost::graph_traits< Graph >::halfedge_descriptor make_tetrahedron (const P &p0, const P &p1, const P &p2, const P &p3, Graph &g)
 
boost::graph_traits< Graph >::halfedge_descriptor make_regular_prism (typename boost::graph_traits< Graph >::vertices_size_type nb_vertices, Graph &g, const P &base_center=P(0, 0, 0), typename CGAL::Kernel_traits< P >::Kernel::FT height=1.0, typename CGAL::Kernel_traits< P >::Kernel::FT radius=1.0, bool is_closed=true)
 
boost::graph_traits< Graph >::halfedge_descriptor make_pyramid (typename boost::graph_traits< Graph >::vertices_size_type nb_vertices, Graph &g, const P &base_center=P(0, 0, 0), typename CGAL::Kernel_traits< P >::Kernel::FT height=1.0, typename CGAL::Kernel_traits< P >::Kernel::FT radius=1.0, bool is_closed=true)
 
boost::graph_traits< Graph >::halfedge_descriptor make_icosahedron (Graph &g, const P &center=P(0, 0, 0), typename CGAL::Kernel_traits< P >::Kernel::FT radius=1.0)
 
boost::graph_traits< Graph >::halfedge_descriptor make_grid (typename boost::graph_traits< Graph >::vertices_size_type i, typename boost::graph_traits< Graph >::vertices_size_type j, Graph &g, const CoordinateFunctor &calculator, bool triangulated=false)
 
OutputIterator expand_face_selection (const FaceRange &selection, FaceGraph &fg, unsigned int k, IsFaceSelectedPMap is_selected, OutputIterator out)
 
OutputIterator reduce_face_selection (const FaceRange &selection, FaceGraph &fg, unsigned int k, IsFaceSelectedPMap is_selected, OutputIterator out)
 
void regularize_face_selection_borders (TriangleMesh &mesh, IsSelectedMap is_selected, double weight, const NamedParameters &np)
 
OutputIterator select_incident_faces (const HalfedgeRange &hedges, FaceGraph &fg, OutputIterator out)
 
OutputIterator expand_edge_selection (const EdgeRange &selection, HalfedgeGraph &fg, unsigned int k, IsEdgeSelectedPMap is_selected, OutputIterator out)
 
OutputIterator reduce_edge_selection (const EdgeRange &selection, HalfedgeGraph &fg, unsigned int k, IsEdgeSelectedPMap is_selected, OutputIterator out)
 
OutputIterator expand_vertex_selection (const VertexRange &selection, HalfedgeGraph &fg, unsigned int k, IsVertexSelectedPMap is_selected, OutputIterator out)
 
OutputIterator reduce_vertex_selection (const VertexRange &selection, HalfedgeGraph &fg, unsigned int k, IsVertexSelectedPMap is_selected, OutputIterator out)
 
void expand_face_selection_for_removal (const FaceRange &faces_to_be_deleted, TriangleMesh &tm, IsSelectedMap is_selected)
 
void split_graph_into_polylines (const Graph &graph, Visitor &polyline_visitor, IsTerminal is_terminal)
 
void copy_face_graph (const SourceMesh &sm, TargetMesh &tm, const NamedParameters1 &np1, const NamedParameters2 &np2)
 
bool read_off (std::istream &is, Graph &g, const NamedParameters &np)
 
bool read_off (const char *fname, Graph &g, const NamedParameters &np)
 
bool write_off (std::ostream &os, const Graph &g, const NamedParameters &np)
 
bool write_off (const char *fname, const Graph &g, const NamedParameters &np)
 
bool write_vtp (std::ostream &os, const Graph &g, const NamedParameters &np)
 
bool write_wrl (std::ostream &os, const Graph &g, const NamedParameters &np)
 
double alpha_expansion_graphcut (const InputGraph &input_graph, EdgeCostMap edge_cost_map, VertexLabelCostMap vertex_label_cost_map, VertexLabelMap vertex_label_map, const NamedParameters &np)
 
void draw (const POLY &apoly)
 
void hilbert_sort (InputPointIterator begin, InputPointIterator end, const Traits &traits=Default_traits, PolicyTag policy=Default_policy)
 
void hilbert_sort_on_sphere (InputPointIterator begin, InputPointIterator end, const Traits &traits=Default_traits, PolicyTag policy=Default_policy, double sqr_radius=1.0, const Traits::Point_3 &center=Default_center)
 
void spatial_sort (InputPointIterator begin, InputPointIterator end, const Traits &traits=Default_traits, PolicyTag policy=Default_policy, std::ptrdiff_t threshold_hilbert=default, std::ptrdiff_t threshold_multiscale=default, double ratio=default)
 
void spatial_sort_on_sphere (InputPointIterator begin, InputPointIterator end, const Traits &traits=Default_traits, PolicyTag policy=Default_policy, double sqr_radius=1.0, const Traits::Point_3 &center=Default_center, std::ptrdiff_t threshold_hilbert=default, std::ptrdiff_t threshold_multiscale=default, double ratio=default)
 
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<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 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<typename Traits , typename Dcel , typename OutputIterator , typename PointLocation >
OutputIterator zone (Arrangement_2< Traits, Dcel > &arr, const typename Traits::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 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. More...
 
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 interior of the given curve is disjoint from all existing arrangement vertices and edges. More...
 
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. More...
 
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. More...
 
template<typename GeometryTraits , typename TopologyTraits >
bool is_valid (const Arrangement_on_surface_2< GeometryTraits, TopologyTraits > &arr)
 Checks the validity of a given arrangement. More...
 
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. More...
 
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. More...
 
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)
 Compute the zone of the given \( x\)-monotone curve in the existing arrangement. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
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. 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)
 
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<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.
 

Variables

 OBTUSE
 
 RIGHT
 
 ACUTE
 
 ON_UNBOUNDED_SIDE
 
 ON_BOUNDARY
 
 ON_BOUNDED_SIDE
 
 SMALLER
 
 EQUAL
 
 LARGER
 
 NEGATIVE
 
 ZERO
 
 POSITIVE
 
 ON_NEGATIVE_SIDE
 
 ON_ORIENTED_BOUNDARY
 
 ON_POSITIVE_SIDE
 
 LEFT_BOUNDARY
 
 RIGHT_BOUNDARY
 
 BOTTOM_BOUNDARY
 
 TOP_BOUNDARY
 
 INTERIOR
 
 EXTERIOR
 
const CGAL::Orientation CLOCKWISE
 
const CGAL::Orientation COUNTERCLOCKWISE
 
const CGAL::Orientation COLLINEAR
 
const CGAL::Orientation LEFT_TURN
 
const CGAL::Orientation RIGHT_TURN
 
const CGAL::Orientation COPLANAR
 
const CGAL::Orientation DEGENERATE
 
const CGAL::Null_vector NULL_VECTOR
 
const CGAL::Origin ORIGIN
 
 ABORT
 
 EXIT
 
 EXIT_WITH_SUCCESS
 
 CONTINUE
 
 THROW_EXCEPTION
 
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
 
class CGAL::Arr_naive_point_location trim_2_object
 
template<typename Traits , typename Dcel , typename Curve , typename PointLocation >
void insert (Arrangement_2< Traits, Dcel > &arr, const Curve &c, const PointLocation &pl=walk_pl)
 % 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, typename Arr_point_location_result< Arrangement_2< Traits, Dcel > >::type obj)
 Inserts the \( x\)-monotone (only) curve xc into the arrangement arr. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...