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	Arr_accessor
class	Arr_algebraic_segment_traits_2
class	Arr_Bezier_curve_traits_2
class	Arr_circle_segment_traits_2
class	Arr_circular_arc_traits_2
class	Arr_circular_line_arc_traits_2
class	Arr_conic_traits_2
class	Arr_consolidated_curve_data_traits_2
class	Arr_curve_data_traits_2
class	Arr_dcel_base
class	Arr_default_dcel
class	Arr_default_overlay_traits
class	Arr_face_overlay_traits
class	Arr_extended_dcel
class	Arr_extended_face
class	Arr_extended_halfedge
class	Arr_extended_vertex
class	Arr_face_extended_dcel
class	Arr_face_index_map
class	Arr_landmarks_point_location
class	Arr_line_arc_traits_2
class	Arr_linear_traits_2
class	Arr_naive_point_location
class	Arr_non_caching_segment_basic_traits_2
class	Arr_non_caching_segment_traits_2
class	Arr_observer
class	Arr_point_location_result
class	Arr_polycurve_traits_2
class	Arr_polyline_traits_2
class	Arr_rational_function_traits_2
class	Arr_segment_traits_2
class	Arr_oblivious_side_tag
class	Arr_open_side_tag
class	Arr_trapezoid_ric_point_location
class	Arr_vertex_index_map
class	Arr_walk_along_line_point_location
class	Arrangement_2
class	Arrangement_with_history_2
class	Arr_extended_dcel_text_formatter
class	Arr_face_extended_text_formatter
class	Arr_text_formatter
class	Arr_with_history_text_formatter
class	Polygon_2
class	Polygon_with_holes_2
class	General_polygon_with_holes_2
class	Partition_is_valid_traits_2
class	Partition_traits_2
class	Is_convex_2
class	Is_vacuously_valid
class	Is_y_monotone_2
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	AABB_polyhedron_segment_primitive
class	AABB_face_graph_triangle_primitive
class	AABB_traits
class	AABB_polyhedron_triangle_primitive
struct	AABB_primitive
class	AABB_segment_primitive
class	AABB_tree
class	AABB_halfedge_graph_segment_primitive
class	AABB_triangle_primitive
class	Constrained_Delaunay_triangulation_2
struct	No_intersection_tag
struct	Exact_intersections_tag
struct	Exact_predicates_tag
class	Constrained_triangulation_2
class	Constrained_triangulation_face_base_2
class	Constrained_triangulation_plus_2
class	Delaunay_triangulation_2
class	Regular_triangulation_2
class	Regular_triangulation_euclidean_traits_2
class	Regular_triangulation_face_base_2
class	Regular_triangulation_filtered_traits_2
class	Regular_triangulation_vertex_base_2
class	Triangulation_2
class	Triangulation_cw_ccw_2
class	Triangulation_euclidean_traits_2
class	Triangulation_face_base_2
class	Triangulation_face_base_with_info_2
class	Triangulation_hierarchy_2
class	Triangulation_hierarchy_vertex_base_2
class	Triangulation_vertex_base_2
class	Triangulation_vertex_base_with_info_2
class	Weighted_point
class	Greene_convex_decomposition_2
	The Greene_convex_decomposition_2 class implements the approximation algorithm of Greene for the decomposition of an input polygon into convex sub-polygons. More...
class	Hertel_Mehlhorn_convex_decomposition_2
	The Hertel_Mehlhorn_convex_decomposition_2 class implements the approximation algorithm of Hertel and Mehlhorn for decomposing a polygon into convex sub-polygons. More...
class	Optimal_convex_decomposition_2
	The Optimal_convex_decomposition_2 class provides an implementation of Greene's dynamic programming algorithm for optimal decomposition of a polygon into convex sub-polygons. More...
class	Polygon_nop_decomposition_2
	The Polygon_nop_decomposition_2 class implements a convex decomposition of a polygon, which merely passes the input polygon to the list of output convex polygons. More...
class	Polygon_triangulation_decomposition_2
	The Polygon_triangulation_decomposition_2 class implements a convex decomposition of a polygon or a polygon with holes into triangles using the Delaunay constrained triangulation functionality of the 2D Triangulation package. More...
class	Polygon_vertical_decomposition_2
	The Polygon_vertical_decomposition_2 class implements a convex decompistion of a polygon or a polygon with holes into pseudo trapezoids utilizing the CGAL::decompose() free function of the 2D Arrangements package. More...
class	Small_side_angle_bisector_decomposition_2
	The Small_side_angle_bisector_decomposition_2 class implements a simple yet efficient heuristic for decomposing an input polygon into convex sub-polygons. More...

Functions
template<class Kernel , class Container , class OutputIterator >
OutputIterator	approximated_inset_2 (const Polygon_2< Kernel, Container > &pgn, const typename Kernel::FT &r, const double &eps, OutputIterator oi)
	Provides a guaranteed approximation of the inset, or inner offset, of the given polygon P by a given radius r. More...
template<class Kernel , class Container >
Gps_circle_segment_traits_2 < Kernel > ::Polygon_with_holes_2	approximated_offset_2 (const Polygon_2< Kernel, Container > &P, const typename Kernel::FT &r, const double &eps)
	Provides a guaranteed approximation of the offset of the given polygon P by a given radius r - namely, the function computes the Minkowski sum \( P \oplus B_r\), where \( B_r\) is a disc of radius r centered at the origin. More...
template<class Kernel , class Container >
Gps_circle_segment_traits_2 < Kernel > ::Polygon_with_holes_2	approximated_offset_2 (const Polygon_with_holes_2< Kernel, Container > &wh, const typename Kernel::FT &r, const double &eps)
	Provides a guaranteed approximation of offset the given polygon with holes pwh by a given radius r, such that the approximation error is bounded by eps. More...
template<class Kernel , class Container , class DecompositionStrategy >
Gps_circle_segment_traits_2 < Kernel > ::Polygon_with_holes_2	approximated_offset_2 (const Polygon_2< Kernel, Container > &P, const typename Kernel::FT &r, const double &eps, const DecompositionStrategy &decomp)
	Provides a guaranteed approximation of the offset of the given polygon P by a radius r, as described above. More...
template<typename Kernel , typename Container >
Polygon_with_holes_2< Kernel, Container >	minkowski_sum_2 (const PolygonType1< Kernel, Container > &P, const PolygonType2< Kernel, Container > &Q)
	Computes the Minkowski sum \( P \oplus Q\) of two given polygons (which may have holes). More...
template<typename Kernel , typename Container >
Polygon_with_holes_2< Kernel, Container >	minkowski_sum_by_reduced_convolution_2 (const PolygonType1< Kernel, Container > &P, const PolygonType2< Kernel, Container > &Q)
	Computes the Minkowski sum \( P \oplus Q\) of the two given polygons. More...
template<typename Kernel , typename Container >
Polygon_with_holes_2< Kernel, Container >	minkowski_sum_by_full_convolution_2 (const Polygon_2< Kernel, Container > &P, const Polygon_2< Kernel, Container > &Q)
	Computes the Minkowski sum \( P \oplus Q\) of the two given polygons. More...
template<typename Kernel , typename Container , typename PolygonConvexDecompositionP_2_ , typename PolygonConvexDecompositionQ_2_ >
Polygon_with_holes_2< Kernel, Container >	minkowski_sum_2 (const PolygonType1< Kernel, Container > &P, const PolygonType2< Kernel, Container > &Q, const PolygonConvexDecompositionP_2_ &decomp_P, const PolygonConvexDecompositionQ_2_ &decomp_Q, const Gps_segment_traits_2 &traits=Gps_segment_traits_2< Kernel, Container, Arr_segment_traits >())
	Computes the Minkowski sum \( P \oplus Q\) of the two given polygons. More...
template<typename Kernel , typename Container , typename PolygonConvexDecomposition_2_ >
Polygon_with_holes_2< Kernel, Container >	minkowski_sum_2 (const PolygonType1< Kernel, Container > &P, const PolygonType2< Kernel, Container > &Q, const PolygonConvexDecomposition_2_ &decomp, const Gps_segment_traits_2 &traits=Gps_segment_traits_2< Kernel, Container, Arr_segment_traits >())
	Computes the Minkowski sum \( P \oplus Q\) of the two given polygons. More...
template<typename Kernel , typename Container , typename PolygonNoHolesConvexDecomposition_2_ , typename PolygonWithHolesConvexDecomposition_2_ >
Polygon_with_holes_2< Kernel, Container >	minkowski_sum_by_decomposition_2 (const PolygonType1< Kernel, Container > &P, const PolygonType2< Kernel, Container > &Q, const PolygonNoHolesConvexDecomposition_2_ &no_holes_decomp, const PolygonWithHolesConvexDecomposition_2_ &with_holes_decomp, const Gps_segment_traits_2 &traits=Gps_segment_traits_2< Kernel, Container, Arr_segment_traits >())
	Computes the Minkowski sum \( P \oplus Q\) of the two given polygons using the decomposition strategy. More...
template<class ConicTraits , class Container , class OutputIterator >
OutputIterator	inset_polygon_2 (const Polygon_2< typename ConicTraits::Rat_kernel, Container > &P, const typename ConicTraits::Rat_kernel::FT &r, const ConicTraits &traits, OutputIterator oi)
	Computes the inset, or inner offset, of the given polygon P by a given radius r - namely, the function computes the set of points inside the polygon whose distance from \( P\)'s boundary is at least \( r\): \( \{ p \in P \;|\; {\rm dist}(p, \partial P) \geq r \}\). More...
template<class ConicTraits , class Container >
Gps_traits_2< ConicTraits > ::Polygon_with_holes_2	offset_polygon_2 (const Polygon_2< typename ConicTraits::Rat_kernel, Container > &P, const typename ConicTraits::Rat_kernel::FT &r, const ConicTraits &traits)
	Computes the offset of the given polygon P by a given radius r - namely, the function computes the Minkowski sum \( P \oplus B_r\), where \( B_r\) is a disc of radius r centered at the origin. More...
template<class ConicTraits , class Container >
Gps_traits_2< ConicTraits > ::Polygon_with_holes_2	offset_polygon_2 (const Polygon_with_holes_2< typename ConicTraits::Rat_kernel, Container > &pwh, const typename ConicTraits::Rat_kernel::FT &r, const ConicTraits &traits)
	Computes the offset of the given polygon with holes pwh by a given radius r. More...
template<class ConicTraits , class Container , class DecompositionStrategy >
Gps_traits_2< ConicTraits > ::Polygon_with_holes_2	offset_polygon_2 (const Polygon_2< typename ConicTraits::Rat_kernel, Container > &P, const typename ConicTraits::Rat_kernel::FT &r, const DecompositionStrategy &decomp, const ConicTraits &traits)
	Computes the exact representation of the offset of the given polygon P by a radius r, as described above. More...