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	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	Delaunay_triangulation

class	Regular_triangulation

class	Regular_triangulation_traits_adapter

class	Triangulation

class	Triangulation_data_structure

class	Triangulation_ds_full_cell

class	Triangulation_ds_vertex

class	Triangulation_face

class	Triangulation_full_cell

class	Triangulation_vertex

class	Euclidean_distance

class	Euclidean_distance_sphere_point

class	Fuzzy_iso_box

class	Fuzzy_sphere

class	Incremental_neighbor_search

class	K_neighbor_search

class	Kd_tree

class	Kd_tree_node

class	Kd_tree_leaf_node

class	Kd_tree_internal_node

class	Kd_tree_rectangle

class	Manhattan_distance_iso_box_point

class	Orthogonal_incremental_neighbor_search

class	Orthogonal_k_neighbor_search

class	Plane_separator

class	Point_container

class	Search_traits

class	Search_traits_2

class	Search_traits_3

class	Distance_adapter

class	Search_traits_adapter

class	Search_traits_d

class	Fair

class	Median_of_max_spread

class	Median_of_rectangle

class	Midpoint_of_max_spread

class	Midpoint_of_rectangle

class	Sliding_fair

class	Sliding_midpoint

class	Weighted_Minkowski_distance

class	Cartesian_d
	A model for `Kernel_d` (and even `KernelWithLifting_d`) that uses Cartesian coordinates to represent the geometric objects. More...

class	Epick_d
	A model for `Kernel_d` that uses Cartesian coordinates to represent the geometric objects. More...

class	Homogeneous_d
	A model for a `Kernel_d` (and even `KernelWithLifting_d`) using homogeneous coordinates to represent the geometric objects. More...

class	Aff_transformation_d
	An instance of the data type `Aff_transformation_d<Kernel>` is an affine transformation of $d$ -dimensional space. More...

class	Direction_d
	A `Direction_d` is a vector in the $d$ -dimensional vector space where we forget about its length. More...

class	Hyperplane_d
	An instance of data type `Hyperplane_d` is an oriented hyperplane in $d$ - dimensional space. More...

class	Iso_box_d
	An object $b$ of the data type `Iso_box_d` is an iso-box in the Euclidean space $\E^d$ with edges parallel to the axes of the coordinate system. More...

class	Line_d
	An instance of data type `Line_d` is an oriented line in $d$ -dimensional Euclidean space. More...

class	Point_d
	An instance of data type `Point_d<Kernel>` is a point of Euclidean space in dimension $d$ . More...

class	Ray_d
	An instance of data type `Ray_d` is a ray in $d$ -dimensional Euclidean space. More...

class	Segment_d
	An instance $s$ of the data type `Segment_d` is a directed straight line segment in $d$ -dimensional Euclidean space connecting two points $p$ and $q$ . More...

class	Sphere_d
	An instance $S$ of the data type `Sphere_d` is an oriented sphere in some $d$ -dimensional space. More...

class	Vector_d
	An instance of data type `Vector_d<Kernel>` is a vector of Euclidean space in dimension $d$ . More...

class	Linear_algebraCd
	The class `Linear_algebraCd` serves as the default traits class for the LA parameter of `CGAL::Cartesian_d<FT,LA>`. More...

class	Linear_algebraHd
	The class `Linear_algebraHd` serves as the default traits class for the LA parameter of `CGAL::Homogeneous_d<RT,LA>`. More...

Functions
template<class ForwardIterator >
Point_d< R >	center_of_sphere (ForwardIterator first, ForwardIterator last)
	returns the center of the sphere spanned by the points in `A = tuple[first,last)`. More...

Point_d< R >	lift_to_paraboloid (const Point_d< R > &p)
	returns the projection of $p = (x_0,\ldots,x_{d-1})$ onto the paraboloid of revolution which is the point $(p_0, \ldots,p_{d-1},\sum_{0 \le i < d}p_i^2)$ in $(d+1)$ -space.

template<class ForwardIterator , class OutputIterator >
OutputIterator	linear_base (ForwardIterator first, ForwardIterator last, OutputIterator result)
	computes a basis of the linear space spanned by the vectors in `A = tuple [first,last)` and returns it via an iterator range starting in `result`. More...

Point_d< R >	midpoint (const Point_d< R > &p, const Point_d< R > &q)
	computes the midpoint of the segment $pq$ . More...

Point_d< R >	project_along_d_axis (const Point_d< R > &p)
	returns $p$ projected along the $d$ -axis onto the hyperspace spanned by the first $d-1$ standard base vectors.

FT	squared_distance (Point_d< R > p, Point_d< R > q)
	computes the square of the Euclidean distance between the two points $p$ and $q$ . More...

bool	do_intersect (Type1< R > obj1, Type2< R > obj2)
	checks whether `obj1` and `obj2` intersect. More...

cpp11::result_of < R::Intersect_d(Type1< R > , Type2< R >)>::type	intersection (Type1< R > f1, Type2< R > f2)
	returns the intersection between `f1` and `f2`. More...

template<class ForwardIterator >
bool	affinely_independent (ForwardIterator first, ForwardIterator last)
	returns true iff the points in `A = tuple [first,last)` are affinely independent. More...

template<class ForwardIterator >
int	affine_rank (ForwardIterator first, ForwardIterator last)
	computes the affine rank of the points in `A = tuple [first,last)`. More...

Comparison_result	compare_lexicographically (const Point_d< R > &p, const Point_d< R > &q)
	Compares the Cartesian coordinates of points `p` and `q` lexicographically in ascending order of its Cartesian components `p[i]` and `q[i]` for $i = 0,\ldots,d-1$ . More...

template<class ForwardIterator >
bool	contained_in_affine_hull (ForwardIterator first, ForwardIterator last, const Point_d< R > &p)
	determines whether $p$ is contained in the affine hull of the points in `A = tuple [first,last)`. More...

template<class ForwardIterator >
bool	contained_in_linear_hull (ForwardIterator first, ForwardIterator last, const Vector_d< R > &v)
	determines whether $v$ is contained in the linear hull of the vectors in `A = tuple [first,last)`. More...

template<class ForwardIterator >
bool	contained_in_simplex (ForwardIterator first, ForwardIterator last, const Point_d< R > &p)
	determines whether $p$ is contained in the simplex of the points in `A = tuple [first,last)`. More...

bool	lexicographically_smaller (const Point_d< R > &p, const Point_d< R > &q)
	returns `true` iff `p` is lexicographically smaller than `q` with respect to Cartesian lexicographic order of points. More...

bool	lexicographically_smaller_or_equal (const Point_d< R > &p, const Point_d< R > &q)
	returns `true` iff $p$ is lexicographically smaller than $q$ with respect to Cartesian lexicographic order of points or equal to $q$ . More...

template<class ForwardIterator >
bool	linearly_independent (ForwardIterator first, ForwardIterator last)
	decides whether the vectors in `A = tuple [first,last)` are linearly independent. More...

template<class ForwardIterator >
int	linear_rank (ForwardIterator first, ForwardIterator last)
	computes the linear rank of the vectors in `A = tuple [first,last)`. More...

template<class ForwardIterator >
Orientation	orientation (ForwardIterator first, ForwardIterator last)
	determines the orientation of the points of the tuple `A = tuple [first,last)` where $A$ consists of $d+1$ points in $d$ -space. More...

template<class ForwardIterator >
Bounded_side	side_of_bounded_sphere (ForwardIterator first, ForwardIterator last, const Point_d< R > &p)
	returns the relative position of point `p` to the sphere defined by `A = tuple [first,last)`. More...

template<class ForwardIterator >
Oriented_side	side_of_oriented_sphere (ForwardIterator first, ForwardIterator last, const Point_d< R > &p)
	returns the relative position of point `p` to the oriented sphere defined by the points in `A = tuple [first,last)` The order of the points in $A$ is important, since it determines the orientation of the implicitly constructed sphere. More...

Namespaces

Classes

Functions