\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11.2 - dD Geometry Kernel
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
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  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...