#include <Concepts/Kernel_d.h>

Definition

The concept of a kernel is defined by a set of requirements on the provision of certain types and access member functions to create objects of these types. The types are function object classes to be used within the algorithms and data structures in the basic library of CGAL. This allows you to use any model of a kernel as a traits class in the CGAL algorithms and data structures, unless they require types beyond those provided by a kernel.

Kernel_d subsumes the concept of a \( d\)-dimensional kernel.

A kernel provides types, construction objects, and generalized predicates. The former replace constructors of the kernel classes and constructive procedures in the kernel. There are also function objects replacing operators, especially for equality testing.

Has models
: CGAL::Cartesian_d<FieldNumberType>
: CGAL::Homogeneous_d<RingNumberType>
: CGAL::Epick_d<DimensionTag>
: CGAL::Epeck_d<DimensionTag>

Classes
class	Affine_rank_d

class	Affinely_independent_d

class	CartesianConstIterator_d
	A type representing an iterator to the Cartesian coordinates of a point in `d` dimensions. More...

class	Center_of_sphere_d

class	Compare_lexicographically_d

class	Component_accessor_d

class	Compute_coordinate_d

class	Construct_max_vertex_d

class	Construct_min_vertex_d

class	ConstructCartesianConstIterator_d

class	Contained_in_affine_hull_d

class	Contained_in_linear_hull_d

class	Contained_in_simplex_d

class	Equal_d

class	Has_on_positive_side_d

class	Intersect_d

class	Less_coordinate_d

class	Less_lexicographically_d

class	Less_or_equal_lexicographically_d

class	Linear_base_d

class	Linear_rank_d

class	Linearly_independent_d

class	Midpoint_d

class	Orientation_d

class	Oriented_side_d

class	Orthogonal_vector_d

class	Point_dimension_d

class	Point_of_sphere_d

class	Point_to_vector_d

class	Side_of_bounded_sphere_d

class	Side_of_oriented_sphere_d

class	Squared_distance_d

class	Value_at_d

class	Vector_to_point_d

Types
typedef unspecified_type	FT
	a number type that is a model for `FieldNumberType`

typedef unspecified_type	RT
	a number type that is a model for `RingNumberType`

typedef unspecified_type	Dimension
	the dimension of the ambient space.

Coordinate Access
typedef unspecified_type	Cartesian_const_iterator_d
	a type that allows to iterate over the Cartesian coordinates

Constructions
typedef unspecified_type	Barycentric_coordinates_d

typedef unspecified_type	Center_of_sphere_d
	a model of `Kernel_d::Center_of_sphere_d`

typedef unspecified_type	Compute_coordinate_d
	a model of `Kernel_d::Compute_coordinate_d`

typedef unspecified_type	Construct_point_d

typedef unspecified_type	Construct_vector_d

typedef unspecified_type	Construct_direction_d

typedef unspecified_type	Construct_hyperplane_d

typedef unspecified_type	Construct_segment_d

typedef unspecified_type	Construct_iso_box_d

typedef unspecified_type	Construct_line_d

typedef unspecified_type	Construct_ray_d

typedef unspecified_type	Construct_sphere_d

typedef unspecified_type	Construct_aff_transformation_d

typedef unspecified_type	Construct_cartesian_const_iterator_d
	a model of `Kernel_d::ConstructCartesianConstIterator_d`

typedef unspecified_type	Intersect_d
	a model of `Kernel_d::Intersect_d`

typedef unspecified_type	Linear_base_d
	a model of `Kernel_d::Linear_base_d`

typedef unspecified_type	Midpoint_d
	a model of `Kernel_d::Midpoint_d`

typedef unspecified_type	Orthogonal_vector_d
	a model of `Kernel_d::Orthogonal_vector_d`

typedef unspecified_type	Point_of_sphere_d
	a model of `Kernel_d::Point_of_sphere_d`

typedef unspecified_type	Point_to_vector_d
	a model of `Kernel_d::Point_to_vector_d`

typedef unspecified_type	Squared_distance_d
	a model of `Kernel_d::Squared_distance_d`

typedef unspecified_type	Value_at_d
	a model of `Kernel_d::Value_at_d`

typedef unspecified_type	Vector_to_point_d
	a model of `Kernel_d::Vector_to_point_d`

Generalized Predicates
typedef unspecified_type	Affine_rank_d
	a model of `Kernel_d::Affine_rank_d`

typedef unspecified_type	Affinely_independent_d
	a model of `Kernel_d::Affinely_independent_d`

typedef unspecified_type	Compare_lexicographically_d
	a model of `Kernel_d::Compare_lexicographically_d`

typedef unspecified_type	Component_accessor_d
	a model of `Kernel_d::Component_accessor_d`

typedef unspecified_type	Contained_in_affine_hull_d
	a model of `Kernel_d::Contained_in_affine_hull_d`

typedef unspecified_type	Contained_in_linear_hull_d
	a model of `Kernel_d::Contained_in_linear_hull_d`

typedef unspecified_type	Contained_in_simplex_d
	a model of `Kernel_d::Contained_in_simplex_d`

typedef unspecified_type	Equal_d
	a model of `Kernel_d::Equal_d`

typedef unspecified_type	Has_on_positive_side_d
	a model of `Kernel_d::Has_on_positive_side_d`

typedef unspecified_type	Less_coordinate_d
	a model of `Kernel_d::Less_coordinate_d`

typedef unspecified_type	Less_lexicographically_d
	a model of `Kernel_d::Less_lexicographically_d`

typedef unspecified_type	Less_or_equal_lexicographically_d
	a model of `Kernel_d::Less_or_equal_lexicographically_d`

typedef unspecified_type	Linear_rank_d
	a model of `Kernel_d::Linear_rank_d`

typedef unspecified_type	Linearly_independent_d
	a model of `Kernel_d::Linearly_independent_d`

typedef unspecified_type	Orientation_d
	a model of `Kernel_d::Orientation_d`

typedef unspecified_type	Oriented_side_d
	a model of `Kernel_d::Oriented_side_d`

typedef unspecified_type	Point_dimension_d
	a model of `Kernel_d::Point_dimension_d`

typedef unspecified_type	Position_on_line_d

typedef unspecified_type	Side_of_bounded_sphere_d
	a model of `Kernel_d::Side_of_bounded_sphere_d`

typedef unspecified_type	Side_of_oriented_sphere_d
	a model of `Kernel_d::Side_of_oriented_sphere_d`

Operations
The following member functions return function objects of the types listed above. The name of the access function is the name of the type returned with an `_object` suffix and no capital letter at the beginning. We only give two examples to show the scheme. For the functors `Construct_point_d` and `Orientation_d` the corresponding functions are:
Kernel_d::Construct_point_d	construct_point_d_object () const

Kernel_d::Orientation_d	orientation_d_object () const

Member Typedef Documentation

◆ Aff_transformation_d

typedef unspecified_type Kernel_d::Aff_transformation_d

◆ Affine_rank_d

typedef unspecified_type Kernel_d::Affine_rank_d

a model of Kernel_d::Affine_rank_d

◆ Affinely_independent_d

typedef unspecified_type Kernel_d::Affinely_independent_d

a model of Kernel_d::Affinely_independent_d

◆ Barycentric_coordinates_d

typedef unspecified_type Kernel_d::Barycentric_coordinates_d

◆ Cartesian_const_iterator_d

typedef unspecified_type Kernel_d::Cartesian_const_iterator_d

a type that allows to iterate over the Cartesian coordinates

◆ Center_of_sphere_d

typedef unspecified_type Kernel_d::Center_of_sphere_d

a model of Kernel_d::Center_of_sphere_d

◆ Compare_lexicographically_d

typedef unspecified_type Kernel_d::Compare_lexicographically_d

a model of Kernel_d::Compare_lexicographically_d

◆ Component_accessor_d

typedef unspecified_type Kernel_d::Component_accessor_d

a model of Kernel_d::Component_accessor_d

◆ Compute_coordinate_d

typedef unspecified_type Kernel_d::Compute_coordinate_d

a model of Kernel_d::Compute_coordinate_d

◆ Construct_aff_transformation_d

typedef unspecified_type Kernel_d::Construct_aff_transformation_d

◆ Construct_cartesian_const_iterator_d

typedef unspecified_type Kernel_d::Construct_cartesian_const_iterator_d

a model of Kernel_d::ConstructCartesianConstIterator_d

◆ Construct_direction_d

typedef unspecified_type Kernel_d::Construct_direction_d

◆ Construct_hyperplane_d

typedef unspecified_type Kernel_d::Construct_hyperplane_d

◆ Construct_iso_box_d

typedef unspecified_type Kernel_d::Construct_iso_box_d

◆ Construct_line_d

typedef unspecified_type Kernel_d::Construct_line_d

◆ Construct_point_d

typedef unspecified_type Kernel_d::Construct_point_d

◆ Construct_ray_d

typedef unspecified_type Kernel_d::Construct_ray_d

◆ Construct_segment_d

typedef unspecified_type Kernel_d::Construct_segment_d

◆ Construct_sphere_d

typedef unspecified_type Kernel_d::Construct_sphere_d

◆ Construct_vector_d

typedef unspecified_type Kernel_d::Construct_vector_d

◆ Contained_in_affine_hull_d

typedef unspecified_type Kernel_d::Contained_in_affine_hull_d

a model of Kernel_d::Contained_in_affine_hull_d

◆ Contained_in_linear_hull_d

typedef unspecified_type Kernel_d::Contained_in_linear_hull_d

a model of Kernel_d::Contained_in_linear_hull_d

◆ Contained_in_simplex_d

typedef unspecified_type Kernel_d::Contained_in_simplex_d

a model of Kernel_d::Contained_in_simplex_d

◆ Dimension

typedef unspecified_type Kernel_d::Dimension

the dimension of the ambient space.

It must be either Dimension_tag<d> for some integer d or Dynamic_dimension_tag.

◆ Direction_d

typedef unspecified_type Kernel_d::Direction_d

◆ Equal_d

typedef unspecified_type Kernel_d::Equal_d

a model of Kernel_d::Equal_d

◆ FT

typedef unspecified_type Kernel_d::FT

a number type that is a model for FieldNumberType

◆ Has_on_positive_side_d

typedef unspecified_type Kernel_d::Has_on_positive_side_d

a model of Kernel_d::Has_on_positive_side_d

◆ Hyperplane_d

typedef unspecified_type Kernel_d::Hyperplane_d

◆ Intersect_d

typedef unspecified_type Kernel_d::Intersect_d

a model of Kernel_d::Intersect_d

◆ Iso_box_d

typedef unspecified_type Kernel_d::Iso_box_d

◆ Less_coordinate_d

typedef unspecified_type Kernel_d::Less_coordinate_d

a model of Kernel_d::Less_coordinate_d

◆ Less_lexicographically_d

typedef unspecified_type Kernel_d::Less_lexicographically_d

a model of Kernel_d::Less_lexicographically_d

◆ Less_or_equal_lexicographically_d

typedef unspecified_type Kernel_d::Less_or_equal_lexicographically_d

a model of Kernel_d::Less_or_equal_lexicographically_d

◆ Line_d

typedef unspecified_type Kernel_d::Line_d

◆ Linear_base_d

typedef unspecified_type Kernel_d::Linear_base_d

a model of Kernel_d::Linear_base_d

◆ Linear_rank_d

typedef unspecified_type Kernel_d::Linear_rank_d

a model of Kernel_d::Linear_rank_d

◆ Linearly_independent_d

typedef unspecified_type Kernel_d::Linearly_independent_d

a model of Kernel_d::Linearly_independent_d

◆ Midpoint_d

typedef unspecified_type Kernel_d::Midpoint_d

a model of Kernel_d::Midpoint_d

◆ Orientation_d

typedef unspecified_type Kernel_d::Orientation_d

a model of Kernel_d::Orientation_d

◆ Oriented_side_d

typedef unspecified_type Kernel_d::Oriented_side_d

a model of Kernel_d::Oriented_side_d

◆ Orthogonal_vector_d

typedef unspecified_type Kernel_d::Orthogonal_vector_d

a model of Kernel_d::Orthogonal_vector_d

◆ Point_d

typedef unspecified_type Kernel_d::Point_d

◆ Point_dimension_d

typedef unspecified_type Kernel_d::Point_dimension_d

a model of Kernel_d::Point_dimension_d

◆ Point_of_sphere_d

typedef unspecified_type Kernel_d::Point_of_sphere_d

a model of Kernel_d::Point_of_sphere_d

◆ Point_to_vector_d

typedef unspecified_type Kernel_d::Point_to_vector_d

a model of Kernel_d::Point_to_vector_d

◆ Position_on_line_d

typedef unspecified_type Kernel_d::Position_on_line_d

◆ Ray_d

typedef unspecified_type Kernel_d::Ray_d

◆ RT

typedef unspecified_type Kernel_d::RT

a number type that is a model for RingNumberType

◆ Segment_d

typedef unspecified_type Kernel_d::Segment_d

◆ Side_of_bounded_sphere_d

typedef unspecified_type Kernel_d::Side_of_bounded_sphere_d

a model of Kernel_d::Side_of_bounded_sphere_d

◆ Side_of_oriented_sphere_d

typedef unspecified_type Kernel_d::Side_of_oriented_sphere_d

a model of Kernel_d::Side_of_oriented_sphere_d

◆ Sphere_d

typedef unspecified_type Kernel_d::Sphere_d

◆ Squared_distance_d

typedef unspecified_type Kernel_d::Squared_distance_d

a model of Kernel_d::Squared_distance_d

◆ Value_at_d

typedef unspecified_type Kernel_d::Value_at_d

a model of Kernel_d::Value_at_d

◆ Vector_d

typedef unspecified_type Kernel_d::Vector_d

◆ Vector_to_point_d

typedef unspecified_type Kernel_d::Vector_to_point_d

a model of Kernel_d::Vector_to_point_d

Member Function Documentation

◆ construct_point_d_object()

Kernel_d::Construct_point_d Kernel_d::construct_point_d_object ( ) const

◆ orientation_d_object()

Kernel_d::Orientation_d Kernel_d::orientation_d_object ( ) const

Geometric Objects
typedef unspecified_type	Point_d

typedef unspecified_type	Vector_d

typedef unspecified_type	Direction_d

typedef unspecified_type	Hyperplane_d

typedef unspecified_type	Line_d

typedef unspecified_type	Ray_d

typedef unspecified_type	Segment_d

typedef unspecified_type	Iso_box_d

typedef unspecified_type	Sphere_d

typedef unspecified_type	Aff_transformation_d