Kernel_d Concept Reference 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> Concepts 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 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 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 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. Kernel_d Generated by 1.17.0

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>

Concepts
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

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

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

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.