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>

Concepts
concept	Affine_rank_d
concept	Affinely_independent_d
concept	CartesianConstIterator_d
	A type representing an iterator to the Cartesian coordinates of a point in d dimensions. More...
concept	Center_of_sphere_d
concept	Compare_lexicographically_d
concept	Component_accessor_d
concept	Compute_coordinate_d
concept	ConstructCartesianConstIterator_d
concept	Contained_in_affine_hull_d
concept	Contained_in_linear_hull_d
concept	Contained_in_simplex_d
concept	Equal_d
concept	Has_on_positive_side_d
concept	Intersect_d
concept	Less_coordinate_d
concept	Less_lexicographically_d
concept	Less_or_equal_lexicographically_d
concept	Linear_base_d
concept	Linear_rank_d
concept	Linearly_independent_d
concept	Midpoint_d
concept	Orientation_d
concept	Oriented_side_d
concept	Orthogonal_vector_d
concept	Point_dimension_d
concept	Point_of_sphere_d
concept	Point_to_vector_d
concept	Side_of_bounded_sphere_d
concept	Side_of_oriented_sphere_d
concept	Squared_distance_d
concept	Value_at_d
concept	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

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