## Kernel_d

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.

### Types

Kernel_d::FT
| a number type that is a model for FieldNumberType
Kernel_d::RT
| a number type that is a model for RingNumberType

### Coordinate Access

Kernel_d::Cartesian_const_iterator_d
| a type that allows to iterate over the Cartesian coordinates

### Geometric Objects

Kernel_d::Point_d

Kernel_d::Vector_d

Kernel_d::Direction_d

Kernel_d::Hyperplane_d

Kernel_d::Line_d

Kernel_d::Ray_d

Kernel_d::Segment_d

Kernel_d::Iso_box_d

Kernel_d::Sphere_d

Kernel_d::Aff_transformation_d

### Constructions

Kernel_d::Construct_point_d

Kernel_d::Construct_vector_d

Kernel_d::Construct_direction_d

Kernel_d::Construct_hyperplane_d

Kernel_d::Construct_segment_d

Kernel_d::Construct_iso_box_d

Kernel_d::Construct_line_d

Kernel_d::Construct_ray_d

Kernel_d::Construct_sphere_d

Kernel_d::Construct_aff_transformation_d

Kernel_d::Construct_cartesian_const_iterator_d

### Generalized Predicates

Kernel_d::Affine_rank_d

Kernel_d::Affinely_independent_d

Kernel_d::Barycentric_coordinates_d

Kernel_d::Center_of_sphere_d

Kernel_d::Compare_lexicographically_d

Kernel_d::Component_accessor_d

Kernel_d::Contained_in_affine_hull_d

Kernel_d::Contained_in_linear_hull_d

Kernel_d::Contained_in_simplex_d

Kernel_d::Equal_d

Kernel_d::Has_on_positive_side_d

Kernel_d::Intersect_d

Kernel_d::Less_lexicographically_d

Kernel_d::Less_or_equal_lexicographically_d

Kernel_d::Lift_to_paraboloid_d

Kernel_d::Linear_base_d

Kernel_d::Linear_rank_d

Kernel_d::Linearly_independent_d

Kernel_d::Midpoint_d

Kernel_d::Orientation_d

Kernel_d::Oriented_side_d

Kernel_d::Orthogonal_vector_d

Kernel_d::Point_of_sphere_d

Kernel_d::Point_to_vector_d

Kernel_d::Position_on_line_d

Kernel_d::Project_along_d_axis_d

Kernel_d::Side_of_bounded_sphere_d

Kernel_d::Side_of_oriented_sphere_d

Kernel_d::Squared_distance_d

Kernel_d::Value_at_d

Kernel_d::Vector_to_point_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::Construct_point_d
| kernel.construct_point_d_object ()
Kernel::Orientation_d
| kernel.orientation_d_object ()

### Has Models

Cartesian_d<FieldNumberType>, Homogeneous_d<RingNumberType>