mirror of https://github.com/CGAL/cgal
168 lines
4.3 KiB
TeX
168 lines
4.3 KiB
TeX
\begin{ccRefConcept}{Kernel_d}
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The concept of a {\em kernel} is defined by a set of requirements on
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the provision of certain types and access member functions to create
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objects of these types. The types are function object classes to be used
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within the algorithms and data structures in the basic library of \cgal.
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This allows you to use any model of a kernel as a traits class in
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the \cgal\ algorithms and data structures, unless they require types
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beyond those provided by a kernel.
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\ccc{Kernel_d} subsumes the concept of a {\em $d$-dimensional kernel}.
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A kernel provides types, construction objects, and generalized
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predicates. The former replace constructors of the kernel classes and
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constructive procedures in the kernel. There are also function objects
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replacing operators, especially for equality testing.
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\ccCreationVariable{kernel}
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\ccTypes
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\ccNestedType{FT}{a number type that is a model for \ccc{FieldNumberType}}
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\ccGlue
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\ccNestedType{RT}{a number type that is a model for \ccc{RingNumberType}}
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\ccHeading{Coordinate Access}
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\ccNestedType{Cartesian_const_iterator_d}{ a type that allows to iterate over
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the \ccHtmlNoLinksFrom{Cartesian} coordinates}
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\ccHeading{Geometric Objects}
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\ccNestedType{Point_d}{}
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\ccGlue
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\ccNestedType{Vector_d}{}
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\ccGlue
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\ccNestedType{Direction_d}{}
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\ccGlue
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\ccNestedType{Hyperplane_d}{}
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\ccGlue
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\ccNestedType{Line_d}{}
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\ccGlue
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\ccNestedType{Ray_d}{}
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\ccGlue
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\ccNestedType{Segment_d}{}
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\ccGlue
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\ccNestedType{Iso_box_d}{}
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\ccGlue
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\ccNestedType{Sphere_d}{}
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\ccGlue
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\ccNestedType{Aff_transformation_d}{}
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\ccHeading{Constructions}
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\ccNestedType{Construct_point_d}{}
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\ccGlue
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\ccNestedType{Construct_vector_d}{}
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\ccGlue
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\ccNestedType{Construct_direction_d}{}
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\ccGlue
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\ccNestedType{Construct_hyperplane_d}{}
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\ccGlue
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\ccNestedType{Construct_segment_d}{}
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\ccGlue
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\ccNestedType{Construct_iso_box_d}{}
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\ccGlue
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\ccNestedType{Construct_line_d}{}
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\ccGlue
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\ccNestedType{Construct_ray_d}{}
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\ccGlue
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\ccNestedType{Construct_sphere_d}{}
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\ccGlue
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\ccNestedType{Construct_aff_transformation_d}{}
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\ccGlue
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\ccNestedType{Construct_cartesian_const_iterator_d}{}
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\ccGlue
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\ccHeading{Generalized Predicates}
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\ccNestedType{Affine_rank_d}{}
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\ccGlue
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\ccNestedType{Affinely_independent_d}{}
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\ccGlue
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\ccNestedType{Barycentric_coordinates_d}{}
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\ccGlue
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\ccNestedType{Center_of_sphere_d}{}
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\ccGlue
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\ccNestedType{Compare_lexicographically_d}{}
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\ccGlue
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\ccNestedType{Component_accessor_d}{}
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\ccGlue
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\ccNestedType{Compute_coordinate_d}{}
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\ccGlue
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\ccNestedType{Contained_in_affine_hull_d}{}
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\ccGlue
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\ccNestedType{Contained_in_linear_hull_d}{}
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\ccGlue
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\ccNestedType{Contained_in_simplex_d}{}
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\ccGlue
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\ccNestedType{Equal_d}{}
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\ccGlue
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\ccNestedType{Has_on_positive_side_d}{}
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\ccGlue
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\ccNestedType{Intersect_d}{}
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\ccGlue
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\ccNestedType{Less_lexicographically_d}{}
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\ccGlue
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\ccNestedType{Less_or_equal_lexicographically_d}{}
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\ccGlue
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\ccNestedType{Lift_to_paraboloid_d}{}
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\ccGlue
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\ccNestedType{Linear_base_d}{}
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\ccGlue
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\ccNestedType{Linear_rank_d}{}
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\ccGlue
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\ccNestedType{Linearly_independent_d}{}
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\ccGlue
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\ccNestedType{Midpoint_d}{}
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\ccGlue
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\ccNestedType{Orientation_d}{}
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\ccGlue
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\ccNestedType{Oriented_side_d}{}
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\ccGlue
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\ccNestedType{Orthogonal_vector_d}{}
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\ccGlue
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\ccNestedType{Point_of_sphere_d}{}
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\ccGlue
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\ccNestedType{Point_to_vector_d}{}
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\ccGlue
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\ccNestedType{Position_on_line_d}{}
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\ccGlue
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\ccNestedType{Project_along_d_axis_d}{}
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\ccGlue
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\ccNestedType{Side_of_bounded_sphere_d}{}
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\ccGlue
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\ccNestedType{Side_of_oriented_sphere_d}{}
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\ccGlue
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\ccNestedType{Squared_distance_d}{}
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\ccGlue
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\ccNestedType{Value_at_d}{}
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\ccGlue
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\ccNestedType{Vector_to_point_d}{}
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\ccGlue
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\ccOperations
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The following member functions return function objects of the types
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listed above. The name of the access function is the name of the type
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returned with an \ccc{_object} suffix and no capital letter at the
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beginning. We only give two examples to show the scheme. For the
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functors \ccc{Construct_point_d} and \ccc{Orientation_d} the
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corresponding functions are:
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\ccTexHtml{\ccSetThreeColumns{Kernel::Construct_point_d}{}{%
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\hspace*{4.5cm}}}{}
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\setlength{\parskip}{0pt}
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\ccMemberFunction{Kernel::Construct_point_d construct_point_d_object() const;}{}
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\ccGlue
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\ccMemberFunction{Kernel::Orientation_d orientation_d_object() const;}{}
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\ccHasModels
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\ccc{Cartesian_d<FieldNumberType>}, \ccc{Homogeneous_d<RingNumberType>}
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\end{ccRefConcept}
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