\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5 - dD Geometry Kernel
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Class and Concept List
Here is the list of all concepts and classes of this package. Classes are inside the namespace CGAL. Concepts are in the global namespace.
[detail level 123]
oNCGAL
|oCCartesian_dA model for Kernel_d (and even KernelWithLifting_d) that uses Cartesian coordinates to represent the geometric objects
|oCEpick_dA model for Kernel_d that uses Cartesian coordinates to represent the geometric objects
||\CPoint_dPoint in the Euclidean space
|oCHomogeneous_dA model for a Kernel_d (and even KernelWithLifting_d) using homogeneous coordinates to represent the geometric objects
|oCAff_transformation_dAn instance of the data type Aff_transformation_d<Kernel> is an affine transformation of \( d\)-dimensional space
|oCDirection_dA Direction_d is a vector in the \( d\)-dimensional vector space where we forget about its length
|oCHyperplane_dAn instance of data type Hyperplane_d is an oriented hyperplane in \( d\) - dimensional space
|oCIso_box_dAn object \( b\) of the data type Iso_box_d is an iso-box in the Euclidean space \( \E^d\) with edges parallel to the axes of the coordinate system
|oCLine_dAn instance of data type Line_d is an oriented line in \( d\)-dimensional Euclidean space
|oCPoint_dAn instance of data type Point_d<Kernel> is a point of Euclidean space in dimension \( d\)
|oCRay_dAn instance of data type Ray_d is a ray in \( d\)-dimensional Euclidean space
|oCSegment_dAn instance \( s\) of the data type Segment_d is a directed straight line segment in \( d\)-dimensional Euclidean space connecting two points \( p\) and \( q\)
|oCSphere_dAn instance \( S\) of the data type Sphere_d is an oriented sphere in some \( d\)-dimensional space
|oCVector_dAn instance of data type Vector_d<Kernel> is a vector of Euclidean space in dimension \( d\)
|oCLinear_algebraCdThe class Linear_algebraCd serves as the default traits class for the LA parameter of CGAL::Cartesian_d<FT,LA>
|\CLinear_algebraHdThe class Linear_algebraHd serves as the default traits class for the LA parameter of CGAL::Homogeneous_d<RT,LA>
oCKernel_dThe 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
|oCAffine_rank_d
|oCAffinely_independent_d
|oCCartesianConstIterator_dA type representing an iterator to the Cartesian coordinates of a point in d dimensions
|oCCenter_of_sphere_d
|oCCompare_lexicographically_d
|oCComponent_accessor_d
|oCCompute_coordinate_d
|oCConstructCartesianConstIterator_d
|oCContained_in_affine_hull_d
|oCContained_in_linear_hull_d
|oCContained_in_simplex_d
|oCEqual_d
|oCHas_on_positive_side_d
|oCIntersect_d
|oCLess_coordinate_d
|oCLess_lexicographically_d
|oCLess_or_equal_lexicographically_d
|oCLinear_base_d
|oCLinear_rank_d
|oCLinearly_independent_d
|oCMidpoint_d
|oCOrientation_d
|oCOriented_side_d
|oCOrthogonal_vector_d
|oCPoint_dimension_d
|oCPoint_of_sphere_d
|oCPoint_to_vector_d
|oCSide_of_bounded_sphere_d
|oCSide_of_oriented_sphere_d
|oCSquared_distance_d
|oCValue_at_d
|\CVector_to_point_d
oCKernelWithLifting_dThe concept of a kernel with lifting is a small refinement of the general kernel concept. It adds 2 functors, the meaning of which would be unclear in kernels of fixed dimension
|oCLift_to_paraboloid_d
|\CProject_along_d_axis_d
oCLinearAlgebraTraits_dThe data type LinearAlgebraTraits_d encapsulates two classes Matrix, Vector and many functions of basic linear algebra. An instance of data type Matrix is a matrix of variables of type NT. Accordingly, Vector implements vectors of variables of type NT. Most functions of linear algebra are checkable, i.e., the programs can be asked for a proof that their output is correct. For example, if the linear system solver declares a linear system \( A x = b\) unsolvable it also returns a vector \( c\) such that \( c^T A = 0\) and \( c^T b \neq 0\)
oCMatrixAn instance of data type Matrix is a matrix of variables of number type NT. The types Matrix and Vector together realize many functions of basic linear algebra
\CVectorAn instance of data type Vector is a vector of variables of number type NT. Together with the type Matrix it realizes the basic operations of linear algebra