CGAL 4.7 - 2D and 3D Linear Geometry Kernel: Class and Concept List

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 2D and 3D Linear Geometry Kernel

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
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 12]

CGAL |
Aff_transformation_2 | The class `Aff_transformation_2` represents two-dimensional affine transformations
Aff_transformation_3 | The class `Aff_transformation_3` represents three-dimensional affine transformations
Identity_transformation | Tag class for affine transformations
Reflection | Tag class for affine transformations
Rotation | Tag class for affine transformations
Scaling | Tag class for affine transformations
Translation | Tag class for affine transformations
Bbox_2 | An object `b` of the class `Bbox_2` is a bounding box in the two-dimensional Euclidean plane \( \E^2\)
Bbox_3 | An object `b` of the class `Bbox_3` is a bounding box in the three-dimensional Euclidean space \( \E^3\)
Cartesian | A model for `Kernel` that uses Cartesian coordinates to represent the geometric objects
Cartesian_converter | `Cartesian_converter` converts objects from the kernel traits `K1` to the kernel traits `K2` using `NTConverter` to do the conversion
Circle_2 | An object `c` of type `Circle_2` is a circle in the two-dimensional Euclidean plane \( \E^2\)
Circle_3 | An object `c` of type `Circle_3` is a circle in the three-dimensional Euclidean space \( \E^3\)
Ambient_dimension | The class `Ambient_dimension` allows to retrieve the dimension of the ambient space of a type `T` in a kernel `K`
Dimension_tag | An object of the class `Dimension_tag` is an empty object which can be used for dispatching functions based on the dimension of an object, as provided by the `dim` parameter
Dynamic_dimension_tag | An object of the class `Dynamic_dimension_tag` is an empty object which can be used for dispatching functions based on the dimension of an object
Feature_dimension | The class `Feature_dimension` allows to retrieve the geometric dimension of a type `T` in a kernel `K`
Direction_2 | An object `d` of the class `Direction_2` is a vector in the two-dimensional vector space \( \mathbb{R}^2\) where we forget about its length
Direction_3 | An object of the class `Direction_3` is a vector in the three-dimensional vector space \( \mathbb{R}^3\) where we forget about their length
Exact_predicates_exact_constructions_kernel | A typedef to a kernel which has the following properties:
Exact_predicates_exact_constructions_kernel_with_kth_root | A typedef to a kernel which has the following properties:
Exact_predicates_exact_constructions_kernel_with_root_of | A typedef to a kernel which has the following properties:
Exact_predicates_exact_constructions_kernel_with_sqrt | A typedef to a kernel which has the following properties:
Exact_predicates_inexact_constructions_kernel | A typedef to a kernel which has the following properties:
Filtered_kernel_adaptor | `Filtered_kernel_adaptor` is a kernel that uses a filtering technique to obtain a kernel with exact and efficient predicate functors
Filtered_kernel | `Filtered_kernel` is a kernel that uses a filtering technique based on interval arithmetic from to achieve exact and efficient predicates
Filtered_predicate | `Filtered_predicate` is an adaptor for predicate function objects that allows one to produce efficient and exact predicates
Homogeneous | A model for a `Kernel` using homogeneous coordinates to represent the geometric objects
Homogeneous_converter | `Homogeneous_converter` converts objects from the kernel traits `K1` to the kernel traits `K2`
Iso_cuboid_3 | An object `c` of the data type `Iso_cuboid_3` is a cuboid in the Euclidean space \( \E^3\) with edges parallel to the \( x\), \( y\) and \( z\) axis of the coordinate system
Iso_rectangle_2 | An object `r` of the data type `Iso_rectangle_2` is a rectangle in the Euclidean plane \( \E^2\) with sides parallel to the \( x\) and \( y\) axis of the coordinate system
Kernel_traits | The class `Kernel_traits` provides access to the kernel model to which the argument type `T` belongs
Line_2 | An object `l` of the data type `Line_2` is a directed straight line in the two-dimensional Euclidean plane \( \E^2\)
Line_3 | An object `l` of the data type `Line_3` is a directed straight line in the three-dimensional Euclidean space \( \E^3\)
Null_vector | CGAL defines a symbolic constant `NULL_VECTOR` to construct zero length vectors
Origin | CGAL defines a symbolic constant `ORIGIN` which denotes the point at the origin
Plane_3 | An object `h` of the data type `Plane_3` is an oriented plane in the three-dimensional Euclidean space \( \E^3\)
Point_2 | An object `p` of the class `Point_2` is a point in the two-dimensional Euclidean plane \( \E^2\)
Point_3 | An object of the class `Point_3` is a point in the three-dimensional Euclidean space \( \E^3\)
Projection_traits_xy_3 | The class `Projection_traits_xy_3` is an adapter to apply 2D algorithms to the projections of 3D data on the `xy`-plane
Projection_traits_xz_3 | The class `Projection_traits_xz_3` is an adapter to apply 2D algorithms to the projections of 3D data on the `xz`-plane
Projection_traits_yz_3 | The class `Projection_traits_yz_3` is an adapter to apply 2D algorithms to the projections of 3D data on the `yz`-plane
Ray_2 | An object `r` of the data type `Ray_2` is a directed straight ray in the two-dimensional Euclidean plane \( \E^2\)
Ray_3 | An object `r` of the data type `Ray_3` is a directed straight ray in the three-dimensional Euclidean space \( \E^3\)
Segment_2 | An object `s` of the data type `Segment_2` is a directed straight line segment in the two-dimensional Euclidean plane \( \E^2\), i.e. a straight line segment \( [p,q]\) connecting two points \( p,q \in \mathbb{R}^2\)
Segment_3 | An object `s` of the data type `Segment_3` is a directed straight line segment in the three-dimensional Euclidean space \( \E^3\), that is a straight line segment \( [p,q]\) connecting two points \( p,q \in \R^3\)
Simple_cartesian | A model for a `Kernel` using Cartesian coordinates to represent the geometric objects
Simple_homogeneous | A model for a `Kernel` using homogeneous coordinates to represent the geometric objects
Sphere_3 | An object of type `Sphere_3` is a sphere in the three-dimensional Euclidean space \( \E^3\)
Tetrahedron_3 | An object `t` of the class `Tetrahedron_3` is an oriented tetrahedron in the three-dimensional Euclidean space \( \E^3\)
Triangle_2 | An object `t` of the class `Triangle_2` is a triangle in the two-dimensional Euclidean plane \( \E^2\)
Triangle_3 | An object `t` of the class `Triangle_3` is a triangle in the three-dimensional Euclidean space \( \E^3\)
Vector_2 | An object `v` of the class `Vector_2` is a vector in the two-dimensional vector space \( \mathbb{R}^2\)
Vector_3 | An object of the class `Vector_3` is a vector in the three-dimensional vector space \( \mathbb{R}^3\)
Kernel |
Angle_2 |
Angle_3 |
AreOrderedAlongLine_2 |
AreOrderedAlongLine_3 |
AreParallel_2 |
AreParallel_3 |
AreStrictlyOrderedAlongLine_2 |
AreStrictlyOrderedAlongLine_3 |
Assign_2 |
Assign_3 |
BoundedSide_2 |
BoundedSide_3 |
CartesianConstIterator_2 | A type representing an iterator to the Cartesian coordinates of a point in two dimensions
CartesianConstIterator_3 | A type representing an iterator to the Cartesian coordinates of a point in three dimensions
CollinearAreOrderedAlongLine_2 |
CollinearAreOrderedAlongLine_3 |
CollinearAreStrictlyOrderedAlongLine_2 |
CollinearAreStrictlyOrderedAlongLine_3 |
CollinearHasOn_2 |
Collinear_2 |
Collinear_3 |
CompareAngleWithXAxis_2 |
CompareDihedralAngle_3 |
CompareDistance_2 |
CompareDistance_3 |
CompareSlope_2 |
CompareSquaredDistance_2 |
CompareSquaredDistance_3 |
CompareSquaredRadius_3 |
CompareXAtY_2 |
CompareXYZ_3 |
CompareXY_2 |
CompareXY_3 |
CompareX_2 |
CompareX_3 |
CompareYAtX_2 |
CompareYX_2 |
CompareY_2 |
CompareY_3 |
CompareZ_3 |
ComputeA_2 |
ComputeA_3 |
ComputeApproximateArea_3 |
ComputeApproximateSquaredLength_3 |
ComputeAreaDividedByPi_3 |
ComputeArea_2 |
ComputeArea_3 |
ComputeB_2 |
ComputeB_3 |
ComputeC_2 |
ComputeC_3 |
ComputeD_3 |
ComputeDeterminant_2 |
ComputeDeterminant_3 |
ComputeDx_2 |
ComputeDx_3 |
ComputeDy_2 |
ComputeDy_3 |
ComputeDz_3 |
ComputeHx_2 |
ComputeHx_3 |
ComputeHy_2 |
ComputeHy_3 |
ComputeHw_2 |
ComputeHw_3 |
ComputeHz_3 |
ComputeScalarProduct_2 |
ComputeScalarProduct_3 |
ComputeSquaredArea_3 |
ComputeSquaredDistance_2 |
ComputeSquaredDistance_3 |
ComputeSquaredLengthDividedByPiSquare_3 |
ComputeSquaredLength_2 |
ComputeSquaredLength_3 |
ComputeSquaredRadius_2 |
ComputeSquaredRadius_3 |
ComputeVolume_3 |
ComputeX_2 |
ComputeX_3 |
ComputeXmax_2 |
ComputeXmax_3 |
ComputeXmin_2 |
ComputeXmin_3 |
ComputeYAtX_2 |
ComputeY_2 |
ComputeY_3 |
ComputeYmax_2 |
ComputeYmax_3 |
ComputeYmin_2 |
ComputeYmin_3 |
ComputeZ_3 |
ComputeZmax_3 |
ComputeZmin_3 |
ConstructBarycenter_2 |
ConstructBarycenter_3 |
ConstructBaseVector_3 |
ConstructBbox_2 |
ConstructBbox_3 |
ConstructBisector_2 |
ConstructBisector_3 |
ConstructCartesianConstIterator_2 |
ConstructCartesianConstIterator_3 |
ConstructCenter_2 |
ConstructCenter_3 |
ConstructCentroid_2 |
ConstructCentroid_3 |
ConstructCircle_2 |
ConstructCircle_3 |
ConstructCircumcenter_2 |
ConstructCircumcenter_3 |
ConstructCrossProductVector_3 |
ConstructDifferenceOfVectors_2 |
ConstructDifferenceOfVectors_3 |
ConstructDirection_2 |
ConstructDirection_3 |
ConstructDividedVector_2 |
ConstructDividedVector_3 |
ConstructEquidistantLine_3 |
ConstructIsoCuboid_3 |
ConstructIsoRectangle_2 |
ConstructLiftedPoint_3 |
ConstructLine_2 |
ConstructLine_3 |
ConstructMaxVertex_2 |
ConstructMaxVertex_3 |
ConstructMidpoint_2 |
ConstructMidpoint_3 |
ConstructMinVertex_2 |
ConstructMinVertex_3 |
ConstructNormal_3 |
ConstructObject_2 |
ConstructObject_3 |
ConstructOppositeCircle_2 |
ConstructOppositeDirection_2 |
ConstructOppositeDirection_3 |
ConstructOppositeLine_2 |
ConstructOppositeLine_3 |
ConstructOppositePlane_3 |
ConstructOppositeRay_2 |
ConstructOppositeRay_3 |
ConstructOppositeSegment_2 |
ConstructOppositeSegment_3 |
ConstructOppositeSphere_3 |
ConstructOppositeTriangle_2 |
ConstructOppositeVector_2 |
ConstructOppositeVector_3 |
ConstructOrthogonalVector_3 |
ConstructPerpendicularDirection_2 |
ConstructPerpendicularLine_2 |
ConstructPerpendicularLine_3 |
ConstructPerpendicularPlane_3 |
ConstructPerpendicularVector_2 |
ConstructPlane_3 |
ConstructPointOn_2 |
ConstructPointOn_3 |
ConstructPoint_2 |
ConstructPoint_3 |
ConstructProjectedPoint_2 |
ConstructProjectedPoint_3 |
ConstructProjectedXYPoint_2 |
ConstructRadicalLine_2 |
ConstructRadicalPlane_3 |
ConstructRay_2 |
ConstructRay_3 |
ConstructScaledVector_2 |
ConstructScaledVector_3 |
ConstructSecondPoint_2 |
ConstructSecondPoint_3 |
ConstructSegment_2 |
ConstructSegment_3 |
ConstructSource_2 |
ConstructSource_3 |
ConstructSphere_3 |
ConstructSumOfVectors_2 |
ConstructSumOfVectors_3 |
ConstructSupportingPlane_3 |
ConstructTarget_2 |
ConstructTarget_3 |
ConstructTetrahedron_3 |
ConstructTranslatedPoint_2 |
ConstructTranslatedPoint_3 |
ConstructTriangle_2 |
ConstructTriangle_3 |
ConstructUnitNormal_3 |
ConstructVector_2 |
ConstructVector_3 |
ConstructVertex_2 |
ConstructVertex_3 |
CoplanarOrientation_3 |
CoplanarSideOfBoundedCircle_3 |
Coplanar_3 |
CounterclockwiseInBetween_2 |
DoIntersect_2 |
DoIntersect_3 |
EqualXY_3 |
EqualX_2 |
EqualX_3 |
EqualY_2 |
EqualY_3 |
EqualZ_3 |
Equal_2 |
Equal_3 |
HasOnBoundary_2 |
HasOnBoundary_3 |
HasOnBoundedSide_2 |
HasOnBoundedSide_3 |
HasOnNegativeSide_2 |
HasOnNegativeSide_3 |
HasOnPositiveSide_2 |
HasOnPositiveSide_3 |
HasOnUnboundedSide_2 |
HasOnUnboundedSide_3 |
HasOn_2 |
HasOn_3 |
Intersect_2 |
Intersect_3 |
IsDegenerate_2 |
IsDegenerate_3 |
IsHorizontal_2 |
IsVertical_2 |
LeftTurn_2 |
LessDistanceToPoint_2 |
LessDistanceToPoint_3 |
LessRotateCCW_2 |
LessSignedDistanceToLine_2 |
LessSignedDistanceToPlane_3 |
LessXYZ_3 |
LessXY_2 |
LessXY_3 |
LessX_2 |
LessX_3 |
LessYX_2 |
LessY_2 |
LessY_3 |
LessZ_3 |
Orientation_2 |
Orientation_3 |
OrientedSide_2 |
OrientedSide_3 |
SideOfBoundedCircle_2 |
SideOfBoundedSphere_3 |
SideOfOrientedCircle_2 |
SideOfOrientedSphere_3 |
Circle_2 | A type representing circles in two dimensions
Circle_3 | A type representing circles in three dimensions
Direction_2 | A type representing directions in two dimensions
Direction_3 | A type representing directions in three dimensions
IsoCuboid_3 | A type representing isocuboids in three dimensions
IsoRectangle_2 | A type representing iso-rectangles in two dimensions
Line_2 | A type representing straight lines (and halfspaces) in two dimensions
Line_3 | A type representing straight lines in three dimensions
Object_2 | A type representing different types of objects in two dimensions
Object_3 | A type representing different types of objects in three dimensions
Plane_3 | A type representing planes (and half-spaces) in three dimensions
Point_2 | A type representing points in two dimensions
Point_3 | A type representing points in three dimensions
Ray_2 | A type representing rays in two dimensions
Ray_3 | A type representing rays in three dimensions
Segment_2 | A type representing segments in two dimensions
Segment_3 | A type representing segments in three dimensions
Sphere_3 | A type representing spheres in three dimensions
Tetrahedron_3 | A type representing tetrahedra in three dimensions
Triangle_2 | A type representing triangles in two dimensions
Triangle_3 | A type representing triangles in three dimensions
Vector_2 | A type representing vectors in two dimensions
Vector_3 | A type representing vectors in three dimensions
Kernel | 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 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