Chapter 7
Reference Pages

7.1   Concepts

• Kernel

• EuclideanRingNumberType

• FieldNumberType

• RingNumberType

• SqrtFieldNumberType

7.2   Kernel Classes and Operations

• Cartesian<FieldNumberType>

• Cartesian_converter<K1, K2, NTConverter>

• cartesian_to_homogeneous

• Filtered_kernel<CK>

• Filtered_kernel_adaptor<CK>

• Filtered_predicate<EP, FP, C2E, C2F>

• Homogeneous<RingNumberType>

• Homogeneous_converter<K1, K2, RTConverter, FTConverter>

• homogeneous_to_cartesian

• homogeneous_to_quotient_cartesian

• Kernel_archetype

• Kernel_traits<T>

• Simple_cartesian<FieldNumberType>

• Simple_homogeneous<RingNumberType>

7.3   Predefined Kernels

• Exact_predicates_exact_constructions_kernel

• Exact_predicates_exact_constructions_kernel_with_sqrt

• Exact_predicates_inexact_constructions_kernel

7.4   Kernel Objects

7.4.1   Two-dimensional Objects

• Aff_transformation_2<Kernel>

• Bbox_2

• Circle_2<Kernel>

• Direction_2<Kernel>

• Iso_rectangle_2<Kernel>

• Line_2<Kernel>

• Point_2<Kernel>

• Ray_2<Kernel>

• Segment_2<Kernel>

• Triangle_2<Kernel>

• Vector_2<Kernel>

7.4.2   Three-dimensional Objects

• Bbox_3

• Aff_transformation_3<Kernel>

• Direction_3<Kernel>

• Iso_cuboid_3<Kernel>

• Line_3<Kernel>

• Plane_3<Kernel>

• Point_3<Kernel>

• Ray_3<Kernel>

• Segment_3<Kernel>

• Sphere_3<Kernel>

• Tetrahedron_3<Kernel>

• Triangle_3<Kernel>

• Vector_3<Kernel>

7.4.3   Polymorphic Objects

• Object

• assign

• make_object

7.5   Constants and Enumerations

• Angle

• Bounded_side

• Comparison_result

• Sign

• Orientation

• Oriented_side

• CLOCKWISE

• COUNTERCLOCKWISE

• COLLINEAR

• LEFT_TURN

• RIGHT_TURN

• COPLANAR

• DEGENERATE

• Null_vector

• NULL_VECTOR

• Origin

• ORIGIN

• Identity_transformation

• Reflection

• Rotation

• Scaling

• Translation

7.6   Global Functions

• angle

• are_ordered_along_line

• are_strictly_ordered_along_line

• area

• bisector

• centroid

• circumcenter

• collinear

• collinear_are_ordered_along_line

• collinear_are_strictly_ordered_along_line

• compare_distance_to_point

• compare_signed_distance_to_line

• compare_signed_distance_to_plane

• compare_slopes

• compare_x

• compare_xy

• compare_xyz

• compare_x_at_y

• compare_y

• compare_y_at_x

• compare_yx

• compare_z

• coplanar

• coplanar_orientation

• coplanar_side_of_bounded_circle

• cross_product

• do_intersect

• do_overlap

• has_larger_distance_to_point

• has_larger_signed_distance_to_line

• has_larger_signed_distance_to_plane

• has_smaller_distance_to_point

• has_smaller_signed_distance_to_line

• has_smaller_signed_distance_to_plane

• intersection

• left_turn

• lexicographically_xyz_smaller

• lexicographically_xyz_smaller_or_equal

• lexicographically_xy_larger

• lexicographically_xy_larger_or_equal

• lexicographically_xy_smaller

• lexicographically_xy_smaller_or_equal

• max_vertex

• midpoint

• min_vertex

• operator+

• operator-

• operator*

• opposite

• orthogonal_vector

• orientation

• parallel

• quotient_cartesian_to_homogeneous

• rational_rotation_approximation

• right_turn

• side_of_bounded_circle

• side_of_bounded_sphere

• side_of_oriented_circle

• side_of_oriented_sphere

• squared_distance

• squared_radius

• volume

• x_equal

• y_equal

• z_equal

7.7   Kernel Function Object Concepts

• Kernel::Angle_2

• Kernel::Angle_3

• Kernel::AreOrderedAlongLine_2

• Kernel::AreOrderedAlongLine_3

• Kernel::AreParallel_2

• Kernel::AreParallel_3

• Kernel::AreStrictlyOrderedAlongLine_2

• Kernel::AreStrictlyOrderedAlongLine_3

• Kernel::Assign_2

• Kernel::Assign_3

• Kernel::BoundedSide_2

• Kernel::BoundedSide_3

• Kernel::Circle_2

• Kernel::CollinearAreOrderedAlongLine_2

• Kernel::CollinearAreOrderedAlongLine_3

• Kernel::CollinearAreStrictlyOrderedAlongLine_2

• Kernel::CollinearAreStrictlyOrderedAlongLine_3

• Kernel::CollinearHasOn_2

• Kernel::Collinear_2

• Kernel::Collinear_3

• Kernel::CompareAngleWithXAxis_2

• Kernel::CompareDistance_2

• Kernel::CompareDistance_3

• Kernel::CompareSlope_2

• Kernel::CompareXAtY_2

• Kernel::CompareXYZ_3

• Kernel::CompareXY_2

• Kernel::CompareXY_3

• Kernel::CompareX_2

• Kernel::CompareX_3

• Kernel::CompareYAtX_2

• Kernel::CompareY_2

• Kernel::CompareY_3

• Kernel::CompareZ_3

• Kernel::ComputeArea_2

• Kernel::ComputeArea_3

• Kernel::ComputeScalarProduct_2

• Kernel::ComputeScalarProduct_3

• Kernel::ComputeSquaredArea_3

• Kernel::ComputeSquaredDistance_2

• Kernel::ComputeSquaredDistance_3

• Kernel::ComputeSquaredLength_2

• Kernel::ComputeSquaredLength_3

• Kernel::ComputeSquaredRadius_2

• Kernel::ComputeSquaredRadius_3

• Kernel::ComputeVolume_3

• Kernel::ConstructBaseVector_3

• Kernel::ConstructBbox_2

• Kernel::ConstructBbox_3

• Kernel::ConstructBisector_2

• Kernel::ConstructBisector_3

• Kernel::ConstructCartesianConstIterator_2

• Kernel::ConstructCartesianConstIterator_3

• Kernel::ConstructCenter_2

• Kernel::ConstructCenter_3

• Kernel::ConstructCentroid_2

• Kernel::ConstructCentroid_3

• Kernel::ConstructCircle_2

• Kernel::ConstructCircumcenter_2

• Kernel::ConstructCircumcenter_3

• Kernel::ConstructCrossProductVector_3

• Kernel::ConstructDirection_2

• Kernel::ConstructDirection_3

• Kernel::ConstructIsoCuboid_3

• Kernel::ConstructIsoRectangle_2

• Kernel::ConstructLiftedPoint_3

• Kernel::ConstructLine_2

• Kernel::ConstructLine_3

• Kernel::ConstructMaxVertex_2

• Kernel::ConstructMaxVertex_3

• Kernel::ConstructMidpoint_2

• Kernel::ConstructMidpoint_3

• Kernel::ConstructMinVertex_2

• Kernel::ConstructMinVertex_3

• Kernel::ConstructObject_2

• Kernel::ConstructObject_3

• Kernel::ConstructOppositeCircle_2

• Kernel::ConstructOppositeDirection_2

• Kernel::ConstructOppositeDirection_3

• Kernel::ConstructOppositeLine_2

• Kernel::ConstructOppositeLine_3

• Kernel::ConstructOppositePlane_3

• Kernel::ConstructOppositeRay_2

• Kernel::ConstructOppositeRay_3

• Kernel::ConstructOppositeSegment_2

• Kernel::ConstructOppositeSegment_3

• Kernel::ConstructOppositeSphere_3

• Kernel::ConstructOppositeTriangle_2

• Kernel::ConstructOppositeVector_2

• Kernel::ConstructOppositeVector_3

• Kernel::ConstructOrthogonalVector_3

• Kernel::ConstructPerpendicularDirection_2

• Kernel::ConstructPerpendicularLine_2

• Kernel::ConstructPerpendicularLine_3

• Kernel::ConstructPerpendicularPlane_3

• Kernel::ConstructPerpendicularVector_2

• Kernel::ConstructPlane_3

• Kernel::ConstructPointOn_2

• Kernel::ConstructPointOn_3

• Kernel::ConstructPoint_2

• Kernel::ConstructPoint_3

• Kernel::ConstructProjectedPoint_2

• Kernel::ConstructProjectedPoint_3

• Kernel::ConstructProjectedXYPoint_2

• Kernel::ConstructRay_2

• Kernel::ConstructRay_3

• Kernel::ConstructScaledVector_2

• Kernel::ConstructScaledVector_3

• Kernel::ConstructSegment_2

• Kernel::ConstructSegment_3

• Kernel::ConstructSphere_3

• Kernel::ConstructSupportingPlane_3

• Kernel::ConstructTetrahedron_3

• Kernel::ConstructTranslatedPoint_2

• Kernel::ConstructTranslatedPoint_3

• Kernel::ConstructTriangle_2

• Kernel::ConstructTriangle_3

• Kernel::ConstructVector_2

• Kernel::ConstructVector_3

• Kernel::ConstructVertex_2

• Kernel::ConstructVertex_3

• Kernel::CartesianConstIterator_2

• Kernel::CartesianConstIterator_3

• Kernel::CoplanarOrientation_3

• Kernel::CoplanarSideOfBoundedCircle_3

• Kernel::Coplanar_3

• Kernel::CounterclockwiseInBetween_2

• Kernel::Direction_2

• Kernel::Direction_3

• Kernel::DoIntersect_2

• Kernel::DoIntersect_3

• Kernel::EqualXY_3

• Kernel::EqualX_2

• Kernel::EqualX_3

• Kernel::EqualY_2

• Kernel::EqualY_3

• Kernel::EqualZ_3

• Kernel::Equal_2

• Kernel::Equal_3

• Kernel::HasOnBoundary_2

• Kernel::HasOnBoundary_3

• Kernel::HasOnBoundedSide_2

• Kernel::HasOnBoundedSide_3

• Kernel::HasOnNegativeSide_2

• Kernel::HasOnNegativeSide_3

• Kernel::HasOnPositiveSide_2

• Kernel::HasOnPositiveSide_3

• Kernel::HasOnUnboundedSide_2

• Kernel::HasOnUnboundedSide_3

• Kernel::HasOn_2

• Kernel::HasOn_3

• Kernel::Intersect_2

• Kernel::Intersect_3

• Kernel::IsDegenerate_2

• Kernel::IsDegenerate_3

• Kernel::IsHorizontal_2

• Kernel::IsoCuboid_3

• Kernel::IsoRectangle_2

• Kernel::IsVertical_2

• Kernel::LeftTurn_2

• Kernel::LessDistanceToPoint_2

• Kernel::LessDistanceToPoint_3

• Kernel::LessRotateCCW_2

• Kernel::LessSignedDistanceToLine_2

• Kernel::LessSignedDistanceToPlane_3

• Kernel::LessXYZ_3

• Kernel::LessXY_2

• Kernel::LessXY_3

• Kernel::LessX_2

• Kernel::LessX_3

• Kernel::LessYX_2

• Kernel::LessY_2

• Kernel::LessY_3

• Kernel::LessZ_3

• Kernel::Line_2

• Kernel::Line_3

• Kernel::Object_2

• Kernel::Object_3

• Kernel::Orientation_2

• Kernel::Orientation_3

• Kernel::OrientedSide_2

• Kernel::OrientedSide_3

• Kernel::Plane_3

• Kernel::Point_2

• Kernel::Point_3

• Kernel::Ray_2

• Kernel::Ray_3

• Kernel::Segment_2

• Kernel::Segment_3

• Kernel::SideOfBoundedCircle_2

• Kernel::SideOfBoundedSphere_3

• Kernel::SideOfOrientedCircle_2

• Kernel::SideOfOrientedSphere_3

• Kernel::Sphere_3

• Kernel::Tetrahedron_3

• Kernel::Triangle_2

• Kernel::Triangle_3

• Kernel::Vector_2

• Kernel::Vector_3

7.8   Tag Classes

• Tag_false

• Tag_true