2D and 3D Kernel
Reference Manual

The following pages give a complete overview on the functionality provided in the kernel.

2.7   Concepts

Kernel

2.8   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>

2.9   Predefined Kernels

Exact_predicates_exact_constructions_kernel

Exact_predicates_exact_constructions_kernel_with_sqrt

Exact_predicates_inexact_constructions_kernel

2.10   Kernel Objects

2.10.1   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>

2.10.2   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>

2.10.3   Polymorphic Objects

Object

2.11   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

2.12   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

enum_cast

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

2.13   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::ComputeA_2

Kernel::ComputeB_2

Kernel::ComputeC_2

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::ComputeX_2

Kernel::ComputeY_2

Kernel::ComputeXmin_2

Kernel::ComputeYmin_2

Kernel::ComputeXmax_2

Kernel::ComputeYmax_2

Kernel::ComputeYAtX_2

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::ConstructDifferenceOfVectors_2

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::ConstructSumOfVectors_2

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

2.14   Tag Classes

Tag_false

Tag_true