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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.

A kernel provides types, construction objects, and generalized predicates. The former replace constructors of the kernel classes and constructive procedures in the kernel. There are also function objects replacing operators, especially for equality testing.

Has Models

CGAL::Cartesian<FieldNumberType>
CGAL::Homogeneous<RingNumberType>
CGAL::Simple_cartesian<FieldNumberType>
CGAL::Simple_homogeneous<RingNumberType>

Types

Kernel::FT
a model of FieldNumberType

Kernel::RT
a model of RingNumberType

The following types describe the return types of predicates. They typically map to bool and CGAL kernel enum types, except when an interval arithmetic number type is used such as within the filtering kernels, in which case it is Uncertain<bool> or similar.

Kernel::Boolean
bool or Uncertain<bool>

Kernel::Sign
CGAL::Sign or Uncertain<CGAL::Sign>

Kernel::Comparison_result
CGAL::Comparison_result or Uncertain<CGAL::Comparison_result>

Kernel::Orientation
CGAL::Orientation or Uncertain<CGAL::Orientation>

Kernel::Oriented_side
CGAL::Oriented_side or Uncertain<CGAL::Oriented_side>

Kernel::Bounded_side
CGAL::Bounded_side or Uncertain<CGAL::Bounded_side>

Kernel::Angle
CGAL::Angle or Uncertain<CGAL::Angle>

Two-dimensional Kernel

Coordinate Access

Kernel::Cartesian_const_iterator_2
a model of Kernel::CartesianConstIterator_2

Geometric Objects

Kernel::Point_2
a model of Kernel::Point_2

Kernel::Vector_2
a model of Kernel::Vector_2

Kernel::Direction_2
a model of Kernel::Direction_2

Kernel::Line_2
a model of Kernel::Line_2

Kernel::Ray_2
a model of Kernel::Ray_2

Kernel::Segment_2
a model of Kernel::Segment_2

Kernel::Triangle_2
a model of Kernel::Triangle_2

Kernel::Iso_rectangle_2
a model of Kernel::IsoRectangle_2

Kernel::Circle_2
a model of Kernel::Circle_2

Kernel::Object_2
a model of Kernel::Object_2

Constructions

Kernel::Construct_point_2
a model of Kernel::ConstructPoint_2

Kernel::Construct_vector_2
a model of Kernel::ConstructVector_2

Kernel::Construct_direction_2
a model of Kernel::ConstructDirection_2

Kernel::Construct_segment_2
a model of Kernel::ConstructSegment_2

Kernel::Construct_line_2
a model of Kernel::ConstructLine_2

Kernel::Construct_ray_2
a model of Kernel::ConstructRay_2

Kernel::Construct_circle_2
a model of Kernel::ConstructCircle_2

Kernel::Construct_triangle_2
a model of Kernel::ConstructTriangle_2

Kernel::Construct_iso_rectangle_2
a model of Kernel::ConstructIsoRectangle_2

Kernel::Construct_object_2
a model of Kernel::ConstructObject_2

Kernel::Construct_scaled_vector_2
a model of Kernel::ConstructScaledVector_2

Kernel::Construct_translated_point_2
a model of Kernel::ConstructTranslatedPoint_2

Kernel::Construct_point_on_2
a model of Kernel::ConstructPointOn_2

Kernel::Construct_projected_point_2
a model of Kernel::ConstructProjectedPoint_2

Kernel::Construct_projected_xy_point_2
a model of Kernel::ConstructProjectedXYPoint_2

Kernel::Construct_cartesian_const_iterator_2
a model of Kernel::ConstructCartesianConstIterator_2

Kernel::Construct_vertex_2
a model of Kernel::ConstructVertex_2

Kernel::Construct_bbox_2
a model of Kernel::ConstructBbox_2

Kernel::Construct_perpendicular_vector_2
a model of Kernel::ConstructPerpendicularVector_2

Kernel::Construct_perpendicular_direction_2
a model of Kernel::ConstructPerpendicularDirection_2

Kernel::Construct_perpendicular_line_2
a model of Kernel::ConstructPerpendicularLine_2

Kernel::Construct_max_vertex_2
a model of Kernel::ConstructMaxVertex_2

Kernel::Construct_midpoint_2
a model of Kernel::ConstructMidpoint_2

Kernel::Construct_equidistant_line_3
a model of Kernel::ConstructEquidistantLine_3

Kernel::Construct_min_vertex_2
a model of Kernel::ConstructMinVertex_2

Kernel::Construct_center_2
a model of Kernel::ConstructCenter_2

Kernel::Construct_centroid_2
a model of Kernel::ConstructCentroid_2

Kernel::Construct_circumcenter_2
a model of Kernel::ConstructCircumcenter_2

Kernel::Construct_bisector_2
a model of Kernel::ConstructBisector_2

Kernel::Construct_opposite_direction_2
a model of Kernel::ConstructOppositeDirection_2

Kernel::Construct_opposite_segment_2
a model of Kernel::ConstructOppositeSegment_2

Kernel::Construct_opposite_ray_2
a model of Kernel::ConstructOppositeRay_2

Kernel::Construct_opposite_line_2
a model of Kernel::ConstructOppositeLine_2

Kernel::Construct_opposite_triangle_2
a model of Kernel::ConstructOppositeTriangle_2

Kernel::Construct_opposite_circle_2
a model of Kernel::ConstructOppositeCircle_2

Kernel::Construct_opposite_vector_2
a model of Kernel::ConstructOppositeVector_2

If the result type is not determined, there is no Construct_ prefix:

Kernel::Intersect_2
a model of Kernel::Intersect_2

Kernel::Assign_2
a model of Kernel::Assign_2

If the result type is a number type, the prefix is Compute_:

Kernel::Compute_squared_distance_2
a model of Kernel::ComputeSquaredDistance_2

Kernel::Compute_squared_length_2
a model of Kernel::ComputeSquaredLength_2

Kernel::Compute_squared_radius_2
a model of Kernel::ComputeSquaredRadius_2

Kernel::Compute_area_2
a model of Kernel::ComputeArea_2

Generalized Predicates

Kernel::Angle_2
a model of Kernel::Angle_2

Kernel::Equal_2
a model of Kernel::Equal_2

Kernel::Equal_x_2
a model of Kernel::EqualX_2

Kernel::Equal_y_2
a model of Kernel::EqualY_2

Kernel::Less_x_2
a model of Kernel::LessX_2

Kernel::Less_y_2
a model of Kernel::LessY_2

Kernel::Less_xy_2
a model of Kernel::LessXY_2

Kernel::Less_yx_2
a model of Kernel::LessYX_2

Kernel::Compare_x_2
a model of Kernel::CompareX_2

Kernel::Compare_x_at_y_2
a model of Kernel::CompareXAtY_2

Kernel::Compare_y_2
a model of Kernel::CompareY_2

Kernel::Compare_xy_2
a model of Kernel::CompareXY_2

Kernel::Compare_xy_2
a model of Kernel::CompareYX_2

Kernel::Compare_y_at_x_2
a model of Kernel::CompareYAtX_2

Kernel::Compare_distance_2
a model of Kernel::CompareDistance_2

Kernel::Compare_angle_with_x_axis_2
a model of Kernel::CompareAngleWithXAxis_2

Kernel::Compare_slope_2
a model of Kernel::CompareSlope_2

Kernel::Less_distance_to_point_2
a model of Kernel::LessDistanceToPoint_2

Kernel::Less_signed_distance_to_line_2
a model of Kernel::LessSignedDistanceToLine_2

Kernel::Less_rotate_ccw_2
a model of Kernel::LessRotateCCW_2

Kernel::Left_turn_2
a model of Kernel::LeftTurn_2

Kernel::Collinear_2
a model of Kernel::Collinear_2

Kernel::Orientation_2
a model of Kernel::Orientation_2

Kernel::Side_of_oriented_circle_2
a model of Kernel::SideOfOrientedCircle_2

Kernel::Side_of_bounded_circle_2
a model of Kernel::SideOfBoundedCircle_2

Kernel::Is_horizontal_2
a model of Kernel::IsHorizontal_2

Kernel::Is_vertical_2
a model of Kernel::IsVertical_2

Kernel::Is_degenerate_2
a model of Kernel::IsDegenerate_2

Kernel::Has_on_2
a model of Kernel::HasOn_2

Kernel::Collinear_has_on_2
a model of Kernel::CollinearHasOn_2

Kernel::Has_on_bounded_side_2
a model of Kernel::HasOnBoundedSide_2

Kernel::Has_on_unbounded_side_2
a model of Kernel::HasOnUnboundedSide_2

Kernel::Has_on_boundary_2
a model of Kernel::HasOnBoundary_2

Kernel::Has_on_positive_side_2
a model of Kernel::HasOnPositiveSide_2

Kernel::Has_on_negative_side_2
a model of Kernel::HasOnNegativeSide_2

Kernel::Oriented_side_2
a model of Kernel::OrientedSide_2

Kernel::Bounded_side_2
a model of Kernel::BoundedSide_2

Kernel::Are_parallel_2
a model of Kernel::AreParallel_2

Kernel::Are_ordered_along_line_2
a model of Kernel::AreOrderedAlongLine_2

Kernel::Are_strictly_ordered_along_line_2
a model of Kernel::AreStrictlyOrderedAlongLine_2

Kernel::Collinear_are_ordered_along_line_2
a model of Kernel::CollinearAreOrderedAlongLine_2

Kernel::Collinear_are_strictly_ordered_along_line_2
a model of Kernel::CollinearAreStrictlyOrderedAlongLine_2

Kernel::Counterclockwise_in_between_2
a model of Kernel::CounterclockwiseInBetween_2

Kernel::Do_intersect_2
a model of Kernel::DoIntersect_2

Three-dimensional Kernel

Coordinate Access

Kernel::Cartesian_const_iterator_3
a model of Kernel::CartesianConstIterator_3

Geometric Objects

Kernel::Point_3
a model of Kernel::Point_3

Kernel::Vector_3
a model of Kernel::Vector_3

Kernel::Direction_3
a model of Kernel::Direction_3

Kernel::Iso_cuboid_3
a model of Kernel::IsoCuboid_3

Kernel::Line_3
a model of Kernel::Line_3

Kernel::Ray_3
a model of Kernel::Ray_3

Kernel::Circle_3
a model of Kernel::Circle_3

Kernel::Sphere_3
a model of Kernel::Sphere_3

Kernel::Segment_3
a model of Kernel::Segment_3

Kernel::Plane_3
a model of Kernel::Plane_3

Kernel::Triangle_3
a model of Kernel::Triangle_3

Kernel::Tetrahedron_3
a model of Kernel::Tetrahedron_3

Kernel::Object_3
a model of Kernel::Object_3

Constructions

Kernel::Construct_point_3
a model of Kernel::ConstructPoint_3

Kernel::Construct_vector_3
a model of Kernel::ConstructVector_3

Kernel::Construct_direction_3
a model of Kernel::ConstructDirection_3

Kernel::Construct_plane_3
a model of Kernel::ConstructPlane_3

Kernel::Construct_iso_cuboid_3
a model of Kernel::ConstructIsoCuboid_3

Kernel::Construct_line_3
a model of Kernel::ConstructLine_3

Kernel::Construct_ray_3
a model of Kernel::ConstructRay_3

Kernel::Construct_sphere_3
a model of Kernel::ConstructSphere_3

Kernel::Construct_segment_3
a model of Kernel::ConstructSegment_3

Kernel::Construct_triangle_3
a model of Kernel::ConstructTriangle_3

Kernel::Construct_tetrahedron_3
a model of Kernel::ConstructTetrahedron_3

Kernel::Construct_object_3
a model of Kernel::ConstructObject_3

Kernel::Construct_scaled_vector_3
a model of Kernel::ConstructScaledVector_3

Kernel::Construct_translated_point_3
a model of Kernel::ConstructTranslatedPoint_3

Kernel::Construct_point_on_3
a model of Kernel::ConstructPointOn_3

Kernel::Construct_projected_point_3
a model of Kernel::ConstructProjectedPoint_3

Kernel::Construct_lifted_point_3
a model of Kernel::ConstructLiftedPoint_3

Kernel::Construct_cartesian_const_iterator_3
a model of Kernel::ConstructCartesianConstIterator_3

Kernel::Construct_vertex_3
a model of Kernel::ConstructVertex_3

Kernel::Construct_bbox_3
a model of Kernel::ConstructBbox_3

Kernel::Construct_supporting_plane_3
a model of Kernel::ConstructSupportingPlane_3

Kernel::Construct_orthogonal_vector_3
a model of Kernel::ConstructOrthogonalVector_3

Kernel::Construct_base_vector_3
a model of Kernel::ConstructBaseVector_3

Kernel::Construct_perpendicular_plane_3
a model of Kernel::ConstructPerpendicularPlane_3

Kernel::Construct_radical_plane_3
a model of Kernel::ConstructRadicalPlane_3

Kernel::Construct_perpendicular_line_3
a model of Kernel::ConstructPerpendicularLine_3

Kernel::Construct_midpoint_3
a model of Kernel::ConstructMidpoint_3

Kernel::Construct_center_3
a model of Kernel::ConstructCenter_3

Kernel::Construct_centroid_3
a model of Kernel::ConstructCentroid_3

Kernel::Construct_circumcenter_3
a model of Kernel::ConstructCircumcenter_3

Kernel::Construct_bisector_3
a model of Kernel::ConstructBisector_3

Kernel::Construct_cross_product_vector_3
a model of Kernel::ConstructCrossProductVector_3

Kernel::Construct_opposite_direction_3
a model of Kernel::ConstructOppositeDirection_3

Kernel::Construct_opposite_segment_3
a model of Kernel::ConstructOppositeSegment_3

Kernel::Construct_opposite_ray_3
a model of Kernel::ConstructOppositeRay_3

Kernel::Construct_opposite_line_3
a model of Kernel::ConstructOppositeLine_3

Kernel::Construct_opposite_plane_3
a model of Kernel::ConstructOppositePlane_3

Kernel::Construct_opposite_sphere_3
a model of Kernel::ConstructOppositeSphere_3

Kernel::Construct_opposite_vector_3
a model of Kernel::ConstructOppositeVector_3

If the result type is not determined, there is no Construct_ prefix:

Kernel::Intersect_3
a model of Kernel::Intersect_3

Kernel::Assign_3
a model of Kernel::Assign_3

If the result type is a number type, the prefix is Compute_:

Kernel::Compute_area_3
a model of Kernel::ComputeArea_3

Kernel::Compute_squared_area_3
a model of Kernel::ComputeSquaredArea_3

Kernel::Compute_area_divided_by_pi_3
a model of Kernel::ComputeAreaDividedByPi_3

Kernel::Compute_approximate_area_3
a model of Kernel::ComputeApproximateArea_3

Kernel::Compute_squared_distance_3
a model of Kernel::ComputeSquaredDistance_3

Kernel::Compute_squared_length_3
a model of Kernel::ComputeSquaredLength_3

Kernel::Compute_squared_length_divided_by_pi_square_3
a model of Kernel::ComputeSquaredLengthDividedByPiSquare_3

Kernel::Compute_approximate_squared_length_3
a model of Kernel::ComputeApproximateSquaredLength_3

Kernel::Compute_squared_radius_3
a model of Kernel::ComputeSquaredRadius_3

Kernel::Compute_volume_3
a model of Kernel::ComputeVolume_3

Generalized Predicates

Kernel::Angle_3
a model of Kernel::Angle_3

Kernel::Equal_3
a model of Kernel::Equal_3

Kernel::Equal_x_3
a model of Kernel::EqualX_3

Kernel::Equal_y_3
a model of Kernel::EqualY_3

Kernel::Equal_z_3
a model of Kernel::EqualZ_3

Kernel::Equal_xy_3
a model of Kernel::EqualXY_3

Kernel::Less_x_3
a model of Kernel::LessX_3

Kernel::Less_y_3
a model of Kernel::LessY_3

Kernel::Less_z_3
a model of Kernel::LessZ_3

Kernel::Less_xy_3
a model of Kernel::LessXY_3

Kernel::Less_xyz_3
a model of Kernel::LessXYZ_3

Kernel::Compare_x_3
a model of Kernel::CompareX_3

Kernel::Compare_y_3
a model of Kernel::CompareY_3

Kernel::Compare_z_3
a model of Kernel::CompareZ_3

Kernel::Compare_xy_3
a model of Kernel::CompareXY_3

Kernel::Compare_xyz_3
a model of Kernel::CompareXYZ_3

Kernel::Less_signed_distance_to_plane_3
a model of Kernel::LessSignedDistanceToPlane_3

Kernel::Less_distance_to_point_3
a model of Kernel::LessDistanceToPoint_3

Kernel::Compare_distance_3
a model of Kernel::CompareDistance_3

Kernel::Collinear_3
a model of Kernel::Collinear_3

Kernel::Coplanar_3
a model of Kernel::Coplanar_3

Kernel::Orientation_3
a model of Kernel::Orientation_3

Kernel::Coplanar_orientation_3
a model of Kernel::CoplanarOrientation_3

Kernel::Coplanar_side_of_bounded_circle_3
a model of Kernel::CoplanarSideOfBoundedCircle_3

Kernel::Side_of_oriented_sphere_3
a model of Kernel::SideOfOrientedSphere_3

Kernel::Side_of_bounded_sphere_3
a model of Kernel::SideOfBoundedSphere_3

Kernel::Is_degenerate_3
a model of Kernel::IsDegenerate_3

Kernel::Has_on_3
a model of Kernel::HasOn_3

Kernel::Has_on_bounded_side_3
a model of Kernel::HasOnBoundedSide_3

Kernel::Has_on_unbounded_side_3
a model of Kernel::HasOnUnboundedSide_3

Kernel::Has_on_boundary_3
a model of Kernel::HasOnBoundary_3

Kernel::Has_on_positive_side_3
a model of Kernel::HasOnPositiveSide_3

Kernel::Has_on_negative_side_3
a model of Kernel::HasOnNegativeSide_3

Kernel::Oriented_side_3
a model of Kernel::OrientedSide_3

Kernel::Bounded_side_3
a model of Kernel::BoundedSide_3

Kernel::Are_parallel_3
a model of Kernel::AreParallel_3

Kernel::Are_ordered_along_line_3
a model of Kernel::AreOrderedAlongLine_3

Kernel::Are_strictly_ordered_along_line_3
a model of Kernel::AreStrictlyOrderedAlongLine_3

Kernel::Collinear_are_ordered_along_line_3
a model of Kernel::CollinearAreOrderedAlongLine_3

Kernel::Collinear_are_strictly_ordered_along_line_3
a model of Kernel::CollinearAreStrictlyOrderedAlongLine_3

Kernel::Do_intersect_3
a model of Kernel::DoIntersect_3

Operations

For each of the function objects above, there must exist a member function that requires no arguments and returns an instance of that function object. The name of the member function is the uncapitalized name of the type returned with the suffix _object appended. For example, for the function object Kernel::Construct_vector_2 the following member function must exist:

Kernel::Construct_vector_2 kernel.construct_vector_2_object ()

See Also

Kernel_d

Next: Cartesian<FieldNumberType>
Navigation: Up   Table of Contents   Package Overview   Bibliography   Index   Title   Acknowledging CGAL
CGAL Open Source Project. Release 3.5.1. 19 December 2009.