Kernel Concept Reference

Definition

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.

Naming convention of constructions
All constructions which result type is a geometric object are prefixed by Construct_. If the result type is a number type, the name is prefixed by Compute_. When the result type is not determined, no prefix is used.

Has Models:

CGAL::Cartesian<FieldNumberType>

CGAL::Homogeneous<RingNumberType>

CGAL::Simple_cartesian<FieldNumberType>

CGAL::Simple_homogeneous<RingNumberType>

CGAL::Filtered_kernel<CK>

CGAL::Exact_predicates_exact_constructions_kernel

CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt

CGAL::Exact_predicates_inexact_constructions_kernel

See Also

Kernel_d

CGAL::Ambient_dimension

CGAL::Feature_dimension

CGAL::Kernel_traits

Todo:

Kernel::ConstructUnitNormal_3 as no model in the concept

Kernel::CompareSquaredRadius_3 as no model in the concept

Examples:

Kernel_23/MyKernel.h.

Types
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.
typedef unspecified_type	FT
	a model of FieldNumberType More...
typedef unspecified_type	RT
	a model of RingNumberType More...
typedef unspecified_type	Boolean
	bool or Uncertain<bool> More...
typedef unspecified_type	Sign
	CGAL::Sign or Uncertain<CGAL::Sign> More...
typedef unspecified_type	Comparison_result
	CGAL::Comparison_result or Uncertain<CGAL::Comparison_result> More...
typedef unspecified_type	Orientation
	CGAL::Orientation or Uncertain<CGAL::Orientation> More...
typedef unspecified_type	Oriented_side
	CGAL::Oriented_side or Uncertain<CGAL::Oriented_side> More...
typedef unspecified_type	Bounded_side
	CGAL::Bounded_side or Uncertain<CGAL::Bounded_side> More...
typedef unspecified_type	Angle
	CGAL::Angle or Uncertain<CGAL::Angle> More...

Constants
static const bool	Has_filtered_predicates
	A Boolean value indicating whether the predicates are filtered (as in CGAL::Filtered_kernel). More...

Two-dimensional Coordinate Access
typedef unspecified_type	Cartesian_const_iterator_2
	a model of Kernel::CartesianConstIterator_2 More...

Two-dimensional Geometric Objects
typedef unspecified_type	Point_2
	a model of Kernel::Point_2 More...
typedef unspecified_type	Vector_2
	a model of Kernel::Vector_2 More...
typedef unspecified_type	Direction_2
	a model of Kernel::Direction_2 More...
typedef unspecified_type	Line_2
	a model of Kernel::Line_2 More...
typedef unspecified_type	Ray_2
	a model of Kernel::Ray_2 More...
typedef unspecified_type	Segment_2
	a model of Kernel::Segment_2 More...
typedef unspecified_type	Triangle_2
	a model of Kernel::Triangle_2 More...
typedef unspecified_type	Iso_rectangle_2
	a model of Kernel::IsoRectangle_2 More...
typedef unspecified_type	Circle_2
	a model of Kernel::Circle_2 More...
typedef unspecified_type	Object_2
	a model of Kernel::Object_2 More...

Two-dimensional Constructions
typedef unspecified_type	Construct_point_2
	a model of Kernel::ConstructPoint_2 More...
typedef unspecified_type	Construct_vector_2
	a model of Kernel::ConstructVector_2 More...
typedef unspecified_type	Construct_direction_2
	a model of Kernel::ConstructDirection_2 More...
typedef unspecified_type	Construct_segment_2
	a model of Kernel::ConstructSegment_2 More...
typedef unspecified_type	Construct_line_2
	a model of Kernel::ConstructLine_2 More...
typedef unspecified_type	Construct_ray_2
	a model of Kernel::ConstructRay_2 More...
typedef unspecified_type	Construct_circle_2
	a model of Kernel::ConstructCircle_2 More...
typedef unspecified_type	Construct_triangle_2
	a model of Kernel::ConstructTriangle_2 More...
typedef unspecified_type	Construct_iso_rectangle_2
	a model of Kernel::ConstructIsoRectangle_2 More...
typedef unspecified_type	Construct_object_2
	a model of Kernel::ConstructObject_2 More...
typedef unspecified_type	Construct_scaled_vector_2
	a model of Kernel::ConstructScaledVector_2 More...
typedef unspecified_type	Construct_difference_of_vectors_2
	a model of Kernel::ConstructDifferenceOfVectors_2 More...
typedef unspecified_type	Construct_sum_of_vectors_2
	a model of Kernel::ConstructSumOfVectors_2 More...
typedef unspecified_type	Construct_divided_vector_2
	a model of Kernel::ConstructDividedVector_2 More...
typedef unspecified_type	Construct_translated_point_2
	a model of Kernel::ConstructTranslatedPoint_2 More...
typedef unspecified_type	Construct_point_on_2
	a model of Kernel::ConstructPointOn_2 More...
typedef unspecified_type	Construct_projected_point_2
	a model of Kernel::ConstructProjectedPoint_2 More...
typedef unspecified_type	Construct_projected_xy_point_2
	a model of Kernel::ConstructProjectedXYPoint_2 More...
typedef unspecified_type	Construct_second_point_2
	a model of Kernel::ConstructSecondPoint_2 More...
typedef unspecified_type	Construct_cartesian_const_iterator_2
	a model of Kernel::ConstructCartesianConstIterator_2 More...
typedef unspecified_type	Construct_vertex_2
	a model of Kernel::ConstructVertex_2 More...
typedef unspecified_type	Construct_bbox_2
	a model of Kernel::ConstructBbox_2 More...
typedef unspecified_type	Construct_perpendicular_vector_2
	a model of Kernel::ConstructPerpendicularVector_2 More...
typedef unspecified_type	Construct_perpendicular_direction_2
	a model of Kernel::ConstructPerpendicularDirection_2 More...
typedef unspecified_type	Construct_perpendicular_line_2
	a model of Kernel::ConstructPerpendicularLine_2 More...
typedef unspecified_type	Construct_max_vertex_2
	a model of Kernel::ConstructMaxVertex_2 More...
typedef unspecified_type	Construct_midpoint_2
	a model of Kernel::ConstructMidpoint_2 More...
typedef unspecified_type	Construct_equidistant_line_3
	a model of Kernel::ConstructEquidistantLine_3 More...
typedef unspecified_type	Construct_min_vertex_2
	a model of Kernel::ConstructMinVertex_2 More...
typedef unspecified_type	Construct_center_2
	a model of Kernel::ConstructCenter_2 More...
typedef unspecified_type	Construct_centroid_2
	a model of Kernel::ConstructCentroid_2 More...
typedef unspecified_type	Construct_barycenter_2
	a model of Kernel::ConstructBarycenter_2 More...
typedef unspecified_type	Construct_circumcenter_2
	a model of Kernel::ConstructCircumcenter_2 More...
typedef unspecified_type	Construct_bisector_2
	a model of Kernel::ConstructBisector_2 More...
typedef unspecified_type	Construct_radical_line_2
	a model of Kernel::ConstructRadicalLine_2 More...
typedef unspecified_type	Construct_opposite_direction_2
	a model of Kernel::ConstructOppositeDirection_2 More...
typedef unspecified_type	Construct_opposite_segment_2
	a model of Kernel::ConstructOppositeSegment_2 More...
typedef unspecified_type	Construct_opposite_ray_2
	a model of Kernel::ConstructOppositeRay_2 More...
typedef unspecified_type	Construct_opposite_line_2
	a model of Kernel::ConstructOppositeLine_2 More...
typedef unspecified_type	Construct_opposite_triangle_2
	a model of Kernel::ConstructOppositeTriangle_2 More...
typedef unspecified_type	Construct_opposite_circle_2
	a model of Kernel::ConstructOppositeCircle_2 More...
typedef unspecified_type	Construct_opposite_vector_2
	a model of Kernel::ConstructOppositeVector_2 More...
typedef unspecified_type	Construct_source_2
	a model of Kernel::ConstructSource_2 More...
typedef unspecified_type	Construct_target_2
	a model of Kernel::ConstructTarget_2 More...
typedef unspecified_type	Construct_max_vertex_2
	a model of Kernel::ConstructMaxVertex_2 More...
typedef unspecified_type	Construct_min_vertex_2
	a model of Kernel::ConstructMinVertex_2 More...
typedef unspecified_type	Intersect_2
	a model of Kernel::Intersect_2 More...
typedef unspecified_type	Assign_2
	a model of Kernel::Assign_2 More...
typedef unspecified_type	Compute_x_2
	a model of Kernel::ComputeX_2 More...
typedef unspecified_type	Compute_y_2
	a model of Kernel::ComputeY_2 More...
typedef unspecified_type	Compute_a_2
	a model of Kernel::ComputeA_2 More...
typedef unspecified_type	Compute_b_2
	a model of Kernel::ComputeB_2 More...
typedef unspecified_type	ComputeC_2
	a model of Kernel::ComputeC_2 More...
typedef unspecified_type	Compute_dx_2
	a model of Kernel::ComputeDx_2 More...
typedef unspecified_type	Compute_dy_2
	a model of Kernel::ComputeDy_2 More...
typedef unspecified_type	Compute_hx_2
	a model of Kernel::ComputeHx_2 More...
typedef unspecified_type	Compute_hy_2
	a model of Kernel::ComputeHy_2 More...
typedef unspecified_type	Compute_hw_2
	a model of Kernel::ComputeHw_2 More...
typedef unspecified_type	Compute_xmax_2
	a model of Kernel::ComputeXmax_2 More...
typedef unspecified_type	Compute_xmin_2
	a model of Kernel::ComputeXmin_2 More...
typedef unspecified_type	Compute_ymax_2
	a model of Kernel::ComputeYmax_2 More...
typedef unspecified_type	Compute_ymin_2
	a model of Kernel::ComputeYmin_2 More...
typedef unspecified_type	Compute_y_at_x_2
	a model of Kernel::ComputeYAtX_2 More...
typedef unspecified_type	Compute_squared_distance_2
	a model of Kernel::ComputeSquaredDistance_2 More...
typedef unspecified_type	Compute_squared_length_2
	a model of Kernel::ComputeSquaredLength_2 More...
typedef unspecified_type	Compute_squared_radius_2
	a model of Kernel::ComputeSquaredRadius_2 More...
typedef unspecified_type	Compute_area_2
	a model of Kernel::ComputeArea_2 More...
typedef unspecified_type	Compute_determinant_2
	a model of Kernel::ComputeDeterminant_2 More...
typedef unspecified_type	Compute_scalar_product_2
	a model of Kernel::ComputeScalarProduct_2 More...

Two-dimensional Generalized Predicates
typedef unspecified_type	Angle_2
	a model of Kernel::Angle_2 More...
typedef unspecified_type	Equal_2
	a model of Kernel::Equal_2 More...
typedef unspecified_type	Equal_x_2
	a model of Kernel::EqualX_2 More...
typedef unspecified_type	Equal_y_2
	a model of Kernel::EqualY_2 More...
typedef unspecified_type	Less_x_2
	a model of Kernel::LessX_2 More...
typedef unspecified_type	Less_y_2
	a model of Kernel::LessY_2 More...
typedef unspecified_type	Less_xy_2
	a model of Kernel::LessXY_2 More...
typedef unspecified_type	Less_yx_2
	a model of Kernel::LessYX_2 More...
typedef unspecified_type	Compare_x_2
	a model of Kernel::CompareX_2 More...
typedef unspecified_type	Compare_x_at_y_2
	a model of Kernel::CompareXAtY_2 More...
typedef unspecified_type	Compare_y_2
	a model of Kernel::CompareY_2 More...
typedef unspecified_type	Compare_xy_2
	a model of Kernel::CompareXY_2 More...
typedef unspecified_type	Compare_yx_2
	a model of Kernel::CompareYX_2 More...
typedef unspecified_type	Compare_y_at_x_2
	a model of Kernel::CompareYAtX_2 More...
typedef unspecified_type	Compare_distance_2
	a model of Kernel::CompareDistance_2 More...
typedef unspecified_type	Compare_square_distance_2
	a model of Kernel::CompareSquaredDistance_2 More...
typedef unspecified_type	Compare_angle_with_x_axis_2
	a model of Kernel::CompareAngleWithXAxis_2 More...
typedef unspecified_type	Compare_slope_2
	a model of Kernel::CompareSlope_2 More...
typedef unspecified_type	Less_distance_to_point_2
	a model of Kernel::LessDistanceToPoint_2 More...
typedef unspecified_type	Less_signed_distance_to_line_2
	a model of Kernel::LessSignedDistanceToLine_2 More...
typedef unspecified_type	Less_rotate_ccw_2
	a model of Kernel::LessRotateCCW_2 More...
typedef unspecified_type	Left_turn_2
	a model of Kernel::LeftTurn_2 More...
typedef unspecified_type	Collinear_2
	a model of Kernel::Collinear_2 More...
typedef unspecified_type	Orientation_2
	a model of Kernel::Orientation_2 More...
typedef unspecified_type	Side_of_oriented_circle_2
	a model of Kernel::SideOfOrientedCircle_2 More...
typedef unspecified_type	Side_of_bounded_circle_2
	a model of Kernel::SideOfBoundedCircle_2 More...
typedef unspecified_type	Is_horizontal_2
	a model of Kernel::IsHorizontal_2 More...
typedef unspecified_type	Is_vertical_2
	a model of Kernel::IsVertical_2 More...
typedef unspecified_type	Is_degenerate_2
	a model of Kernel::IsDegenerate_2 More...
typedef unspecified_type	Has_on_2
	a model of Kernel::HasOn_2 More...
typedef unspecified_type	Collinear_has_on_2
	a model of Kernel::CollinearHasOn_2 More...
typedef unspecified_type	Has_on_bounded_side_2
	a model of Kernel::HasOnBoundedSide_2 More...
typedef unspecified_type	Has_on_unbounded_side_2
	a model of Kernel::HasOnUnboundedSide_2 More...
typedef unspecified_type	Has_on_boundary_2
	a model of Kernel::HasOnBoundary_2 More...
typedef unspecified_type	Has_on_positive_side_2
	a model of Kernel::HasOnPositiveSide_2 More...
typedef unspecified_type	Has_on_negative_side_2
	a model of Kernel::HasOnNegativeSide_2 More...
typedef unspecified_type	Oriented_side_2
	a model of Kernel::OrientedSide_2 More...
typedef unspecified_type	Bounded_side_2
	a model of Kernel::BoundedSide_2 More...
typedef unspecified_type	Are_parallel_2
	a model of Kernel::AreParallel_2 More...
typedef unspecified_type	Are_ordered_along_line_2
	a model of Kernel::AreOrderedAlongLine_2 More...
typedef unspecified_type	Are_strictly_ordered_along_line_2
	a model of Kernel::AreStrictlyOrderedAlongLine_2 More...
typedef unspecified_type	Collinear_are_ordered_along_line_2
	a model of Kernel::CollinearAreOrderedAlongLine_2 More...
typedef unspecified_type	Collinear_are_strictly_ordered_along_line_2
	a model of Kernel::CollinearAreStrictlyOrderedAlongLine_2 More...
typedef unspecified_type	Counterclockwise_in_between_2
	a model of Kernel::CounterclockwiseInBetween_2 More...
typedef unspecified_type	Do_intersect_2
	a model of Kernel::DoIntersect_2 More...

Three-dimensional Coordinate Access
typedef unspecified_type	Cartesian_const_iterator_3
	a model of Kernel::CartesianConstIterator_3 More...

Three-dimensional Geometric Objects
typedef unspecified_type	Point_3
	a model of Kernel::Point_3 More...
typedef unspecified_type	Vector_3
	a model of Kernel::Vector_3 More...
typedef unspecified_type	Direction_3
	a model of Kernel::Direction_3 More...
typedef unspecified_type	Iso_cuboid_3
	a model of Kernel::IsoCuboid_3 More...
typedef unspecified_type	Line_3
	a model of Kernel::Line_3 More...
typedef unspecified_type	Ray_3
	a model of Kernel::Ray_3 More...
typedef unspecified_type	Circle_3
	a model of Kernel::Circle_3 More...
typedef unspecified_type	Sphere_3
	a model of Kernel::Sphere_3 More...
typedef unspecified_type	Segment_3
	a model of Kernel::Segment_3 More...
typedef unspecified_type	Plane_3
	a model of Kernel::Plane_3 More...
typedef unspecified_type	Triangle_3
	a model of Kernel::Triangle_3 More...
typedef unspecified_type	Tetrahedron_3
	a model of Kernel::Tetrahedron_3 More...
typedef unspecified_type	Object_3
	a model of Kernel::Object_3 More...

Three-dimensional Constructions
typedef unspecified_type	Construct_point_3
	a model of Kernel::ConstructPoint_3 More...
typedef unspecified_type	Construct_vector_3
	a model of Kernel::ConstructVector_3 More...
typedef unspecified_type	Construct_direction_3
	a model of Kernel::ConstructDirection_3 More...
typedef unspecified_type	Construct_plane_3
	a model of Kernel::ConstructPlane_3 More...
typedef unspecified_type	Construct_iso_cuboid_3
	a model of Kernel::ConstructIsoCuboid_3 More...
typedef unspecified_type	Construct_line_3
	a model of Kernel::ConstructLine_3 More...
typedef unspecified_type	Construct_ray_3
	a model of Kernel::ConstructRay_3 More...
typedef unspecified_type	Construct_sphere_3
	a model of Kernel::ConstructSphere_3 More...
typedef unspecified_type	Construct_segment_3
	a model of Kernel::ConstructSegment_3 More...
typedef unspecified_type	Construct_triangle_3
	a model of Kernel::ConstructTriangle_3 More...
typedef unspecified_type	Construct_tetrahedron_3
	a model of Kernel::ConstructTetrahedron_3 More...
typedef unspecified_type	Construct_circle_3
	a model of Kernel::ConstructCircle_3 More...
typedef unspecified_type	Construct_object_3
	a model of Kernel::ConstructObject_3 More...
typedef unspecified_type	Construct_scaled_vector_3
	a model of Kernel::ConstructScaledVector_3 More...
typedef unspecified_type	Construct_translated_point_3
	a model of Kernel::ConstructTranslatedPoint_3 More...
typedef unspecified_type	Construct_point_on_3
	a model of Kernel::ConstructPointOn_3 More...
typedef unspecified_type	Construct_projected_point_3
	a model of Kernel::ConstructProjectedPoint_3 More...
typedef unspecified_type	Construct_lifted_point_3
	a model of Kernel::ConstructLiftedPoint_3 More...
typedef unspecified_type	Construct_cartesian_const_iterator_3
	a model of Kernel::ConstructCartesianConstIterator_3 More...
typedef unspecified_type	Construct_vertex_3
	a model of Kernel::ConstructVertex_3 More...
typedef unspecified_type	Construct_source_3
	a model of Kernel::ConstructSource_3 More...
typedef unspecified_type	Construct_target_3
	a model of Kernel::ConstructTarget_3 More...
typedef unspecified_type	Construct_max_vertex_3
	a model of Kernel::ConstructMaxVertex_3 More...
typedef unspecified_type	Construct_min_vertex_3
	a model of Kernel::ConstructMinVertex_3 More...
typedef unspecified_type	Construct_bbox_3
	a model of Kernel::ConstructBbox_3 More...
typedef unspecified_type	Construct_supporting_plane_3
	a model of Kernel::ConstructSupportingPlane_3 More...
typedef unspecified_type	Construct_orthogonal_vector_3
	a model of Kernel::ConstructOrthogonalVector_3 More...
typedef unspecified_type	Construct_base_vector_3
	a model of Kernel::ConstructBaseVector_3 More...
typedef unspecified_type	Construct_difference_of_vectors_3
	a model of Kernel::ConstructDifferenceOfVectors_3 More...
typedef unspecified_type	Construct_sum_of_vectors_3
	a model of Kernel::ConstructSumOfVectors_3 More...
typedef unspecified_type	Construct_divided_vector_3
	a model of Kernel::ConstructDividedVector_3 More...
typedef unspecified_type	Construct_normal_3
	a model of Kernel::ConstructNormal_3 More...
typedef unspecified_type	Construct_perpendicular_plane_3
	a model of Kernel::ConstructPerpendicularPlane_3 More...
typedef unspecified_type	Construct_radical_plane_3
	a model of Kernel::ConstructRadicalPlane_3 More...
typedef unspecified_type	Construct_perpendicular_line_3
	a model of Kernel::ConstructPerpendicularLine_3 More...
typedef unspecified_type	Construct_midpoint_3
	a model of Kernel::ConstructMidpoint_3 More...
typedef unspecified_type	Construct_center_3
	a model of Kernel::ConstructCenter_3 More...
typedef unspecified_type	Construct_centroid_3
	a model of Kernel::ConstructCentroid_3 More...
typedef unspecified_type	Construct_circumcenter_3
	a model of Kernel::ConstructCircumcenter_3 More...
typedef unspecified_type	Construct_bisector_3
	a model of Kernel::ConstructBisector_3 More...
typedef unspecified_type	Construct_cross_product_vector_3
	a model of Kernel::ConstructCrossProductVector_3 More...
typedef unspecified_type	Construct_barycenter_3
	a model of Kernel::ConstructBarycenter_3 More...
typedef unspecified_type	Construct_second_point_3
	a model of Kernel::ConstructSecondPoint_3 More...
typedef unspecified_type	Construct_opposite_direction_3
	a model of Kernel::ConstructOppositeDirection_3 More...
typedef unspecified_type	Construct_opposite_segment_3
	a model of Kernel::ConstructOppositeSegment_3 More...
typedef unspecified_type	Construct_opposite_ray_3
	a model of Kernel::ConstructOppositeRay_3 More...
typedef unspecified_type	Construct_opposite_line_3
	a model of Kernel::ConstructOppositeLine_3 More...
typedef unspecified_type	Construct_opposite_plane_3
	a model of Kernel::ConstructOppositePlane_3 More...
typedef unspecified_type	Construct_opposite_sphere_3
	a model of Kernel::ConstructOppositeSphere_3 More...
typedef unspecified_type	Construct_opposite_vector_3
	a model of Kernel::ConstructOppositeVector_3 More...
typedef unspecified_type	Intersect_3
	a model of Kernel::Intersect_3 More...
typedef unspecified_type	Assign_3
	a model of Kernel::Assign_3 More...
typedef unspecified_type	Compute_x_3
	a model of Kernel::ComputeX_3 More...
typedef unspecified_type	Compute_y_3
	a model of Kernel::ComputeY_3 More...
typedef unspecified_type	Compute_z_3
	a model of Kernel::ComputeZ_3 More...
typedef unspecified_type	Compute_a_3
	a model of Kernel::ComputeA_3 More...
typedef unspecified_type	Compute_b_3
	a model of Kernel::ComputeB_3 More...
typedef unspecified_type	Compute_c_3
	a model of Kernel::ComputeC_3 More...
typedef unspecified_type	Compute_d_3
	a model of Kernel::ComputeD_3 More...
typedef unspecified_type	Compute_hx_3
	a model of Kernel::ComputeHx_3 More...
typedef unspecified_type	Compute_hy_3
	a model of Kernel::ComputeHy_3 More...
typedef unspecified_type	Compute_hz_3
	a model of Kernel::ComputeHz_3 More...
typedef unspecified_type	Compute_hw_3
	a model of Kernel::ComputeHw_3 More...
typedef unspecified_type	Compute_dx_3
	a model of Kernel::ComputeDx_3 More...
typedef unspecified_type	Compute_dy_3
	a model of Kernel::ComputeDy_3 More...
typedef unspecified_type	Compute_dz_3
	a model of Kernel::ComputeDz_3 More...
typedef unspecified_type	Compute_xmax_3
	a model of Kernel::ComputeXmax_3 More...
typedef unspecified_type	Compute_xmin_3
	a model of Kernel::ComputeXmin_3 More...
typedef unspecified_type	Compute_ymax_3
	a model of Kernel::ComputeYmax_3 More...
typedef unspecified_type	Compute_ymin_3
	a model of Kernel::ComputeYmin_3 More...
typedef unspecified_type	Compute_zmax_3
	a model of Kernel::ComputeZmax_3 More...
typedef unspecified_type	Compute_zmin_3
	a model of Kernel::ComputeZmin_3 More...
typedef unspecified_type	Compute_area_3
	a model of Kernel::ComputeArea_3 More...
typedef unspecified_type	Compute_squared_area_3
	a model of Kernel::ComputeSquaredArea_3 More...
typedef unspecified_type	Compute_area_divided_by_pi_3
	a model of Kernel::ComputeAreaDividedByPi_3 More...
typedef unspecified_type	Compute_approximate_area_3
	a model of Kernel::ComputeApproximateArea_3 More...
typedef unspecified_type	Compute_determinant_3
	a model of Kernel::ComputeDeterminant_3 More...
typedef unspecified_type	Compute_scalar_product_3
	a model of Kernel::ComputeScalarProduct_3 More...
typedef unspecified_type	Compute_squared_distance_3
	a model of Kernel::ComputeSquaredDistance_3 More...
typedef unspecified_type	Compute_squared_length_3
	a model of Kernel::ComputeSquaredLength_3 More...
typedef unspecified_type	Compute_squared_length_divided_by_pi_square_3
	a model of Kernel::ComputeSquaredLengthDividedByPiSquare_3 More...
typedef unspecified_type	Compute_approximate_squared_length_3
	a model of Kernel::ComputeApproximateSquaredLength_3 More...
typedef unspecified_type	Compute_squared_radius_3
	a model of Kernel::ComputeSquaredRadius_3 More...
typedef unspecified_type	Compute_volume_3
	a model of Kernel::ComputeVolume_3 More...

Three-dimensional Generalized Predicates
typedef unspecified_type	Angle_3
	a model of Kernel::Angle_3 More...
typedef unspecified_type	Equal_3
	a model of Kernel::Equal_3 More...
typedef unspecified_type	Equal_x_3
	a model of Kernel::EqualX_3 More...
typedef unspecified_type	Equal_y_3
	a model of Kernel::EqualY_3 More...
typedef unspecified_type	Equal_z_3
	a model of Kernel::EqualZ_3 More...
typedef unspecified_type	Equal_xy_3
	a model of Kernel::EqualXY_3 More...
typedef unspecified_type	Less_x_3
	a model of Kernel::LessX_3 More...
typedef unspecified_type	Less_y_3
	a model of Kernel::LessY_3 More...
typedef unspecified_type	Less_z_3
	a model of Kernel::LessZ_3 More...
typedef unspecified_type	Less_xy_3
	a model of Kernel::LessXY_3 More...
typedef unspecified_type	Less_xyz_3
	a model of Kernel::LessXYZ_3 More...
typedef unspecified_type	Compare_x_3
	a model of Kernel::CompareX_3 More...
typedef unspecified_type	Compare_y_3
	a model of Kernel::CompareY_3 More...
typedef unspecified_type	Compare_z_3
	a model of Kernel::CompareZ_3 More...
typedef unspecified_type	Compare_xy_3
	a model of Kernel::CompareXY_3 More...
typedef unspecified_type	Compare_xyz_3
	a model of Kernel::CompareXYZ_3 More...
typedef unspecified_type	Compare_squared_distance_3
	a model of Kernel::CompareSquaredDistance_3 More...
typedef unspecified_type	Less_signed_distance_to_plane_3
	a model of Kernel::LessSignedDistanceToPlane_3 More...
typedef unspecified_type	Less_distance_to_point_3
	a model of Kernel::LessDistanceToPoint_3 More...
typedef unspecified_type	Compare_dihedral_angle_3
	a model of Kernel::CompareDihedralAngle_3 More...
typedef unspecified_type	Compare_distance_3
	a model of Kernel::CompareDistance_3 More...
typedef unspecified_type	Collinear_3
	a model of Kernel::Collinear_3 More...
typedef unspecified_type	Coplanar_3
	a model of Kernel::Coplanar_3 More...
typedef unspecified_type	Orientation_3
	a model of Kernel::Orientation_3 More...
typedef unspecified_type	Coplanar_orientation_3
	a model of Kernel::CoplanarOrientation_3 More...
typedef unspecified_type	Coplanar_side_of_bounded_circle_3
	a model of Kernel::CoplanarSideOfBoundedCircle_3 More...
typedef unspecified_type	Side_of_oriented_sphere_3
	a model of Kernel::SideOfOrientedSphere_3 More...
typedef unspecified_type	Side_of_bounded_sphere_3
	a model of Kernel::SideOfBoundedSphere_3 More...
typedef unspecified_type	Is_degenerate_3
	a model of Kernel::IsDegenerate_3 More...
typedef unspecified_type	Has_on_3
	a model of Kernel::HasOn_3 More...
typedef unspecified_type	Has_on_bounded_side_3
	a model of Kernel::HasOnBoundedSide_3 More...
typedef unspecified_type	Has_on_unbounded_side_3
	a model of Kernel::HasOnUnboundedSide_3 More...
typedef unspecified_type	Has_on_boundary_3
	a model of Kernel::HasOnBoundary_3 More...
typedef unspecified_type	Has_on_positive_side_3
	a model of Kernel::HasOnPositiveSide_3 More...
typedef unspecified_type	Has_on_negative_side_3
	a model of Kernel::HasOnNegativeSide_3 More...
typedef unspecified_type	Oriented_side_3
	a model of Kernel::OrientedSide_3 More...
typedef unspecified_type	Bounded_side_3
	a model of Kernel::BoundedSide_3 More...
typedef unspecified_type	Are_parallel_3
	a model of Kernel::AreParallel_3 More...
typedef unspecified_type	Are_ordered_along_line_3
	a model of Kernel::AreOrderedAlongLine_3 More...
typedef unspecified_type	Are_strictly_ordered_along_line_3
	a model of Kernel::AreStrictlyOrderedAlongLine_3 More...
typedef unspecified_type	Collinear_are_ordered_along_line_3
	a model of Kernel::CollinearAreOrderedAlongLine_3 More...
typedef unspecified_type	Collinear_are_strictly_ordered_along_line_3
	a model of Kernel::CollinearAreStrictlyOrderedAlongLine_3 More...
typedef unspecified_type	Do_intersect_3
	a model of Kernel::DoIntersect_3 More...

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	construct_vector_2_object () const

Member Typedef Documentation

typedef unspecified_type Kernel::Angle

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

typedef unspecified_type Kernel::Angle_2

a model of Kernel::Angle_2

typedef unspecified_type Kernel::Angle_3

a model of Kernel::Angle_3

typedef unspecified_type Kernel::Are_ordered_along_line_2

a model of Kernel::AreOrderedAlongLine_2

typedef unspecified_type Kernel::Are_ordered_along_line_3

a model of Kernel::AreOrderedAlongLine_3

typedef unspecified_type Kernel::Are_parallel_2

a model of Kernel::AreParallel_2

typedef unspecified_type Kernel::Are_parallel_3

a model of Kernel::AreParallel_3

typedef unspecified_type Kernel::Are_strictly_ordered_along_line_2

a model of Kernel::AreStrictlyOrderedAlongLine_2

typedef unspecified_type Kernel::Are_strictly_ordered_along_line_3

a model of Kernel::AreStrictlyOrderedAlongLine_3

typedef unspecified_type Kernel::Assign_2

a model of Kernel::Assign_2

typedef unspecified_type Kernel::Assign_3

a model of Kernel::Assign_3

typedef unspecified_type Kernel::Boolean

bool or Uncertain<bool>

typedef unspecified_type Kernel::Bounded_side

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

typedef unspecified_type Kernel::Bounded_side_2

a model of Kernel::BoundedSide_2

typedef unspecified_type Kernel::Bounded_side_3

a model of Kernel::BoundedSide_3

typedef unspecified_type Kernel::Cartesian_const_iterator_2

a model of Kernel::CartesianConstIterator_2

typedef unspecified_type Kernel::Cartesian_const_iterator_3

a model of Kernel::CartesianConstIterator_3

typedef unspecified_type Kernel::Circle_2

a model of Kernel::Circle_2

typedef unspecified_type Kernel::Circle_3

a model of Kernel::Circle_3

typedef unspecified_type Kernel::Collinear_2

a model of Kernel::Collinear_2

typedef unspecified_type Kernel::Collinear_3

a model of Kernel::Collinear_3

typedef unspecified_type Kernel::Collinear_are_ordered_along_line_2

a model of Kernel::CollinearAreOrderedAlongLine_2

typedef unspecified_type Kernel::Collinear_are_ordered_along_line_3

a model of Kernel::CollinearAreOrderedAlongLine_3

typedef unspecified_type Kernel::Collinear_are_strictly_ordered_along_line_2

a model of Kernel::CollinearAreStrictlyOrderedAlongLine_2

typedef unspecified_type Kernel::Collinear_are_strictly_ordered_along_line_3

a model of Kernel::CollinearAreStrictlyOrderedAlongLine_3

typedef unspecified_type Kernel::Collinear_has_on_2

a model of Kernel::CollinearHasOn_2

typedef unspecified_type Kernel::Compare_angle_with_x_axis_2

a model of Kernel::CompareAngleWithXAxis_2

typedef unspecified_type Kernel::Compare_dihedral_angle_3

a model of Kernel::CompareDihedralAngle_3

typedef unspecified_type Kernel::Compare_distance_2

a model of Kernel::CompareDistance_2

typedef unspecified_type Kernel::Compare_distance_3

a model of Kernel::CompareDistance_3

typedef unspecified_type Kernel::Compare_slope_2

a model of Kernel::CompareSlope_2

typedef unspecified_type Kernel::Compare_square_distance_2

a model of Kernel::CompareSquaredDistance_2

typedef unspecified_type Kernel::Compare_squared_distance_3

a model of Kernel::CompareSquaredDistance_3

typedef unspecified_type Kernel::Compare_x_2

a model of Kernel::CompareX_2

typedef unspecified_type Kernel::Compare_x_3

a model of Kernel::CompareX_3

typedef unspecified_type Kernel::Compare_x_at_y_2

a model of Kernel::CompareXAtY_2

typedef unspecified_type Kernel::Compare_xy_2

a model of Kernel::CompareXY_2

typedef unspecified_type Kernel::Compare_xy_3

a model of Kernel::CompareXY_3

typedef unspecified_type Kernel::Compare_xyz_3

a model of Kernel::CompareXYZ_3

typedef unspecified_type Kernel::Compare_y_2

a model of Kernel::CompareY_2

typedef unspecified_type Kernel::Compare_y_3

a model of Kernel::CompareY_3

typedef unspecified_type Kernel::Compare_y_at_x_2

a model of Kernel::CompareYAtX_2

typedef unspecified_type Kernel::Compare_yx_2

a model of Kernel::CompareYX_2

typedef unspecified_type Kernel::Compare_z_3

a model of Kernel::CompareZ_3

typedef unspecified_type Kernel::Comparison_result

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

typedef unspecified_type Kernel::Compute_a_2

a model of Kernel::ComputeA_2

typedef unspecified_type Kernel::Compute_a_3

a model of Kernel::ComputeA_3

typedef unspecified_type Kernel::Compute_approximate_area_3

a model of Kernel::ComputeApproximateArea_3

typedef unspecified_type Kernel::Compute_approximate_squared_length_3

a model of Kernel::ComputeApproximateSquaredLength_3

typedef unspecified_type Kernel::Compute_area_2

a model of Kernel::ComputeArea_2

typedef unspecified_type Kernel::Compute_area_3

a model of Kernel::ComputeArea_3

typedef unspecified_type Kernel::Compute_area_divided_by_pi_3

a model of Kernel::ComputeAreaDividedByPi_3

typedef unspecified_type Kernel::Compute_b_2

a model of Kernel::ComputeB_2

typedef unspecified_type Kernel::Compute_b_3

a model of Kernel::ComputeB_3

typedef unspecified_type Kernel::Compute_c_3

a model of Kernel::ComputeC_3

typedef unspecified_type Kernel::Compute_d_3

a model of Kernel::ComputeD_3

typedef unspecified_type Kernel::Compute_determinant_2

a model of Kernel::ComputeDeterminant_2

typedef unspecified_type Kernel::Compute_determinant_3

a model of Kernel::ComputeDeterminant_3

typedef unspecified_type Kernel::Compute_dx_2

a model of Kernel::ComputeDx_2

typedef unspecified_type Kernel::Compute_dx_3

a model of Kernel::ComputeDx_3

typedef unspecified_type Kernel::Compute_dy_2

a model of Kernel::ComputeDy_2

typedef unspecified_type Kernel::Compute_dy_3

a model of Kernel::ComputeDy_3

typedef unspecified_type Kernel::Compute_dz_3

a model of Kernel::ComputeDz_3

typedef unspecified_type Kernel::Compute_hw_2

a model of Kernel::ComputeHw_2

typedef unspecified_type Kernel::Compute_hw_3

a model of Kernel::ComputeHw_3

typedef unspecified_type Kernel::Compute_hx_2

a model of Kernel::ComputeHx_2

typedef unspecified_type Kernel::Compute_hx_3

a model of Kernel::ComputeHx_3

typedef unspecified_type Kernel::Compute_hy_2

a model of Kernel::ComputeHy_2

typedef unspecified_type Kernel::Compute_hy_3

a model of Kernel::ComputeHy_3

typedef unspecified_type Kernel::Compute_hz_3

a model of Kernel::ComputeHz_3

typedef unspecified_type Kernel::Compute_scalar_product_2

a model of Kernel::ComputeScalarProduct_2

typedef unspecified_type Kernel::Compute_scalar_product_3

a model of Kernel::ComputeScalarProduct_3

typedef unspecified_type Kernel::Compute_squared_area_3

a model of Kernel::ComputeSquaredArea_3

typedef unspecified_type Kernel::Compute_squared_distance_2

a model of Kernel::ComputeSquaredDistance_2

typedef unspecified_type Kernel::Compute_squared_distance_3

a model of Kernel::ComputeSquaredDistance_3

typedef unspecified_type Kernel::Compute_squared_length_2

a model of Kernel::ComputeSquaredLength_2

typedef unspecified_type Kernel::Compute_squared_length_3

a model of Kernel::ComputeSquaredLength_3

typedef unspecified_type Kernel::Compute_squared_length_divided_by_pi_square_3

a model of Kernel::ComputeSquaredLengthDividedByPiSquare_3

typedef unspecified_type Kernel::Compute_squared_radius_2

a model of Kernel::ComputeSquaredRadius_2

typedef unspecified_type Kernel::Compute_squared_radius_3

a model of Kernel::ComputeSquaredRadius_3

typedef unspecified_type Kernel::Compute_volume_3

a model of Kernel::ComputeVolume_3

typedef unspecified_type Kernel::Compute_x_2

a model of Kernel::ComputeX_2

typedef unspecified_type Kernel::Compute_x_3

a model of Kernel::ComputeX_3

typedef unspecified_type Kernel::Compute_xmax_2

a model of Kernel::ComputeXmax_2

typedef unspecified_type Kernel::Compute_xmax_3

a model of Kernel::ComputeXmax_3

typedef unspecified_type Kernel::Compute_xmin_2

a model of Kernel::ComputeXmin_2

typedef unspecified_type Kernel::Compute_xmin_3

a model of Kernel::ComputeXmin_3

typedef unspecified_type Kernel::Compute_y_2

a model of Kernel::ComputeY_2

typedef unspecified_type Kernel::Compute_y_3

a model of Kernel::ComputeY_3

typedef unspecified_type Kernel::Compute_y_at_x_2

a model of Kernel::ComputeYAtX_2

typedef unspecified_type Kernel::Compute_ymax_2

a model of Kernel::ComputeYmax_2

typedef unspecified_type Kernel::Compute_ymax_3

a model of Kernel::ComputeYmax_3

typedef unspecified_type Kernel::Compute_ymin_2

a model of Kernel::ComputeYmin_2

typedef unspecified_type Kernel::Compute_ymin_3

a model of Kernel::ComputeYmin_3

typedef unspecified_type Kernel::Compute_z_3

a model of Kernel::ComputeZ_3

typedef unspecified_type Kernel::Compute_zmax_3

a model of Kernel::ComputeZmax_3

typedef unspecified_type Kernel::Compute_zmin_3

a model of Kernel::ComputeZmin_3

typedef unspecified_type Kernel::ComputeC_2

a model of Kernel::ComputeC_2

typedef unspecified_type Kernel::Construct_barycenter_2

a model of Kernel::ConstructBarycenter_2

typedef unspecified_type Kernel::Construct_barycenter_3

a model of Kernel::ConstructBarycenter_3

typedef unspecified_type Kernel::Construct_base_vector_3

a model of Kernel::ConstructBaseVector_3

typedef unspecified_type Kernel::Construct_bbox_2

a model of Kernel::ConstructBbox_2

typedef unspecified_type Kernel::Construct_bbox_3

a model of Kernel::ConstructBbox_3

typedef unspecified_type Kernel::Construct_bisector_2

a model of Kernel::ConstructBisector_2

typedef unspecified_type Kernel::Construct_bisector_3

a model of Kernel::ConstructBisector_3

typedef unspecified_type Kernel::Construct_cartesian_const_iterator_2

a model of Kernel::ConstructCartesianConstIterator_2

typedef unspecified_type Kernel::Construct_cartesian_const_iterator_3

a model of Kernel::ConstructCartesianConstIterator_3

typedef unspecified_type Kernel::Construct_center_2

a model of Kernel::ConstructCenter_2

typedef unspecified_type Kernel::Construct_center_3

a model of Kernel::ConstructCenter_3

typedef unspecified_type Kernel::Construct_centroid_2

a model of Kernel::ConstructCentroid_2

typedef unspecified_type Kernel::Construct_centroid_3

a model of Kernel::ConstructCentroid_3

typedef unspecified_type Kernel::Construct_circle_2

a model of Kernel::ConstructCircle_2

typedef unspecified_type Kernel::Construct_circle_3

a model of Kernel::ConstructCircle_3

typedef unspecified_type Kernel::Construct_circumcenter_2

a model of Kernel::ConstructCircumcenter_2

typedef unspecified_type Kernel::Construct_circumcenter_3

a model of Kernel::ConstructCircumcenter_3

typedef unspecified_type Kernel::Construct_cross_product_vector_3

a model of Kernel::ConstructCrossProductVector_3

typedef unspecified_type Kernel::Construct_difference_of_vectors_2

a model of Kernel::ConstructDifferenceOfVectors_2

typedef unspecified_type Kernel::Construct_difference_of_vectors_3

a model of Kernel::ConstructDifferenceOfVectors_3

typedef unspecified_type Kernel::Construct_direction_2

a model of Kernel::ConstructDirection_2

typedef unspecified_type Kernel::Construct_direction_3

a model of Kernel::ConstructDirection_3

typedef unspecified_type Kernel::Construct_divided_vector_2

a model of Kernel::ConstructDividedVector_2

typedef unspecified_type Kernel::Construct_divided_vector_3

a model of Kernel::ConstructDividedVector_3

typedef unspecified_type Kernel::Construct_equidistant_line_3

a model of Kernel::ConstructEquidistantLine_3

typedef unspecified_type Kernel::Construct_iso_cuboid_3

a model of Kernel::ConstructIsoCuboid_3

typedef unspecified_type Kernel::Construct_iso_rectangle_2

a model of Kernel::ConstructIsoRectangle_2

typedef unspecified_type Kernel::Construct_lifted_point_3

a model of Kernel::ConstructLiftedPoint_3

typedef unspecified_type Kernel::Construct_line_2

a model of Kernel::ConstructLine_2

typedef unspecified_type Kernel::Construct_line_3

a model of Kernel::ConstructLine_3

typedef unspecified_type Kernel::Construct_max_vertex_2

a model of Kernel::ConstructMaxVertex_2

typedef unspecified_type Kernel::Construct_max_vertex_2

a model of Kernel::ConstructMaxVertex_2

typedef unspecified_type Kernel::Construct_max_vertex_3

a model of Kernel::ConstructMaxVertex_3

typedef unspecified_type Kernel::Construct_midpoint_2

a model of Kernel::ConstructMidpoint_2

typedef unspecified_type Kernel::Construct_midpoint_3

a model of Kernel::ConstructMidpoint_3

typedef unspecified_type Kernel::Construct_min_vertex_2

a model of Kernel::ConstructMinVertex_2

typedef unspecified_type Kernel::Construct_min_vertex_2

a model of Kernel::ConstructMinVertex_2

typedef unspecified_type Kernel::Construct_min_vertex_3

a model of Kernel::ConstructMinVertex_3

typedef unspecified_type Kernel::Construct_normal_3

a model of Kernel::ConstructNormal_3

typedef unspecified_type Kernel::Construct_object_2

a model of Kernel::ConstructObject_2

typedef unspecified_type Kernel::Construct_object_3

a model of Kernel::ConstructObject_3

typedef unspecified_type Kernel::Construct_opposite_circle_2

a model of Kernel::ConstructOppositeCircle_2

typedef unspecified_type Kernel::Construct_opposite_direction_2

a model of Kernel::ConstructOppositeDirection_2

typedef unspecified_type Kernel::Construct_opposite_direction_3

a model of Kernel::ConstructOppositeDirection_3

typedef unspecified_type Kernel::Construct_opposite_line_2

a model of Kernel::ConstructOppositeLine_2

typedef unspecified_type Kernel::Construct_opposite_line_3

a model of Kernel::ConstructOppositeLine_3

typedef unspecified_type Kernel::Construct_opposite_plane_3

a model of Kernel::ConstructOppositePlane_3

typedef unspecified_type Kernel::Construct_opposite_ray_2

a model of Kernel::ConstructOppositeRay_2

typedef unspecified_type Kernel::Construct_opposite_ray_3

a model of Kernel::ConstructOppositeRay_3

typedef unspecified_type Kernel::Construct_opposite_segment_2

a model of Kernel::ConstructOppositeSegment_2

typedef unspecified_type Kernel::Construct_opposite_segment_3

a model of Kernel::ConstructOppositeSegment_3

typedef unspecified_type Kernel::Construct_opposite_sphere_3

a model of Kernel::ConstructOppositeSphere_3

typedef unspecified_type Kernel::Construct_opposite_triangle_2

a model of Kernel::ConstructOppositeTriangle_2

typedef unspecified_type Kernel::Construct_opposite_vector_2

a model of Kernel::ConstructOppositeVector_2

typedef unspecified_type Kernel::Construct_opposite_vector_3

a model of Kernel::ConstructOppositeVector_3

typedef unspecified_type Kernel::Construct_orthogonal_vector_3

a model of Kernel::ConstructOrthogonalVector_3

typedef unspecified_type Kernel::Construct_perpendicular_direction_2

a model of Kernel::ConstructPerpendicularDirection_2

typedef unspecified_type Kernel::Construct_perpendicular_line_2

a model of Kernel::ConstructPerpendicularLine_2

typedef unspecified_type Kernel::Construct_perpendicular_line_3

a model of Kernel::ConstructPerpendicularLine_3

typedef unspecified_type Kernel::Construct_perpendicular_plane_3

a model of Kernel::ConstructPerpendicularPlane_3

typedef unspecified_type Kernel::Construct_perpendicular_vector_2

a model of Kernel::ConstructPerpendicularVector_2

typedef unspecified_type Kernel::Construct_plane_3

a model of Kernel::ConstructPlane_3

typedef unspecified_type Kernel::Construct_point_2

a model of Kernel::ConstructPoint_2

typedef unspecified_type Kernel::Construct_point_3

a model of Kernel::ConstructPoint_3

typedef unspecified_type Kernel::Construct_point_on_2

a model of Kernel::ConstructPointOn_2

typedef unspecified_type Kernel::Construct_point_on_3

a model of Kernel::ConstructPointOn_3

typedef unspecified_type Kernel::Construct_projected_point_2

a model of Kernel::ConstructProjectedPoint_2

typedef unspecified_type Kernel::Construct_projected_point_3

a model of Kernel::ConstructProjectedPoint_3

typedef unspecified_type Kernel::Construct_projected_xy_point_2

a model of Kernel::ConstructProjectedXYPoint_2

typedef unspecified_type Kernel::Construct_radical_line_2

a model of Kernel::ConstructRadicalLine_2

typedef unspecified_type Kernel::Construct_radical_plane_3

a model of Kernel::ConstructRadicalPlane_3

typedef unspecified_type Kernel::Construct_ray_2

a model of Kernel::ConstructRay_2

typedef unspecified_type Kernel::Construct_ray_3

a model of Kernel::ConstructRay_3

typedef unspecified_type Kernel::Construct_scaled_vector_2

a model of Kernel::ConstructScaledVector_2

typedef unspecified_type Kernel::Construct_scaled_vector_3

a model of Kernel::ConstructScaledVector_3

typedef unspecified_type Kernel::Construct_second_point_2

a model of Kernel::ConstructSecondPoint_2

Todo:

This is used in CGAL::Ray_2<K>::second_point() but is not documented

typedef unspecified_type Kernel::Construct_second_point_3

a model of Kernel::ConstructSecondPoint_3

Todo:

This is used in CGAL::Ray_2<K>::second_point() but is not documented

typedef unspecified_type Kernel::Construct_segment_2

a model of Kernel::ConstructSegment_2

typedef unspecified_type Kernel::Construct_segment_3

a model of Kernel::ConstructSegment_3

typedef unspecified_type Kernel::Construct_source_2

a model of Kernel::ConstructSource_2

typedef unspecified_type Kernel::Construct_source_3

a model of Kernel::ConstructSource_3

typedef unspecified_type Kernel::Construct_sphere_3

a model of Kernel::ConstructSphere_3

typedef unspecified_type Kernel::Construct_sum_of_vectors_2

a model of Kernel::ConstructSumOfVectors_2

typedef unspecified_type Kernel::Construct_sum_of_vectors_3

a model of Kernel::ConstructSumOfVectors_3

typedef unspecified_type Kernel::Construct_supporting_plane_3

a model of Kernel::ConstructSupportingPlane_3

typedef unspecified_type Kernel::Construct_target_2

a model of Kernel::ConstructTarget_2

typedef unspecified_type Kernel::Construct_target_3

a model of Kernel::ConstructTarget_3

typedef unspecified_type Kernel::Construct_tetrahedron_3

a model of Kernel::ConstructTetrahedron_3

typedef unspecified_type Kernel::Construct_translated_point_2

a model of Kernel::ConstructTranslatedPoint_2

typedef unspecified_type Kernel::Construct_translated_point_3

a model of Kernel::ConstructTranslatedPoint_3

typedef unspecified_type Kernel::Construct_triangle_2

a model of Kernel::ConstructTriangle_2

typedef unspecified_type Kernel::Construct_triangle_3

a model of Kernel::ConstructTriangle_3

typedef unspecified_type Kernel::Construct_vector_2

a model of Kernel::ConstructVector_2

typedef unspecified_type Kernel::Construct_vector_3

a model of Kernel::ConstructVector_3

typedef unspecified_type Kernel::Construct_vertex_2

a model of Kernel::ConstructVertex_2

typedef unspecified_type Kernel::Construct_vertex_3

a model of Kernel::ConstructVertex_3

typedef unspecified_type Kernel::Coplanar_3

a model of Kernel::Coplanar_3

typedef unspecified_type Kernel::Coplanar_orientation_3

a model of Kernel::CoplanarOrientation_3

typedef unspecified_type Kernel::Coplanar_side_of_bounded_circle_3

a model of Kernel::CoplanarSideOfBoundedCircle_3

typedef unspecified_type Kernel::Counterclockwise_in_between_2

a model of Kernel::CounterclockwiseInBetween_2

typedef unspecified_type Kernel::Direction_2

a model of Kernel::Direction_2

typedef unspecified_type Kernel::Direction_3

a model of Kernel::Direction_3

typedef unspecified_type Kernel::Do_intersect_2

a model of Kernel::DoIntersect_2

typedef unspecified_type Kernel::Do_intersect_3

a model of Kernel::DoIntersect_3

typedef unspecified_type Kernel::Equal_2

a model of Kernel::Equal_2

typedef unspecified_type Kernel::Equal_3

a model of Kernel::Equal_3

typedef unspecified_type Kernel::Equal_x_2

a model of Kernel::EqualX_2

typedef unspecified_type Kernel::Equal_x_3

a model of Kernel::EqualX_3

typedef unspecified_type Kernel::Equal_xy_3

a model of Kernel::EqualXY_3

typedef unspecified_type Kernel::Equal_y_2

a model of Kernel::EqualY_2

typedef unspecified_type Kernel::Equal_y_3

a model of Kernel::EqualY_3

typedef unspecified_type Kernel::Equal_z_3

a model of Kernel::EqualZ_3

typedef unspecified_type Kernel::FT

a model of FieldNumberType

typedef unspecified_type Kernel::Has_on_2

a model of Kernel::HasOn_2

typedef unspecified_type Kernel::Has_on_3

a model of Kernel::HasOn_3

typedef unspecified_type Kernel::Has_on_boundary_2

a model of Kernel::HasOnBoundary_2

typedef unspecified_type Kernel::Has_on_boundary_3

a model of Kernel::HasOnBoundary_3

typedef unspecified_type Kernel::Has_on_bounded_side_2

a model of Kernel::HasOnBoundedSide_2

typedef unspecified_type Kernel::Has_on_bounded_side_3

a model of Kernel::HasOnBoundedSide_3

typedef unspecified_type Kernel::Has_on_negative_side_2

a model of Kernel::HasOnNegativeSide_2

typedef unspecified_type Kernel::Has_on_negative_side_3

a model of Kernel::HasOnNegativeSide_3

typedef unspecified_type Kernel::Has_on_positive_side_2

a model of Kernel::HasOnPositiveSide_2

typedef unspecified_type Kernel::Has_on_positive_side_3

a model of Kernel::HasOnPositiveSide_3

typedef unspecified_type Kernel::Has_on_unbounded_side_2

a model of Kernel::HasOnUnboundedSide_2

typedef unspecified_type Kernel::Has_on_unbounded_side_3

a model of Kernel::HasOnUnboundedSide_3

typedef unspecified_type Kernel::Intersect_2

a model of Kernel::Intersect_2

typedef unspecified_type Kernel::Intersect_3

a model of Kernel::Intersect_3

typedef unspecified_type Kernel::Is_degenerate_2

a model of Kernel::IsDegenerate_2

typedef unspecified_type Kernel::Is_degenerate_3

a model of Kernel::IsDegenerate_3

typedef unspecified_type Kernel::Is_horizontal_2

a model of Kernel::IsHorizontal_2

typedef unspecified_type Kernel::Is_vertical_2

a model of Kernel::IsVertical_2

typedef unspecified_type Kernel::Iso_cuboid_3

a model of Kernel::IsoCuboid_3

typedef unspecified_type Kernel::Iso_rectangle_2

a model of Kernel::IsoRectangle_2

typedef unspecified_type Kernel::Left_turn_2

a model of Kernel::LeftTurn_2

typedef unspecified_type Kernel::Less_distance_to_point_2

a model of Kernel::LessDistanceToPoint_2

typedef unspecified_type Kernel::Less_distance_to_point_3

a model of Kernel::LessDistanceToPoint_3

typedef unspecified_type Kernel::Less_rotate_ccw_2

a model of Kernel::LessRotateCCW_2

typedef unspecified_type Kernel::Less_signed_distance_to_line_2

a model of Kernel::LessSignedDistanceToLine_2

typedef unspecified_type Kernel::Less_signed_distance_to_plane_3

a model of Kernel::LessSignedDistanceToPlane_3

typedef unspecified_type Kernel::Less_x_2

a model of Kernel::LessX_2

typedef unspecified_type Kernel::Less_x_3

a model of Kernel::LessX_3

typedef unspecified_type Kernel::Less_xy_2

a model of Kernel::LessXY_2

typedef unspecified_type Kernel::Less_xy_3

a model of Kernel::LessXY_3

typedef unspecified_type Kernel::Less_xyz_3

a model of Kernel::LessXYZ_3

typedef unspecified_type Kernel::Less_y_2

a model of Kernel::LessY_2

typedef unspecified_type Kernel::Less_y_3

a model of Kernel::LessY_3

typedef unspecified_type Kernel::Less_yx_2

a model of Kernel::LessYX_2

typedef unspecified_type Kernel::Less_z_3

a model of Kernel::LessZ_3

typedef unspecified_type Kernel::Line_2

a model of Kernel::Line_2

typedef unspecified_type Kernel::Line_3

a model of Kernel::Line_3

typedef unspecified_type Kernel::Object_2

a model of Kernel::Object_2

typedef unspecified_type Kernel::Object_3

a model of Kernel::Object_3

typedef unspecified_type Kernel::Orientation

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

typedef unspecified_type Kernel::Orientation_2

a model of Kernel::Orientation_2

typedef unspecified_type Kernel::Orientation_3

a model of Kernel::Orientation_3

typedef unspecified_type Kernel::Oriented_side

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

typedef unspecified_type Kernel::Oriented_side_2

a model of Kernel::OrientedSide_2

typedef unspecified_type Kernel::Oriented_side_3

a model of Kernel::OrientedSide_3

typedef unspecified_type Kernel::Plane_3

a model of Kernel::Plane_3

typedef unspecified_type Kernel::Point_2

a model of Kernel::Point_2

typedef unspecified_type Kernel::Point_3

a model of Kernel::Point_3

typedef unspecified_type Kernel::Ray_2

a model of Kernel::Ray_2

typedef unspecified_type Kernel::Ray_3

a model of Kernel::Ray_3

typedef unspecified_type Kernel::RT

a model of RingNumberType

typedef unspecified_type Kernel::Segment_2

a model of Kernel::Segment_2

typedef unspecified_type Kernel::Segment_3

a model of Kernel::Segment_3

typedef unspecified_type Kernel::Side_of_bounded_circle_2

a model of Kernel::SideOfBoundedCircle_2

typedef unspecified_type Kernel::Side_of_bounded_sphere_3

a model of Kernel::SideOfBoundedSphere_3

typedef unspecified_type Kernel::Side_of_oriented_circle_2

a model of Kernel::SideOfOrientedCircle_2

typedef unspecified_type Kernel::Side_of_oriented_sphere_3

a model of Kernel::SideOfOrientedSphere_3

typedef unspecified_type Kernel::Sign

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

typedef unspecified_type Kernel::Sphere_3

a model of Kernel::Sphere_3

typedef unspecified_type Kernel::Tetrahedron_3

a model of Kernel::Tetrahedron_3

typedef unspecified_type Kernel::Triangle_2

a model of Kernel::Triangle_2

typedef unspecified_type Kernel::Triangle_3

a model of Kernel::Triangle_3

typedef unspecified_type Kernel::Vector_2

a model of Kernel::Vector_2

typedef unspecified_type Kernel::Vector_3

a model of Kernel::Vector_3

Member Function Documentation

Kernel::Construct_vector_2 Kernel::construct_vector_2_object

(

)

const

Member Data Documentation

const bool Kernel::Has_filtered_predicates

static

A Boolean value indicating whether the predicates are filtered (as in CGAL::Filtered_kernel).

This helps propagating such decisions to traits classes which are built on top of a kernel, so that they can decide to filter their own predicates or not.