2D and 3D Linear Geometry Kernel Reference

Hervé Brönnimann, Andreas Fabri, Geert-Jan Giezeman, Susan Hert, Michael Hoffmann, Lutz Kettner, Sylvain Pion, and Stefan Schirra

This package contains kernels each containing objects of constant size, such as point, vector, direction, line, ray, segment, circle as well as predicates and constructions for these objects. The kernels mainly differ in the way they handle robustness issues.

Introduced in: CGAL 0.9
BibTeX: cgal:bfghhkps-lgk23-15a
License: LGPL

Classified Reference Pages

Concepts

• Kernel

Kernel Classes and Operations

• CGAL::Cartesian<FieldNumberType>
• CGAL::Cartesian_converter<K1, K2, NTConverter>
• CGAL::cartesian_to_homogeneous
• CGAL::Filtered_kernel<CK>
• CGAL::Filtered_kernel_adaptor<CK>
• CGAL::Filtered_predicate<EP, FP, C2E, C2F>
• CGAL::Homogeneous<RingNumberType>
• CGAL::Homogeneous_converter<K1, K2, RTConverter, FTConverter>
• CGAL::homogeneous_to_cartesian
• CGAL::homogeneous_to_quotient_cartesian
• CGAL::Kernel_traits<T>
• CGAL::Simple_cartesian<FieldNumberType>
• CGAL::Simple_homogeneous<RingNumberType>
• CGAL::Projection_traits_xy_3<K>

Predefined Kernels

• CGAL::Exact_predicates_exact_constructions_kernel
• CGAL::Exact_predicates_exact_constructions_kernel_with_sqrt
• CGAL::Exact_predicates_inexact_constructions_kernel

Kernel Objects

Two-dimensional Objects

• CGAL::Aff_transformation_2<Kernel>
• CGAL::Bbox_2
• CGAL::Circle_2<Kernel>
• CGAL::Direction_2<Kernel>
• CGAL::Iso_rectangle_2<Kernel>
• CGAL::Line_2<Kernel>
• CGAL::Point_2<Kernel>
• CGAL::Ray_2<Kernel>
• CGAL::Segment_2<Kernel>
• CGAL::Triangle_2<Kernel>
• CGAL::Vector_2<Kernel>

Three-dimensional Objects

• CGAL::Bbox_3
• CGAL::Aff_transformation_3<Kernel>
• CGAL::Direction_3<Kernel>
• CGAL::Iso_cuboid_3<Kernel>
• CGAL::Line_3<Kernel>
• CGAL::Plane_3<Kernel>
• CGAL::Point_3<Kernel>
• CGAL::Ray_3<Kernel>
• CGAL::Segment_3<Kernel>
• CGAL::Circle_3<Kernel>
• CGAL::Sphere_3<Kernel>
• CGAL::Tetrahedron_3<Kernel>
• CGAL::Triangle_3<Kernel>
• CGAL::Vector_3<Kernel>

Constants and Enumerations

• CGAL::Angle
• CGAL::Bounded_side
• CGAL::Comparison_result
• CGAL::Sign
• CGAL::Orientation
• CGAL::Oriented_side
• CGAL::CLOCKWISE
• CGAL::COUNTERCLOCKWISE
• CGAL::COLLINEAR
• CGAL::LEFT_TURN
• CGAL::RIGHT_TURN
• CGAL::COPLANAR
• CGAL::DEGENERATE
• CGAL::Null_vector
• CGAL::NULL_VECTOR
• CGAL::Origin
• CGAL::ORIGIN
• CGAL::Identity_transformation
• CGAL::Reflection
• CGAL::Rotation
• CGAL::Scaling
• CGAL::Translation

Global Functions

• CGAL::angle()
• CGAL::are_ordered_along_line()
• CGAL::are_strictly_ordered_along_line()
• CGAL::area()
• CGAL::barycenter()
• CGAL::bisector()
• CGAL::centroid()
• CGAL::circumcenter()
• CGAL::collinear()
• CGAL::collinear_are_ordered_along_line()
• CGAL::collinear_are_strictly_ordered_along_line()
• CGAL::compare_distance_to_point()
• CGAL::compare_lexicographically()
• CGAL::compare_signed_distance_to_line()
• CGAL::compare_signed_distance_to_plane()
• CGAL::compare_slopes()
• CGAL::compare_dihedral_angle()
• CGAL::compare_squared_distance()
• CGAL::compare_squared_radius()
• CGAL::compare_x()
• CGAL::compare_xy()
• CGAL::compare_xyz()
• CGAL::compare_x_at_y()
• CGAL::compare_y()
• CGAL::compare_y_at_x()
• CGAL::compare_yx()
• CGAL::compare_z()
• CGAL::coplanar()
• CGAL::coplanar_orientation()
• CGAL::coplanar_side_of_bounded_circle()
• CGAL::cross_product()
• CGAL::determinant()
• CGAL::do_intersect()
• CGAL::do_overlap()
• CGAL::enum_cast()
• CGAL::equidistant_line()
• CGAL::has_larger_distance_to_point()
• CGAL::has_larger_signed_distance_to_line()
• CGAL::has_larger_signed_distance_to_plane()
• CGAL::has_smaller_distance_to_point()
• CGAL::has_smaller_signed_distance_to_line()
• CGAL::has_smaller_signed_distance_to_plane()
• CGAL::intersection()
• CGAL::left_turn()
• CGAL::lexicographically_xyz_smaller()
• CGAL::lexicographically_xyz_smaller_or_equal()
• CGAL::lexicographically_xy_larger()
• CGAL::lexicographically_xy_larger_or_equal()
• CGAL::lexicographically_xy_smaller()
• CGAL::lexicographically_xy_smaller_or_equal()
• CGAL::max_vertex()
• CGAL::midpoint()
• CGAL::normal()
• CGAL::min_vertex()
• CGAL::operator+()
• CGAL::operator-()
• CGAL::operator*()
• CGAL::opposite()
• CGAL::orthogonal_vector()
• CGAL::orientation()
• CGAL::parallel()
• CGAL::quotient_cartesian_to_homogeneous()
• CGAL::radical_plane()
• CGAL::radical_line()
• CGAL::rational_rotation_approximation()
• CGAL::right_turn()
• CGAL::side_of_bounded_circle()
• CGAL::side_of_bounded_sphere()
• CGAL::side_of_oriented_circle()
• CGAL::side_of_oriented_sphere()
• CGAL::squared_area()
• CGAL::squared_distance()
• CGAL::squared_radius()
• CGAL::unit_normal()
• CGAL::volume()
• CGAL::x_equal()
• CGAL::y_equal()
• CGAL::z_equal()

Kernel Geometric Object Concepts

• Kernel::Circle_2
• Kernel::Circle_3
• Kernel::Direction_2
• Kernel::Direction_3
• Kernel::IsoCuboid_3
• Kernel::IsoRectangle_2
• Kernel::Line_2
• Kernel::Line_3
• Kernel::Object_2
• Kernel::Object_3
• Kernel::Plane_3
• Kernel::Point_2
• Kernel::Point_3
• Kernel::Ray_2
• Kernel::Ray_3
• Kernel::Segment_2
• Kernel::Segment_3
• Kernel::Sphere_3
• Kernel::Tetrahedron_3
• Kernel::Triangle_2
• Kernel::Triangle_3
• Kernel::Vector_2
• Kernel::Vector_3

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::CollinearAreOrderedAlongLine_2
• Kernel::CollinearAreOrderedAlongLine_3
• Kernel::CollinearAreStrictlyOrderedAlongLine_2
• Kernel::CollinearAreStrictlyOrderedAlongLine_3
• Kernel::CollinearHasOn_2
• Kernel::Collinear_2
• Kernel::Collinear_3
• Kernel::CompareAngleWithXAxis_2
• Kernel::CompareDihedralAngle_3
• Kernel::CompareDistance_2
• Kernel::CompareDistance_3
• Kernel::CompareSlope_2
• Kernel::CompareSquaredDistance_2
• Kernel::CompareSquaredDistance_3
• Kernel::CompareSquaredRadius_3
• 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::CompareYX_2
• Kernel::CompareZ_3
• Kernel::ComputeA_2
• Kernel::ComputeB_2
• Kernel::ComputeC_2
• Kernel::ComputeApproximateArea_3
• Kernel::ComputeApproximateSquaredLength_3
• Kernel::ComputeArea_2
• Kernel::ComputeArea_3
• Kernel::ComputeAreaDividedByPi_3
• Kernel::ComputeDeterminant_2
• Kernel::ComputeDeterminant_3
• Kernel::ComputeDx_2
• Kernel::ComputeDy_2
• Kernel::ComputeHx_2
• Kernel::ComputeHy_2
• Kernel::ComputeScalarProduct_2
• Kernel::ComputeScalarProduct_3
• Kernel::ComputeSquaredArea_3
• Kernel::ComputeSquaredDistance_2
• Kernel::ComputeSquaredDistance_3
• Kernel::ComputeSquaredLength_2
• Kernel::ComputeSquaredLength_3
• Kernel::ComputeSquaredLengthDividedByPiSquare_3
• Kernel::ComputeSquaredRadius_2
• Kernel::ComputeSquaredRadius_3
• Kernel::ComputeVolume_3
• Kernel::ComputeX_2
• Kernel::ComputeX_3
• Kernel::ComputeY_2
• Kernel::ComputeY_3
• Kernel::ComputeZ_3
• Kernel::ComputeXmin_2
• Kernel::ComputeYmin_2
• Kernel::ComputeXmax_2
• Kernel::ComputeYmax_2
• Kernel::ComputeYAtX_2
• Kernel::ConstructBarycenter_2
• Kernel::ConstructBarycenter_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::ConstructCircle_3
• Kernel::ConstructCircumcenter_2
• Kernel::ConstructCircumcenter_3
• Kernel::ConstructCrossProductVector_3
• Kernel::ConstructDifferenceOfVectors_2
• Kernel::ConstructDifferenceOfVectors_3
• Kernel::ConstructDirection_2
• Kernel::ConstructDirection_3
• Kernel::ConstructDividedVector_2
• Kernel::ConstructDividedVector_3
• Kernel::ConstructEquidistantLine_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::ConstructNormal_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::ConstructRadicalLine_2
• Kernel::ConstructRadicalPlane_3
• Kernel::ConstructRay_2
• Kernel::ConstructRay_3
• Kernel::ConstructScaledVector_2
• Kernel::ConstructScaledVector_3
• Kernel::ConstructSecondPoint_2
• Kernel::ConstructSegment_2
• Kernel::ConstructSegment_3
• Kernel::ConstructSource_2
• Kernel::ConstructSphere_3
• Kernel::ConstructSumOfVectors_2
• Kernel::ConstructSumOfVectors_3
• Kernel::ConstructSupportingPlane_3
• Kernel::ConstructTarget_2
• Kernel::ConstructTetrahedron_3
• Kernel::ConstructTranslatedPoint_2
• Kernel::ConstructTranslatedPoint_3
• Kernel::ConstructTriangle_2
• Kernel::ConstructTriangle_3
• Kernel::ConstructUnitNormal_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::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::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::Orientation_2
• Kernel::Orientation_3
• Kernel::OrientedSide_2
• Kernel::OrientedSide_3
• Kernel::SideOfBoundedCircle_2
• Kernel::SideOfBoundedSphere_3
• Kernel::SideOfOrientedCircle_2
• Kernel::SideOfOrientedSphere_3

Dimension handling tools

• CGAL::Ambient_dimension<T, K>
• CGAL::Feature_dimension<T, K>
• CGAL::Dimension_tag<int dim>
• CGAL::Dynamic_dimension_tag

Modules
	Concepts
	Predefined Kernels
	2D Kernel Objects
	3D Kernel Objects
	Kernel Classes
	Global Kernel Functions
	Enumerations and Related Functions
	Cartesian/Homogenous Conversion
	Dimension Handling Tools

Classes
class	CGAL::Null_vector
	CGAL defines a symbolic constant NULL_VECTOR to construct zero length vectors. More...
class	CGAL::Origin
	CGAL defines a symbolic constant ORIGIN which denotes the point at the origin. More...