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-lgk23-19a
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>
• CGAL::Weighted_point_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>
• CGAL::Weighted_point_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::l_infinity_distance()
• 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::scalar_product()
• 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::WeightedPoint_2
• Kernel::WeightedPoint_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::CompareSlope_3
• Kernel::ComparePowerDistance_2
• Kernel::ComparePowerDistance_3
• Kernel::CompareSquaredDistance_2
• Kernel::CompareSquaredDistance_3
• Kernel::CompareSquaredRadius_3
• Kernel::CompareWeightedSquaredRadius_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::ComputeApproximateDihedralAngle_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::ComputeLInfinityDistance_2
• Kernel::ComputeLInfinityDistance_3
• Kernel::ComputePowerDistanceToPowerSphere_3
• Kernel::ComputePowerProduct_2
• Kernel::ComputePowerProduct_3
• 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::ComputeSquaredRadiusSmallestOrthogonalCircle_2
• Kernel::ComputeSquaredRadiusSmallestOrthogonalSphere_3
• Kernel::ComputeVolume_3
• Kernel::ComputeWeight_2
• Kernel::ComputeWeight_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::ConstructRadicalAxis_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::ConstructWeightedCircumcenter_3
• Kernel::ConstructWeightedPoint_2
• Kernel::ConstructWeightedPoint_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::PowerSideOfBoundedPowerCircle_2
• Kernel::PowerSideOfBoundedPowerSphere_3
• Kernel::PowerSideOfOrientedPowerCircle_2
• Kernel::PowerSideOfOrientedPowerSphere_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...