\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 2D and 3D Linear Geometry Kernel
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Refinement Relationships
Concept Kernel::AreOrderedAlongLine_2
AdaptableFunctor (with three arguments)
Concept Kernel::AreOrderedAlongLine_3
AdaptableFunctor (with three arguments)
Concept Kernel::AreParallel_2
AdaptableFunctor (with two arguments)
Concept Kernel::AreParallel_3
AdaptableFunctor (with two arguments)
Concept Kernel::AreStrictlyOrderedAlongLine_2
AdaptableFunctor (with three arguments)
Concept Kernel::AreStrictlyOrderedAlongLine_3
AdaptableFunctor (with three arguments)
Concept Kernel::Assign_2
AdaptableFunctor (with two arguments)
Concept Kernel::Assign_3
AdaptableFunctor (with two arguments)
Concept Kernel::BoundedSide_2
AdaptableFunctor (with two arguments)
Concept Kernel::BoundedSide_3
AdaptableFunctor (with two arguments)
Concept Kernel::CartesianConstIterator_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::CartesianConstIterator_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Circle_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Circle_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Collinear_2
AdaptableFunctor (with three arguments)
Concept Kernel::Collinear_3
AdaptableFunctor (with three arguments)
Concept Kernel::CollinearAreOrderedAlongLine_2
AdaptableFunctor (with three arguments)
Concept Kernel::CollinearAreOrderedAlongLine_3
AdaptableFunctor (with three arguments)
Concept Kernel::CollinearAreStrictlyOrderedAlongLine_2
AdaptableFunctor (with three arguments)
Concept Kernel::CollinearAreStrictlyOrderedAlongLine_3
AdaptableFunctor (with three arguments)
Concept Kernel::CollinearHasOn_2
AdaptableFunctor (with two arguments)
Concept Kernel::CompareAngleWithXAxis_2
AdaptableFunctor (with two arguments)
Concept Kernel::CompareDistance_2
AdaptableFunctor (with three arguments)
Concept Kernel::CompareDistance_3
AdaptableFunctor (with three arguments)
Concept Kernel::CompareSlope_2
AdaptableFunctor (with two arguments)
Concept Kernel::CompareSquaredDistance_2
AdaptableFunctor (with three arguments)
Concept Kernel::CompareSquaredDistance_3
AdaptableFunctor (with three arguments)
Concept Kernel::CompareSquaredRadius_3
AdaptableFunctor (with three arguments)
Concept Kernel::CompareX_2
AdaptableFunctor (with two arguments)
Concept Kernel::CompareX_3
AdaptableFunctor (with two arguments)
Concept Kernel::CompareXAtY_2
AdaptableFunctor (with three arguments)
Concept Kernel::CompareXY_2
AdaptableFunctor (with two arguments)
Concept Kernel::CompareXY_3
AdaptableFunctor (with two arguments)
Concept Kernel::CompareXYZ_3
AdaptableFunctor (with two arguments)
Concept Kernel::CompareY_2
AdaptableFunctor (with two arguments)
Concept Kernel::CompareY_3
AdaptableFunctor (with two arguments)
Concept Kernel::CompareYAtX_2
AdaptableFunctor (with three arguments)
Concept Kernel::CompareYX_2
AdaptableFunctor (with two arguments)
Concept Kernel::CompareZ_3
AdaptableFunctor (with two arguments)
Concept Kernel::ComputeA_2
AdaptableFunctor
Concept Kernel::ComputeA_3
AdaptableFunctor
Concept Kernel::ComputeApproximateArea_3
AdaptableFunctor
Concept Kernel::ComputeApproximateSquaredLength_3
AdaptableFunctor (with one argument)
Concept Kernel::ComputeArea_2
AdaptableFunctor (with one argument)
Concept Kernel::ComputeArea_3
AdaptableFunctor (with one argument)
Concept Kernel::ComputeAreaDividedByPi_3
AdaptableFunctor (with one argument)
Concept Kernel::ComputeB_2
AdaptableFunctor
Concept Kernel::ComputeB_3
AdaptableFunctor
Concept Kernel::ComputeC_2
AdaptableFunctor
Concept Kernel::ComputeC_3
AdaptableFunctor
Concept Kernel::ComputeD_3
AdaptableFunctor
Concept Kernel::ComputeDeterminant_2
AdaptableFunctor (with two arguments)
Concept Kernel::ComputeDeterminant_3
AdaptableFunctor (with three arguments)
Concept Kernel::ComputeDx_2
AdaptableFunctor
Concept Kernel::ComputeDx_3
AdaptableFunctor
Concept Kernel::ComputeDy_2
AdaptableFunctor
Concept Kernel::ComputeDy_3
AdaptableFunctor
Concept Kernel::ComputeDz_3
AdaptableFunctor
Concept Kernel::ComputeHw_2
AdaptableFunctor
Concept Kernel::ComputeHw_3
AdaptableFunctor
Concept Kernel::ComputeHx_2
AdaptableFunctor
Concept Kernel::ComputeHx_3
AdaptableFunctor
Concept Kernel::ComputeHy_2
AdaptableFunctor
Concept Kernel::ComputeHy_3
AdaptableFunctor
Concept Kernel::ComputeHz_3
AdaptableFunctor
Concept Kernel::ComputeScalarProduct_2
AdaptableFunctor (with two arguments)
Concept Kernel::ComputeScalarProduct_3
AdaptableFunctor (with two arguments)
Concept Kernel::ComputeSquaredArea_3
AdaptableFunctor (with one argument)
Concept Kernel::ComputeSquaredDistance_2
AdaptableFunctor (with two arguments)
Concept Kernel::ComputeSquaredDistance_3
AdaptableFunctor (with two arguments)
Concept Kernel::ComputeSquaredLength_2
AdaptableFunctor (with one argument)
Concept Kernel::ComputeSquaredLength_3
AdaptableFunctor (with one argument)
Concept Kernel::ComputeSquaredLengthDividedByPiSquare_3
AdaptableFunctor (with one argument)
Concept Kernel::ComputeSquaredRadius_2
AdaptableFunctor (with one argument)
Concept Kernel::ComputeSquaredRadius_3
AdaptableFunctor (with one argument)
Concept Kernel::ComputeVolume_3
AdaptableFunctor (with one argument)
Concept Kernel::ComputeX_2
AdaptableFunctor
Concept Kernel::ComputeX_3
AdaptableFunctor
Concept Kernel::ComputeXmax_2
AdaptableFunctor
Concept Kernel::ComputeXmax_3
AdaptableFunctor
Concept Kernel::ComputeXmin_2
AdaptableFunctor
Concept Kernel::ComputeXmin_3
AdaptableFunctor
Concept Kernel::ComputeY_2
AdaptableFunctor
Concept Kernel::ComputeY_3
AdaptableFunctor
Concept Kernel::ComputeYAtX_2
AdaptableFunctor
Concept Kernel::ComputeYmax_2
AdaptableFunctor
Concept Kernel::ComputeYmax_3
AdaptableFunctor
Concept Kernel::ComputeYmin_2
AdaptableFunctor
Concept Kernel::ComputeYmin_3
AdaptableFunctor
Concept Kernel::ComputeZ_3
AdaptableFunctor
Concept Kernel::ComputeZmax_3
AdaptableFunctor
Concept Kernel::ComputeZmin_3
AdaptableFunctor
Concept Kernel::ConstructBarycenter_2
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructBarycenter_3
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructBaseVector_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructBbox_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructBbox_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructBisector_2
AdaptableFunctor
Concept Kernel::ConstructBisector_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructCartesianConstIterator_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructCartesianConstIterator_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructCenter_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructCenter_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructCentroid_2
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructCentroid_3
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructCircle_2
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructCircle_3
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructCircumcenter_2
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructCircumcenter_3
AdaptableFunctor (with four arguments)
Concept Kernel::ConstructCrossProductVector_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructDifferenceOfVectors_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructDifferenceOfVectors_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructDirection_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructDirection_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructDividedVector_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructDividedVector_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructEquidistantLine_3
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructIsoCuboid_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructIsoRectangle_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructLiftedPoint_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructLine_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructLine_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructMaxVertex_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructMaxVertex_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructMidpoint_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructMidpoint_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructMinVertex_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructMinVertex_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructNormal_3
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructObject_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructObject_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeCircle_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeDirection_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeDirection_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeLine_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeLine_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositePlane_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeRay_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeRay_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeSegment_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeSegment_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeSphere_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeTriangle_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeVector_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOppositeVector_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructOrthogonalVector_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructPerpendicularDirection_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructPerpendicularLine_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructPerpendicularLine_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructPerpendicularPlane_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructPerpendicularVector_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructPlane_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructPoint_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructPoint_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructPointOn_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructPointOn_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructProjectedPoint_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructProjectedPoint_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructProjectedXYPoint_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructRadicalLine_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructRadicalPlane_3
AdaptableFunctor (with two argument)
Concept Kernel::ConstructRay_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructRay_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructScaledVector_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructScaledVector_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructSecondPoint_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructSecondPoint_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructSegment_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructSegment_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructSource_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructSource_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructSphere_3
AdaptableFunctor (with four arguments)
Concept Kernel::ConstructSumOfVectors_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructSumOfVectors_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructSupportingPlane_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructTarget_2
AdaptableFunctor (with one argument)
Concept Kernel::ConstructTarget_3
AdaptableFunctor (with one argument)
Concept Kernel::ConstructTetrahedron_3
AdaptableFunctor (with four arguments)
Concept Kernel::ConstructTranslatedPoint_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructTranslatedPoint_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructTriangle_2
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructTriangle_3
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructUnitNormal_3
AdaptableFunctor (with three arguments)
Concept Kernel::ConstructVector_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructVector_3
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructVertex_2
AdaptableFunctor (with two arguments)
Concept Kernel::ConstructVertex_3
AdaptableFunctor (with two arguments)
Concept Kernel::Coplanar_3
AdaptableFunctor (with four arguments)
Concept Kernel::CoplanarOrientation_3
AdaptableFunctor (with four arguments)
Concept Kernel::CoplanarSideOfBoundedCircle_3
AdaptableFunctor (with four arguments)
Concept Kernel::CounterclockwiseInBetween_2
AdaptableFunctor (with three arguments)
Concept Kernel::Direction_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Direction_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::DoIntersect_2
AdaptableFunctor (with two arguments)
Concept Kernel::DoIntersect_3
AdaptableFunctor (with two arguments)
Concept Kernel::Equal_2
AdaptableFunctor (with two arguments)
Concept Kernel::Equal_3
AdaptableFunctor (with two arguments)
Concept Kernel::EqualX_2
AdaptableFunctor (with two arguments)
Concept Kernel::EqualX_3
AdaptableFunctor (with two arguments)
Concept Kernel::EqualXY_3
AdaptableFunctor (with two arguments)
Concept Kernel::EqualY_2
AdaptableFunctor (with two arguments)
Concept Kernel::EqualY_3
AdaptableFunctor (with two arguments)
Concept Kernel::EqualZ_3
AdaptableFunctor (with two arguments)
Concept Kernel::HasOn_2
AdaptableFunctor (with two arguments)
Concept Kernel::HasOn_3
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnBoundary_2
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnBoundary_3
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnBoundedSide_2
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnBoundedSide_3
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnNegativeSide_2
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnNegativeSide_3
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnPositiveSide_2
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnPositiveSide_3
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnUnboundedSide_2
AdaptableFunctor (with two arguments)
Concept Kernel::HasOnUnboundedSide_3
AdaptableFunctor (with two arguments)
Concept Kernel::Intersect_2
AdaptableFunctor (with two arguments)
Concept Kernel::Intersect_3
AdaptableFunctor (with two or three arguments)
Concept Kernel::IsDegenerate_2
AdaptableFunctor (with one argument)
Concept Kernel::IsDegenerate_3
AdaptableFunctor (with one argument)
Concept Kernel::IsHorizontal_2
AdaptableFunctor (with one argument)
Concept Kernel::IsoCuboid_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::IsoRectangle_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::IsVertical_2
AdaptableFunctor (with one argument)
Concept Kernel::LeftTurn_2
AdaptableFunctor (with three arguments)
Concept Kernel::LessDistanceToPoint_2
AdaptableFunctor (with three arguments)
Concept Kernel::LessDistanceToPoint_3
AdaptableFunctor (with three arguments)
Concept Kernel::LessRotateCCW_2
AdaptableFunctor (with three arguments)
Concept Kernel::LessSignedDistanceToLine_2
AdaptableFunctor` (with four arguments)
Concept Kernel::LessSignedDistanceToPlane_3
AdaptableFunctor (with three arguments)
Concept Kernel::LessX_2
AdaptableFunctor (with two arguments)
Concept Kernel::LessX_3
AdaptableFunctor (with two arguments)
Concept Kernel::LessXY_2
AdaptableFunctor (with two arguments)
Concept Kernel::LessXY_3
AdaptableFunctor (with two arguments)
Concept Kernel::LessXYZ_3
AdaptableFunctor (with two arguments)
Concept Kernel::LessY_2
AdaptableFunctor (with two arguments)
Concept Kernel::LessY_3
AdaptableFunctor (with two arguments)
Concept Kernel::LessYX_2
AdaptableFunctor (with two arguments)
Concept Kernel::Line_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Line_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Object_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Object_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Orientation_2
AdaptableFunctor (with three arguments)
Concept Kernel::Orientation_3
AdaptableFunctor (with four arguments)
Concept Kernel::OrientedSide_2
AdaptableFunctor (with two arguments)
Concept Kernel::OrientedSide_3
AdaptableFunctor (with two arguments)
Concept Kernel::Plane_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Point_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Point_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Ray_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Ray_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Segment_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Segment_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::SideOfBoundedCircle_2
AdaptableFunctor (with four arguments)
Concept Kernel::SideOfBoundedSphere_3
AdaptableFunctor (with five arguments)
Concept Kernel::SideOfOrientedCircle_2
AdaptableFunctor (with four arguments)
Concept Kernel::SideOfOrientedSphere_3
AdaptableFunctor (with five arguments)
Concept Kernel::Sphere_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Tetrahedron_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Triangle_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Triangle_3

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Vector_2

CopyConstructible

Assignable

DefaultConstructible

Concept Kernel::Vector_3

CopyConstructible

Assignable

DefaultConstructible