CGAL 5.5 - 2D Arrangements
Geometry Traits Concepts

## Concepts

conceptArrangementApproximateTraits_2
The concept ArrangementApproximateTraits_2 refines the basic traits concept ArrangementBasicTraits_2. A model of this concept is able to approximate a point. More...

conceptArrangementBasicTraits_2
The concept ArrangementBasicTraits_2 defines the minimal set of geometric predicates needed for the construction and maintenance of objects of the class Arrangement_2, as well as performing simple queries (such as point-location queries) on such arrangements. More...

conceptArrangementBottomSideTraits_2
ArrangementBottomSideTraits_2 is an abstract concept. It generalizes all concepts that handle curves that either reach or approach the bottom boundary side of the parameter space. (An "abstract" concept is a concept that is useless on its own.) Only a combination of this concept and additional concepts that handle curves that either reach or approach the remaining boundary sides (that is, left, right, and top) are purposeful, and can have models. More...

conceptArrangementClosedBottomTraits_2
A model of the concept ArrangementClosedBottomTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is closed on the left side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the left boundary side when it is closed. More...

conceptArrangementClosedLeftTraits_2
A model of the concept ArrangementClosedLeftTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is closed on the left side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the left boundary side when it is closed. More...

conceptArrangementClosedRightTraits_2
A model of the concept ArrangementClosedRightTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is closed on the right side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the right boundary side when it is closed. More...

conceptArrangementClosedTopTraits_2
A model of the concept ArrangementClosedTopTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is closed on the top side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the top boundary side when it is closed. More...

conceptArrangementConstructCurveTraits_2
The concept ArrangementConstructCurveTraits_2 refines the basic traits concept ArrangementBasicTraits_2. A model of this concept is able to construct a curve from two points. More...

conceptArrangementConstructXMonotoneCurveTraits_2
The concept ArrangementConstructXMonotoneCurveTraits_2 refines the basic traits concept ArrangementBasicTraits_2. A model of this concept is able to construct an $$x$$-monotone curve from two points. More...

conceptArrangementContractedBottomTraits_2
A model of the concept ArrangementContractedBottomTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is contracted on the bottom side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the bottom boundary side when it is contracted. More...

conceptArrangementContractedLeftTraits_2
A model of the concept ArrangementContractedLeftTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is contracted on the left side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the left boundary side when it is contracted. More...

conceptArrangementContractedRightTraits_2
A model of the concept ArrangementContractedRightTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is contracted on the right side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the right boundary side when it is contracted. More...

conceptArrangementContractedTopTraits_2
A model of the concept ArrangementContractedTopTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is contracted on the top side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the top boundary side when it is contracted. More...

conceptArrangementHorizontalSideTraits_2
ArrangementHorizontalSideTraits_2 is an abstract concept. It generalizes all concepts that handle curves that either reach or approach either the bottom or top sizeds of the boundary of the parameter space. (An "abstract" concept is a concept that is useless on its own.) Only a combination of this concept and one or more concepts that handle curves that either reach or approach the remaining boundary sides (that is, left and right) are purposeful, and can have models. More...

conceptArrangementIdentifiedHorizontalTraits_2
A model of the concept ArrangementIdentifiedHorizontalTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is identified on the bottom and top sides and curves inserted into the arrangement are expected to reach these boundary sides. More...

conceptArrangementIdentifiedVerticalTraits_2
A model of the concept ArrangementIdentifiedVerticalTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is identified on the left and right sides and curves inserted into the arrangement are expected to reach these boundary sides. More...

conceptArrangementLandmarkTraits_2
The concept ArrangementLandmarkTraits_2 refines the traits concepts ArrangementApproximateTraits_2 and ArrangementConstructXMonotoneCurveTraits_2. The type of an arrangement associated with the landmark point-location strategy (see CGAL::Arr_landmarks_point_location) must be an instance of the CGAL::Arrangement_2<Traits,Dcel> class template, where the Traits parameter is substituted with a model of this concept. More...

conceptArrangementLeftSideTraits_2
ArrangementLeftSideTraits_2 is an abstract concept. It generalizes all concepts that handle curves that either reach or approach the left boundary side of the parameter space. (An "abstract" concept is a concept that is useless on its own.) Only a combination of this concept and additional concepts that handle curves that either reach or approach the remaining boundary sides (that is, right, bottom, and top) are purposeful, and can have models. More...

conceptArrangementOpenBottomTraits_2
A model of the concept ArrangementOpenBottomTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is open on the bottom side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the bottom boundary side when it is open. More...

conceptArrangementOpenBoundaryTraits_2
Several predicates are required to handle $$x$$-monotone curves that approach infinity and thus approach the boundary of the parameter space. These predicates are sufficient to handle not only curves embedded in an unbounded parameter space, but also curves embedded in a bounded parameter space with open boundaries. Models of the concept ArrangementOpenBoundaryTraits_2 handle curves that approach the boundary of a parameter space. This concept refines the concept ArrangementBasicTraits_2. The arrangement template instantiated with a traits class that models this concept can handle $$x$$-monotone curves that are unbounded in any direction. The concept ArrangementOpenBoundaryTraits_2, nontheless, also supports planar $$x$$-monotone curves that reach the boundary of an open yet bounded parameter space. More...

conceptArrangementOpenLeftTraits_2
A model of the concept ArrangementOpenLeftTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is open on the left side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the left boundary side when it is open. More...

conceptArrangementOpenRightTraits_2
A model of the concept ArrangementOpenRightTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is open on the right side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the right boundary side when it is open. More...

conceptArrangementOpenTopTraits_2
A model of the concept ArrangementOpenTopTraits_2 must be used when the parameter space of the surface, the arrangement is embedded on, is open on the top side and curves inserted into the arrangement are expected to reach this boundary side. A model of this concept can handle curves that reach the top boundary side when it is open. More...

conceptArrangementRightSideTraits_2
ArrangementRightSideTraits_2 is an abstract concept. It generalizes all concepts that handle curves that either reach or approach the right boundary side of the parameter space. (An "abstract" concept is a concept that is useless on its own.) Only a combination of this concept and additional concepts that handle curves that either reach or approach the remaining boundary sides (that is, left, bottom, and top) are purposeful, and can have models. More...

conceptArrangementSphericalBoundaryTraits_2
Models of the concept ArrangementSphericalBoundaryTraits_2 handle curves on a sphere or a surface that is topological equivalent to a sphere. The sphere is oriented in such a way that the boundary of the rectangular parameter space, the sphere is the mapping of which, is identified on the left and right sides and contracted at the top and bottom sides. More...

conceptArrangementTopSideTraits_2
ArrangementTopSideTraits_2 is an abstract concept. It generalizes all concepts that handle curves that either reach or approach the top boundary side of the parameter space. (An "abstract" concept is a concept that is useless on its own.) Only a combination of this concept and additional concepts that handle curves that either reach or approach the remaining boundary sides (that is, left, right, and bottom) are purposeful, and can have models. More...

conceptArrangementTraits_2
The concept ArrangementTraits_2 allows the construction of arrangement of general planar curves. Models of this concept are used by the free CGAL::insert() functions of the arrangement package and by the CGAL::Arrangement_with_history_2 class. More...

conceptArrangementVerticalSideTraits_2
ArrangementVerticalSideTraits_2 is an abstract concept. It generalizes all concepts that handle curves that either reach or approach either the left or right sizeds of the boundary of the parameter space. (An "abstract" concept is a concept that is useless on its own.) Only a combination of this concept and one or more concepts that handle curves that either reach or approach the remaining boundary sides (that is, bottom and top) are purposeful, and can have models. More...

conceptArrangementXMonotoneTraits_2
The concept ArrangementXMonotoneTraits_2 refines the basic arrangement-traits concept. A model of this concept is able to handle $$x$$-monotone curves that intersect in their interior (and points that coincide with curve interiors). This is necessary for constructing arrangements of sets of intersecting $$x$$-monotone curves. More...

conceptOverlayTraits
A model for the OverlayTraits should be able to operate on records (namely, vertices, halfedges and faces) of two input DCEL classes, named Dcel_A and Dcel_B, and construct the records of an output DCEL class, referred to as Dcel_R. More...