CGAL 6.2 - 2D Arrangements

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Geometry Traits Concepts
Reference Manual » Concepts

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## Concepts
concept | AosApproximatePointTraits_2
| The concept `AosApproximatePointTraits_2` refines the basic traits concept `AosBasicTraits_2`. A model of this concept is able to approximate a point. More...
concept | AosApproximateTraits_2
| The concept `AosApproximateTraits_2` refines the concept `AosApproximatePointTraits_2`. A model of this concept is able to approximate a point and a curve (in addition to the ability to approximate the coordinates of a point). More...
concept | AosApproximateUnboundedTraits_2
| The concept `AosApproximateUnboundedTraits_2` refines the concept `AosApproximateTraits_2`. A model of this concept is able to approximate a curve constrained to a given bounding box (in addition to the ability to approximate a point and a curve without constraints). More...
concept | AosBasicTraits_2
| The concept `AosBasicTraits_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...
concept | AosBottomSideTraits_2
| `AosBottomSideTraits_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...
concept | AosClosedBottomTraits_2
| A model of the concept `AosClosedBottomTraits_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...
concept | AosClosedLeftTraits_2
| A model of the concept `AosClosedLeftTraits_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...
concept | AosClosedRightTraits_2
| A model of the concept `AosClosedRightTraits_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...
concept | AosClosedTopTraits_2
| A model of the concept `AosClosedTopTraits_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...
concept | AosConstructCurveTraits_2
| The concept `AosConstructCurveTraits_2` refines the basic traits concept `AosBasicTraits_2`. A model of this concept is able to construct a curve from two points. More...
concept | AosConstructXMonotoneCurveTraits_2
| The concept `AosConstructXMonotoneCurveTraits_2` refines the basic traits concept `AosBasicTraits_2`. A model of this concept is able to construct an \(x\)-monotone curve from two points. More...
concept | AosContractedBottomTraits_2
| A model of the concept `AosContractedBottomTraits_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...
concept | AosContractedLeftTraits_2
| A model of the concept `AosContractedLeftTraits_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...
concept | AosContractedRightTraits_2
| A model of the concept `AosContractedRightTraits_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...
concept | AosContractedTopTraits_2
| A model of the concept `AosContractedTopTraits_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...
concept | AosHorizontalSideTraits_2
| `AosHorizontalSideTraits_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...
concept | AosIdentifiedHorizontalTraits_2
| A model of the concept `AosIdentifiedHorizontalTraits_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...
concept | AosIdentifiedVerticalTraits_2
| A model of the concept `AosIdentifiedVerticalTraits_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...
concept | AosLandmarkTraits_2
| The concept `AosLandmarkTraits_2` refines the traits concepts `AosApproximatePointTraits_2` and `AosConstructXMonotoneCurveTraits_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 by a model of this concept. More...
concept | AosLeftSideTraits_2
| `AosLeftSideTraits_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...
concept | AosOpenBottomTraits_2
| A model of the concept `AosOpenBottomTraits_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...
concept | AosOpenBoundaryTraits_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 `AosOpenBoundaryTraits_2` handle curves that approach the boundary of a parameter space. This concept refines the concept `AosBasicTraits_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 `AosOpenBoundaryTraits_2`, nonetheless, also supports planar \(x\)-monotone curves that reach the boundary of an open yet bounded parameter space. More...
concept | AosOpenLeftTraits_2
| A model of the concept `AosOpenLeftTraits_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...
concept | AosOpenRightTraits_2
| A model of the concept `AosOpenRightTraits_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...
concept | AosOpenTopTraits_2
| A model of the concept `AosOpenTopTraits_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...
concept | AosRightSideTraits_2
| `AosRightSideTraits_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...
concept | AosSphericalBoundaryTraits_2
| Models of the concept `AosSphericalBoundaryTraits_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...
concept | AosTopSideTraits_2
| `AosTopSideTraits_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...
concept | AosTraits_2
| The concept `AosTraits_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...
concept | AosVerticalSideTraits_2
| `AosVerticalSideTraits_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...
concept | AosXMonotoneTraits_2
| The concept `AosXMonotoneTraits_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...
concept | OverlayTraits
| 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...