Geometry Traits Concepts

Classes
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	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...
class	AosTraits_2
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class	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...
class	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...
class	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...