Class and Concept List

Here is the list of all concepts and classes of this package. Classes are inside the namespace CGAL. Concepts are in the global namespace.

[detail level 123]

►NArrTraits	The namespace containing concepts specific to Arrangements
CApproximate_2
CAreMergeable_2
CCompareX_2
CCompareXNearBoundary_2
CCompareXOnBoundary_2
CCompareXOnBoundaryOfCurveEnd_2
CCompareXy_2
CCompareYAtX_2
CCompareYAtXLeft_2
CCompareYAtXRight_2
CCompareYNearBoundary_2
CCompareYOnBoundary_2
CConstructCurve_2
CConstructMaxVertex_2
CConstructMinVertex_2
CConstructXMonotoneCurve_2
CCurve_2	General planar curve
CEqual_2
CIntersect_2
CIsOnXIdentification_2
CIsOnYIdentification_2
CIsVertical_2
CMakeXMonotone_2
CMerge_2
CParameterSpaceInX_2
CParameterSpaceInY_2
CPoint_2	Represents a point in the plane
CSplit_2
CXMonotoneCurve_2	Represents a planar (weakly) \(x\)-monotone curve
►NCGAL
CAos_observer
CArr_accessor
►CArr_algebraic_segment_traits_2	The traits class Arr_algebraic_segment_traits_2 is a model of the ArrangementTraits_2 concept that handles planar algebraic curves of arbitrary degree, and \( x\)-monotone of such curves
CConstruct_curve_2
CConstruct_point_2
CConstruct_x_monotone_segment_2
CCurve_2	Models the ArrangementTraits_2::Curve_2 concept
CPoint_2	Models the ArrangementBasicTraits_2::Point_2 concept
CX_monotone_curve_2	Models the ArrangementBasicTraits_2::X_monotone_curve_2 concept
►CArr_Bezier_curve_traits_2	The traits class Arr_Bezier_curve_traits_2 is a model of the ArrangementTraits_2 concept that handles planar Bézier curves
CCurve_2	The Curve_2 class nested within the Bézier traits class is used to represent a Bézier curve of arbitrary degree, which is defined by a sequence of rational control points
CPoint_2	The Point_2 class nested within the Bézier traits class is used to represent: (i) an endpoint of a Bézier curve, (ii) a vertical tangency point of a curve, used to subdivide it into \( x\)-monotone subcurve, and (iii) an intersection point between two curves
CTrim_2
CX_monotone_curve_2	The X_monotone_curve_2 class nested within the Bézier traits is used to represent \( x\)-monotone subcurves of Bézier curves
CArr_bounded_planar_topology_traits_2
►CArr_circle_segment_traits_2	The class Arr_circle_segment_traits_2 is a model of the ArrangementTraits_2 concept and can be used to construct and maintain arrangements of circular arcs and line segments
CCurve_2	The Curve_2 class nested within the traits class can represent arbitrary circular arcs, full circles and line segments and support their construction in various ways
CPoint_2	The Point_2 number-type nested within the traits class represents a Cartesian point whose coordinates are algebraic numbers of type CoordNT
CTrim_2
CX_monotone_curve_2	The X_monotone_curve_2 class nested within the traits class can represent \( x\)-monotone and line segments (which are always weakly \(x\)-monotone)
CArr_circular_arc_traits_2	This class is a traits class for CGAL arrangements, built on top of a model of concept CircularKernel
CArr_circular_line_arc_traits_2	This class is a traits class for CGAL arrangements, built on top of a model of concept CircularKernel
CArr_closed_side_tag	This type tag is used to indicate that a side of the parameter space, either left, right, bottom, or top, is closed, and curves that reach this side might be inserted into the arrangement
►CArr_conic_traits_2	The class Arr_conic_traits_2 is a model of the ArrangementTraits_2 concept and can be used to construct and maintain arrangements of bounded segments of algebraic curves of degree \(2\) at most, also known as conic curves
CApproximate_2	A functor that approximates a point and an \(x\)-monotone curve
CConstruct_bbox_2	A functor that constructs a bounding box of a conic arc
CConstruct_curve_2	A functor that constructs a conic arc
CConstruct_x_monotone_curve_2	A functor that constructs an \(x\)-monotone conic arc
CCurve_2	The Curve_2 class nested within the conic-arc traits can represent arbitrary conic arcs and support their construction in various ways
CPoint_2	The Point_2 class nested within the conic-arc traits is used to represent points
CTrim_2	A functor that trims a conic arc
CX_monotone_curve_2	The X_monotone_curve_2 class nested within the conic-arc traits is used to represent \(x\)-monotone conic arcs
►CArr_consolidated_curve_data_traits_2	The class Arr_consolidated_curve_data_traits_2 is a model of the concept ArrangementTraits_2, and serves as a decorator class that enables the extension of the curve type defined by the Traits parameter
CData_container	The Data_container class nested within the consolidated curve-data traits and associated with the Traits::X_monotone_curve_2 type is maintained as a list with unique data objects
CArr_contracted_side_tag	This type tag is used to indicate that a side of the parameter space, either left, right, bottom, or top, is contracted, and curves that approach this side might be inserted into the arrangement
►CArr_curve_data_traits_2	The class Arr_curve_data_traits_2 is a model of the ArrangementTraits_2 concept and serves as a decorator class that allows the extension of the curves defined by the base traits-class (the Tr parameter), which serves as a geometric traits-class (a model of the ArrangementTraits_2 concept), with extraneous (non-geometric) data fields
CCurve_2	The Curve_2 class nested within the curve-data traits extends the Base_traits_2::Curve_2 type with an extra data field of type Data
CX_monotone_curve_2	The X_monotone_curve_2 class nested within the curve-data traits extends the Base_traits_2::X_monotone_curve_2 type with an extra data field
CArr_dcel	The DCEL class used by the Arrangement_2, Arr_bounded_planar_topology_traits_2, Arr_unb_planar_topology_traits_2 class templates and other templates
►CArr_dcel_base
CArr_face_base	The basic DCEL face type
CArr_halfedge_base	The basic DCEL halfedge type
CArr_vertex_base	The basic DCEL vertex type
CArr_default_overlay_traits	An instance of Arr_default_overlay_traits should be used for overlaying two arrangements of type Arrangement that store no auxiliary data with their DCEL records, where the resulting overlaid arrangement stores no auxiliary DCEL data as well
CArr_extended_dcel	The Arr_extended_dcel class-template extends the topological-features of the DCEL namely the vertex, halfedge, and face types
CArr_extended_dcel_text_formatter	Arr_extended_dcel_text_formatter defines the format of an arrangement in an input or output stream (typically a file stream), thus enabling reading and writing an Arrangement instance using a simple text format
CArr_extended_face	The Arr_extended_face class-template extends the face topological-features of the DCEL
CArr_extended_halfedge	The Arr_extended_halfedge class-template extends the halfedge topological-features of the DCEL
CArr_extended_vertex	The Arr_extended_vertex class-template extends the vertex topological-features of the DCEL
CArr_face_extended_dcel	The Arr_face_extended_dcel class-template extends the DCEL face-records, making it possible to store extra (non-geometric) data with the arrangement faces
CArr_face_extended_text_formatter	Arr_face_extended_text_formatter defines the format of an arrangement in an input or output stream (typically a file stream), thus enabling reading and writing an Arrangement instance using a simple text format
CArr_face_index_map	Arr_face_index_map maintains a mapping of face handles of an attached arrangement object to indices (of type unsigned int)
CArr_face_overlay_traits	An instance of Arr_face_overlay_traits should be used for overlaying two arrangements of types Arr_A and Arr_B, which are instantiated using the same geometric traits-class and with the DCEL classes Dcel_A and Dcel_B respectively, in order to store their overlay in an arrangement of type Arr_R, which is instantiated using a third DCEL class Dcel_R
►CArr_geodesic_arc_on_sphere_traits_2	The traits class Arr_geodesic_arc_on_sphere_traits_2 is a model of the ArrangementTraits_2 concept
CConstruct_curve_2	Construction functor of geodesic arcs
CConstruct_point_2	Construction functor of a point
CConstruct_x_monotone_curve_2	Construction functor of \(x\)-monotone geodesic arcs
CCurve_2
CPoint_2	The Point_2 class nested within the traits is used to represent a point on a sphere centered at the origin
CX_monotone_curve_2	The X_monotone_curve_2 class nested within the traits is used to represent an \(x\)-monotone geodesic arc on the a sphere centered at the origin
CArr_identified_side_tag	This type tag is used to indicate that a side of the parameter space, either left, right, bottom, or top, is identified, and curves that approach this side might be inserted into the arrangement
CArr_landmarks_point_location
CArr_line_arc_traits_2	This class is a traits class for CGAL arrangements, built on top of a model of concept CircularKernel
►CArr_linear_traits_2	The traits class Arr_linear_traits_2 is a model of the ArrangementTraits_2 concept, which enables the construction and maintenance of arrangements of linear objects
CTrim_2
CX_monotone_curve_2	The X_monotone_curve_2 (and the Curve_2) class nested within the linear-traits can represent all types of linear objects
CArr_naive_point_location
CArr_non_caching_segment_basic_traits_2	The traits class Arr_non_caching_segment_basic_traits_2 is a model of the ArrangementTraits_2 concept that allow the construction and maintenance of arrangements of sets of pairwise interior-disjoint line segments
CArr_non_caching_segment_traits_2	The traits class Arr_non_caching_segment_traits_2 is a model of the ArrangementTraits_2 concept that allows the construction and maintenance of arrangements of line segments
CArr_oblivious_side_tag	This type tag is used to indicate that the condition of a boundary side of the parameter space is irrelevant
CArr_open_side_tag	This type tag is used to indicate that a side of the parameter space, either left, right, bottom, or top, is open, and curves that approach this side might be inserted into the arrangement
CArr_point_location_result	A unary metafunction to determine the return type of a point-location or vertical ray-shoot query
►CArr_polycurve_traits_2	Note: The SubcurveTraits_2 can comprise of Line_segments, Conic_arcs, Circular_arc, Bezier_curves, or Linear_curves
CConstruct_curve_2	Construction functor of a general (not necessarily \(x\)-monotone) polycurve
CConstruct_x_monotone_curve_2	Construction functor of \(x\)-monotone polycurve
CCurve_2	The Curve_2 type nested in the Arr_polycurve_traits_2 represents general continuous piecewise-linear subcurves (a polycurve can be self-intersecting) and support their construction from range of subcurves
CMake_x_monotone_2	Subdivide a given subcurve into \(x\)-monotone subcurves and isolated points, and insert them into an output container
CNumber_of_points_2	Function object which returns the number of subcurve end-points of a polycurve
CPush_back_2	Functor to augment a polycurve by either adding a vertex or a subcurve at the back
CPush_front_2	Functor to augment a polycurve by either adding a vertex or a subcurve at the front
CTrim_2
CX_monotone_curve_2	The X_monotone_curve_2 class nested within the polycurve traits is used to represent \( x\)-monotone piecewise linear subcurves
►CArr_polyline_traits_2	The traits class Arr_polyline_traits_2 handles piecewise linear curves, commonly referred to as polylines
CConstruct_curve_2	Construction functor of a general (not necessarily \(x\)-monotone) polyline
CConstruct_x_monotone_curve_2	Construction functor of \(x\)-monotone polyline
CCurve_2	The Curve_2 type nested within the traits class respresnts polylines
CPush_back_2	Functor to augment a polyline by either adding a vertex or a segment at the back
CPush_front_2	Functor to augment a polyline by either adding a vertex or a segment at the front
CX_monotone_curve_2	The X_monotone_curve_2 type nested within the traits class respresnts \(x\)-monotone polylines
►CArr_rational_function_traits_2	The traits class Arr_rational_function_traits_2 is a model of the ArrangementTraits_2 concept
CConstruct_curve_2	Functor to construct a Curve_2
CConstruct_x_monotone_curve_2	Functor to construct a X_monotone_curve_2
CCurve_2	The Curve_2 class nested within the traits is used to represent rational functions which may be restricted to a certain x-range
CPoint_2
CX_monotone_curve_2	The X_monotone_curve_2 class nested within the traits is used to represent \( x\)-monotone parts of rational functions
►CArr_segment_traits_2	The traits class Arr_segment_traits_2 is a model of the ArrangementTraits_2 concept, which allows the construction and maintenance of arrangements of line segments
CTrim_2	A functor that trims curves
CX_monotone_curve_2	The X_monotone_curve_2 class nested within the traits class is used to represent segments
CArr_spherical_topology_traits_2
CArr_text_formatter	Arr_text_formatter defines the format of an arrangement in an input or output stream (typically a file stream), thus enabling reading and writing an Arrangement instance using a simple text format
CArr_trapezoid_ric_point_location
CArr_triangulation_point_location
CArr_unb_planar_topology_traits_2
CArr_vertex_index_map	Arr_vertex_index_map maintains a mapping of vertex handles of an attached arrangement object to indices (of type unsigned int)
CArr_walk_along_line_point_location
CArr_with_history_text_formatter	Arr_with_history_text_formatter defines the format of an arrangement in an input or output stream (typically a file stream), thus enabling reading and writing an arrangement-with-history instance using a simple text format
CArrangement_2
►CArrangement_on_surface_2
CFace	An object of the class Face represents an arrangement face, namely, a \(2\)-dimensional arrangement cell
CHalfedge	An object \( e\) of the class Halfedge represents a halfedge in the arrangement
CVertex	An object \( v\) of the class Vertex represents an arrangement vertex, that is a \( 0\)-dimensional cell, associated with a point on the ambient surface
CArrangement_on_surface_with_history_2
CArrangement_with_history_2
CCORE_algebraic_number_traits	CORE_algebraic_number_traits is a traits class for CORE's algebraic number types
CArrangementApproximateTraits_2	The concept ArrangementApproximateTraits_2 refines the basic traits concept ArrangementBasicTraits_2. A model of this concept is able to approximate a point
CArrangementBasicTopologyTraits	The concept ArrangementBasicTopologyTraits defines the minimal functionality needed for a model of a topology traits, which can substitutes the TopolTraits template parameters when the class template Arrangement_on_surface_2<GeomTraits, TopolTraits> is instantiated. In particular. a model of this concept holds the Dcel data structure used to represent the arrangement cells (i.e., vertices, edges, and facets) and the incident relations between them
CArrangementBasicTraits_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
CArrangementBottomSideTraits_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
CArrangementClosedBottomTraits_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
CArrangementClosedLeftTraits_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
CArrangementClosedRightTraits_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
CArrangementClosedTopTraits_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
CArrangementConstructCurveTraits_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
CArrangementConstructXMonotoneCurveTraits_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
CArrangementContractedBottomTraits_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
CArrangementContractedLeftTraits_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
CArrangementContractedRightTraits_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
CArrangementContractedTopTraits_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
CArrangementDcel	A doubly-connected edge-list (DCEL for short) data-structure. It consists of three containers of records: vertices \( V\), halfedges \( E\), and faces \( F\). It maintains the incidence relation among them. The halfedges are ordered in pairs sometimes referred to as twins, such that each halfedge pair represent an edge
CArrangementDcelFace	A face record in a DCEL data structure. A face represents a region, which may have outer and inner boundaries. A boundary conists of a chain of incident halfedges, referred to as a Connected Component of the Boundary (CCB). A face may be unbounded. Otherwise, it has one or more outer CCBs. A face may also be bounded by inner CCBs, and it may contain isolated vertices in its interior. A planar face may have only one outer CCBs and its inner CCBs are referred to as holes
CArrangementDcelHalfedge	A halfedge record in a DCEL data structure. Two halfedges with opposite directions always form an edge (a halfedge pair). The halfedges form together chains, defining the boundaries of connected components, such that all halfedges along a chain have the same incident face. Note that the chain the halfedge belongs to may form the outer boundary of a bounded face (an outer CCB) or the boundary of a hole inside a face (an inner CCB)
CArrangementDcelInnerCcb	A hole record in a Dcel data structure, which stores the face that contains the hole in its interior, along with an iterator for the hole in the holes' container of this face
CArrangementDcelIsolatedVertex	An isolated vertex-information record in a DCEL data structure, which stores the face that contains the isolated vertex in its interior, along with an iterator for the isolated vertex in the isolated vertices' container of this face
CArrangementDcelOuterCcb	A hole record in a DCEL data structure, which stores the face that contains the hole in its interior, along with an iterator for the hole in the holes' container of this face
CArrangementDcelVertex	A vertex record in a DCEL data structure. A vertex is always associated with a point. However, the vertex record only stores a pointer to the associated point, and the actual Point object is stored elsewhere
CArrangementDcelWithRebind	The concept ArrangementDcelWithRebind refines the ArrangementDcel concept by adding a policy clone idiom in form of a rebind struct-template
CArrangementHorizontalSideTraits_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
CArrangementIdentifiedHorizontalTraits_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
CArrangementIdentifiedVerticalTraits_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
CArrangementInputFormatter	A model for the ArrangementInputFormatter concept supports a set of functions that enable reading an arrangement from an input stream using a specific format
CArrangementLandmarkTraits_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 by a model of this concept
CArrangementLeftSideTraits_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
CArrangementOpenBottomTraits_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
CArrangementOpenBoundaryTraits_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, nonetheless, also supports planar \( x\)-monotone curves that reach the boundary of an open yet bounded parameter space
CArrangementOpenLeftTraits_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
CArrangementOpenRightTraits_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
CArrangementOpenTopTraits_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
CArrangementOutputFormatter	A model for the ArrangementOutputFormatter concept supports a set of functions that enable writing an arrangement to an output stream using a specific format
CArrangementPointLocation_2	A model of the ArrangementPointLocation_2 concept can answer point-location queries on an arrangement attached to it. Namely, given a Arrangement_2::Point_2 object, representing a point in the plane, it returns the arrangement cell containing it. In the general case, the query point is contained inside an arrangement face, but in degenerate situations it may lie on an edge or coincide with an arrangement vertex
CArrangementRightSideTraits_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
CArrangementSphericalBoundaryTraits_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
CArrangementTopologyTraits	A geometry traits class encapsulates the definitions of the geometric entities and implements the geometric predicates and constructions needed by instances of the CGAL::Arrangement_on_surface_2 class template and by the peripheral algorithms that operate on objects of such instances. Essentially, it maintains the doubly-connected connected edge list (DCEL) used by the arrangement
CArrangementTopSideTraits_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
CArrangementTraits_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
CArrangementVerticalRayShoot_2	A model of the ArrangementVerticalRayShoot_2 concept can answer vertical ray-shooting queries on an arrangement attached to it. Namely, given a Arrangement_2::Point_2 object, representing a point in the plane, it returns the arrangement feature (edge or vertex) that lies strictly above it (or below it). By "strictly" we mean that if the query point lies on an arrangement edge (or on an arrangement vertex) this edge will not be the query result, but the feature lying above or below it. (An exception to this rule is the degenerate case where the query point lies in the interior of a vertical edge.) Note that it may happen that the query point lies above the upper envelope (or below the lower envelope) of the arrangement, and the vertical ray emanating from the query point goes to infinity without hitting any arrangement feature on its way. In this case the unbounded face is returned
CArrangementVerticalSideTraits_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
CArrangementWithHistoryInputFormatter	A model for the ArrangementWithHistoryInputFormatter concept supports a set of functions that enable reading an arrangement-with-history instance from an input stream using a specific format
CArrangementWithHistoryOutputFormatter	A model for the ArrangementWithHistoryOutputFormatter concept supports a set of functions that enable writing an arrangement-with-history instance to an output stream using a specific format
CArrangementXMonotoneTraits_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
COverlayTraits	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