CGAL 6.1.1 - 2D Arrangements

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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 1 2 3]

►N AosTraits | The namespace containing concepts specific to Arrangements
C Approximate_2 |
C AreMergeable_2 |
C CompareX_2 |
C CompareXNearBoundary_2 |
C CompareXOnBoundary_2 |
C CompareXOnBoundaryOfCurveEnd_2 |
C CompareXy_2 |
C CompareYAtX_2 |
C CompareYAtXLeft_2 |
C CompareYAtXRight_2 |
C CompareYNearBoundary_2 |
C CompareYOnBoundary_2 |
C ConstructCurve_2 |
C ConstructMaxVertex_2 |
C ConstructMinVertex_2 |
C ConstructXMonotoneCurve_2 |
C Curve_2 | General planar curve
C Equal_2 |
C Intersect_2 |
C IsOnXIdentification_2 |
C IsOnYIdentification_2 |
C IsVertical_2 |
C MakeXMonotone_2 |
C Merge_2 |
C ParameterSpaceInX_2 |
C ParameterSpaceInY_2 |
C Point_2 | Represents a point in the plane
C Split_2 |
C XMonotoneCurve_2 | Represents a planar (weakly) \(x\)-monotone curve
►N CGAL | Copyright (c) 2007,2009,2010,2011 Tel-Aviv University (Israel)
C Aos_observer |
C Arr_accessor |
►C Arr_algebraic_segment_traits_2 | The traits class `Arr_algebraic_segment_traits_2` is a model of the `AosTraits_2` concept that handles planar algebraic curves of arbitrary degree, and \(x\)-monotone of such curves
C Construct_curve_2 |
C Construct_point_2 |
C Construct_x_monotone_segment_2 |
C Curve_2 | A model of the the `AosTraits_2::Curve_2` concept
C Point_2 | A model of the `AosBasicTraits_2::Point_2` concept
C X_monotone_curve_2 | A model of the `AosBasicTraits_2::X_monotone_curve_2` concept
►C Arr_Bezier_curve_traits_2 | The traits class `Arr_Bezier_curve_traits_2` is a model of the `AosTraits_2` concept that handles planar Bézier curves
C Curve_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
C Point_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
C Trim_2 |
C X_monotone_curve_2 | The `X_monotone_curve_2` class nested within the Bézier traits is used to represent \(x\)-monotone subcurves of Bézier curves
C Arr_bounded_planar_topology_traits_2 |
►C Arr_circle_segment_traits_2 | The class `Arr_circle_segment_traits_2` is a model of the `AosTraits_2` concept and can be used to construct and maintain arrangements of circular arcs and line segments
C Curve_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
C Point_2 | The `Point_2` number-type nested within the traits class represents a Cartesian point whose coordinates are algebraic numbers of type `CoordNT`
C Trim_2 |
C X_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)
C Arr_circular_arc_traits_2 | This class is a traits class for CGAL arrangements, built on top of a model of concept `CircularKernel`
C Arr_circular_line_arc_traits_2 | This class is a traits class for CGAL arrangements, built on top of a model of concept `CircularKernel`
C Arr_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
►C Arr_conic_traits_2 | The class `Arr_conic_traits_2` is a model of the `AosTraits_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
C Construct_bbox_2 | A functor that constructs a bounding box of a conic arc
C Construct_curve_2 | A functor that constructs a conic arc
C Construct_x_monotone_curve_2 | A functor that constructs an \(x\)-monotone conic arc
C Curve_2 | The `Curve_2` class nested within the conic-arc traits can represent arbitrary conic arcs and support their construction in various ways
C Point_2 | The `Point_2` class nested within the conic-arc traits is used to represent points
C Trim_2 | A functor that trims a conic arc
C X_monotone_curve_2 | The `X_monotone_curve_2` class nested within the conic-arc traits is used to represent \(x\)-monotone conic arcs
►C Arr_consolidated_curve_data_traits_2 | The class `Arr_consolidated_curve_data_traits_2` is a model of the concept `AosTraits_2`, and serves as a decorator class that enables the extension of the curve type defined by the `Traits` parameter
C Data_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
C Arr_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
C Arr_counting_traits_2 | A metadata traits-class decorator for the arrangement package
►C Arr_curve_data_traits_2 | The class `Arr_curve_data_traits_2` is a model of the `AosTraits_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 `AosTraits_2` concept), with extraneous (non-geometric) data fields
C Curve_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`
C X_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
C Arr_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
►C Arr_dcel_base |
C Arr_face_base | The basic DCEL face type
C Arr_halfedge_base | The basic DCEL halfedge type
C Arr_vertex_base | The basic DCEL vertex type
C Arr_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
C Arr_extended_dcel | The `Arr_extended_dcel` class-template extends the topological-features of the DCEL namely the vertex, halfedge, and face types
C Arr_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
C Arr_extended_face | The `Arr_extended_face` class-template extends the face topological-features of the DCEL
C Arr_extended_halfedge | The `Arr_extended_halfedge` class-template extends the halfedge topological-features of the DCEL
C Arr_extended_vertex | The `Arr_extended_vertex` class-template extends the vertex topological-features of the DCEL
C Arr_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
C Arr_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
C Arr_face_index_map | `Arr_face_index_map` maintains a mapping of face handles of an attached arrangement object to indices (of type `unsigned int`)
C Arr_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`
►C Arr_geodesic_arc_on_sphere_traits_2 | The traits class `Arr_geodesic_arc_on_sphere_traits_2` is a model of the `AosTraits_2` concept
C Construct_curve_2 | Construction functor of geodesic arcs
C Construct_point_2 | Construction functor of a point
C Construct_x_monotone_curve_2 | Construction functor of \(x\)-monotone geodesic arcs
C Curve_2 |
C Point_2 | The `Point_2` class nested within the traits is used to represent a point on a sphere centered at the origin
C X_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
C Arr_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
C Arr_landmarks_point_location |
C Arr_line_arc_traits_2 | This class is a traits class for CGAL arrangements, built on top of a model of concept `CircularKernel`
►C Arr_linear_traits_2 | The traits class `Arr_linear_traits_2` is a model of the `AosTraits_2` concept, which enables the construction and maintenance of arrangements of linear objects
C Trim_2 |
C X_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
C Arr_naive_point_location |
C Arr_non_caching_segment_basic_traits_2 | The traits class `Arr_non_caching_segment_basic_traits_2` is a model of the `AosTraits_2` concept that allow the construction and maintenance of arrangements of sets of pairwise interior-disjoint line segments
C Arr_non_caching_segment_traits_2 | The traits class `Arr_non_caching_segment_traits_2` is a model of the `AosTraits_2` concept that allows the construction and maintenance of arrangements of line segments
C Arr_oblivious_side_tag | This type tag is used to indicate that the condition of a boundary side of the parameter space is irrelevant
C Arr_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
C Arr_point_location_result | A unary metafunction to determine the return type of a point-location or vertical ray-shoot query
►C Arr_polycurve_traits_2 | Note: The `SubcurveTraits_2` can comprise of Line_segments, Conic_arcs, Circular_arc, Bezier_curves, or Linear_curves
C Construct_curve_2 | Construction functor of a general (not necessarily \(x\)-monotone) polycurve
C Construct_x_monotone_curve_2 | Construction functor of \(x\)-monotone polycurve
C Curve_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
C Make_x_monotone_2 | Subdivides a given subcurve into \(x\)-monotone subcurves and isolated points, and insert them into an output container
C Number_of_points_2 | Function object which returns the number of subcurve end-points of a polycurve
C Push_back_2 | Functor to augment a polycurve by either adding a vertex or a subcurve at the back
C Push_front_2 | Functor to augment a polycurve by either adding a vertex or a subcurve at the front
C Trim_2 |
C X_monotone_curve_2 | The `X_monotone_curve_2` class nested within the polycurve traits is used to represent \(x\)-monotone piecewise linear subcurves
►C Arr_polyline_traits_2 | The traits class `Arr_polyline_traits_2` handles piecewise linear curves, commonly referred to as polylines
C Construct_curve_2 | Construction functor of a general (not necessarily \(x\)-monotone) polyline
C Construct_x_monotone_curve_2 | Construction functor of \(x\)-monotone polyline
C Curve_2 | The `Curve_2` type nested within the traits class respresnts polylines
C Push_back_2 | Functor to augment a polyline by either adding a vertex or a segment at the back
C Push_front_2 | Functor to augment a polyline by either adding a vertex or a segment at the front
C X_monotone_curve_2 | The `X_monotone_curve_2` type nested within the traits class respresnts \(x\)-monotone polylines
►C Arr_rational_function_traits_2 | The traits class `Arr_rational_function_traits_2` is a model of the `AosTraits_2` concept
C Construct_curve_2 | Functor to construct a `Curve_2`
C Construct_x_monotone_curve_2 | Functor to construct a `X_monotone_curve_2`
C Curve_2 | The `Curve_2` class nested within the traits is used to represent rational functions which may be restricted to a certain \(x\)-range
C Point_2 |
C X_monotone_curve_2 | The `X_monotone_curve_2` class nested within the traits is used to represent \(x\)-monotone parts of rational functions
►C Arr_segment_traits_2 | The traits class `Arr_segment_traits_2` is a model of the `AosTraits_2` concept, which allows the construction and maintenance of arrangements of line segments
C Trim_2 | A functor that trims curves
C X_monotone_curve_2 | The `X_monotone_curve_2` class nested within the traits class is used to represent segments
C Arr_spherical_topology_traits_2 |
C Arr_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
C Arr_tracing_traits_2 | A metadata traits-class decorator for the arrangement package
C Arr_trapezoid_ric_point_location |
C Arr_triangulation_point_location |
C Arr_unb_planar_topology_traits_2 |
C Arr_vertex_index_map | `Arr_vertex_index_map` maintains a mapping of vertex handles of an attached arrangement object to indices (of type `unsigned int`)
C Arr_walk_along_line_point_location |
C Arr_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
C Arrangement_2 |
►C Arrangement_on_surface_2 |
C Face | An object of the class `Face` represents an arrangement face, namely, a \(2\)-dimensional arrangement cell
C Halfedge | An object \(e\) of the class `Halfedge` represents a halfedge in the arrangement
C Vertex | 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
C Arrangement_on_surface_with_history_2 |
C Arrangement_with_history_2 |
C CORE_algebraic_number_traits | `CORE_algebraic_number_traits` is a traits class for CORE's algebraic number types
C AosApproximatePointTraits_2 | The concept `AosApproximatePointTraits_2` refines the basic traits concept `AosBasicTraits_2`. A model of this concept is able to approximate a point
C 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)
C AosBasicTopologyTraits | The concept `AosBasicTopologyTraits` 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
C 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
C 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
C 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
C 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
C 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
C 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
C 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
C 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
C 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
C 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
C 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
C 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
C AosDcel | 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
C AosDcelFace | 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
C AosDcelHalfedge | 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)
C AosDcelInnerCcb | 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
C AosDcelIsolatedVertex | 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
C AosDcelOuterCcb | 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
C AosDcelVertex | 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
C AosDcelWithRebind | The concept `AosDcelWithRebind` refines the `AosDcel` concept by adding a policy clone idiom in form of a rebind struct-template
C 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
C 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
C 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
C AosInputFormatter | A model for the `AosInputFormatter` concept supports a set of functions that enable reading an arrangement from an input stream using a specific format
C 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
C 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
C 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
C 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
C 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
C 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
C 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
C AosOutputFormatter | A model for the `AosOutputFormatter` concept supports a set of functions that enable writing an arrangement to an output stream using a specific format
C AosPointLocation_2 | A model of the `AosPointLocation_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
C 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
C 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
C AosTopologyTraits | 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
C 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
C 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
C AosVerticalRayShoot_2 | A model of the `AosVerticalRayShoot_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
C 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
C AosWithHistoryInputFormatter | A model for the `AosWithHistoryInputFormatter` concept supports a set of functions that enable reading an arrangement-with-history instance from an input stream using a specific format
C AosWithHistoryOutputFormatter | A model for the `AosWithHistoryOutputFormatter` concept supports a set of functions that enable writing an arrangement-with-history instance to an output stream using a specific format
C 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
C 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`