| ▼NArrTraits | The namespace containing concepts specific to Arrangements |
| CApproximate_2 | |
| CAreMergeable_2 | |
| CCompareX_2 | |
| CCompareXAtLimit_2 | |
| CCompareXNearLimit_2 | |
| CCompareXy_2 | |
| CCompareYAtX_2 | |
| CCompareYAtXLeft_2 | |
| CCompareYAtXRight_2 | |
| CCompareYNearBoundary_2 | |
| CConstructMaxVertex_2 | |
| CConstructMinVertex_2 | |
| CConstructXMonotoneCurve_2 | |
| CCurve_2 | General planar curve |
| CEqual_2 | |
| CIntersect_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 | |
| 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_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_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 |
| CCurve_2 | The Curve_2 class nested within the conic-arc traits can represent arbitrary conic arcs and support their construction in various ways |
| CTrim_2 | |
| 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_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_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_dcel | The default Dcel class used by the Arrangement_2 class-template is parameterized by a traits class, which is a model of the ArrangementBasicTraits_2 concept |
| 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_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 |
| CCurve_2 | The Curve_2 (and the X_monotone_curve_2) class nested within the linear-traits can represent all types of linear objects |
| CTrim_2 | |
| 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 | The categories Left_side_category, Right_side_category, Bottom_side_category, and Top_side_category, nested in any model of the ArrangementBasicTraits_2, must be convertible to Arr_oblivious_side_tag |
| CArr_observer | |
| CArr_open_side_tag | All the four types Left_side_category, Right_side_category, Bottom_side_category, and Top_side_category nested in any model of the concept ArrangementOpenBoundaryTraits must be convertible to Arr_open_side_tag, which derives from Arr_oblivious_side_tag |
| 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 the given subcurve into x-monotone subcurves and insert them into the given output iterator |
| 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 |
| 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 |
| ►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 |
| 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_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 | |
| 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 plane |
| CArrangement_with_history_2 | |
| CArrangementApproximateTraits_2 | The concept ArrangementApproximateTraits_2 refines the basic traits concept ArrangementBasicTraits_2. A model of this concept is able to approximate a point |
| 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 |
| 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 |
| 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 may either be unbounded, otherwise it has an incident halfedge along the chain defining its outer boundary. A face may also contain holes and isolated vertices in its interior |
| 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) |
| CArrangementDcelHole | 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 |
| 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 |
| 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 with a model of this concept |
| 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, nontheless, also supports planar x-monotone curves that reach the boundary of an open yet bounded parameter space |
| 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 |
| 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 |
| 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 |
1.8.13 