ArrangementBasicTraits_2 Concept Reference

Definition

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.

A model of this concept must define nested Point_2 and X_monotone_curve_2 types, which represent planar points and continuous \( x\)-monotone curves (a vertical segment is also considered to be weakly \( x\)-monotone), respectively. The \( x\)-monotone curves are assumed to be pairwise disjoint in their interiors, so they do not intersect except at their endpoints.

The X_monotone_curve_2 curves of an arrangement are confined to an iso-rectangular area called the parameter space. The iso-rectangule can be unbounded, open, or closed. The set of predicates provided by a model the concept ArrangementBasicTraits_2 is sufficient for constructing arrangements of \( x\)-monotone curves that do not reach or approach the boundary of the parameter space. The nature of the input curves, whether they are expected to reach or approach the left, right, bottom, or top side of the boundary of the parameter space, are conveyed through the definition of four additional nested types, namely Left_side_category, Right_side_category, Bottom_side_category, and Top_side_category. Each such type must be convertible to the type CGAL::Arr_oblivious_side_tag.

Refines:

DefaultConstructible

CopyConstructible

Assignable

Has Models:

CGAL::Arr_segment_traits_2<Kernel>

CGAL::Arr_non_caching_segment_basic_traits_2<Kernel>

CGAL::Arr_non_caching_segment_traits_2<Kernel>

CGAL::Arr_linear_traits_2<Kernel>

CGAL::Arr_polyline_traits_2<SegmentTraits>

CGAL::Arr_circle_segment_traits_2<Kernel>

CGAL::Arr_line_arc_traits_2<CircularKernel>

CGAL::Arr_circular_arc_traits_2<CircularKernel>

CGAL::Arr_circular_line_arc_traits_2<CircularKernel>

CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>

CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>

CGAL::Arr_Bezier_curve_traits_2<RatKernel,AlgKernel,NtTraits>

CGAL::Arr_algebraic_segment_traits_2<Coefficient>

CGAL::Arr_curve_data_traits_2<Tr,XData,Mrg,CData,Cnv>

CGAL::Arr_consolidated_curve_data_traits_2<Traits,Data>

Types
typedef unspecified_type	Point_2
	models the concept ArrTraits::Point_2.
typedef unspecified_type	X_monotone_curve_2
	models the concept ArrTraits::XMonotoneCurve_2.

Categories
typedef unspecified_type	Has_left_category
	indicates whether the nested functor Compare_at_x_left_2 is provided.
typedef unspecified_type	Left_side_category
	Must be convertible to CGAL::Arr_oblivious_side_tag.
typedef unspecified_type	Bottom_side_category
	Must be convertible to CGAL::Arr_oblivious_side_tag.
typedef unspecified_type	Top_side_category
	Must be convertible to CGAL::Arr_oblivious_side_tag.
typedef unspecified_type	Right_side_category
	Must be convertible to CGAL::Arr_oblivious_side_tag.

Functor Types
typedef unspecified_type	Compare_x_2
	models the concept ArrTraits::CompareX_2.
typedef unspecified_type	Compare_xy_2
	models the concept ArrTraits::CompareXy_2.
typedef unspecified_type	Construct_min_vertex_2
	models the concept ArrTraits::ConstructMinVertex_2.
typedef unspecified_type	Construct_max_vertex_2
	models the concept ArrTraits::ConstructMaxVertex_2.
typedef unspecified_type	Is_vertical_2
	models the concept ArrTraits::IsVertical_2.
typedef unspecified_type	Compare_y_at_x_2
	models the concept ArrTraits::CompareYAtX_2.
typedef unspecified_type	Compare_y_at_x_left_2
	models the concept ArrTraits::CompareYAtXLeft_2. More...
typedef unspecified_type	Compare_y_at_x_right_2
	models the concept ArrTraits::CompareYAtXRight_2.
typedef unspecified_type	Equal_2
	models the concept ArrTraits::Equal_2.

Accessing Functor Objects
Compare_x_2	compare_x_2_object () const
Compare_xy_2	compare_xy_2_object () const
Construct_min_vertex_2	construct_min_vertex_2_object () const
Construct_max_vertex_2	construct_max_vertex_2_object () const
Is_vertical_2	is_vertical_2_object () const
Compare_y_at_x_2	compare_y_at_x_2_object () const
Compare_y_at_x_left_2	compare_y_at_x_left_2_object () const
Compare_y_at_x_right_2	compare_y_at_x_right_2_object () const
Equal_2	equal_2_object () const

Member Typedef Documentation

Compare_y_at_x_left_2

typedef unspecified_type ArrangementBasicTraits_2::Compare_y_at_x_left_2

models the concept ArrTraits::CompareYAtXLeft_2.

Required only if the Has_left_category category is convertible to Tag_true.