\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11.3 - 2D Arrangements
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ArrangementBasicTraits_2 Concept Reference
Traits Concepts

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 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 Arr_oblivious_side_tag.
 
typedef unspecified_type Bottom_side_category
 Must be convertible to Arr_oblivious_side_tag.
 
typedef unspecified_type Top_side_category
 Must be convertible to Arr_oblivious_side_tag.
 
typedef unspecified_type Right_side_category
 Must be convertible to 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

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.