CGAL 5.3 - 2D Arrangements
ArrangementXMonotoneTraits_2 Concept Reference

## Definition

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.

As the resulting structure, represented by the Arrangement_2 class, stores pairwise interior-disjoint curves, the input curves are split at the intersection points before being inserted into the arrangement. A model of this refined concept therefore needs to compute the intersections (and possibly overlaps) between two $$x$$-monotone curves and to support curve splitting.

Refines:
ArrangementBasicTraits_2
Has Models:

CGAL::Arr_segment_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>

ArrangementBasicTraits_2

## Types

typedef unspecified_type Multiplicity
the multiplicity type.

## Tags

typedef unspecified_type Has_merge_category
indicates whether the nested functors Are_mergeable_2 and Merge_2 are provided.

## Functor Types

typedef unspecified_type Intersect_2
models the concept ArrTraits::Intersect_2.

typedef unspecified_type Split_2
models the concept ArrTraits::Split_2.

Attention
The two following function-object types are optional. If they are supported, the Has_merge_category tag should be defined as Tag_true and otherwise as Tag_false.
typedef unspecified_type Are_mergeable_2
models the concept ArrTraits::AreMergeable_2.

typedef unspecified_type Merge_2
models the concept ArrTraits::Merge_2.

## Accessing Functor Objects

Intersect_2 intersect_2_object () const

Split_2 split_2_object () const

The two following methods are optional.

If they are supported, the Has_merge_category tag should be defined as Tag_true and otherwise as Tag_false.

Are_mergeable_2 are_mergeable_2_object () const

Merge_2 merge_2_object () const