\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Regularized Boolean Set-Operations

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ArrangementDirectionalXMonotoneTraits_2 Concept Reference
Concepts

## Definition

This concept refines the basic arrangement \( x\)-monotone traits concept. A model of this concept is able to handle directed \( x\)-monotone curves that intersect in their interior. Namely, an instance of the `X_monotone_curve_2` type defined by a model of the concept `ArrangementXMonotoneTraits_2` is only required to have a left (lexicographically smaller) endpoint and a right endpoint. If the traits class is also a model of `ArrangementDirectionalXMonotoneTraits_2`, the \( x\)-monotone curve is also required to have a direction, namely one of these two endpoint serves as its source and the other as its target.

Refines:
  `ArrangementXMonotoneTraits_2`

Has Models:

  `CGAL::Arr_segment_traits_2<Kernel>`

  `CGAL::Arr_non_caching_segment_traits_2<Kernel>`

  `CGAL::Arr_circle_segment_traits_2<Kernel>`

  `CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>`

  `CGAL::Arr_rational_function_traits_2<AlgKernel,NtTraits>`

  `CGAL::Arr_Bezier_curve_traits_2<RatKernel,AlgKernel,NtTraits>`

  `CGAL::Arr_algebraic_segment_traits_2<Coefficient>`

See Also
  `ArrangementXMonotoneTraits_2`

## Functor Types
typedef unspecified_type | Compare_endpoints_xy_2
| models the concept `ArrDirectionalTraits::CompareEndpointsXy_2`.
typedef unspecified_type | Construct_opposite_2
| models the concept `ArrDirectionalTraits::ConstructOpposite_2`.
typedef unspecified_type | Intersect_2
| models the concept `ArrDirectionalTraits::Intersect_2`.
typedef unspecified_type | Split_2
| models the concept `ArrDirectionalTraits::Split_2`.
typedef unspecified_type | Are_mergeable_2
| models the concept `ArrDirectionalTraits::AreMergeable_2`.
typedef unspecified_type | Merge_2
| models the concept `ArrDirectionalTraits::Merge_2`.

## Creation
| ArrangementDirectionalXMonotoneTraits_2 ()
| default constructor.
| ArrangementDirectionalXMonotoneTraits_2 (ArrangementDirectionalXMonotoneTraits_2 other)
| copy constructor
ArrangementDirectionalXMonotoneTraits_2 | operator= (other)
| assignment operator.

## Accessing Functor Objects
Compare_endpoints_xy_2 | compare_endpoints_xy_2_object ()
Construct_opposite_2 | construct_opposite_2_object ()