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

CGAL 4.8 - 2D Arrangements

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
Classes
CGAL::Arr_linear_traits_2< Kernel > Class Template Reference
Traits Classes

`#include <CGAL/Arr_linear_traits_2.h>`

## Definition

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.

The linear objects may be bounded (line segments) or unbounded (rays and lines). Thus, it is also a model of the concept `ArrangementOpenBoundaryTraits_2`. The traits class is parameterized parameterized with a CGAL-kernel model; see the reference page of `Arr_segment_traits_2<Kernel>` for further explanations and recommendations on choosing a kernel.

`Arr_linear_traits_2` defines `Kernel::Point_2` as its point type. The nested `X_monotone_curve_2` and `Curve_2` types defined by the traits class (as is the case with the various segment-traits classes, both types refer to the same class, as every linear object is (weakly) \( x\)-monotone), are constructible from a point, a line segment, a ray and from a line (objects of types `Kernel::Point_2`, `Kernel::Segment_2`, `Kernel::Ray_2` and `Kernel::Line_2`, respectively). On the other hand, when we are given a curve we can find out its actual type and convert it to the respective kernel object (say, to a `Kernel::Ray_2`).

Is Model Of:

  `ArrangementTraits_2`

  `ArrangementLandmarkTraits_2`

  `ArrangementOpenBoundaryTraits_2`

Examples:
  Arrangement_on_surface_2/dual_lines.cpp, Arrangement_on_surface_2/dual_with_data.cpp, Arrangement_on_surface_2/global_removal.cpp, Arrangement_on_surface_2/overlay_unbounded.cpp, and Arrangement_on_surface_2/unbounded_non_intersecting.cpp.

## Classes
class | Curve_2
| The `Curve_2` (and the `X_monotone_curve_2`) class nested within the linear-traits can represent all types of linear objects. More...