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

CGAL 4.8 - 2D Arrangements

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CGAL::Arr_non_caching_segment_traits_2< Kernel > Class Template Reference
Traits Classes

`#include <CGAL/Arr_non_caching_segment_traits_2.h>`

## Inherits from

CGAL::Arr_non_caching_segment_basic_traits_2< Kernel >.

## Definition

The traits class `Arr_non_caching_segment_traits_2` is a model of the `ArrangementTraits_2` concept that allows the construction and maintenance of arrangements of line segments.

It is parameterized with a CGAL-Kernel type, and it is derived from it. This traits class is a thin layer above the parameterized kernel. It inherits the `Point_2` from the kernel and its `X_monotone_curve_2` and `Curve_2` types are both defined as `Kernel::Segment_2`. Most traits-class functor are inherited from the kernel functor, and the traits class only supplies the necessary functors that are not provided by the kernel. The kernel is parameterized with a number type, which should support exact rational arithmetic in order to avoid robustness problems, although other number types could be used at the user's own risk.

The traits-class implementation is very simple, yet may lead to a cascaded representation of intersection points with exponentially long bit-lengths, especially if the kernel is parameterized with a number type that does not perform normalization (e.g. `Quotient<MP_Float>`). The `Arr_segment_traits_2` traits class avoids this cascading problem, and should be the default choice for implementing arrangements of line segments. It is recommended to use `Arr_non_caching_segment_traits_2` only for very sparse arrangements of huge sets of input segments.

While `Arr_non_caching_segment_traits_2` models the concept `ArrangementDirectionalXMonotoneTraits_2`, the implementation of the `Are_mergeable_2` operation does not enforce the input curves to have the same direction as a precondition. Moreover, `Arr_non_caching_segment_traits_2` supports the merging of curves of opposite directions.

Is Model Of:

  `ArrangementTraits_2`

  `ArrangementLandmarkTraits_2`

  `ArrangementDirectionalXMonotoneTraits_2`

See Also
  `Arr_segment_traits_2<Kernel>`