\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5 - 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>