The traits class Arr_non_caching_segment_traits_2<Kernel> 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 sgements. It is recommended to use Arr_non_caching_segment_traits_2<Kernel> only for very sparse arrangements of huge sets of input segments.