The traits class *Arr_segment_traits_2<Kernel>* is a model of the *ArrangementTraits_2*
concept that allow the construction and maintenance of arrangements of
line segments. It should be parameterized with a Cgal-kernel model that is
templated in turn with a number type. To avoid numerical errors and
robustness problems, the number type should support exact rational
arithmetic - that is, the number type should support the arithmetic
operations +, -, × and ÷ that should be carried out
without loss of precision.

For example, instatiating the traits
template with kernels such as *Cartesian<Quotient<MP_Float> >*,
or *Homogeneous<Gmpz>* ensures the exact and robust operation of
the application. In particular, the *Cartesian<Gmpq>* achieves
the fastest running times in most cases. Using other (inexact) number
types (for example, instatiating the template with
*Simple_cartesian<double>*) is possible at the user's own risk:
selecting an inexact number type usually leads to faster running time at
the expence of possible robustness problems.

For optimal performance, we recommend instantiating the traits class with
the default *Exact_predicates_exact_constructions_kernel* provided by
Cgal. Using this kernel guarantees exactness and robustness, while it incurs
only a minor overhead (in comparison to working with a fast, inexact number
type) for most inputs.

*Arr_segment_traits_2<Kernel>* defines *Kernel::Point_2* as its point type. However, it
does *not* define *Kernel::Segment_2* as its curve type, as one may
expect. The reason is that the kernel segment is represented by its
two endpoints only, while the traits class needs to store extra data
with its segments, in order to efficiently operate on them. Nevertheless,
the nested *X_monotone_curve_2* and *Curve_2* types (in this
case both types refer to the same class, as *every* line segement
is (weakly) x-monotone) are however convertable to the
*Kernel::Segment_2*.

*Arr_segment_traits_2<Kernel>* achieves faster running times than the
*Arr_non_caching_segment_traits_2<Kernel>* traits-class, when
arrangements with relatively many intersection points are constructed.
It also allows for working with less accurate, yet computationally
efficient number types, such as *Quotient<MP_Float>*, which
represents floating-point numbers with an unbounded mantissa, but with
a bounded exponent. Using this traits class is therefore highly recommended
for almost all applications that rely on arrangements of line segments.
On the other hand, *Arr_segment_traits_2<Kernel>* uses more space and stores extra data with
each segment, so constructing arrangements of huge sets of non-intersecting
segments (or segments that intersect very sparsely) could be more efficient
with the *Arr_non_caching_segment_traits_2* traits-class.

*#include <CGAL/Arr_segment_traits_2.h>*

CGAL Open Source Project.
Release 3.5.
1 October 2009.