## Summary of Changes
This addresses issue #9084. In particular, I replaced `Cartesian` with
`Simple_cartesian` in all traits.
I also defined Multiplicity to be `std::size_t` in all traits. In
addition, I replaced `typedef` with `using` and properly indented and
cleaned up the code in the source files I touched. I simplified the code
that approximates a point of the traits classes `Arr_linear_traits_2`,
`Arr_segment_traits_2`, and `Arr_non_caching_segment_basic_traits_2.h`.
I did not use the
[GAL::Cartesian_coverter](https://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Cartesian__converter.html)
(mentioned in issue #9084) because the code is now simple as it is(just
one line in each traits class).
I also added a missing `inline` in draw_arrangement_2. This is unrelated
to the above.
## Release Management
* Affected package(s): Arrangement_on_surface_2
* Issue(s) solved (if any): fix#9084
* Feature/Small Feature (if any):
* Link to compiled documentation (obligatory for small feature) [*wrong
link name to be changed*](httpssss://wrong_URL_to_be_changed/Manual/Pkg)
* License and copyright ownership: TAU
## Summary of Changes
Optimized `do_intersect(polygon, polygon)`, `do_intersect(begin, end)`,
and `do_intersect(begin1, end1, begin2, end2)`:
(i) Terminated the execution once an intersection is detected. (In the
past, the intersection was computed in one phase and examined in a
subsequent phase.)
(ii) Made the variants of the free functions `do_intersect()` that apply
to linear polygons, robust even with an inexact-construction kernel. The
variants that apply to generalized polygons endure inexact constructions
much more than before; however, there are rare degenerate cases that are
still require an exact construction kernel.
In general, the changes described here do not affect the default
interface, so a small feature is not required. However, it is a major
impact, and it does affect the interface as described bellow, and even
somehow break backward compatibility.
Recently, the code of the package "2D Regularized Boolean Set
Operations" was optimized. In particular, a 3rd optional parameter was
introduced in the free functions. It determined whether the boundaries
of the input polygons are treated as cyclic sequences of single
(`x`-monotone) segments or as a cyclic sequences of (`x`-monotone)
polylines. The change described here eliminates this 3rd parameter, and
brings the interface of the `do_intersect() function back to the
original design with two input polygons.
## Release Management
* Affected package(s): Boolean_set_operations_2, Surface_sweep,
Arrangement_on_surface_2
* Feature/Small Feature (if any):
[here](https://cgalwiki.geometryfactory.com/CGAL/Members/wiki/Features/Small_Features/do_intersect_polygon_2_predicates_only)
* Link to compiled documentation (obligatory for small feature) [*wrong
link name to be changed*](httpssss://wrong_URL_to_be_changed/Manual/Pkg)
* License and copyright ownership: TAU