CGAL 5.4.4  2D Arrangements

The concept ArrangementTraits_2
allows the construction of arrangement of general planar curves. Models of this concept are used by the free CGAL::insert()
functions of the arrangement package and by the CGAL::Arrangement_with_history_2
class.
A model of this concept must define the nested Curve_2
type, which represents a general planar curve that is not necessarily \( x\)monotone and is not necessarily connected. Such curves are eventually subdivided into \( x\)monotone subcurves and isolated points (represented by the Point_2
and X_monotone_curve_2
types, defined in the basic traits concept).
A model of the concept ArrangementTraits_2
that handles arbitrary curves, which are always \( x\)monotone, such as a traits class that handles linear curves may define the nested types Curve_2
and X_monotone_curve_2
to be of equivalent types. Moreover, defining them as of equivalent types is advantageous, as it enables a generic simple implementation of the nested Functor Make_x_monotone_2
.
On the other hand, a model of the ArrangementTraits_2
concept that handles arbitrary curves, which may be not \( x\)monotone must define the Curve_2
and X_monotone_curve_2
nested types to be of different types to allow proper dispatching of the free functions that accept such curves, such as intsert()
.
CGAL::Arr_segment_traits_2<Kernel>
CGAL::Arr_non_caching_segment_traits_2<Kernel>
CGAL::Arr_linear_traits_2<Kernel>
CGAL::Arr_polyline_traits_2<SegmentTraits>
CGAL::Arr_circle_segment_traits_2<Kernel>
CGAL::Arr_line_arc_traits_2<CircularKernel>
CGAL::Arr_circular_arc_traits_2<CircularKernel>
CGAL::Arr_circular_line_arc_traits_2<CircularKernel>
CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>
CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>
CGAL::Arr_Bezier_curve_traits_2<RatKernel,AlgKernel,NtTraits>
CGAL::Arr_algebraic_segment_traits_2<Coefficient>
CGAL::Arr_curve_data_traits_2<Tr,XData,Mrg,CData,Cnv>
CGAL::Arr_consolidated_curve_data_traits_2<Traits,Data>
Types  
typedef unspecified_type  Curve_2 
models the concept ArrTraits::Curve_2 .  
Functor Types  
typedef unspecified_type  Make_x_monotone_2 
models the concept ArrTraits::MakeXMonotone_2 .  
Accessing Functor Objects  
Make_x_monotone_2  make_x_monotone_2_object () const 