Definition

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().