ArrangementOpenBoundaryTraits_2 Concept Reference

Definition

Several predicates are required to handle \( x\)-monotone curves that approach infinity and thus approach the boundary of the parameter space. These predicates are sufficient to handle not only curves embedded in an unbounded parameter space, but also curves embedded in a bounded parameter space with open boundaries. Models of the concept ArrangementOpenBoundaryTraits_2 handle curves that approach the boundary of a parameter space. This concept refines the concept ArrangementBasicTraits_2. The arrangement template instantiated with a traits class that models this concept can handle \( x\)-monotone curves that are unbounded in any direction. The concept ArrangementOpenBoundaryTraits_2, nonetheless, also supports planar \( x\)-monotone curves that reach the boundary of an open yet bounded parameter space.

An \( x\)-monotone curve may be closed, in which case its endpoints are representable as Point_2 objects, or open at the boundary of the parameter space. It can have one open end and one closed end (e.g., a ray). The nature of the \( x\)-monotone curves, whether they are expected to be closed or not at any one of the four boundary-sides, is conveyed through the definition of the four nested types Left_side_category, Right_side_category, Bottom_side_category, and Top_side_category. If some curves handled by a model of the concept ArrangementOpenBoundaryTraits_2 are expected to be open on the left, the nested type Left_side_category must be convertible to CGAL::Arr_open_side_tag. Similarly, if some curves handled by the concept are expected to be open on the right, open at the bottom, or open at the top, the corresponding nested type must be convertible to CGAL::Arr_open_side_tag. A model of the concept ArrangementOpenBoundaryTraits_2 must have all the four categories convertible to CGAL::Arr_open_side_tag.We intend to introduce more concepts that require only a subset of the categories to be convertible to CGAL::Arr_open_side_tag. In this case the DCEL of the arrangement instantiated with the model is initialized with an implicit bounding rectangle. When the parameter space is bounded, it is the exact geometric embedding of the implicit bounding rectangle.

Refines

ArrangementBasicTraits_2

Has models

CGAL::Arr_linear_traits_2<Kernel>

CGAL::Arr_rational_function_traits_2<AlgebraicKernel_d_1>

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>

See also

ArrangementBasicTraits_2

ArrangementXMonotoneTraits_2

ArrangementLandmarkTraits_2

ArrangementTraits_2

Categories
typedef unspecified_type	Left_side_category
	Must be convertible to CGAL::Arr_open_side_tag.
typedef unspecified_type	Bottom_side_category
	Must be convertible to CGAL::Arr_open_side_tag.
typedef unspecified_type	Top_side_category
	Must be convertible to CGAL::Arr_open_side_tag.
typedef unspecified_type	Right_side_category
	Must be convertible to CGAL::Arr_open_side_tag.

Functor Types
typedef unspecified_type	Parameter_space_in_x_2
	models the concept ArrTraits::ParameterSpaceInX_2.
typedef unspecified_type	Compare_y_near_boundary_2
	models the concept ArrTraits::CompareYNearBoundary_2.
typedef unspecified_type	Parameter_space_in_y_2
	models the concept ArrTraits::ParameterSpaceInY_2.
typedef unspecified_type	Compare_x_on_boundary_2
	models the concept ArrTraits::CompareXOnBoundaryOfCurveEnd_2.
typedef unspecified_type	Compare_x_near_boundary_2
	models the concept ArrTraits::CompareXNearBoundary_2.

Accessing Functor Objects
Parameter_space_in_x_2	parameter_space_in_x_2_object () const
Compare_y_near_boundary_2	compare_y_near_boundary_2_object () const
Parameter_space_in_y_2	parameter_space_in_y_2_object () const
Compare_x_on_boundary_2	compare_x_on_boundary_2_object () const
Compare_x_near_boundary_2	compare_x_near_boundary_2_object () const

Member Typedef Documentation

Compare_x_near_boundary_2

typedef unspecified_type ArrangementOpenBoundaryTraits_2::Compare_x_near_boundary_2

models the concept ArrTraits::CompareXNearBoundary_2.

Required only if the traits class supports unbounded curves that approach the bottom or the top sides (the Bottom_side_category or the Top_side_category categories are convertible to CGAL::Arr_open_side_tag).

Compare_x_on_boundary_2

typedef unspecified_type ArrangementOpenBoundaryTraits_2::Compare_x_on_boundary_2

models the concept ArrTraits::CompareXOnBoundaryOfCurveEnd_2.

Required only if the traits class supports unbounded curves that approach the bottom or the top sides (the Bottom_side_category or the Top_side_category categories are convertible to CGAL::Arr_open_side_tag).

Compare_y_near_boundary_2

typedef unspecified_type ArrangementOpenBoundaryTraits_2::Compare_y_near_boundary_2

models the concept ArrTraits::CompareYNearBoundary_2.

Required only if the traits class supports unbounded curves that approach the left or the right sides (the Left_side_category or the Right_side_category categories are convertible to CGAL::Arr_open_side_tag).

Parameter_space_in_x_2

typedef unspecified_type ArrangementOpenBoundaryTraits_2::Parameter_space_in_x_2

models the concept ArrTraits::ParameterSpaceInX_2.

Required only if the traits class supports unbounded curves that approach the left or the right sides (the Left_side_category or the Right_side_category categories are convertible to CGAL::Arr_open_side_tag).

Parameter_space_in_y_2

typedef unspecified_type ArrangementOpenBoundaryTraits_2::Parameter_space_in_y_2

models the concept ArrTraits::ParameterSpaceInY_2.

Required only if the traits class supports unbounded curves that approach the bottom or the top sides (the Bottom_side_category or the Top_side_category categories are convertible to CGAL::Arr_open_side_tag).