ArrangementBasicTraits_2

Definition

The basic arrangement-traits concept defines the minimal set of geometric predicates needed for the constrcution and maintenance of instances of the Arrangement_2 class, as well as performing simple queries (such as point-location queries) on such arrangements.

A model of this concept must define nested Point_2 and X_monotone_curve_2 types, which represent planar points and $$x-monotone curves (a vertical segment is also considered to be weakly $$x-monotone), respectively. The $$x-monotone curves are assumed to be pairwise disjoint in their interiors, so they do not intersect, and their endpoints are representable as Point_2 objects.

Types

ArrangementBasicTraits_2::Point_2
	represents a point on the plane.
ArrangementBasicTraits_2::X_monotone_curve_2
	represents a planar (weakly) $$x-monotone curve.

Tags

ArrangementBasicTraits_2::Has_left_category
	indicates whether the nested functor Compare_at_x_left_2 is provided.

Functor Types

ArrangementBasicTraits_2::Compare_x_2
	provides the operator : Comparison_result operator() (Point_2 p1, Point_2 p2) which returns SMALLER, EQUAL or LARGER according to the $$x-ordering of points p1 and p2.
ArrangementBasicTraits_2::Compare_xy_2
	provides the operator : Comparison_result operator() (Point_2 p1, Point_2 p2) which returns SMALLER, EQUAL, or LARGER according to the lexicographic $$xy-order of the points p1 and p2.
ArrangementBasicTraits_2::Construct_min_vertex_2
	provides the operator : Point_2 operator() (X_monotone_curve_2 c) which returns the lexicographically smaller (left) endpoint of c.
ArrangementBasicTraits_2::Construct_max_vertex_2
	provides the operator : Point_2 operator() (X_monotone_curve_2 c) which returns the lexicographically larger (right) endpoint of c.
ArrangementBasicTraits_2::Is_vertical_2
	provides the operator : bool operator() (X_monotone_curve_2 c) which determines whether c is a vertical segment.
ArrangementBasicTraits_2::Compare_y_at_x_2
	provides the operator : Comparison_result operator() (Point_2 p, X_monotone_curve_2 c) which compares the $$y-coordinates of p and the vertical projection of p on c, and returns SMALLER, EQUAL or LARGER according to the result.
ArrangementBasicTraits_2::Compare_y_at_x_left_2
	provides the operator : Comparison_result operator() (X_monotone_curve_2 c1, X_monotone_curve_2 c2, Point_2 p) which accepts two $$x-monotone curves c1 and c2 that have a common right endpoint p, and returns SMALLER, EQUAL or LARGER according to the relative position of the two curves immediately to the left of $$p. Note that in case one of the $$x-monotone curves is a vertical segment (emanating downward from p), it is always considered to be below the other curve.
ArrangementBasicTraits_2::Compare_y_at_x_right_2
	provides the operator : Comparison_result operator() (X_monotone_curve_2 c1, X_monotone_curve_2 c2, Point_2 p) which accepts two $$x-monotone curves c1 and c2 that have a common left endpoint p, and returns SMALLER, EQUAL or LARGER according to the relative position of the two curves immediately to the right of $$p. Note that in case one of the $$x-monotone curves is a vertical segment emanating upward from p, it is always considered to be above the other curve.
ArrangementBasicTraits_2::Equal_2
	provides the operators : bool operator() (Point_2 p1, Point_2 p2) which determines whether p1 and p2 are geometrically equivalent; and : bool operator() (X_monotone_curve_2 c1, X_monotone_curve_2 c2) which determines whether c1 and c2 are geometrically equivalent (have the same graph).

Creation

ArrangementBasicTraits_2 traits;
	default constructor.
ArrangementBasicTraits_2 traits ( other);
	copy constructor

ArrangementBasicTraits_2
	traits = other	assignment operator.

Accessing Functor Objects

Compare_x_2	traits.compare_x_2_object ()
Compare_xy_2	traits.compare_xy_2_object ()
Construct_min_vertex_2
	traits.construct_min_vertex_2_object ()
Construct_max_vertex_2
	traits.construct_max_vertex_2_object ()
Is_vertical_2	traits.is_vertical_2_object ()
Compare_y_at_x_2	traits.compare_y_at_x_2_object ()
Compare_y_at_x_left_2
	traits.compare_y_at_x_left_2_object ()
Compare_y_at_x_right_2
	traits.compare_y_at_x_right_2_object ()
Equal_2	traits.equal_2_object ()

Has Models

CGAL::Arr_segment_traits_2<Kernel>
CGAL::Arr_non_caching_segment_basic_traits_2<Kernel>
CGAL::Arr_non_caching_segment_traits_2<Kernel>
CGAL::Arr_polyline_traits_2<SegmentTraits>
CGAL::Arr_circle_segment_traits_2<Kernel>
CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>
CGAL::Arr_rational_arc_traits_2<AlgKernel,NtTraits>
CGAL::Arr_curve_data_traits_2<Tr,XData,Mrg,CData,Cnv>
CGAL::Arr_consolidated_curve_data_traits_2<Traits,Data>