ArrTraits::CompareXNearBoundary_2 Concept Reference

Definition

Refines

AdaptableTernaryFunction

Has models

ArrangementOpenBoundaryTraits_2::Compare_x_near_boundary_

Operations
A model of this concept must provide:
Comparison_result	operator() (const ArrTraits::X_monotone_curve_2 &xcv1, const ArrTraits::X_monotone_curve_2 &xcv2, CGAL::Arr_curve_end ce)
	Given two \(x\)-monotone curves xcv1 and xcv2 and an enumeration ce that specifies either the minimum ends or the maximum ends of the curves where the curves have a vertical asymptote, compares the \(x\)-coordinate of the curves near their respective ends.

Member Function Documentation

operator()()

Comparison_result ArrTraits::CompareXNearBoundary_2::operator()	(	const ArrTraits::X_monotone_curve_2 &	xcv1,
		const ArrTraits::X_monotone_curve_2 &	xcv2,
		CGAL::Arr_curve_end	ce
	)

Given two \(x\)-monotone curves xcv1 and xcv2 and an enumeration ce that specifies either the minimum ends or the maximum ends of the curves where the curves have a vertical asymptote, compares the \(x\)-coordinate of the curves near their respective ends.

Returns CGAL::SMALLER, CGAL::EQUAL, or CGAL::LARGER accordingly. More precisely, compares the \(x\)-coordinates of the horizontal projection of a point \(p\) onto xcv1 and xcv2. If xcv1 and xcv2 approach the bottom boundary-side, \(p\) is located far to the bottom, such that the result is invariant under a translation of \( p\) farther to the bottom. If xcv1 and xcv2 approach the top boundary-side, \(p\) is located far to the top in a similar manner.

Precondition

The \(x\)-coordinates of the limits of the curves at their respective ends are equal. That is, compare_x_on_boundary_2(xcv1, xcv2, ce) = CGAL::EQUAL.

parameter_space_in_y_2(xcv1, ce) = parameter_space_in_y_2(xcv2, ce).

parameter_space_in_y_2(xcv1, ce) \( \neq\) CGAL::ARR_INTERIOR.