CGAL 5.1.3 - 2D Arrangements
ArrTraits::CompareXAtLimit_2 Concept Reference

## Operations

A model of this concept must provide:

Comparison_result operator() (const ArrTraits::Point_2 &p, const ArrTraits::X_monotone_curve_2 &xcv, Arr_curve_end ce)
Given a point p, an $$x$$-monotone curve xcv, and an enumeration ce that specifies either the minimum or the maximum end of the curve where the curve has a vertical asymptote, compares the $$x$$-coordinate of p and the $$x$$-coordinate of the limit of the curve at its specificed end. More...

Comparison_result operator() (const ArrTraits::X_monotone_curve_2 &xcv1, Arr_curve_end ce1, const ArrTraits::X_monotone_curve_2 &xcv2, Arr_curve_end ce2)
Given two $$x$$-monotone curves xcv1 and xcv2 and two indices ce1 and ce2 that specify either the minimum or the maximum ends of xcv1 and xcv2, respectively, where the curves have vertical asymptotes, compares the $$x$$-coordinates of the limits of the curves at their specificed ends. More...

## ◆ operator()() [1/2]

 Comparison_result ArrTraits::CompareXAtLimit_2::operator() ( const ArrTraits::Point_2 & p, const ArrTraits::X_monotone_curve_2 & xcv, Arr_curve_end ce )

Given a point p, an $$x$$-monotone curve xcv, and an enumeration ce that specifies either the minimum or the maximum end of the curve where the curve has a vertical asymptote, compares the $$x$$-coordinate of p and the $$x$$-coordinate of the limit of the curve at its specificed end.

The variable xcv identifies the parametric curve $$C(t) = (X(t),Y(t))$$ defined over an open or half-open interval with endpoints $$0$$ and $$1$$. The enumeration ce identifies an open end $$d \in\{0,1\}$$ of $$C$$. Formally, compares the $$x$$-coordinate of p and $$\lim_{t \rightarrow d} X(t)$$. Returns SMALLER, EQUAL, or LARGER accordingly.

Precondition
parameter_space_in_y_2(xcv, ce) $$\neq$$ ARR_INTERIOR.
If the parameter space is unbounded, $$C$$ has a vertical asymptote at its $$d$$-end; that is, parameter_space_in_x_2(xcv, ce) = ARR_INTERIOR.

## ◆ operator()() [2/2]

 Comparison_result ArrTraits::CompareXAtLimit_2::operator() ( const ArrTraits::X_monotone_curve_2 & xcv1, Arr_curve_end ce1, const ArrTraits::X_monotone_curve_2 & xcv2, Arr_curve_end ce2 )

Given two $$x$$-monotone curves xcv1 and xcv2 and two indices ce1 and ce2 that specify either the minimum or the maximum ends of xcv1 and xcv2, respectively, where the curves have vertical asymptotes, compares the $$x$$-coordinates of the limits of the curves at their specificed ends.

The variables xcv1 and xcv2 identify the parametric curves $$C_1(t) = (X_1(t),Y_1(t))$$ and $$C_2(t) = (X_2(t),Y_2(t))$$, respectively, defined over open or half-open intervals with endpoints $$0$$ and $$1$$. The indices ce1 and ce2 identify open ends $$d_1 \in\{0,1\}$$ and $$d_2 \in\{0,1\}$$ of $$C_1$$ and $$C_2$$, respectively. Formally, compares $$\lim_{t \rightarrow d_1} X_1(t)$$ and $$\lim_{t \rightarrow d_2} X_2(t)$$. Returns SMALLER, EQUAL, or LARGER accordingly.

Precondition
parameter_space_in_y_2(xcv1, ce1) $$\neq$$ ARR_INTERIOR.
parameter_space_in_y_2(xcv2, ce2) $$\neq$$ ARR_INTERIOR.
If the parameter space is unbounded, $$C_1$$ has a vertical asymptote at its respective end; that is, parameter_space_in_x_2(xcv1, ce1) = ARR_INTERIOR.
If the parameter space is unbounded, $$C_2$$ has a vertical asymptote at its respective end; that is, parameter_space_in_x_2(xcv2, ce2) = ARR_INTERIOR.