\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.12 - 2D Arrangements
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ArrTraits::CompareXNearLimit_2 Concept Reference
2D Arrangement Reference » Concepts » Function Object Concepts

Definition

Refines:
AdaptableTernaryFunction
Has Models:
ArrangementOpenBoundaryTraits_2::Compare_x_near_limit_2

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, 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. More...
 

Member Function Documentation

◆ operator()()

Comparison_result ArrTraits::CompareXNearLimit_2::operator() ( const ArrTraits::X_monotone_curve_2 &  xcv1,
const ArrTraits::X_monotone_curve_2 &  xcv2,
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 SMALLER, EQUAL, or 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_at_limit_2(xcv1, xcv2, ce) = EQUAL.
parameter_space_in_y_2(xcv1, ce) = parameter_space_in_y_2(xcv2, ce).
parameter_space_in_y_2(xcv1, ce) \( \neq\) ARR_INTERIOR.