\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Arrangements

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ArrTraits::CompareXNearLimit_2 Concept Reference
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

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`.