\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5.1 - 2D Arrangements
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ArrTraits::CompareYNearBoundary_2 Concept Reference
Function Object Concepts

Definition

Refines:
AdaptableTernaryFunction
Has Models:
ArrangementOpenBoundaryTraits_2::Compare_y_near_boundary_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 or the maximum ends of the curves, compares the \( y\)-coordinate of the curves near their respective ends. More...
 

Member Function Documentation

Comparison_result ArrTraits::CompareYNearBoundary_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 or the maximum ends of the curves, compares the \( y\)-coordinate of the curves near their respective ends.

Returns SMALLER, EQUAL, or LARGER accordingly. More precisely, compares the \( y\)-coordinates of the vertical projection of a point \( p\) onto predicate Parameter_space_in_x_2 evaluates to ARR_LEFT_BOUNDARY when applied to xcv1 and ce and when applied to xcv2 and ce. In this case \( p\) is located far to the left, such that the result is invariant under a translation of \( p\) farther to the left. If ce is evaluates to ARR_RIGHT_BOUNDARY when applied to xcv1 and ce and when applied to xcv2 and ce. In that case \( p\) is located far to the right in a similar manner.

Precondition
parameter_space_in_x_2(xcv2, ce) = parameter_space_in_x_2(xcv1, ce).
parameter_space_in_x_2(xcv1, ce) \( \neq\) ARR_INTERIOR.