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

CGAL 4.8 - 2D Arrangements

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ArrTraits::ParameterSpaceInY_2 Concept Reference
Function Object Concepts

## Definition

Refines:
  AdaptableBinaryFunction

Has Models:
  ArrangementOpenBoundaryTraits_2::Parameter_space_in_y_2

## Operations
A model of this concept must provide:
Arr_parameter_space | operator() (const ArrTraits::X_monotone_curve_2 &xcv, Arr_curve_end ce)
| Given an \( x\)-monotone curve `xcv` and an enumeration `ce` that specifies either the minimum or the maximum end of the curve, determines the location of the curve end along the \( y\)-dimension. More...

## Member Function Documentation

Arr_parameter_space ArrTraits::ParameterSpaceInY_2::operator() | ( | const ArrTraits::X_monotone_curve_2 & | xcv,
|  | Arr_curve_end | ce
| ) |  |

Given an \( x\)-monotone curve `xcv` and an enumeration `ce` that specifies either the minimum or the maximum end of the curve, determines the location of the curve end along the \( y\)-dimension.

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, determines whether \( \lim_{t \rightarrow d} Y(t)\) evaluates to \( b_b\), \( b_t\), or a value in between, where \( b_b\) and \( b_t\) are the \( y\)-coordinates of the bottom and top boundaries of the parameter space, respectively. Returns `ARR_BOTTOM_BOUNDARY`, `ARR_TOP_BOUNDARY`, or `ARR_INTERIOR`, accordingly.

Postcondition
  If `ArrTraits::Bottom_side_category` is not convertible to `Arr_open_side_tag` then the result is not `ARR_BOTTOM_BOUNDARY`.
  If `ArrTraits::Top_side_category` is not convertible to `Arr_open_side_tag` then the result is not `ARR_TOP_BOUNDARY`.