\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11.2 - 2D Arrangements
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ArrTraits::ParameterSpaceInY_2 Concept Reference

Definition

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.