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

CGAL 4.8 - 2D Arrangements

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CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Curve_2 Class Reference

`#include <CGAL/Arr_rational_function_traits_2.h>`

## Definition

The `Curve_2` class nested within the traits is used to represent rational functions which may be restricted to a certain x-range.

Is Model Of:
  `ArrTraits::Curve_2`

## Types
typedef AlgebraicKernel_d_1::Polynomial_1 | Polynomial_1
typedef AlgebraicKernel_d_1::Algebraic_real_1 | Algebraic_real_1

## Operations
const Polynomial_1 & | numerator () const
| returns the numerator of the supporting rational function.
const Polynomial_1 & | denominator () const
| returns the denominator of the supporting rational function.
bool | is_continuous () const
| returns whether çurve is continuous, namely whether it does not contains any vertical asymptotes in its interior.
Arr_parameter_space | left_parameter_space_in_x () const
| returns whether the \( x\)-coordinate of çurve's left end is finite or whether it is \( \pm\infty\).
Arr_parameter_space | right_parameter_space_in_x () const
| returns whether the \( x\)-coordinate of çurve's right end is finite or whether it is \( \pm\infty\).
Algebraic_real_1 | left_x () const
| returns the \( x\)-coordinate of the left end. More...
Algebraic_real_1 | right_x () const
| returns the \( x\)-coordinate of the right end. More...

## Member Function Documentation

template<typename AlgebraicKernel_d_1 >

Algebraic_real_1 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Curve_2::left_x | ( | ) |  | const

returns the \( x\)-coordinate of the left end.

Precondition
  left_boundary_in_x()==ARR_INTERIOR

template<typename AlgebraicKernel_d_1 >

Algebraic_real_1 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Curve_2::right_x | ( | ) |  | const

returns the \( x\)-coordinate of the right end.

Precondition
  right_boundary_in_x()==ARR_INTERIOR