\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.14.2 - 2D Arrangements
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_1numerator () const
 returns the numerator of the supporting rational function.
 
const Polynomial_1denominator () 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

◆ left_x()

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

◆ right_x()

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