CGAL 5.3 - 2D Arrangements
CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2 Class Reference

#include <CGAL/Arr_rational_function_traits_2.h>

Definition

The X_monotone_curve_2 class nested within the traits is used to represent \( x\)-monotone parts of rational functions.

In particular, such an \( x\)-monotone curve may not contain a vertical asymptote in its interior \( x\)-range.

Is Model Of:
ArrTraits::XMonotoneCurve_2

Types

typedef AlgebraicKernel_d_1::Polynomial_1 Polynomial_1
 
typedef AlgebraicKernel_d_1::Algebraic_real_1 Algebraic_real_1
 
typedef Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2 Point_2
 

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.
 
Arr_parameter_space source_parameter_space_in_x () const
 returns whether the \( x\)-coordinate of the source is finite or whether it is \( \pm\infty\).
 
Arr_parameter_space source_parameter_space_in_y () const
 returns whether the \( y\)-coordinate of the source is finite or whether it is \( \pm\infty\).
 
const Point_2source () const
 returns the source point of the arc. More...
 
Algebraic_real_1 source_x () const
 returns the \( x\)-coordinate of the source point. More...
 
Arr_parameter_space target_parameter_space_in_x () const
 returns whether the \( x\)-coordinate of the target is finite or whether it is \( \pm\infty\).
 
Arr_parameter_space target_parameter_space_in_y () const
 returns whether the \( y\)-coordinate of the target is finite or whether it is \( \pm\infty\).
 
const Point_2target () const
 returns the target point of the arc. More...
 
Algebraic_real_1 target_x () const
 returns the \( x\)-coordinate of the target point. More...
 
Arr_parameter_space left_parameter_space_in_x () const
 returns whether the \( x\)-coordinate of the left curve end is finite or whether it is \( \pm\infty\).
 
Arr_parameter_space left_parameter_space_in_y () const
 returns whether the \( y\)-coordinate of the left curve end is finite or whether it is \( \pm\infty\).
 
const Point_2left () const
 returns the left point of the arc. More...
 
Algebraic_real_1 left_x () const
 returns the \( x\)-coordinate of the left point. More...
 
Arr_parameter_space right_parameter_space_in_x () const
 returns whether the \( x\)-coordinate of the right curve end is finite or whether it is \( \pm\infty\).
 
Arr_parameter_space right_parameter_space_in_y () const
 returns whether the \( y\)-coordinate of the right curve end is finite or whether it is \( \pm\infty\).
 
const Point_2right () const
 returns the right point of the arc. More...
 
Algebraic_real_1 right_x () const
 returns the \( x\)-coordinate of the right point. More...
 
bool is_left_to_right () const
 returns whether the curve is oriented from left to right.
 

Member Function Documentation

◆ left()

template<typename AlgebraicKernel_d_1 >
const Point_2& CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2::left ( ) const

returns the left point of the arc.

Precondition
Both the \( x\)- and \( y\)-coordinates of the left point is finite.

◆ left_x()

template<typename AlgebraicKernel_d_1 >
Algebraic_real_1 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2::left_x ( ) const

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

Precondition
The \( x\)-coordinate of the left point is finite.

◆ right()

template<typename AlgebraicKernel_d_1 >
const Point_2& CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2::right ( ) const

returns the right point of the arc.

Precondition
Both the \( x\)- and \( y\)-coordinates of The right point is finite.

◆ right_x()

template<typename AlgebraicKernel_d_1 >
Algebraic_real_1 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2::right_x ( ) const

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

Precondition
The \( x\)-coordinate of the right point is finite.

◆ source()

template<typename AlgebraicKernel_d_1 >
const Point_2& CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2::source ( ) const

returns the source point of the arc.

Precondition
Both the \( x\)- and \( y\)-coordinates of the source point is finite.

◆ source_x()

template<typename AlgebraicKernel_d_1 >
Algebraic_real_1 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2::source_x ( ) const

returns the \( x\)-coordinate of the source point.

Precondition
The \( x\)-coordinate of the source point is finite.

◆ target()

template<typename AlgebraicKernel_d_1 >
const Point_2& CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2::target ( ) const

returns the target point of the arc.

Precondition
Both the \( x\)- and \( y\)-coordinates of the target point is finite.

◆ target_x()

template<typename AlgebraicKernel_d_1 >
Algebraic_real_1 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::X_monotone_curve_2::target_x ( ) const

returns the \( x\)-coordinate of the target point.

Precondition
The \( x\)-coordinate of the target point is finite.