CGAL 5.6.1 - 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.

## ◆ 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.