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_1 &	numerator () const
	returns the numerator of the supporting rational function.
const Polynomial_1 &	denominator () 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_2 &	source () 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_2 &	target () 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_2 &	left () 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_2 &	right () 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.