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 CGAL 4.14.2 - 2D Arrangements
CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2 Class Reference

#include <CGAL/Arr_rational_function_traits_2.h>

## Definition

Functor to construct a X_monotone_curve_2.

To enable caching the class is not default constructible and must be obtained via the function construct_x_monotone_curve_2_object(), which is a member of the traits.

Is Model Of:

Assignable

CopyConstructible

AdaptableBinaryFunction

AdaptableUnaryFunction

## 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 >::X_monotone_curve_2 result_type

typedef Polynomial_1 argument_type

typedef Polynomial_1 first_argument_type

typedef Polynomial_1 second_argument_type

## Operations

X_monotone_curve_2 operator() (Polynomial_1 P) const
Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$.

X_monotone_curve_2 operator() (Polynomial_1 P, const Algebraic_real_1 &x, bool right) const
Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$. More...

X_monotone_curve_2 operator() (Polynomial_1 P, const Algebraic_real_1 &lower, const Algebraic_real_1 &upper)
Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$. More...

const X_monotone_curve_2 operator() (Polynomial_1 P, Polynomial_1 Q)
Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$. More...

const X_monotone_curve_2 operator() (Polynomial_1 P, Polynomial_1 Q, const Algebraic_real_1 &x, bool right)
Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$. More...

const X_monotone_curve_2 operator() (Polynomial_1 P, Polynomial_1 Q, const Algebraic_real_1 &lower, const Algebraic_real_1 &upper)
Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$. More...

template<typename InputIterator >
const X_monotone_curve_2 operator() (InputIterator begin, InputIterator end) const
Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$, where the coefficients of $$P$$ are given in the range [begin,end).

template<typename InputIterator >
X_monotone_curve_2 operator() (InputIterator begin, InputIterator end, const Algebraic_real_1 &x, bool right) const
Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$, where the coefficients of $$P$$ are given in the range [begin,end). More...

template<typename InputIterator >
X_monotone_curve_2 operator() (InputIterator begin, InputIterator end const Algebraic_real_1 &lower, const Algebraic_real_1 &upper)
Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$, where the coefficients of $$P$$ are given in the range [begin,end). More...

template<typename InputIterator >
const X_monotone_curve_2 operator() (InputIterator begin_numer, InputIterator end_numer, InputIterator begin_denom, InputIterator end_denom)
Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$, where the coefficients of $$P$$ and $$Q$$ are given in the ranges [begin_numer,end_numer) and [begin_denom,end_denom), respectively. More...

template<typename InputIterator >
const X_monotone_curve_2 operator() (InputIterator begin_numer, InputIterator end_numer, InputIterator begin_denom, InputIterator end_denom, const Algebraic_real_1 &x, bool right)
Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$, where the coefficients of $$P$$ and $$Q$$ are given in the ranges [begin_numer,end_numer) and [begin_denom,end_denom), respectively. More...

template<typename InputIterator >
const X_monotone_curve_2 operator() (InputIterator begin_numer, InputIterator end_numer, InputIterator begin_denom, InputIterator end_denom, const Algebraic_real_1 &lower, const Algebraic_real_1 &upper)
Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$, where the coefficients of $$P$$ and $$Q$$ are given in the ranges [begin_numer,end_numer) and [begin_denom,end_denom), respectively. More...

## ◆ operator()() [1/10]

template<typename AlgebraicKernel_d_1 >
 X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( Polynomial_1 P, const Algebraic_real_1 & x, bool right ) const

Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$.

The function is defined over the interval $$[x,+\infty)$$ if $$right$$ is true and $$(-\infty,x]$$ otherwise.

## ◆ operator()() [2/10]

template<typename AlgebraicKernel_d_1 >
 X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( Polynomial_1 P, const Algebraic_real_1 & lower, const Algebraic_real_1 & upper )

Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$.

The function is defined over the interval $$[lower,upper]$$.

## ◆ operator()() [3/10]

template<typename AlgebraicKernel_d_1 >
 const X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( Polynomial_1 P, Polynomial_1 Q )

Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$.

Precondition
$$Q$$ has no real roots.

## ◆ operator()() [4/10]

template<typename AlgebraicKernel_d_1 >
 const X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( Polynomial_1 P, Polynomial_1 Q, const Algebraic_real_1 & x, bool right )

Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$.

The function is defined over the interval $$I=[x,+\infty)$$ if $$right$$ is true and $$I=(-\infty,x]$$ otherwise.

Precondition
$$Q$$ has no real roots in the interior of $$I$$.

## ◆ operator()() [5/10]

template<typename AlgebraicKernel_d_1 >
 const X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( Polynomial_1 P, Polynomial_1 Q, const Algebraic_real_1 & lower, const Algebraic_real_1 & upper )

Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$.

The function is defined over the interval $$I=[lower,upper]$$.

Precondition
$$Q$$ has no real roots in the interior of $$I$$.

## ◆ operator()() [6/10]

template<typename AlgebraicKernel_d_1 >
template<typename InputIterator >
 X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( InputIterator begin, InputIterator end, const Algebraic_real_1 & x, bool right ) const

Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$, where the coefficients of $$P$$ are given in the range [begin,end).

The function is defined over the interval $$[x,+\infty)$$ if $$right$$ is true and $$(-\infty,x]$$ otherwise.

## ◆ operator()() [7/10]

template<typename AlgebraicKernel_d_1 >
template<typename InputIterator >
 X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( InputIterator begin, InputIterator end const Algebraic_real_1 & lower, const Algebraic_real_1 & upper )

Constructs an $$x$$-monotone curve supported by the polynomial function $$y = P(x)$$, where the coefficients of $$P$$ are given in the range [begin,end).

The function is defined over the interval $$[lower,upper]$$.

## ◆ operator()() [8/10]

template<typename AlgebraicKernel_d_1 >
template<typename InputIterator >
 const X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( InputIterator begin_numer, InputIterator end_numer, InputIterator begin_denom, InputIterator end_denom )

Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$, where the coefficients of $$P$$ and $$Q$$ are given in the ranges [begin_numer,end_numer) and [begin_denom,end_denom), respectively.

Precondition
$$Q$$ has no real roots.

## ◆ operator()() [9/10]

template<typename AlgebraicKernel_d_1 >
template<typename InputIterator >
 const X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( InputIterator begin_numer, InputIterator end_numer, InputIterator begin_denom, InputIterator end_denom, const Algebraic_real_1 & x, bool right )

Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$, where the coefficients of $$P$$ and $$Q$$ are given in the ranges [begin_numer,end_numer) and [begin_denom,end_denom), respectively.

The function is defined over the interval $$I=[x,+\infty)$$ if $$right$$ is true and $$I=(-\infty,x]$$ otherwise.

Precondition
$$Q$$ has no real roots in the interior of $$I$$.

## ◆ operator()() [10/10]

template<typename AlgebraicKernel_d_1 >
template<typename InputIterator >
 const X_monotone_curve_2 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Construct_x_monotone_curve_2::operator() ( InputIterator begin_numer, InputIterator end_numer, InputIterator begin_denom, InputIterator end_denom, const Algebraic_real_1 & lower, const Algebraic_real_1 & upper )

Constructs an $$x$$-monotone curve supported by the rational function $$y = P(x)/Q(x)$$, where the coefficients of $$P$$ and $$Q$$ are given in the ranges [begin_numer,end_numer) and [begin_denom,end_denom), respectively.

The function is defined over the interval $$I=[lower,upper]$$.

Precondition
$$Q$$ has no real roots in the interior of $$I$$.