\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Arrangements

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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...

## Member Function Documentation

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.

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 \( [lower,upper]\).

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.

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 \( I\).

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 \( I\).

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.

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 \( [lower,upper]\).

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.

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 \( I\).

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 \( I\).