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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...
 

Member Function Documentation

◆ 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 \( I\).