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 \( I\).