CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2 Class Reference

#include <CGAL/Arr_rational_function_traits_2.h>

Definition

template<typename AlgebraicKernel_d_1>
class CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2

Is model of

ArrTraits::Point_2

Types
typedef AlgebraicKernel_d_1::Polynomial_1	Polynomial_1
typedef AlgebraicKernel_d_1::Algebraic_real_1	Algebraic_real_1
typedef AlgebraicKernel_d_1::Bound	Bound

Operations
Polynomial_1	numerator () const
	returns the numerator of the supporting rational function.
Polynomial_1	denominator () const
	returns the denominator of the supporting rational function.
std::pair< double, double >	to_double () const
	returns double-approximations of the x- and y-coordinates.
Algebraic_real_1	x () const
	returns the \(x\)-coordinate of the point.
Algebraic_real_1	y () const
	obtains the \(y\)-coordinates of the point.
std::pair< Bound, Bound >	approximate_absolute_x (int a) const
	Computes a pair \(p\) approximating the \(x\)-coordinate with respect to the given absolute precision \(a\).
std::pair< Bound, Bound >	approximate_absolute_y (int a) const
	Computes a pair \(p\) approximating the \(y\)-coordinate with respect to the given absolute precision \(a\).
std::pair< Bound, Bound >	approximate_relative_x (int r) const
	Computes a pair \(p\) approximating the \(x\)-coordinate with respect to the given relative precision \(r\).
std::pair< Bound, Bound >	approximate_relative_y (int r) const
	computes a pair \(p\) approximating the \(y\)-coordinate with respect to the given relative precision \(r\).

Member Function Documentation

approximate_absolute_x()

template<typename AlgebraicKernel_d_1 >

std::pair< Bound, Bound > CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2::approximate_absolute_x

(

int

a

)

const

Computes a pair \(p\) approximating the \(x\)-coordinate with respect to the given absolute precision \(a\).

Postcondition

\(p.first \leq x \leq p.second\)

\(p.second - p.first \leq 2^{-a}\)

approximate_absolute_y()

template<typename AlgebraicKernel_d_1 >

std::pair< Bound, Bound > CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2::approximate_absolute_y

(

int

a

)

const

Computes a pair \(p\) approximating the \(y\)-coordinate with respect to the given absolute precision \(a\).

Postcondition

\(p.first \leq y \leq p.second\)

\(p.second - p.first \leq 2^{-a}\)

approximate_relative_x()

template<typename AlgebraicKernel_d_1 >

std::pair< Bound, Bound > CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2::approximate_relative_x

(

int

r

)

const

Computes a pair \(p\) approximating the \(x\)-coordinate with respect to the given relative precision \(r\).

Postcondition

\(p.first \leq x \leq p.second\)

\(p.second - p.first \leq2^{-r}|x|\)

approximate_relative_y()

template<typename AlgebraicKernel_d_1 >

std::pair< Bound, Bound > CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2::approximate_relative_y

(

int

r

)

const

computes a pair \(p\) approximating the \(y\)-coordinate with respect to the given relative precision \(r\).

Postcondition

\(p.first \leq y \leq p.second\)

\(p.second - p.first \leq2^{-r}|y|\)

y()

template<typename AlgebraicKernel_d_1 >

Algebraic_real_1 CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2::y

(

)

const

obtains the \(y\)-coordinates of the point.

Attention: As described above, points are not stored by their \(y\)-coordinate in Algebraic_real_1 representation. In fact, this representation must be computed on demand, and might become quite costly for points defined by high-degree polynomials. Therefore, it is recommended to avoid calls to this function as much as possible.