 CGAL 5.0 - 2D Arrangements
CGAL::Arr_rational_function_traits_2< AlgebraicKernel_d_1 >::Point_2 Class Reference

#include <CGAL/Arr_rational_function_traits_2.h>

## Definition

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. More...

std::pair< Bound, Boundapproximate_absolute_x (int a) const
Computes a pair $$p$$ approximating the $$x$$-coordinate with respect to the given absolute precision $$a$$. More...

std::pair< Bound, Boundapproximate_absolute_y (int a) const
Computes a pair $$p$$ approximating the $$y$$-coordinate with respect to the given absolute precision $$a$$. More...

std::pair< Bound, Boundapproximate_relative_x (int r) const
Computes a pair $$p$$ approximating the $$x$$-coordinate with respect to the given relative precision $$r$$. More...

std::pair< Bound, Boundapproximate_relative_y (int r) const
Computes a pair $$p$$ approximating the $$y$$-coordinate with respect to the given relative precision $$r$$. More...

## ◆ approximate_absolute_x()

template<typename AlgebraicKernel_d_1 >
 std::pair 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
$$p.first \leq x \leq p.second$$
$$p.second - p.first \leq2^{-a}$$

## ◆ approximate_absolute_y()

template<typename AlgebraicKernel_d_1 >
 std::pair 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
$$p.first \leq y \leq p.second$$
$$p.second - p.first \leq2^{-a}$$

## ◆ approximate_relative_x()

template<typename AlgebraicKernel_d_1 >
 std::pair 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 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.