 CGAL 5.4 - 2D Arrangements
CGAL::Arr_algebraic_segment_traits_2< Coefficient >::Point_2 Class Reference

#include <CGAL/Arr_algebraic_segment_traits_2.h>

## Definition

Models the ArrangementBasicTraits_2::Point_2 concept.

Represents points in $$\mathbb{R}^2$$. Intersection points of algebraic curves are in general non-rational, so we need a data structure that is capable of representing arbitrary points with algebraic coordinates.

The traits class represents algebraic coordinates by the type Algebraic_real_1, which is a model of the AlgebraicReal_1 concept. A point $$p$$ is stored by a triple $$(x,cv,arcno)$$, where $$x$$ is the $$x$$-coordinate of a point, $$cv$$ is an instance of Curve_2 that contains the point, (and has no vertical line at $$x$$), and $$arcno$$ is an int, denoting that $$p$$ is met as the $$arcno$$-th point when shooting a vertical ray at $$x$$, starting from $$-\infty$$ (where counting starts with $$0$$).

In addition to the methods listed below, the copy constructor and assignment operator for Point_2 objects are also supported.

The functor Construct_point_2 constructs Point_2 instances.

## Modifiers

Algebraic_real_1 x () const
returns the $$x$$-coordinate of p.

Algebraic_real_1 y () const
returns the $$y$$-coordinates of p. More...

Curve_2 curve () const
returns a Curve_2 instance that pis part of.

int arcno () const
returns the arc number of p.

std::pair< double, double > to_double () const
returns double-approximations of the $$x$$- and $$y$$-coordinates.

## ◆ y()

template<typename Coefficient >
 Algebraic_real_1 CGAL::Arr_algebraic_segment_traits_2< Coefficient >::Point_2::y ( ) const

returns the $$y$$-coordinates of p.

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 to call this function as much as possible.