CGAL 5.4  2D Arrangements

#include <CGAL/Arr_algebraic_segment_traits_2.h>
Models the ArrangementBasicTraits_2::Point_2
concept.
Represents points in \( \mathbb{R}^2\). Intersection points of algebraic curves are in general nonrational, 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 p is part of.  
int  arcno () const 
returns the arc number of p .  
std::pair< double, double >  to_double () const 
returns doubleapproximations of the \( x\) and \( y\)coordinates.  
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 highdegree polynomials. Therefore, it is recommended to avoid to call this function as much as possible.