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[Morteza Manavi <>]

Thanks Efi,

Is it possible to define Kernel such that accept Sqrt_extension coordinates as input? 

On Sun, Sep 16, 2018 at 5:26 PM Efi Fogel <> wrote:

If you absolutely need to use a vertex position as a circle center, you cannot use Arr_circle_segment_traits_2.

In this case you need to resort to a more "powerful" traits, such as the Arr_algebraic_segment_traits_2 traits.

Sqrt_extension cannot be converted to Rational without loss of data.

Naturally, managing, for example, segments, by the Arr_algebraic_segment_traits_2 is more time-consuming then by the Arr_circle_segment_traits_2.

So, make sure that the above is a must. (That is, circle centers may need to have Sqrt_extension coordinates.)
For example, consider a point p = (x,y) with Sqrt_extension coordinates that lies on some circle C.

You can approximating p with p' = (x', y'), such that p' also lies on C while bounding the difference between p and p'; see, e.g.,  CGAL::rational_rotation_approximation().

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  /_____/_) o    /__________  __  //
 (____ (   (    (    (_/ (_/-(-'_(/
                         _/

On Sun, 16 Sep 2018 at 15:48, Efi Fogel <> wrote:

If you absolutely need to use a vertex position as a circle center, you cannot use Arr_circle_segment_traits_2.

In this case you need to resort to a more "powerful" traits, such as the Arr_algebraic_segment_traits_2 traits.

Sqrt_extension cannot be converted to Rational without loss of data.

Naturally, managing, e.g., segments, by the Arr_algebraic_segment_traits_2 is less efficient then by the Arr_circle_segment_traits_2.

So, make sure that the above is a must. For example

   ____  _        ____             _
  /_____/_) o    /__________  __  //
 (____ (   (    (    (_/ (_/-(-'_(/
                         _/

On Sun, 16 Sep 2018 at 13:36, Morteza Manavi <> wrote:

Hi,

I define arrangement:

typedef CGAL::Cartesian<CGAL::Exact_rational>                   Kernel;

typedef Kernel::Circle_2                                        Circle_2;

typedef CGAL::Arr_circle_segment_traits_2<Kernel>               Traits_2;
typedef CGAL::Arrangement_with_history_2<Traits_2>              Arr_with_hist_2;

and I want to get a vertex position and use it for creation new circle in the arrangement but I should use a Point with rational type as circle position while the type of vertex position is 
Sqrt_extension and CGAL do not convert Sqrt_extension to Rational. Now I do not know how to convert Sqrt_extension to Rational such that do not loss data.(convert exactly)