CGAL users discussion list

[Menelaos Karavelas <>]

On 9 Apr 2012, at 13:06, Andrii Sydorchuk wrote:

>> 
>> In the traits class there is a functor: Construct_svd_vertex_2. This
>> gives you the Voronoi vertex.
> 
> 
> Does it mean that coordinates of the Voronoi vertices are not computed
> during segment Delaunay graph construction (only topology is built)?
> 

Yes. The dual graph (the Delaunay graph) is computed.

> However, in order to work correctly you need to use a number type that
>> supports field operations and square roots.
> 
> 
> Let's say I provided proper number types that support field operations and
> square roots, what is the precision I should expect for coordinates of the
> Voronoi vertices in case they are doubles (64 bit floating-point type)?

Suppose you use CORE::Expr's together with exact traits. Then the Voronoi 
vertices are computed exactly as CORE::Expr's. If you want to convert their 
coordinates to doubles, then you obviously loose some accuracy (they become 
approximate). The doubles you get are whatever the CGAL::to_double function 
gives you. I am not sure there are any guaranties on the precision of the 
to_double function.

Now suppose you use CORE::Expr's together with filtered traits. In this case 
you can access the Voronoi vertices exactly (via the exact traits hidden 
inside the filtered traits), and my comments above apply, or you can access 
approximations of the Voronoi vertices by calling the Construct_svd_vertex_2 
functor. In the second case, you get an approximate answer, and the 
approximations again depend on how precise is the to_double function.

Hope I have somehow answered your questions.

- m.

> Regards,
> Andrii
> 
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