CGAL users discussion list

[Bernd Gaertner <>]

 wrote:
> I work with the CGAL library to compute a bounded voronoi diagram for my 
> academic research project.
> I use the Delaunay_triangulation_2 class, the Voronoi_diagram_2 class, the 
> Min_sphere_of_spheres_d class et other functions like "intersection".
>
> I would like to write an article about my subject but I need to know the 
> computing precision. I use C++ double type and I would like to know what is 
> the precision that CGAL can ensure?
> I work with real number (in double) in the interval [0,1], so how many figures after the comma without precision's error can I publish? 

I'm assuming that you speak about the coordinates of the vertices,
say, of the computed Voronoi diagram.

If your programs exclusively work with type double, and no exact
fallback number types (like CGAL::Gmpq or CGAL::MP_Float) are being
used, then CGAL cannot give you any strict precision guarantees.
The programs may even fail completely for certain inputs.

However, if you compute exactly (this is possible by various means
in CGAL) and only round the computed results to double in the end,
you typically incur only unit roundoff, i.e. the results are correct
to around 17 decimal digits. See http://www.cgal.org/philosophy.html
for more on the exact computing paradigm in CGAL.

Best,
Bernd.