CGAL users discussion list

[Monique Teillaud <>]

Hi,

I am travelling these days and cannot spend a lot of time on emails, so my 
answer right now will not be very detailed.  

It seems to me that you would need a general purpose hyperbolic geometry 
kernel, similar to what CGAL has for Euclidean geometry. I agree that it 
would be nice if we could have that in CGAL, but it would require some 
manpower...
What CGAL currently has for hyperbolic geometry is only Traits classes, 
specifically targeted at being used by the hyperbolic Delaunay triangulations 
package (rather than by users), that's why you don't find everything you 
need. 

In fact, directly using the 2D circular geometry kernel could be better for 
you
see https://doc.cgal.org/latest/Manual/packages.html#PkgCircularKernel2
Its interface is about circles and circular arcs in Euclidean plane, not 
about hyperbolic geometry. Still, as a mathematician, you know how hyperbolic 
segments are constructed in the Poincaré disk and you can probably easily 
translate between the two geometries. 

Note that the circular kernel is using some number types for quadratic 
extensions of Q (see "Roots of Polynomials" in the Reference Manual), in 
which you might feed your point coordinates. 

Hope this helps.
Best,
--
Monique Teillaud 
https://members.loria.fr/Monique.Teillaud/
INRIA Nancy - Grand Est, LORIA 
Institut National de Recherche en Informatique et Automatique

----- Le 20 Juin 19, à 9:31, Stefan Witzel 

 a écrit :

> Hi,
> 
> Am Do., 20. Juni 2019 um 14:46 Uhr schrieb Stefan Witzel 
> <>:
>> Here is an obscure issue: I have two points p and q for which
>> Construct_hyperbolic_segment_2 does not terminate. The points are
>> approximately Hyperbolic_point_2(0.9666536103464638,-0.0141826279439945)
>> and Hyperbolic_point_2(0.9666536103464638,0.0141826279439945) but I
>> don't know how I can dump them exactly. They arise as vertices of a
>> hyperbolic Voronoi diagram. Any suggestions?
> 
> Actually it did terminate after minutes. So this must have to do with
> the exact calculations, climbing up some tower of quadratic
> extensions?
> I will use the occasion to ask a bit more about exact/inexact calculations:
> 1. My points do actually come from a quadratic extension of Q (but
> from a different program); is there a good way to feed them exactly
> into cgal?
> 2. What would be a good alternative to the time-consuming exact
> calculations? If I use
> 
>  typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
>  typedef CGAL::Hyperbolic_Delaunay_triangulation_traits_2<K> Gt;
> 
> the program is very fast but also the outcome is very unsatisfactory.
> Am I right to assume that I should use
> 
>  typedef CGAL::Hyperbolic_Delaunay_triangulation_CK_traits_2<> Gt;
> 
> ? In that case, can someone indicate how to cast a
> Hyperbolic_segment_2 to a segment or a circular arc? In principle I
> appreciate this abstraction between interface and implementation but
> in practice I find that the interface doesn't provide what I need (see
> a previous discussion) so I need to access the actual implementation
> and then digging into a template with three nested template parameters
> is beyond me.
> 
> Best,
> Stefan
> 
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