CGAL users discussion list

[Monique Teillaud <>]

----- Le 19 Juin 19, à 3:16, Stefan Witzel 

 a écrit :

> Am Di., 18. Juni 2019 um 19:54 Uhr schrieb Monique Teillaud
> <>:
>> ----- Le 18 Juin 19, à 12:06, Stefan Witzel 
>> <>
>>  a écrit :
>> Yes of course, that was the starting point of the discussion. But I cannot
>> (easily) turn them into a closed path because the endpoints of the dual
>> segments don't match up.
>>
>> Aren't you using the recommended kernels? they make sure that you don't
>> encounter arithmetic issues.
>> Even if you are using your own rounded arithmetics, then you _know_ by
>> definition that the two Voronoi vertices are the same. For this, it is 
>> better
>> to rely on the combinatorics rather than arithmetic constructions.
> 
> When I say "don't match up" I mean target() of one is not source() of
> the next (not because of imprecision but because they happen to lie in
> a region of the Poincaré disk where the cgal convention stipulates
> that the source() of one should be the source() of the next).
> What I take from this discussion is that hyperbolic segments are not
> useful and are not meant to represent edges of combinatorial polygons.

Hyperbolic segments are only useful to what the manual says. They are 
standard geometric hyperbolic (non-oriented) segments, not combinatorial 
objects. 

> So to do things in the cgal spirit one should probably represent
> polygons by their vertices and only create the hyperbolic segments
> when drawing the polygon. In that situation one would then have the
> vertices as well as the segments available and could sort out the
> right orientation.

If I understand correctly, this goes along the same lines as what I proposed 
in my previous email: 
* use circulators to get the combinatorial structure (the polygon is left 
implicit)
* use segments as (non-oriented) geometric objects. 

> Just to make sure: this cgal convention on counterclockwise
> orientation of circular arcs is just an internal convention, not
> guaranteed behavior, correct? So if I have a hyperbolic segment I
> really know nothing about the role of source() and target()?

If I am not mistaken, source() and target() are not even mentioned in the 
manual.

> Perhaps I should say this at least once (and it should probably have
> been earlier): it's great that cgal provides the power of computing
> hyperbolic Voronoi diagrams in such a robust way! I wouldn't have
> started the discussion if your software wasn't so useful.

We are glad that this new package can already be useful to some users! 
Thank you for your comments.

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