CGAL users discussion list

[Stefan Witzel <>]

Hi again,

If I understand correctly in lines 135-136 of

Hyperbolic_triangulation_2/include/CGAL/internal/Hyperbolic_Delaunay_triangulation_traits_2_functions.h

the orientation of hyperbolic segments is chosen so that circular arcs
are always (counter-?)clockwise, discarding potential combinatorial
information. That is, a hyperbolic segment from p to q may end up
going from q to p. Is this correct and is there a good reason for it?

Best,
Stefan

Am Fr., 14. Juni 2019 um 14:13 Uhr schrieb Stefan Witzel 
<>:
>
> Hello again,
>
> I have the following piece of code where dt is a hyperbolic Delaunay
> triangulation, and vt is a vertex handle.
>
>   ecr = vt->incident_edges();
>  do
>   {
>     if (!dt.is_Delaunay_hyperbolic(*ecr)) {
>       break;
>     }
>     process(dt.dual(*ecr));
>   } while (++ecr != vt->incident_edges());
>
> Now I would like that the ecr->target() in one iteration is
> ecr->source() of the next iteration (I'm sweeping casting of ecr to a
> Euclidean_segment_2 respectively Circular_arc_2 under the rug). Now my
> problem is that not only is this not the case but neither does there
> seem to be any kind of pattern. So my question is: is there any way to
> predict the orientation of the dual segment of a (hyperbolic) Delaunay
> triangulation? Thanks in advance!
>
> Best,
> Stefan
>
> Am Fr., 14. Juni 2019 um 11:20 Uhr schrieb Stefan Witzel 
> <>:
> >
> > Dear Mael,
> >
> > Thank you for this nice explanation! I have in fact run into issues
> > with non-hyperbolic faces which I had understood mathematically and
> > thanks to you now understand also on the software level.
> >
> > Best,
> > Stefan
> >
> > Am Fr., 14. Juni 2019 um 08:12 Uhr schrieb Mael
> > <>:
> > >
> > > Hello,
> > >
> > > This is usually the case, if you look at the documentation page of e.g.
> > > Regular_triangulation_2, you'll see a section "Additional Inherited
> > > Members", which contains exactly what you have in mind (typedefs and
> > > functions from Triangulation_2).
> > >
> > > Hyperbolic_Delaunay_triangulation_2 (HDT2) is a little bit different
> > > because it inherits Delaunay_triangulation_2 (DT2), but in a private
> > > way. This is done exactly so that not everything from DT2 is shown in
> > > the documentation. This is because the simplicies in a HDT2 form only a
> > > subset of the simplices of a DT2. Thus, we are internally building a DT2
> > > and the class HDT2 is just a filter on top of the DT2.
> > >
> > > You can use the functions from DT2 (or even T2, which DT2 inherits), but
> > > be careful that you will then be working with the full DT2 structure and
> > > not the HDT2. You can apply hyperbolic filtering manually via the
> > > "is_hyperbolic()" family of functions to bring things back to HDT2.
> > >
> > > Best,
> > > Mael
> > >
> > > On 13/06/2019 22:15, Stefan Witzel wrote:
> > > > Hi,
> > > >
> > > > Sorry about my last question! In case someone is actually wondering:
> > > > the answer are face circulators [1]. The documentation would be much
> > > > more accessible if one could see all the inherited methods somewhere.
> > > > I was looking at the documentation for
> > > > Hyperbolic_Delaunay_triangulation_2 and from there it's a bit of a way
> > > > down to Triangulation_2, especially when you are wondering about the
> > > > traits and data structures along the way.
> > > >
> > > > Best,
> > > > Stefan
> > > >
> > > > [1] 
> > > > https://doc.cgal.org/latest/Triangulation_2/classCGAL_1_1Triangulation__2.html#a1bda2ab92ccf638bb22fc223ae281b96
> > > >
> > > > Am Do., 13. Juni 2019 um 16:32 Uhr schrieb Stefan Witzel 
> > > > <>:
> > > >> Hello,
> > > >>
> > > >> I do not have any previous experience with cgal and my question is a
> > > >> rather conceptual one without much technical insight: I would like to
> > > >> iterate over the faces of a Voronoi diagram and then over the edges 
> > > >> of
> > > >> each face (to obtain a closed polygon); in other words this means to
> > > >> iterate over the vertices of a Delaunay triangulation and then over
> > > >> the edges incident with this vertex. Am I right to assume that this 
> > > >> is
> > > >> fundamentally problematic with the default parameters for
> > > >> Delaunay_triangulation_2 (Triangulation_vertex_base_2,
> > > >> Triangulation_face_base_2) as a vertex does not ``know'' the edges it
> > > >> is incident with? Is there a kind of dual assignment that I could use
> > > >> (like ``(Tessellation_face_base, Tessellation_vertex_base)'')?
> > > >>
> > > >> Since tessellations into non-triangles may be more complicated, would
> > > >> it be a possibility to first produce the (common) barycentric
> > > >> subdivision?
> > > >>
> > > >> Best,
> > > >> Stefan
> > >
> > > --
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> > >
> > >