CGAL users discussion list

[Stefan Witzel <>]

Hi,

I realize that the documentation does not guarantee any kind of behavior 
but I would like say that it would be very useful if the result of 
Construct_hyperbolic_segment_2 *was* guaranteed to be oriented (which 
actually amounts to a simplification of code, see below). I have code 
that needs this property and without it I would essentially start 
reimplementing them just to lift that restriction.

I would also like to point out that, unlike for circular arcs, the 
property of running clockwise or counterclockwise is not an intrinsic 
property of a hyperbolic segment. So one could apply a Moebius 
transformation and the orientation would change.

Generally I agree that the term "segment" doesn't suggest any kind of 
orientation, so one might want to call it differently. However, I found 
that throwing away the order of the endpoints (even of circular arcs) is 
a loss of information that is hard to recover, whereas the property of 
running clockwise or counterclockwise can be checked in a single line 
(which might be a method).

I don't mean to question your design decisions just humbly report on my 
user experience. I'll just work with my patched header for now.

Best,
Stefan

--- 
a/Hyperbolic_triangulation_2/include/CGAL/internal/Hyperbolic_Delaunay_triangulation_traits_2_functions.h
+++ 
b/Hyperbolic_triangulation_2/include/CGAL/internal/Hyperbolic_Delaunay_triangulation_traits_2_functions.h
@@ -132,10 +132,7 @@ public:
     // uncomment!!!
     //assert(circle.has_on_boundary(p) && circle.has_on_boundary(q));

-    if(_gt.orientation_2_object()(p, q, center) == LEFT_TURN)
-      return Circular_arc_2(circle, p, q);
-
-    return Circular_arc_2(circle, q, p);
+    return Circular_arc_2(circle, p, q);
   }


On 17.06.19 15:32, Monique Teillaud wrote:
> Hi,
>
> I don't remember details but I guess that we have followed the same 
> conventions as the CGAL circular kernel, see
> https://doc.cgal.org/latest/Manual/packages.html#PkgCircularKernel2
> The orientation is chosen to be globally consistent.
>
> I have checked the documentation quickly. As far as I can see, neither the 
> traits concept
> (https://doc.cgal.org/latest/Hyperbolic_triangulation_2/classHyperbolicDelaunayTriangulationTraits__2.html)
> nor the two models (note that one of them is based on the abovementioned 
> circular kernel) is explicitly saying anything on the orientation of circular 
> arcs. There is no guarantee that undocumented properties stay the same 
> forever, so, it might be risky to rely on them.
>
> Best,
> --
> Monique Teillaud
> https://members.loria.fr/Monique.Teillaud/
> INRIA Nancy - Grand Est, LORIA
> Institut National de Recherche en Informatique et Automatique
>
> ----- Le 14 Juin 19, à 9:10, Stefan Witzel 
>
>  a écrit :
>
> > 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

--
Stefan Witzel
Faculty of Mathematics
Bielefeld University
Universitätsstraße 25
33501 Bielefeld
http://www.math.uni-bielefeld.de/~switzel/