CGAL users discussion list

[Monique Teillaud <>]

Le 12/05/11 01:14, jahikae a écrit :
> I'm working with arrangements using conics as traits-type.
> Now, in my application I sometimes have to replace straight line segments of
> the arrangement with circular arcs.

Dear Jan-Hinrich,

> The problem is that circular arcs can only be constructed with the rational
> number Kernel.

Not only. More precisely, the centers and squared radius of circles are 
rational, but not necessarily the endpoints of circular arcs.

I am not sure I fully get your question, so let me first write how I 
understand it:
The endpoints of your input line segments have non-rational coordinates, 
apparently because they are constructed from lines and conics. So, their 
coordinates are algebraic numbers of degree 2.
Then you want to construct circular arcs whose endpoints are such 
algebraic points.

> The two original endpoints of the straight segment however can be
> irrational.
> So there is no way to preserve these original vertices and at the same time
> have the new circular arc passing through them.

If you use CGAL::Arr_circular_line_arc_traits_2<CircularKernel>
then there are several ways in which circular arcs can be constructed, 
and some of them take algebraic points and endpoints, and keep their 
coordinates exact.
Hopefully you can find one constructor that works for you, see
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Circular_kernel_2_ref/FunctionObjectConcept_CircularKernel--ConstructCircularArc_2.html#Cross_link_anchor_803 


But CGAL::Arr_circular_line_arc_traits_2<CircularKernel> cannot handle 
conics. Do you actually need arrangements of conics?
I am not very familiar with the arrangement package, maybe other traits 
classes can construct circular arcs from algebraic endpoints, too. There 
are other people who know better.

Still, I hope this helps.

Best regards,
        Monique

> What I do until now is taking rational coordinates very close to the
> original endpoints and use those as endpoints for the circular arc. But this
> messes up my arrangement, because the nearby faces all get merged because of
> the gap that I introduce. I have to avoid this somehow.
>
> Is there any way to construct circular arcs having the exact two endpoints
> of the original straight line?
> And if not, how could I best fix the problem?
>
> Thanks!
>
>
> --
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> http://cgal-discuss.949826.n4.nabble.com/Circular-Arc-imprecision-in-arrangements-tp3516105p3516105.html
> Sent from the cgal-discuss mailing list archive at Nabble.com.


--
Monique Teillaud
INRIA Sophia Antipolis - Méditerranée
http://www.inria.fr/sophia/members/Monique.Teillaud/