CGAL users discussion list

[Jan-Hinrich Kaemper <>]

Eric Berberich wrote:
> jahikae wrote:
>   
> > 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.
> > The problem is that circular arcs can only be constructed with the rational
> > number Kernel.
> > 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.
> >
> > 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!
> >     
>
> Dear Jan-Hinrich,
>
> can you give some more background on the application. With the given 
> information the answer is: It requires a non-rational number type for 
> the endpoints of the segments. Conversion is not immediate, but possible.
>
> With more background, we maybe have more ideas to help you.
>
> Best regards, eriC
>
>   
Hello Eric,

basically what my application does is to begin with an arrangement
where all edges are straight line segments.
Depending on the input data it bends some of these edges, i.e. replaces 
them with circular arcs.
So, for a new circular arc two points (source and target) are always 
given by the endpoints
of the previous straight line to be replaced and the third point can be 
calculated from the data.
Now, as I'm obliged to construct the circular arc with rational 
coordinate points only,
I can't  make the arc fit exactly in the place where the straight line 
was before.
So what happens is that I have to approximate the endpoints of the 
circular arc (to rational numbers), which
isn't satisfying as faces of my arrangement on the two sides of circular 
arc are merged into one face, because
the arc is disconnected from the previously neighboring edges.
I hope this has made it a bit clearer.
For the arrangement I use non-rational number-types.
So this should meet the requirement you mentioned I guess?

Thanks a lot, Jan