CGAL users discussion list

[Wolfgang Aigner <>]

On Monday 08 October 2007 12:08, 

 wrote:
> 
>  wrote:
> > I am new to the CGAL environment, and had the luck to start right away
> > with the rather new Circular_Kernel, as I need Intersections of Arcs;
>
> Hi,
>
> welcome
>
> > To come to the problem: the intersection of arcs has as results points
> > with coordinates of the Root_of_2 type; how is it now possible to lay a
> > simple line_2 through two of such points,
>
> If there exists a rational line containing them both then it is possible
> to use a line in Cartesian<MP_Float> for instance.
> This is not (/not yet?) implemented in CGAL but you can probably code
> this in your program.

Ok, I'll work on this; as linear Kernel i used Cartesian<Quotient<MP_Float>> 
so far, should even be a larger number area; the problem is: given the two
Points in Root_of_2 type, how do I find out if there exists such a line?

>
> > respectively how can I convert Root_of_2 to any type which can be used in
> > the linear kernel, without loss of accuracy;
> >
> > when I came to the conclusion that the conversion to double is the only
> > possible way (d'oh),
>
> well, you will lose accurracy when converting to doubles...
>
> I guess CGAL should propose a conversion from Root_of_2 to Core number
> types. then you would be able to use Cartesian<Core::Expr> since
> Core::Expr is a Field number type. However, this would not always be
> very fast.

This sounds very promising, I'll have a look; when I have to work on larger
data it will probably be anyway necessary to make some compromises

>
> > i was confronted by another, even more crucial problem:
> >
> > Is it in any way possible, to get the intersection point(s) of a line_2
> > with a circluar_arc_2 yet? It is possible to cut a line_arc with a
> > circular_arc, so why not a line?
>
> yes, I think Intersect_2 in the circular kernel offers this. Still, I
> just checked the manual and it is not written. Did you try? It might
> just be something forgotten in the manual...

I tried rather hard before; I was able to cut line_arcs and circular_arcs as 
said, but when choosing a line and a circular_arc, then no matching call of 
the function is complained; and that is a real restriction ;)

>
> best
>       Monique Teillaud

Thank you for the fast answer,
mfg, Wolfgang Aigner