CGAL users discussion list

Wolfgang Aigner wrote:

> > > 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

this linear kernel is completely fine

> Points in Root_of_2 type, how do I find out if there exists such a line?

well, I guess you just write ax+by+c=0 for the two points, and cancel 
sqrt's and solve in a,b,c (up to a constact factor).
Note that if point P is a Circular_arc_point then its x and y have the 
same sqrt.

> > 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

The choice of kernel depends on what you want to do with your points and 
of their nature, not on the size of data.

> > > 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 ;)

I checked in the source code. In fact there is an interal function 
computing this intersection, but it seems it was forgotten in the 
functor Intersect_2.
In case it may help, the internal piece of code is in 
include/CGAL/Circular_kernel_2/internal_functions_on_line_2.h
Sorry... this will be fixed in future releases...

best
        Monique Teillaud