CGAL users discussion list

[Monique Teillaud <>]

Efraim Fogel wrote:
> Dennis Schieferdecker wrote:
> > Ophir Setter schrieb:
> >  
> > > The problem is probably that 0.01 is not translated to 1/100 in an
> > > exact manner.
> > > You should construct 1/100 using a rational number constructor;
> > > probably something like: Kernel::FT(1, 100).
> > >
> > >     
> > Thanks that did the trick (and significantly decreased the number of
> > faces with my larger setup). Maybe you could help me with another type
> > problem later in my program?
> >
> > After having computed the circular arrangement, I need to perform
> > several calculations with the vertices of the arrangement. Unfortunately
> > the points they represent are of type Traits::Point_2 instead od
> > Kernel::Point_2 and use a different numerical type ( Traits::CoordNT,
> > i.e. one_root_number< Kermel::FT >). Here, I run into a problem, since I
> > cannot perform the typical operations I can with type Kernel::Point_2
> > and by converting Traits::Point_2 to Kernel::Point_2 I losse my
> > exactness.

> > In principle I need to compute the point that lies in the
> > middle of two vertices and the orientation of three vertices.

> There are two traits that support circular arcs and segments in the 
> arrangement package, namely, Arr_circle_segment_traits_2 and 
> Arr_circular_line_arc_traits_2. The latter may support more operations, 
> as it is based on a CircularKernel.

Hi Dennis,

The Circular kernel does not provide the orientation of three 
Circular_arc_point_2's either. The coordinates of such 3 points are 
algebraic numbers of degree 2 that do not necessarily lie in the same 
extension.
We are thinking of adding new operations in the CGAL::Root_of_2 number 
type, to allow such computations, this will not be available in a close 
future.

What you might want to do is convert the Circular_arc_point_2's computed 
by the arrangement into Point_2< Cartesian< Core::Expr > >, then all 
functionalities of the cgal Kernel would be available on them.
I have not tried but I guess it would work (you probably have to do the 
conversion of coordinates "by hand"). I am afraid this would be rather 
slow, though.

Best
        Monique Teillaud