CGAL users discussion list

 wrote:
> My problem is the following: I have three points on arcs (therefor circular 
> arc points), and from these three points I want to construct a circle;
> A circle can only be constructed from normal points, so i need to convert the 
> CAP to points, without loosing the has_on property of these points concerning 
> their origin arcs;
>
> I see that the conversion from Root_of_2 isn't trivial, and not implemented 
> yet, anyhow: does someone have an idea how to implement this in a clean / 
> exact way, if the Root_of_2 number is of rational form?

Hi,

In the current implementation, a Root_of_2 is represented as alpha + 
beta sqrt(gamma). There is no clever simplification, checking that gamma 
is a square and simplifying the sqrt.

If your algebraic number is actually rational (if I understand 
correctly, this is the case for your question), then it basically means 
that the number is equal to alpha. There is an [undocumented] access 
function alpha() that returns an element of the underlying field number 
type FT. beta() and gamma() are also provided.
This should allow you to do what you need and construct a Point_2< 
Cartesian<FT> >.

If the number is not rational, the access functions alpha(), beta(), 
gamma() can be used to construct a CORE::Expr.

As usual, using undocumented functions is not completely safe since they 
are not part of the specifications and may change in the future. But I 
guess these access functions should perhaps be documented...

Best,
        Monique Teillaud