CGAL users discussion list

Thomas Zangl wrote:
> Dear List,

> typedef CGAL::Exact_predicates_exact_constructions_kernel K;

Then the coordinates of K::Point_2 are basically rationals (roughly, 
filtered Quotient<MP_float>).

> How to convert from Circular_Arc_Point to Point

You cannot: a circular arc point has coordinates that are algebraic 
numbers of degree 2 (CGAL::Root_of_2).
But a K::Point_2 has coordinates lying in a field type.

As you know, algebraic numbers of degree 2 do not form a field.
Otherwise we would not have invented a new name for circular arc point, 
we would just have re-used Point_2.

> and vice versa as loss-less as possible?

you should use the constructor from Point_2 to Circular_arc_point_2

> E.g. I get an Circular_Arc_Point as the result of an intersection using
> the Circular_Kernel. Now I want to check if the Point is inside or
> outside of an Polygon_2 (defined by K):

This functionality is not provided. The basic predicates would involve 
computations in an extension field of degree > 2.

You may want to try to play with Cartesian<CORE::Expr> but then you will 
have to do many things 'by hand'.

I guess the manual chapter Arithmetic and Algebra could help on 
generalities about number types.

Best,
        List