CGAL users discussion list

[Marc Glisse <>]

On Fri, 26 Feb 2016, Frédérik Paradis wrote:

> Thank you for your answer Sebastien.
>
> There are several factors to take into account:
> > - would there be a significant speed up when using dimension specific
> > implementation?
> > - can the implementation be made easily dimension generic?
>
> The answer to the first question is no and the second is yes. So I guess I
> should just make a dimension generic implementation. However, since the
> CGAL::Ipelet_base class return instances of Point_2, I have to convert
> these instances into Point_d.

You could look at Search_traits_3 (there may be better examples in CGAL, I 
just picked the first one I found). It handles the difference through 
typedefs.

> Is there a way to do do that? Right now, I do
> something like that:
>
>  Point_d point_2_to_point_d(Point_2 p) {
>    return Point_d(CGAL::to_double(p.x()), CGAL::to_double(p.y()));
>  }
>
>  Point_2 point_d_to_point_2(Point_d p) {
>    return Point_2(CGAL::to_double(p[0]), CGAL::to_double(p[1]));
>  }
>
> This class is not documented so it cannot appear in examples but it can
> > certainly be used in the implementation of algorithms of CGAL. Actually
> > it is even better to reuse something existing than creating an almost
> > identical duplicate. At the same time if you need some improvements
> > or new functions in this class they should be welcome.
>
>
> Perfect.
>
> I would need a more precise definition to answer correctly. However,
> > there is the traits Root_of_traits that depending on the number type
> > used will provide an exact representation of algebraic numbers of degree
> > 2  when using an exact number type.
> >
> > http://doc.cgal.org/latest/Number_types/classCGAL_1_1Root__of__traits.html
> >
> > http://doc.cgal.org/latest/Number_types/classCGAL_1_1Sqrt__extension.html
>
>
> So, let r_v and r_v be the radius of two circles v and w. We get r =
> max(r_v, r_w). Let d be the distance between the circles v and w. Let s be
> a constant greater than 0. We want to verify if d >= s*r.

One common trick is to compare the square of distances instead of the 
distances directly, to avoid square roots. Something like d^2 >= s^2*r^2.

> Here is how I've done the calculation:
>
>  bool are_well_separated(const Node* v, const Node* w) const  {
>    Sphere_d cir_v = v->enclosing_circle();
>    Sphere_d cir_w = w->enclosing_circle();
>    FT max_rad =  CGAL::sqrt(std::max(cir_v.squared_radius(),
> cir_w.squared_radius()));
>    FT distance_vw = CGAL::sqrt(CGAL::squared_distance(cir_v.center(),
> cir_w.center()));
>    return (distance_vw - 2.*max_rad) > s*max_rad;
>  }
>
> I do not really understand how to use the two classes that mentionned.
>
> Thank you for your answer.
>
> Frédérik

--
Marc Glisse