CGAL users discussion list

[Matthias Teich <>]

Hm,

my Kernel is CGAL::Simple_cartesian<double>.

I am computing intersections of offset planes of faces of my polyhedra.
I construct offset-planes with the help of three points of the original 
facet which were translated in the direction of the normal vector of the 
facet.
Then I let CGAL compute the intersection lines of this plane with the 
offsetted planes of its adjacent facets.

Each pair of consecutive intersection-lines has to intersect. Due to 
rounding errors (which may have happened before) 
CGAL::squared_distance(line_i, line_j) says there is a distance of 
aproximately 10^-14, so I cant use CGAL to compute the approximately 
intersection point, is this right?
Is there a function to compute the points of nearest approach?

I wrote a function which computes the approximate intersection point, 
but I have problems with getting usable points of the lines with the 
function Line_3::point(). Sometimes Line_3::point() seems to return 
overflown values.

Any hint on how I could solve my problem are very appreciated

Best Regards,
Matthias

Max schrieb:
> > I am using CGAL::Simple_cartesian<double>  as Kernel. for Polyhedron_3.
> > In my algorithm I need to compute the intersections of the planes
> > induced by the faces of the polyhedra. That seems to work fine.
> > But when I try to compute the intersections of the resulting
> > intersection lines there seems to be a problem.
> > CGAL says there is no intersection, but when I display the lines there
> > is an intersection.
> >
> > I guess what I need is an intersection test which accepts a delta value
> > to be more stable.
> > I tried to find a function which computes the minimum distance between
> > the lines and the point where this minimum distance occurs, but without
> > success.
> >
> > Do I need to implement my own tests or can I do this with CGAL? A hint
> > would be nice :)
> >
> > Best Regards,
> > Matthias
> >     
>
> CGAL will give the exact result, more exact than what you can see with your
> eyes, as long as you are using an exact kernel.
>
> Generally, you should use exact kernel types playing with (nef_)polyhedra.
>
> The predefined Exact_predicates_exact_constructions_kernel is a good choice.
>
> HTH.
>
> B/Rgds
> Max
>
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