CGAL users discussion list

[Andreas Fabri <>]

Hi Marc,

Even with an Exact_predicates_exact_constructions_kernel you should pay 
attention
not to construct something and later use it in a predicate where you 
could exploit
combinatorial information.

Say you construct the midpoint mp  of a segment seg and later call 
seg.has_on(mp).

As in the exact construction kernel the predicate is first computed with 
interval arithmetic
the collinearity test has all chances to fail with interval arithmetic, 
and  it will
be done with arbitrary precision rational numbers.

And such mistakes are sometimes still made even in CGAL, if you look at 
some
recent pull requests concerning Boolean operations with Nef Polyhedra.

Best,

Andreas

On 5/18/21 11:20 AM, Michael Hoffmann wrote:
> Hi Marc,
>
> the coordinates of your points look nice in decimal, but they (e.g., 1.1, 
> 0.3, 0.7) get pretty ugly once converted to binary…
>
> Best, Michael
>
> > On 18 May 2021, at 11:16, Marc Alexa <> wrote:
> >
> > Hi Andreas,
> >
> > Thanks for the quick answer.
> >
> > I think I just now fully understood the consequences of “inexact 
> > constructions”. It does lead to some interesting results, I have to say. I 
> > put a minimal program together that generates such a result, which is of 
> > course unsurprising in general, but still a bit surprising to me for the 
> > ‘exact predicates’ statement.
> >
> > Best,
> > Marc
> >
> > #include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
> > #include <CGAL/intersections.h>
> >
> > typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
> > typedef K::Point_3 Point;
> > typedef K::Line_3 Line;
> > typedef K::Plane_3 Plane;
> > typedef K::Triangle_3 Triangle;
> >
> > int main()
> > {
> >      Point V0(1.0,0.3,0.7);
> >      Point V1(0.3,1.1,0.2);
> >      Point V2(3.3,4.7,5.1);
> >
> >      Plane p(V0,V1,V2);
> >      
> >      std::cerr << "V0 on plane? " << p.has_on(V0) << std::endl;
> >      std::cerr << "V1 on plane? " << p.has_on(V1) << std::endl;
> >      std::cerr << "V2 on plane? " << p.has_on(V2) << std::endl;
> >
> >      Triangle t(V0,V1,V2);
> >      
> >      std::cerr << "Triangle intersects plane? " << CGAL::do_intersect(p,t) << std::endl;
> >      
> >      Line l(V0,V1);
> >      std::cerr << "V0 on line? " << l.has_on(V0) << std::endl;
> >      std::cerr << "V1 on line? " << l.has_on(V1) << std::endl;
> >
> >      std::cerr << "Triangle intersects line? " << CGAL::do_intersect(l,t) << 
> > std::endl;
> >
> >      std::cerr << "Plane intersects line? " << CGAL::do_intersect(l,p) << 
> > std::endl;
> >
> >      return 0;
> > }
> >
> >
> >
> > > On 17. May 2021, at 20:53, Andreas Fabri <> 
> > > wrote:
> > >
> > > Hi Marc,
> > >
> > > As the plane is internally a point and a normal  this is a construction.
> > > So if the point is slightly off the plane of the triangle and the normal
> > > happens to be correct the plane and the triangle plane  are parallel.
> > >
> > > Even if one takes a vertex of the triangle as base for the plane
> > > there is no guarantee that the intersection is  the full triangle.
> > >
> > > andreas
> > >
> > > On 5/17/21 7:07 PM, Marc Alexa ( via cgal-discuss Mailing 
> > > List) wrote:
> > > > Dear all,
> > > >
> > > > I’m a checking the intersection between Triangle_3 and Plane_3 objects. If 
> > > > both are constructed from the same triple of points, the result is false for 
> > > > most triples, but sometimes true. I’m using the exact predicates / inexact 
> > > > constructions kernel. Is this the expected / desired behavior? I had hope 
> > > > because of the exact predicates that the result for such intersection tests 
> > > > is at least consistent (and actually consistently true).
> > > >
> > > > Thanks!
> > > > -Marc
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