CGAL users discussion list

[Michael Hoffmann <>]

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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> 
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