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[Marc Alexa <>]

Ah, this is good to know. Because this is exactly what I wanted to do: being 
lazy, not keeping track of how I subdivide the triangle, but then identify 
the elements of the subdivided triangle using the plane through the triangle. 
So, I guess, I have to do the bookkeeping…

Best,
Marc



> On 18. May 2021, at 12:01, Andreas Fabri 
> <> wrote:
> 
> 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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>>>> 
>>> 
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>> 
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