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[Marc Alexa <>]

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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