CGAL users discussion list

[Andre Massing <>]

Hi!

Maybe I should have asked a short question before I digged into the details:
It is in principle possible to use Nef_polyhedrons to compute the 
intersection 
of a triangle and tetrahedron? I assumed it from the documentation of the 
package since it seems quite powerful... Or am I doing the conversion from 
Polyhdron to Nef_Polyhedron wrong?

Onsdag 5. mai 2010 10.48.05 skrev Andre Massing :
> Hi!
> 
> I found (many) example(s) of a strange intersection results for a triangle
>  and a and tetrahedron when converted to Nef_polyhedron_3. Background is
>  that I implemented a barycenter quadrature for arbitrary polyhedrons as
>  part of a the FEM library DOLFIN (http://www.fenics.org/wiki/DOLFIN).
> 
> In the code I first create a tetrahedron and a triangle as Polyhedron_3 via
>  the make_triangle and make_tetrahedron. Afterwards I assign them to
>  Nef_polyhedron objects and intersect them via operator*.
> Here a 2 examples, the second (which is the first in the attached code)
>  gives reasonable results (at least if I compute volume and barycenter),
>  but I don't understand the result of the  first (2nd in attached code) at
>  all:
> 
>   Point_3 a3(0.35, 0.35 ,0.35);
>   Point_3 a4(0.45, 0.35 ,0.35);
>   Point_3 a5(0.45, 0.45 ,0.35);
> 
>   Polyhedron_3 tri_1;
>   tri_1.make_triangle(a3,a4,a5);
>   Nef_polyhedron_3 Ntri_1(tri_1);
> 
>   Point_3 b0(0.333333, 0.333333, 0.333333);
>   Point_3 b1(0.333333, 0.666667, 0.333333);
>   Point_3 b2(0.666667, 0.666667, 0.333333);
>   Point_3 b3(0.666667, 0.666667, 0.666667);
> 
>   Polyhedron_3 tet_1;
>   tet_1.make_tetrahedron(b0,b1,b2,b3);
>   Nef_polyhedron_3 Ntet_1(tet_1);
> 
> At least my understanding of how the Nef_polyhedron intersections works
>  tells me that there should be nontrivial polygonal intersection if I do
> Ntet_1*Ntri_1. The triangle is a triangle located in a x-y plane shifted to
>  z = 0.35 and the (solid) tetrahedron  clearly intersects this triangle in
>  a polygonal region.
> 
> But the output says:
> cut_polygon is non_empty (): 0
> Number of number_of_vertices (): 0
>                                                     ^^^? Why 0 vertices?
> Number of number_of_egdes (): 1
>                                                     ^^^? One edge but no
> vertices??
> Number of number_of_halfegdes (): 2
> Number of number_of_halffacets (): 0
> Number of number_of_facets (): 0
>                                                ^^There should be a facet 
> (representing the polygonal intersection
>  as part of the triangle, shouldn't there?
> Number of number_of_volumes (): 1
> 
> Opposed to the other example:
> 
>   Point_3 a0(0.0, 0.0, 0.5);
>   Point_3 a1(2.0, -0.1, 0.5);
>   Point_3 a2(-0.1, 2.0, 0.5);
> 
>   Polyhedron_3 tri;
>   tri.make_triangle(a0,a1,a2);
>   Nef_polyhedron_3 Ntri(tri);
> 
> and
> 
>   Point_3 e0(0.0, 0.0, 0.0);
>   Point_3 e1(1.0, 0.0, 0.0);
>   Point_3 e2(0.0, 1.0, 0.0);
>   Point_3 e3(0.0, 0.0, 1.0);
> 
>   Polyhedron_3 tet;
>   tet.make_tetrahedron(e0,e1,e2,e3);
>   Nef_polyhedron_3 Ntet(tet);
> 
> Ntri*Ntet gives
> 
> Cut_polygon is non_empty (): 0
> Number of number_of_vertices (): 2
>                                               ^^^ Also strange...
> Number of number_of_egdes (): 3
> Number of number_of_halfegdes (): 6
> Number of number_of_halffacets (): 2
> Number of number_of_facets (): 1
> Number of number_of_volumes (): 1
> 
> Can anybody come up with a explanation for that behaviour? Or do I use the
> classes the wrong way? Any  help/enlightment are really appreciated!
> Example code is attached, you can compile it with (one line)
> g++ -o strange_poyhedron_cuts strange_poyhedron_cuts.cpp -frounding-math \
> -lCGAL -L/<YOUR CGAL LIBPATH>
> 
> 
> Kind regards,
> Andre
>