CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

The infinite vertex should not be used as a point embedded in 3D as its
coordinates are undefined and have no meaning.

Sebastien


 wrote:
> Hi,
> I meshed a sphere and I considered a set of lines crossing each mesh
> vertex. Then I calculate the intersections (CGAL::intersections) of these
> lines with the triangles opposite to the vertex under study and belonging
> to the cells incident to the vertex
> (c3t3.triangulation().incident_cells(vit,std::back_inserter(incident_cells))).
> When calculating the intersection with a triangle of an infinite cell
> (that is the vertex is on the convex hull) I notice that two triangle
> vertexes are on the sphere surface  and one gives me "vertex coordinates:
> 0 0 0, squared distance from the sphere center 0". I guess this is because
> this is the infinite vertex.
>
> My question is: how the intersection is evaluated in this case? (in the
> manual I see "Notice that the infinite vertex has no significant
> coordinates and that no geometric predicate can be applied on it.")
>
> I find, indeed, that for each direction two (or 0) intersections are
> recovered at the end of each loop on the incident cells. I mean also the
> intersection with the opposite facet on the infinite incident cell seems
> to be detected. Nevertheless, also for the infinite incident cell, the
> intersection point is in the interior of the sphere although it belongs to
> the triangle which has two vertexes on the sphere surface, and the third
> is the infinite vertex (the fourth vertex of the cell is the vertex of
> interest and it is on the convex hull).
> Thank you in advance