CGAL users discussion list

[Andreas Fabri <>]

Wesley Smith wrote:
> I'm working on getting 3D voronoi information from
> Delaunay_triangulation_3 and am getting some information I'm not sure
> is valid.  The points in the triangulation are:
>
> (0, 0, 0)
> (1, 0, 0)
> (0, 1, 0)
> (0, 0, 1)
> (1, 1, 1)
>
> These are the cells
> p0: 0 0 0
> p1: 1 0 0
> p2: 0 1 0
> p3: 0 0 1
> dual: 0.5 0.5 0.5
>
> p0: 1 0 0
> p1: 1 1 1
> p2: 0 1 0
> p3: 0 0 1
> dual: 0.5 0.5 0.5
>
>
> And the duals for the finite facets:
>
> segment:
> p0: 0.5 0.5 0.5
> p1: 0.5 0.5 0.5
>
> What I'm trying to figure out is why I get a degenerate segment
> (basically a point) as the only dual.  

Let me only reply to this question, as you found the answers to
the others.  The Voronoi edge connects the duals of the two
adjacent cells.  The dual of the cells is not the point of gravity
of the tetrahedron, but the center of the circumsphere. In your
case, this point coincides for the two neighboring cells.

andreas