following examples successfully merge pinched vertices.  Substantially smaller or larger balls do
not lead to pinched horizons.
<pre>
        rbox 2000 C1,1e-13 D4 s t | qhull Q14
        rbox 500 C1,1e-13 t | qhull Q14 d Qbb
</pre>
For Delaunay triangulations, a bounding box may alleviate this issue (e.g.,  <tt>rbox 500 C1,1E-13 D4 t c G1.0 | qhull Q14 d Qbb</tt>).
The Delaunay triangulation of a regular mesh is likewise sensitive to nearly adjacent vertices.
<pre>
        rbox 2000 M3,4,5 D4 C1,1e-8 | qhu