[Octave-bug-tracker] [bug #34604] Trivial delaunay throws qhull error

[Rik]

Follow-up Comment #5, bug #34604 (project octave):

The error message does appear to be accurate.  The center point of the square
is exactly on a facet line (the diagonal from the corners of the square).  The
warning message suggests using two options--both of which work for me.

The first option is 'QJ' which "Joggles" the input points.  This does
eliminate the exact co-planarity.  However, its use isn't particularly
recommended because it reduces the accuracy of the triangulation.

The second option is 'Qz' which adds a point at infinity.  This option seems
to work well.


y = [0 1 1 0];
x = [0 0 1 1];
tri = delaunay (x,y, 'Qz')
tri =

   4   2   3
   4   2   1


Perhaps this option should always be added to low-dimensional data?  The
relevant code is in src/__delaunayn__.cc:89.


  // default options
  if (dim <= 3)
    options = "Qt Qbb Qc";
  else
    options = "Qt Qbb Qc Qx";


Interestingly, I tried the same trial figure in three dimensions, i.e., a unit
cube and delaunay3 fails in exactly the same way.  By adding 'Qz' I can get
delaunay3 to pass as well.  


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