Why does the DELAUNAY function in MATLAB 7.0 (R14) produce an error when passed colinear points?

When I specify the following colinear points on the xy-plane:

x = [5 5 5 5 5]

y = 1:5

then try to compute the Delaunay triangulation:

tri = delaunay(x,y)

I receive the following error message:

 ??? qhull input error: input is less than 3-dimensional since it has the same x coordinate

 While executing:  | qhull d Qt Qbb Qc

 Options selected for Qhull 2003.1 2003/12/30:

   delaunay  Qtriangulate  Qbbound-last  Qcoplanar-keep  _pre-merge

   _zero-centrum  Pgood  Qinterior-keep  _max-width  4  Error-roundoff 6.9e-015

   _one-merge 4.9e-014  Visible-distance 1.4e-014  U-coplanar-distance 1.4e-014

   Width-outside 2.8e-014  _wide-facet 8.3e-014

 Error in ==> delaunayn at 81

 t = qhullmx(x', 'd ', opt);

 Error in ==> delaunay at 49

     tri = delaunayn([x(:) y(:)]);

Answer 1

[MathWorks Support Team]

The DELAUNAY function in MATLAB is based on Qhull. This error message is generated by the Qhull routine. For information about Qhull, see http://www.qhull.org/.

To avoid this error, you can joggle the data by specifying the 'QJ' option to the DELAUNAY function.

tri = delaunay(x,y,{'QJ'})

For information about Qhull options, see the following URL:

http://www.qhull.org/html/qh-quick.htm#options

For information about the 'QJ' options, see:

http://www.qhull.org/html/qh-optq.htm#QJn

Note that the above command produces the following warning:

 Warning: qhull precision warning: 

 The initial hull is narrow (cosine of min. angle is 1.0000000000000000).

 A coplanar point may lead to a wide facet.  Options 'QbB' (scale to unit box)

 or 'Qbb' (scale last coordinate) may remove this warning.  Use 'Pp' to skip

 this warning.  See 'Limitations' in qh-impre.htm.

As this warning indicates, you can skip this message using the command:

tri = delaunay(x,y,{'QJ','Pp'})