odd griddata error message

[Søren Hauberg]

Hi,
I'm using griddata from octave-forge in octave 2.1.72 to interpolate
unevenly spaced data. However, I get the following long error message
from QHull. I don't know what this message means, so if anybody has some
insight I would be very interested...

Søren

qhull precision error: initial simplex is not convex. Distance=2.1e-17

While executing:  | qhull d Qbb T0
Options selected for Qhull 2003.1 2003/12/30:
  delaunay  Qbbound-last  _pre-merge  _zero-centrum  Pgood  _max-width
1.6e+02
  Error-roundoff 2.2e-13  _one-merge 1.6e-12  _near-inside 7.8e-12
  Visible-distance 4.4e-13  U-coplanar-distance 4.4e-13  Width-outside
8.9e-13
  _wide-facet 2.7e-12

The input to qhull appears to be less than 3 dimensional, or a
computation has overflowed.

Qhull could not construct a clearly convex simplex from points:
- p588 (v3): 1.2e+02 1.6e+02 1.6e+02
- p469 (v2):     1 1.6e+02 1e+02
- p119 (v1): 1.2e+02     1    57
- p0 (v0):     1     1 5.6e-19

The center point is coplanar with a facet, or a vertex is coplanar
with a neighboring facet.  The maximum round off error for
computing distances is 2.2e-13.  The center point, facets and distances
to the center point are as follows:

center point     60.5     80.5     79.5

facet p469 p119 p0 distance= -4.4e-15
facet p588 p119 p0 distance= -4.4e-15
facet p588 p469 p0 distance= -7.7e-15
facet p588 p469 p119 distance= -7.7e-15

These points either have a maximum or minimum x-coordinate, or
they maximize the determinant for k coordinates.  Trial points
are first selected from points that maximize a coordinate.

The min and max coordinates for each dimension are:
  0:         1       120  difference=  119
  1:         1       160  difference=  159
  2:  5.565e-19       159  difference=  159

If the input should be full dimensional, you have several options that
may determine an initial simplex:
  - use 'QJ'  to joggle the input and make it full dimensional
  - use 'QbB' to scale the points to the unit cube
  - use 'QR0' to randomly rotate the input for different maximum points
  - use 'Qs'  to search all points for the initial simplex
  - use 'En'  to specify a maximum roundoff error less than 2.2e-13.
  - trace execution with 'T3' to see the determinant for each point.

If the input is lower dimensional:
  - use 'QJ' to joggle the input and make it full dimensional
  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should
    pick the coordinate with the least range.  The hull will have the
    correct topology.
  - determine the flat containing the points, rotate the points
    into a coordinate plane, and delete the other coordinates.
  - add one or more points to make the input full dimensional.


This is a Delaunay triangulation and the input is co-circular or
co-spherical:
  - use 'Qz' to add a point "at infinity" (i.e., above the paraboloid)
  - or use 'QJ' to joggle the input and avoid co-circular data
error: invalid column index = 2
error: evaluating argument list element number 1
error: evaluating assignment expression near line 75, column 7
error: evaluating if command near line 55, column 3
error: called from `griddata' in file
`/usr/share/octave/site/m/octave-forge/geometry/griddata.m'
error: evaluating assignment expression near line 101, column 15