Why do I receive a "??? qhull precision error: initial facet 2 is coplanar with the interior point" message when using the GRIDDATA function in MATLAB?

When I execute the following commands:

X1 = linspace(1e5, 1e6,50);

[X1 Y1] = meshgrid(X1);

V = X1.^2+Y1.^2;

XI = 2e5; YI = 2e5;

val = griddata(X1,Y1,V, XI, YI, 'linear');

I receive the following error message:

 ??? qhull precision error: initial facet 2 is coplanar with the interior point

 ERRONEOUS FACET:

 While executing:  | qhull d Qt Qbb Qc

 Options selected for Qhull 2002.1 2002/8/20:

   delaunay  Qtriangulate  Qbbound-last  Qcoplanar-keep  _pre-merge

   _zero-centrum  Pgood  Qinterior-keep  _max-width 9e+005

   Error-roundoff 1.4e-009  _one-merge 9.7e-009  Visible-distance 2.8e-009

   U-coplanar-distance 2.8e-009  Width-outside 5.5e-009  _wide-facet 1.7e-008

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

 [SNIP]

Answer 1

[MathWorks Support Team]

The key part of this error message is the statement:

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

This data is obviously 3-dimensional, therefore the error is due to a computation that has overflowed.

There error occurs because the data points are either consistently larger than 1e3, or consistently smaller than 1e-3.

To workaround this issue, scale the data points so that they are within the range >1e-3 and <1e3. For this example, use the commands:

val = griddata(X1/1e5,Y1/1e5,V, XI/1e5, YI/1e5, 'linear');