[SciPy-Dev] Problem with N-dimensional interpolation using a new griddata function for N>=3

[Pauli Virtanen]

Tue, 21 Sep 2010 09:57:03 -0500, Robert Kern wrote:
> On Tue, Sep 21, 2010 at 09:17, Adam Machnik <amachnik at gmail.com> wrote:
>> Hello,
>> I am concerned in the difference in triangulation. I think that on such
>> a simple grid there should be no difference from qhull results.
> 
> What you call a "simple grid" is actually a degenerate set of points for
> Delaunay triangulation. There are a a large number of valid
> triangulations that satisfy the Delaunay condition. The way that qhull
> deals with degeneracy is to randomly perturb the points. 

That's the "joggle" mode of Qhull. The 2003.1 version included in Scipy 
can also work so that it first produces non-simplical facets, and in a 
second step splits them into simplices in an arbitrary way. See
http://qhull.org/html/qh-optq.htm#Qt

This is still sensitive to rounding error, and so it seems that results 
obtained with different optimization levels in the compiler are different.

The problem here seems to be that degenerate facets with zero volume 
appear in the result, which the interpolation routines do not at the 
moment handle sensibly. This should be fixable.

-- 
Pauli Virtanen