RE: Bug resampling field with Irregular2DSet to Linear2DSet

  • To: Ian Graham <ian@xxxxxxxxxx>
  • Subject: RE: Bug resampling field with Irregular2DSet to Linear2DSet
  • From: Bill Hibbard <billh@xxxxxxxxxxxxx>
  • Date: Wed, 30 Apr 2003 06:58:56 -0500 (CDT)
Hi Ian,

> Thanks Bill, it works!

Glad to hear it. Let us know if you have more problems.

> As for my data being weird, well<grin>, it doesn't seem it to me!  It
> consists of measurements that are taken over as close to a perfect grid as
> possible, but likely rotated and certainly with many gaps and offsets due to
> physical obstructions in the field.  As for the larger sizes, I was enjoying
> Curtis's DelaunayFast until I started getting triangulation errors.

If you can organize your data into a curvy grid, and use
a Gridded2DSet, you'll be much better of.

> I worry when you mention that co-linear points cause problems, because
> almost all of my data is similarly co-linear, although often not orthogonal
> to the axes.  That invites my implementing my  own triangulation and using a
> CustomDelaunay that exploits this co-linear tendency, but that doesn't seem
> trivial even in my near-gridded cases, and I still have to support the
> general case.  I was hoping that in the medium-term I could use well-known
> algorithms _that_work_ even if they're imperfect:  I'm not terribly fussy
> how equilateral my triangles are, but I do care that the coverage is
> complete and non-overlapping so that interpolation can work.  Can none of
> the Delaunay algorithms guarantee this?

Delaunay triangulation is a terribly hard problem. Watson's
and Clarkson's algorithm are among the best, and they still
have problems and are slow for large data sets. The offending
triangles in your data set were microscopically thin, which
is what happens with bunches of co-linear points. If you can
generate an explicit topology, either gridded or irregular,
you will be better off.

> And Curtis, thanks for the DelaunayFast.  Unfortunately, I'm getting a fair
> number of "Delaunay.finish_triang:  error in triangulation!" exceptions.
> But fortunately it's fast enough that I can always try it first!
>
> My apologies for the large attachment, I just never succeeded in reproducing
> the problem with a smaller dataset.  It's just as well that it didn't make
> it to the list.  I guess I should've written the data in binary form instead
> of ascii.

Not a problem. I got your attachment, and figured the list
could wait for my reply.

Cheers,
Bill