Delaunay3D -- Statistical Analysis of Mesh?

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Delaunay3D -- Statistical Analysis of Mesh?

Stewart.Dickson
In the example code for Delaynay3D
http://public.kitware.com/cgi-bin/viewcvs.cgi/*checkout*/Examples/Modelling/Python/Delaunay3D.py?root=VTK&content-type=text/plain
It is written:

# Delaunay3D is used to triangulate the points. The Tolerance is the
# distance that nearly coincident points are merged
# together. (Delaunay does better if points are well spaced.) The
# alpha value is the radius of circumcircles, circumspheres. Any mesh
# entity whose circumcircle is smaller than this value is output.
delny.SetTolerance(0.01)
delny.SetAlpha(0.2)
# The points to be triangulated (25) are generated randomly in the unit
# cube located at the origin.

What does one do when one has 860,000  points on the range (-194742,
-104476, 11.), (246342, 189827, 3900)?

It seems to me that Tolerance and Alpha are the lower and upper bounds
(respectively) of the triangulation -- and, to properly set these, we
need to do a statistical analysis of the distances between data points
and disjoint iso-value domains, which is what I need to eventually
arrive at.

Does anyone have any examples or references to literature which might
elucidate the solution short of trial-and-error?

Thanks,

-Stewart Dickson
NOAA National Climatic Data Center
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Re: Delaunay3D -- Statistical Analysis of Mesh?

Kevin H. Hobbs
On Tue, 2006-02-07 at 09:36 -0500, [hidden email] wrote:
> What does one do when one has 860,000  points on the range (-194742,
> -104476, 11.), (246342, 189827, 3900)?

I can't add.

octave:2> [194742,-104476, 11.]-[246342, 189827, 3900]
ans =

   -51600  -294303    -3889

So your ranges are vastly different in x, y, and z. Does this mean that
the distances between points are vastly different in the three
directions?  So different that an alpha large enough to bridge the
smallest Dy will bridge the largest Dz?  If that's the case, then a
single radius will have trouble.



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Re: Delaunay3D -- Statistical Analysis of Mesh?

Stewart.Dickson
In reply to this post by Stewart.Dickson
Kevin,

Thanks for the reply.

I am checking with the Domain Experts at this moment -- but, I expect that
you are correct.  The aspect ratio of the data is very flat -- because it is
the Troposphere -- the height is on the order of 30,000-70,000 feet
(6-12 miles), while the width of the data is on the order of 300 miles.

I suppose that the solution would be to pre-scale the vertical axis by ~50
before triangulation, then flatten it back again afterward?

Thanks,

-Stewart    http://us.imdb.com/Name?Stewart+Dickson
http://www.cs.unca.edu/~dickson

On Tue, 2006-02-07 at 09:36 -0500, [hidden email] wrote:
> What does one do when one has 860,000  points on the range (-194742,
> -104476, 11.), (246342, 189827, 3900)?

I can't add.

octave:2> [194742,-104476, 11.]-[246342, 189827, 3900]
ans =

   -51600  -294303    -3889

So your ranges are vastly different in x, y, and z. Does this mean that
the distances between points are vastly different in the three
directions?  So different that an alpha large enough to bridge the
smallest Dy will bridge the largest Dz?  If that's the case, then a
single radius will have trouble.



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Re: Delaunay3D -- Statistical Analysis of Mesh?

Kevin H. Hobbs
On Tue, 2006-02-07 at 10:30 -0500, [hidden email] wrote:
> Kevin,
>
> Thanks for the reply.
>
> I am checking with the Domain Experts at this moment -- but, I expect that
> you are correct.  The aspect ratio of the data is very flat -- because it is
> the Troposphere -- the height is on the order of 30,000-70,000 feet
> (6-12 miles), while the width of the data is on the order of 300 miles.
>

Well it would depend on how the samples are distributed in that volume.
I was just guessing based on the extent.

> I suppose that the solution would be to pre-scale the vertical axis by ~50
> before triangulation, then flatten it back again afterward?
>
> Thanks,

This way would not require changes to Delaunay3D and avoids nasty new
words like circumellipsoid.

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