[vtkusers] Delaunay3D -- Statistical Analysis of Mesh?

[Stewart.Dickson at noaa.gov]

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