Re: Minimum spanning circles and Voronoi diagrams

[Chris Albertson <chrisalbertson90278@yahoo.com>]

I think you want to simply define a minimum angle threshold
based on the error bars on the astrometry.  15 arcseconds
worked for the Mk III.

Near the equator why not just use SQRT(ra^2 + dec^2) with
ra and dec in degrees to compute the distance.  It's fast.
You can cut down the search by first applying a simple box
function

If you want to do it right up by the poles you need to 
compute the great circle distance between two points on a
sphere.  This is not as hard as it looks.  The center of
the Earth and your two points define a circle.  You need to
compute the distance along that arc between your two
points.  MUCH faster then intersecting circles and it
works across the poles.  I would first convert
the (ra,dec) point to a unit vector in (x,y,z) and then
compute the angle between the two unit vectors.

Or you could simply link to a good library like "SLALIB"
and call the "DESEP" function and get an debugged, exact
answer.  This is in FORTRAN but I have a C wrapper library
that makes using it easy from C.  Works for me on both
Linux and Solaris.

http://www.starlink.rl.ac.uk/star/docs/sun67.htx/sun67.html#xref_

the SLA library was recommended to me by people on this list.
I agree now.  You really need this if you are going to do
anything connected with astronomical coordinates.  It is the
"standard" library that is in wide use.  This problem is
not hard but others are
For example, pretty soon you may want to match catalog data
that is in a different referance system or you need to precess
the data to a diffent epoc.  



--- "Creager, Robert S" <CreagRS@LOUISVILLE.STORTEK.COM> wrote:
> 
> Hello,
> 
> I've been working on generating minimum spanning circles for the data
> going
> into a star.  I'm looking to see when the error increases in my data,
> if I
> have an actual location outlier, rather than magnitude outlier.  To
> this
> end, I am working the MSC.  I've got the convex hull figured out,
> along with
> the set diameter (easy), but am having a devil of a time
> understanding how
> to construct farthest point Voronoi diagrams.  I picked up a book on
> computational geometry, and will chew through that in the near
> future, but
> though I'd check this list for any pointers.
> 
> Thoughts?
> Rob
> 
> Robert Creager
> Senior Software Engineer
> ATS Library Engineering
> 303.673.2365 V
> 303.661.5379 F
> 888.912.4458 P
> StorageTek
> INFORMATION made POWERFUL
> 
> 
> 


=====
Chris Albertson 
  Home:   310-376-1029  chrisalbertson90278@yahoo.com
  Cell:   310-990-7550
  Office: 310-336-5189  Christopher.J.Albertson@aero.org

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