| Re: Matching Lats and Lons from two arrays [message #62419 is a reply to message #62136] |
Fri, 05 September 2008 15:53  |
JD Smith
Messages: 850
Registered: December 1999
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Senior Member |
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I should point out that the MATCH_2D routine mentioned in the above
thread and at:
http://www.dfanning.com/code_tips/matchlists.html
assumes euclidean distance measures apply, which of course is *not*
strictly correct on a sphere. For points of latitude and longitude
(or ra/dec), this will work for small patches of earth (or sky), but
if you are near either pole, or cover appreciable areas, the 2D
distance measure will falter.
You can "fake" a "pretty good" euclidean distance measure by pre-
multiplying all longitudes by the cos of latitude. This works if the
latitude range is not overly large, and if you don't cross any poles.
Do do this correctly would require replacing the d=dx^2 + dy^2 with:
d = 2 asin( sqrt( sin(ddec/2)^2 + cos(dec1)cos(dec2)sin(dra/2)^2 ) )
which is obviously much costlier to evaluate. More importantly,
you'll need to think a bit about whether the stock "platte carre"
projection (i.e. (ra, dec) -> (x,y)) is wasteful or not for your
distribution of points on the sphere, or adversely affects your
matching radius criterion. Adopting another projection prior to
binning and running the histogram might offer gains in efficiency and
more "uniform" distance performance (the issue being that square bins
in a projected sphere do not have constant area). It should be
straightforward to "wrap-around" the poles.
JD
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