[task #15713] Make quad structure to make unique hashes of 4 objects

[Mohammad Akhlaghi]

Follow-up Comment #5, task #15713 (project gnuastro):

There is another major problem with selecting the three nearest points:

The resolution of the reference catalog may be much more than the images! As a
result there will not be any match at all (since all the quads of the
reference catalog will be much smaller than the smallest possible quad of the
catalog to match with!).

But if we use quads that are roughly the size of the healpix, the users just
have to worry about the healpix size being smaller than their image.

Another thing just occurred to me that may provide a good improvement compared
to astrometry.net's implementation: in the hash structure (and thus the
kd-tree), besides the geometry of the points, use their relative brightness
too. 

For example you can define a four-element array (of type 'uint8' only keeping
integer values 0, 1, 2, 3) to store sorted brightness of the points. 

For example, let's assume the quad points (from the example of your blog,
based on their geometry) are called A, B, C and D. Let's assume that after
sorting their flux, B is the brightest, then C, then A and then D is the
faintest.

Then the proposed array would have these values: [2,0,1,3], because point A is
the third brightest (index 2), point B is the brightest (index 0) and so
on...

In the matching we can then use this information also to get even more
accurate fits of the quads ;-)!

Does astrometry.net have any way to account for the relative brightness of the
points in the match?

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