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

[Mohammad Akhlaghi]

Follow-up Comment #2, task #15713 (project gnuastro):

I enjoyed looking through the blog, nice work!

I am just a little confused by the notation. If I understand correctly, you
are now using ".orig" to differentiate between the before/after scaled phase.
Since you have already defined '.' to be for the coordinates, this notation
causes some confusion.

Maybe you can call the initial (original scale) points with capital letters
(A, B, C and D) and the scaled/shifted points with small letters like (a, b, c
and d). 

Since we are talking about two systems (original and shifted), the term
"scale" (in "Scale calculation" section) can be confusing: I initially thought
you are calculating the transformation of the original to scaled coordinates!


But what you mean by "scale" is the length of AC and AD in the newly rotated
coordinates, right? so maybe you can call it "newlength", or any other
less-confusing term ;-).

I also wonder: finding the diagonal of the quad is great for separating A and
B from C and D. But how do you select the reference point (coordinate 0,0)
from A and B? We need to select a method that makes the reference point unique
in any rotation. Maybe the one where the lengths r1+r2 is smaller? But this is
just a raw brainstorm. If you have a solution to this, it would be good
explain it here too ;-).

Finally, it would be good to highlight that you are following the recipe of
Astrometry.net and say which parts follow a similar logic and which parts are
new/different ;-).

I really enjoyed reading the blog, very nice!

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