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

[Mohammad Akhlaghi]

Follow-up Comment #20, task #15713 (project gnuastro):

Thanks for a nice review of the problem Sachin.

I think I understood the problem, but since my knowledge of kd-trees is very
general and not yet as detailed as yours, please look at the following reply
critically and feel free to correct any mis-understanding you may find ;-).

Given that you already know the number of points you want to put into the
kd-tree before hand, pre-allocating the array/space before the hashes does
generally seem like a good option. 

In fact, in Gnuastro, I have done this in several places (for simply-linked
lists
<https://www.gnu.org/software/gnuastro/manual/html_node/Linked-lists.html>):
when I already know the total number of nodes in the list, I just allocate
space once at the start for all of them, then write the values as they come
in. In the end, I also just have to "free" one allocated space! This is also
more efficient than allocating space for each node individually at different
times, because each allocation/free-ing is itself computationally costly.

On a side-note, it would be interesting to see how astrometry.net implements
its kd-tree. 

Just one extra thing: try to keep the kd-tree related functions and structure
nicely separate from this particular problem and modular (ideally in a
separate .c and .h file). In this way, we can later generalize the kd-tree
solution for other problems too ;-).

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