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[task #15637] Match RA and Dec catalog to X and Y catalog to find WCS

From: Mohammad Akhlaghi
Subject: [task #15637] Match RA and Dec catalog to X and Y catalog to find WCS
Date: Mon, 20 Jul 2020 09:41:46 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:78.0) Gecko/20100101 Firefox/78.0

Follow-up Comment #7, task #15637 (project gnuastro):

During the rough outline mentioned before we found out that healpixs are only
necessary to ensure a homogenous sampling of quads across the field. That is
why we decided to ignore the healpix library for now to avoid an extra

In most scenarios, it is indeed not needed and we can simply build a grid
ourselves. But one scenario where healpixs will be necessary just occurred to
me: if the desired field includes the celestial poles. In this case, a simple
gridding of the range of RA and Dec will not properly sample the input RA and

So without healpixs, we will only have problems if the field includes the
celestial poles. However, for now (in the development phase) this isn't a
problem and we can simply use a cartesian grid and progress with the main
work. We can add healpixs as an optional feature to ensure homogenity in the
future (instead of a simple cartesian grid) once all the other steps are

In fact this will be a good feature for Gnuastro: if someone doesn't want to
do astrometry near the celestial poles, they don't need to install healpix as
a dependency of Gnuastro :-). But if healpix is present it will be used (as
implemented later).

Sachin, to allow an easy optional usage of healpix later take the following
step: define two functions very similar to healpix's API: 

* One function to define a "grid" structure over the coordinate range (just
find the minimum and maximum in each dimension, and store them with the number
of grid boxes in each dimension).

* One function to take the "grid" structure and the coordinates of a point and
return the index of the grid element that the coordinate falls in. By "index
of grid element", I mean that if we start counting the grid tiles from the
minimum in both dimensions to to the maximum, which index would correspond to
the tile that the given coordinate falls into.

In this way, later, we can easily optionally call our own simple cartesian
grid-ing function or healpix (if the user has it). 


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