[Proj] A rHealPix bug or I am misunderstanding something

[Rubén Béjar]

Hi all,

After some additional tests and readings I think I finally have this 
figured out. For the record:

- The values of the coordinates of rHealPix are not radians. They are 
projected and in units of the authalic radius. By using all the time 
+a=1 in my tests they looked similar and that got me confused.

- The authalic sphere of the WGS84 ellipsoid with semi-major axis == 1 
does not have a radius of 1 but slightly smaller. This would be the 
reason why some values on the "edges" were not converted. If I use 
+a=1.00336409 with +ellps=WGS84 (ratio between its semi-major and 
semi-minor axes) the authalic sphere has a radius just barely larger 
than 1 and I can convert those points on the "edges".

Best regards,

   Rubén

El 9/10/18 a las 11:21, Thomas Knudsen escribió:
> Rubén,
>
> first, I recommend not mixing "minus style" general options with "plus 
> style" projection definitions. It works for proj and cs2cs, but will 
> not for the next generation tool, cct, so I suggest saying:
>
> proj -EIf '%.4f' +proj=rhealpix +lon_0=0 +a=1 +ellps=WGS84 
> +north_square=0 +south_square=0
>
> second: I can replicate your results, but...
>
> third: I have no idea what it means, and cannot help - any rHealpix 
> users here? Please speak up!
>
> /thomas
>
> Den tir. 9. okt. 2018 kl. 10.19 skrev Rubén Béjar <rbejar at unizar.es 
> <mailto:rbejar at unizar.es>>:
>
>     Hi people,
>
>     I am having some problems with the rHealPix projection and maybe
>     you can help me.
>
>     In (0,0)-rHealPix (i.e. north_square = south_square = 0), I
>     understand that the top left corner is (-PI, 3*PI/4).
>
>     However trying to project that point to lon-lat WGS84 fails.
>
>     I am running proj 5.2.0 (September 15th, 2018) in a terminal in
>     Ubuntu 18.04 (I have compiled it from sources, I am not using the
>     older version from the repositories).
>
>     I assumed that it could be due to some tolerances/epsilon issues.
>     However it does not seem to be so. I have tried with this command:
>
>     proj +proj=rhealpix -f '%.4f' -I +lon_0=0 +a=1 +ellps=WGS84
>     +north_square=0 +south_square=0 -E
>
>     and some of the results I get are these:
>
>     -3.14 2.35
>     -3.14 2.35      *       *
>     -3.13 2.34
>     -3.13 2.34      90.3176 42.4654
>     -3.138 2.348
>     -3.138 2.348    90.3144 41.9431
>     -3.139 2.349
>     -3.139 2.349    *       *
>
>
>     So even after "pushing" the top left corner to the right (from -PI
>     to -3.14, big difference) and down (from 3*PI/4 to 2.35, again big
>     difference) I still don't get a conversion. The closest to the
>     "real" point that seems to work is around (-3.138, 2.349) which is
>     far from that corner (much further than a tolerance).
>
>     This corner is a simple, easily reproducible case. I am having
>     similar problems close to the edges of the N square (and possibly
>     close to some of the edges of other squares too).
>
>     Am I doing something wrong, or is this a problem with rHeallPix in
>     Proj.4?
>
>     Thanks in advance!
>
>     Rubén
>
>
>
-- 

Dr. Rubén Béjar
*Universidad* Zaragoza <https://www.unizar.es>
Advanced Information Systems Laboratory <https://www.iaaa.es/>
Aragon Institute of Engineering Research <http://i3a.unizar.es/>

rbejar at unizar.es <mailto:rbejar at unizar.es> (@rubejar in Twitter) 
<https://twitter.com/rubejar>
*rubenbejar*.com <https://www.rubenbejar.com>
----

Departamento de Informática e Ingeniería de Sistemas

María de Luna 1 / 50018 / Zaragoza (Spain)
Tlf: +34 876 555534 / Fax: +34 976 761914

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