[bug #64617] gal_polygon_area_sky not fully on spherical coordinates

[Mohammad Akhlaghi]

URL:
  <https://savannah.gnu.org/bugs/?64617>

                 Summary: gal_polygon_area_sky not fully on spherical
coordinates
                   Group: GNU Astronomy Utilities
               Submitter: makhlaghi
               Submitted: Sat 02 Sep 2023 11:20:38 PM BST
                Category: Libraries
                Severity: 3 - Normal
              Item Group: Output not reasonable
                  Status: Postponed
                 Privacy: Public
             Assigned to: None
             Open/Closed: Open
         Discussion Lock: Any


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Follow-up Comments:


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Date: Sat 02 Sep 2023 11:20:38 PM BST By: Mohammad Akhlaghi <makhlaghi>
As of Gnuastro 0.20.66, the 'gal_polygon_area_sky' function just applies a
relatively basic correction to the method used in 'gal_polygon_area_flat' (for
a euclidean coordinate system). 

However, as described in the
[https://en.wikipedia.org/wiki/Spherical_trigonometry#Area_and_spherical_excess
Area and spherical excess] section of the Wikipedia page for spherical
trigonometry, there is an analytic solution to this problem that we should
implement in 'gal_polygon_area_sky'.







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