[postgis-tickets] [PostGIS] #4840: ST_Azimuth with geography provides wrong results

[PostGIS]

#4840: ST_Azimuth with geography provides wrong results
----------------------+---------------------------
 Reporter:  postlude  |      Owner:  pramsey
     Type:  defect    |     Status:  new
 Priority:  medium    |  Milestone:  PostGIS 3.1.2
Component:  postgis   |    Version:  3.1.x
 Keywords:            |
----------------------+---------------------------
 Hi,
 I noticed that the azimuth angles reported by ST_Azimuth are obviously
 wrong in some cases.

 The following simple example demonstrates this. The central point C is
 located at 5°E,55°N. All other points are shifted by 1° in the respective
 directions:
 {{{
 SELECT
 degrees(ST_azimuth(C,N))  AS az_n,
 degrees(ST_azimuth(C,NE)) AS az_ne,
 degrees(ST_azimuth(C,E))  AS az_e,
 degrees(ST_azimuth(C,SE)) AS az_se,
 degrees(ST_azimuth(C,S))  AS az_s,
 degrees(ST_azimuth(C,SW)) AS az_sw,
 degrees(ST_azimuth(C,W))  AS az_w,
 degrees(ST_azimuth(C,NW)) AS az_nw
 FROM (SELECT
 ST_GeogFromText('SRID=4326;POINT(5 55)') AS C,
 ST_GeogFromText('SRID=4326;POINT(5 56)') AS N,
 ST_GeogFromText('SRID=4326;POINT(6 56)') AS NE,
 ST_GeogFromText('SRID=4326;POINT(6 55)') AS E,
 ST_GeogFromText('SRID=4326;POINT(6 54)') AS SE,
 ST_GeogFromText('SRID=4326;POINT(5 54)') AS S,
 ST_GeogFromText('SRID=4326;POINT(4 54)') AS SW,
 ST_GeogFromText('SRID=4326;POINT(4 55)') AS W,
 ST_GeogFromText('SRID=4326;POINT(4 56)') AS NW ) points
 }}}

 The result is (I manually removed some decimals for easier readability)
 {{{
  az_n | az_ne | az_e  | az_se  | az_s | az_sw  | az_w   | az_nw
 ------+-------+-------+--------+------+--------+--------+-------
   180 | 29.16 | 89.59 | 149.39 |  360 | 329.39 | 269.59 | 209.16
 }}}

 This is not what I expect. I am well aware that a difference of 1° in N
 and E does not result in an azimuth of 45° due to the convergence of the
 meridians. The azimuth angles az_ne, az_e, az_se and az_w seem correct (I
 checked these angles in a conformal map projection in QGIS). However, what
 I expect is
 {{{
  az_n | az_ne | az_e  | az_se  | az_s | az_sw  | az_w   | az_nw
 ------+-------+-------+--------+------+--------+--------+-------
   0 ! | 29.16 | 89.59 | 149.39 | 180 !|  211 ! | 269.59 | 331 !
 }}}
 What was going wrong for az_n, az_s, az_sw and az_nw?

 The version of my DB is
 {{{
                                                              version
 |            postgis_version
 ---------------------------------------------------------------------------------------------------------------------------------+---------------------------------------
  PostgreSQL 13.1 (Ubuntu 13.1-1.pgdg18.04+1) on x86_64-pc-linux-gnu,
 compiled by gcc (Ubuntu 7.5.0-3ubuntu1~18.04) 7.5.0, 64-bit | 3.1
 USE_GEOS=1 USE_PROJ=1 USE_STATS=1
 }}}
 installed via the apt.postgresql.org repositories for Ubuntu 18.04.

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Ticket URL: <https://trac.osgeo.org/postgis/ticket/4840>
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