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Add +proj=mod_krovak projection method for Modified Krovak that applies to S-JTSK/05 in the Czech Republic #4021

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merged 1 commit into from
Feb 2, 2024

Commits on Feb 1, 2024

  1. Add +proj=mod_krovak projection method for Modified Krovak that appli…

    …es to S-JTSK/05 in the Czech Republic
    
    Validated with the test point given in EPSG Guidance Note 7-2
    
    Also validated with CUZK online calculator at https://geoportal.cuzk.cz/(S(g4ipaut0ckzb5lellu153lvf))/Default.aspx?head_tab=sekce-01-gp&mode=TextMeta&text=wcts&menu=19
    
    Unfortunately this calculator does not offer 'elementary'
    transformations, and cannot just validate Modified Krovak alone.
    The best we can do is to use ETRS89 <--> S-JTSK/05 / Krovak modified,
    which involves a Helmert transformation as well for the datum
    transformation.
    
    * Validation of reverse modified Krovak:
    
      Online calculator:
      - Souřadnice/input: -5568990.91 -6050538.71 100
      - Source CRS: S-JTSK/05 + Bpv (-Y-XH /east-north)
      - Destination CRS: ETRS89 (BLh / DEG)
      - Výsledek/result: 50.208297081 16.848326835 143.762
    
      With PROJ:
      echo -5568990.91 -6050538.71 100 | bin/cs2cs -d 9 EPSG:5516 EPSG:4937 --3d
      50.208297081 16.848326833 143.143233569
    
      Note the different on longitude is totally neglectable: 0.1 mm, as computed by:
    
      $ echo 50.208297081 16.848326835 50.208297081 16.848326833 | bin/geod -F "%.4f" -I +ellps=GRS80
      -90d 90d 0.0001
    
      and that when outputing Krovak modified, the online calculator displays Y/X with
      a precision of 1 cm.
    
      The difference on Z is significant, but can be explained from the fact that
      the online calculator using Baltic Height for S-JTSK/05 and thus apply a
      Baltic Height<-->ETRS89 geoid that we don't apply here.
    
    * Validation of forward Krovak using same point:
    
      Online calculator:
      - Souřadnice/input: 50.208297081 16.848326835 143.762
      - Source: ETRS89 (BLh / DEG)
      - Destination: S-JTSK/05 + Bpv (-Y-XH /east-north)
      - Výsledek/result: -5568990.91 -6050538.71 100
    
      With PROJ:
      $ echo 50.208297081 16.848326835 143.762 | bin/cs2cs -d 2 EPSG:4937 EPSG:5516 --3d
      -5568990.91 -6050538.71 100.62
    rouault committed Feb 1, 2024
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