The triptychial projection of the world
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Author
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      Björn Grieger


References
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      Grieger, B. (2019). "Quincuncial adaptive closed Kohonen (QuACK)
      map for the irregularly shaped comet 67P/Churyumov-Gerasimenko".
      A&A 630, A1. https://doi.org/10.1051/0004-6361/201834841
 
      Grieger, B. (2020). "Optimized global map projections
      for specific applications: the triptychial projection
      and the Spilhaus projection". EGU2020-9885.
      https://doi.org/10.5194/egusphere-egu2020-9885
 

The projection
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   The triptychial projection provides a map of the whole world showing
   all continents including Antarctica with minimal distortion and without
   any intersection. It is an oblique aspect of the Peirce quincuncial
   projection. The image

      blue-marble_triptychial.png

   shows an example. The surface data is from the file

      world.topo.bathy.200407.3x5400x2700.png

   in NASA's Blue Marble collection at

      https://visibleearth.nasa.gov/collection/1484/blue-marble


Tables to apply the triptychial projection
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   There are tables for two different resolutions. The file

      triptychial_lonlat_small.txt.gz

   provides a table for a map with a final resolution of 2160 x 1080
   pixels, while the file

      triptychial_lonlat_full.txt.gz

   is for a resolution of 21600 x 10800 pixels.

   Both are gzip compressed text files. Each record has four entries. The
   first two are pixel column (from left to right) and pixel row (from
   top to bottom), the third and forth are longitude and latitude,
   respectively. These longitudes and latitudes can be used to obtain
   the surface data for the pixel listed in the record.

   When using surface data provided as a map in equidistant cylindrical
   projection (x evenly spaced in longitude, y evenly spaced in latitude)
   with a resolution of 2n x n pixels, please note that pixel (1,1)
   corresponds to longitude -180*(n-1/2)/n, latitude 90*(n/2-1/2)/(n/2)
   and pixel (2n,n) corresponds to longitude 180*(n-1/2)/n, latitude
   -90*(n/2-1/2)/(n/2).