Peirce Quincuncial Projection in QGIS

Question

I'd like to use a Peirce quincuncial projection in QGIS to produce a whole sphere map, but struggling. (To see some nice examples of the projection:- https://github.com/cspersonal/peirce-quincuncial-projection https://en.wikipedia.org/wiki/Peirce_quincuncial_projection) Recent versions of the PROJ library include a relevant option (see https://proj.org/operations/projections/peirce_q.html), and recent versions of QGIS also include ESRI-derived CRS descriptions (ESRI:54091 diamond and ESRI:54090 square).

I'm using QGIS 3.22 which includes PROJ8.1.1.

Selecting the ESRI-derived projections produces no geometry in on-the-fly projection. This appears to be a bug or requires additional implementation: https://github.com/qgis/QGIS/issues/43776 )

Alternatively, creating a custom-CRS with the PROJ4 string of +proj=peirce_q does project the northern hemisphere correctly, but the southern hemisphere is missing:-

It is unclear to me whether these issues are due to implementation in PROJ or QGIS. (This pull request suggests that the problem may lie in the implementation in PROJ: https://github.com/OSGeo/PROJ/pull/2230 )

Any ideas on how to expand to a full-sphere (or even a full tesselation)?... Does this need a re-implementation?

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Note that an earlier similar question on stack was answered before PROJ had included peirce_q as a projection:

• Creating Peirce quincuncial map in QGIS?

Or instead pointed to alternative libraries/software:

• Producing Peirce quincuncial map?

Answer 1

After some investigation, confirmed that the problem with PQ projection in QGIS was due to the partial implementation in PROJ that restricted to northern hemipshere.

I have now contributed code to PROJ which should make it into the next 8.2 branch release of that library which fixes this issue. This should trickle down to QGIS when they update links to latest PROJ.

So by the time the next person reads this, hopefully there will no longer be an issue.

Note that any polygons which stretch over the edges of the map may need splitting to avoid odd visual effects (equivalent problems to stretching over date-line).