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As far as I know neither PROJ4 nor ESRI tools can apply the Peirce quincuncial projection. Does anybody know what libraries/softwares can manage it?

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I recently noticed that the D3js lib can reproject to the Peirce Quincuncial projection (with the geo plugin) :

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Mapthematics Geocart is commercial software that appears to support the Peirce quincuncial projection. (I haven't used it myself, so I can't verify how it works.)

I see this projection is also used for creating a certain kind of panoramic photo. If you only need to project an image (as opposed to vector datasets), you may be able to find an image-processing solution. For example, here is a tutorial on creating Peirce quincuncial panoramas with Photoshop plugins, and here is a discussion (with scripts) for applying the projection to images with MathMap.

The paper Warping Peirce Quincuncial Panoramas by Chamberlain Fong and Brian K. Vogel includes a MatLab implementation of their approach. It is image-oriented as well, but MatLab can read shapefiles, so perhaps a vector projection could be cobbled together…

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