Quincuncial adaptive closed Kohonen (QuACK) map for the irregularly shaped comet 67P/Churyumov-Gerasimenko

Context. Standard global map projections cannot display the complete surface of a highly irregular body such as the Rosetta target comet 67P/Churyumov-Gerasimenko because different points on the surface can have the same longitude and latitude.
Aims: We present a concept of generalized longitudes and latitudes that allows us to display the complete comet in generalized versions of any standard map projection.
Methods: A self-organizing Kohonen map can be used to sample the surface of any 3D shape, but the unfolded map misses some area beyond its edges. Here, we combine two square grids into an inherently closed structure that really maps the complete surface of the comet. Beyond this, the closed map is topologically equivalent to the Peirce quincuncial projection of the world, which enables the definition of generalized longitudes and latitudes.
Results: While the generalized version of any map projection does not exactly share the properties of the original, such as preservation of area or shape, it behaves very similar. In particular, the generalized version of the quincuncial projection behaves very well over most of the surface area and shares the tessellation properties with its original.
Conclusions: The quincuncial adaptive closed Kohonen (QuACK) map and the concept of generalized longitudes and latitudes provide means for global maps of arbitrarily irregular shapes.