These transformations are useful for plotting and analyzing global climate model (GCM) simulations of slowly rotating tidally locked planets, i.e., Earth-like planets inside the habitable zone of small stars. They can be used to leverage the fact that a slowly rotating planet's climate will start to look approximately symmetric about the axis of insolation.
For derivations and definitions, see Koll & Abbot (2015), Appendix B.
Adapted from Koll & Abbot 2015, Fig.1.
The resulting outputs look like this.
Original code by dkoll. Thanks to Huanzhou Yang for testing and improvements.