Posted question to PIXLS.
In the meantime generated the following transformations using CIRCLEtoSQUARE/SQUAREtoCIRCLE currently available on G'mic.
Attachment:
Floral Poincare Disk CIRCLEtoSQUARE.jpg [ 2.35 MiB | Viewed 1042 times ]
Attachment:
Floral Poincare Disk.SQUAREtoCIRCLE.jpg [ 1.72 MiB | Viewed 1042 times ]
A divertissement...PS:But they reveal also that the function you found and used seems to be not perfect (in the sense of being a perfectly composed "circle"). Or maybe the input was not suitable. IDK.