> rotate ~ sounds like transpose matrix, what is not true in this case.
The various definitions that I can see, such as http://dictionary.reference.com/browse/rotate make no mention of matrices. It applies to anything that moves around a pivot or axis.
Overall I don't see the evidence that "rotate" alone would suggest transposing a matrix.
Now it appears that there is a concept in linear algebra named "rotation matrix", defined as: https://en.wikipedia.org/wiki/Rotation_matrix that seems quite relevant for 3D software.
But as psql is not a tool for linear algebra or 3D in the first place, who could realistically be deceived?
in the help inside your last patch, you are using "crosstab". Cannto be crosstab the name for this feature?