Hi,
I am trying to understrand the transformation matrices used in "transform" node. According to maya docs, the final transformation is :
matrix = SP(-1) * S * SH * SP * ST * RP(-1) * RA * R * RP * RT * T
I know it's a row major, so if we use a fixed frame logic (i.e. fixing world coordinates and actively transform objects), we can read the matrix from left to right (i.e. post multiplication) as : scale pivot inverse translation SP(-1), then scale S , then shear SH, then going back to the same pivot point...

My question: I don't understand why we need
(1) scale pivot correction ST (SP-1 cancels SP, so why need ST? getAttr transform.spt always returns 0 0 0 )
(2) rotation pivot correction RT, (as above RP-1 then RP, why need RT) and
(3) RA

Can anyone provide a case where ST/RT/RA are needed? Is there any document/pdf/papers that explain the needed for these three matrices? I found lots of resources on transformation matrices but could not find any these docs that explain any possible need for these matrices...

Thanks in advance,