Local Coordinate Is Left Or Right Hand Coordinate System ?

Hi everyone !

I am reading a paper names "Light Scattering from Human Hair Fibers".
In this paper it shows that everying is computed in right-hand
coordinate system, includes incident angle, azimuths in normal plane.

I have known that in renderman's surface shader, the dPdu,dPdv,Ng is
the local orthonomal basis, and it's a left-handed coordinate
system.as renderman. So How can I make a right hand coordinate in
surface shader if I want to use curve to represent the hair and fur ?
Use dPdu^dPdv or dPdv^dPdu ? or just using dPdv and forwarded N ?

How can I transform the vector into local coordinate ? just like cg
and glsl, just like this?

                 |Tx Bx Nx|
VinLocal = |Ty By Ny|*transpose( VinCamera )
                 |Tz Bz Nz|

I want to obain correct shading result, and I do not know whether the
different coordinate system will affect this.

Thanks very much !