I am using the transdata material for incorporating BTDF's in
Radiance. In this context, I have to convert cartesian coordinates in
polar coordinates.
For a surface (i.e. rectangle) the normal is determined by the right-
hand rule. So far - so good. Unfortunately, I am not sure how the
local coordinate system for the rectangle is defined?! How are the x-
axis, y-axis and z-axis are oriented? The source ray direction
(x,y,z) and the transmitted ray direction (Dx,Dy,Dz) are referring to
this local coordinate system, aren't they?

I am using the transdata material for incorporating BTDF's in
Radiance. In this context, I have to convert cartesian coordinates in
polar coordinates.
For a surface (i.e. rectangle) the normal is determined by the right-
hand rule. So far - so good. Unfortunately, I am not sure how the
local coordinate system for the rectangle is defined?! How are the x-
axis, y-axis and z-axis are oriented? The source ray direction
(x,y,z) and the transmitted ray direction (Dx,Dy,Dz) are referring to
this local coordinate system, aren't they?

no- All coordinates refer to world coordinates. Radiance doesn't
support a local coordinate attached to the primitive. If you want one,
you have a calculate it manually using the surface normal and a
reference axis and do some vector crosspoducts.
Other programs (e.g. Rayshade) supply a default local coordinate system,

I guess Greg hasn't build one into it since it's not clear what
'default'
means: For one large polygon it *might* seem obvious, for a tesselated
surface it would be not.