How do I align the UVW_Modifier's Gizmo to a selected face?

fn alignUVGizmo theObj theFace =
(
-- First get the face normal vector. -- It is shown in BLUE on the image
faceNormal = in coordsys theObj (getFaceNormal theObj theFace)

 -- This is the desired up vector in world space -- It is shown in YELLOW on the image
worldUpVector = [0,0,1]

 -- Now get the cross-product of the face normal and the up vector. -- This will give you a vector that is perpendicular to the plane defined -- by the normal and the up vector. Normalize it to get a normal vector -- pointing to the right. -- It is shown in RED on the image
rightVector = normalize (cross worldUpVector faceNormal)

 -- Now using the face normal and the new vector, -- get a vector that is perpendicular to the plane defined by the two. -- This is the "local up vector", the vector that is the projection of -- the world up vector on the face you selected. This one is perpendicular -- to both the face normal and the right vector, and you have 3 normals now -- that define the X, Y and Z of your new orthogonal coordinate system -- for the UVW gizmo! -- Note that this new vector can be seen as the SHADOW of the World Up vector -- on the face of the object in the above image. -- It is now displayed in green in the image below:
upVector = normalize ( cross rightVector faceNormal )

 -- Using the 3 vectors, define a matrix3 value which represents the -- coordinate system of the gizmo. The face normal is the Z axis, -- the right vector is the X axis, and the local up vector is the Y axis:
theMatrix =matrix3 rightVector upVector faceNormal [0,0,0]

theMap = Uvwmap()
modPanel.addModToSelection theMap ui: on
theMap.gizmo.transform = theMatrix
)