cycles hair strand uv coordinate

Question

I would like to create uv coordinate locally for each hair particule ribbons strand

I have created a plane with ribbon hair particules:

I would like my texture to be aligned for each strand.

Here are the piece of information I have found on nodes:

HairInfo.Intercept contains 0 to 1 value from root to tip. Which could make the v value for example

But I cannot find anything for the other coordinate (u). Is there a way to get this information in material nodes?