Streamslice on 3D surface

I have a magnetoencephalography dataset sampled across a head surface. For each of N locations at a given time point, I have a 3D vector indicating magnetic field strength and direction (all directions are tangential to the head surface at that point). I would like to visualize the magnetic field using something like the streamslice function, but instead of on a 2D plane, as the documentation describes, I would like to see it on the 3D surface, without inter-/extra- polation inside or outside the head.

My first thought is to perform an arc length transformation to make the coordinates planar, then project the vectors onto that plane, streamslice the data, and transform the streamslice back onto the surface. I don't think this would be valid, however, since parts of the surface would be more stretched than others and so the resulting field lines wouldn't accurately represent field strength. So what I would really like is an explanation of how to do this in 3D with streamslice or another function that would accomplish the same goal.