This is assuming we are on a curve across 2D space like the equator and face east or west. This sentence was puzzling me at first glance. In usual 3D space, direction/orientation is represented as a 3 dimensonal vector with length one, so on top of the position dimensions, that makes six dimensions, even if we dont care about magnitude of direction a.k.a. speed. Using angle coordinates changes the support domain, but still three dimensions are needed for direction.