I'm wondering if there is a piece of terminology for a path that does not "undo" the previous movement of the path. To be more precise: for every pair of points $ (p_1, p_2) $ on the path with normalized tangent vectors $ (t_1, t_2) $, the vector projection $ t_1 \cdot t_2 \geq 0. $
I am also interested in any algorithm that can determine whether a new point on a discrete path will cause this property to be violated. Ideally such an algorithm would be able to do so without having to explicitly remember the previous points. I was thinking about some sort of additive polygon algorithm that would add together "invalid regions" on the n-sphere, but if there is a better solution I'd like to know.