It is important to emphasize that the members of \(\mathcal{P}\) represent possible or actual paths of arbitrary massive particles that may have some internal structure such as higher order gravitational and electromagnetic multipole moments and that may therefore interact in complicated ways with various physical fields. In order to constructively establish the projective structure of spacetime, it is necessary to single out a subset of \(\mathcal{P}\), namely \(\mathcal{P}_{f}\), the set of po