  We propose a geometrical explanation for periodically and nonperiodically
repeating fast radio bursts (FRBs) under neutron star (NS)-companion systems.
We suggest a constant critical binary separation, $r_{\rm c}$, within which the
interaction between the NS and companion can trigger FRB bursts. For an
elliptic orbit with the minimum and maximum binary separations, $r_{\rm min}$
and $r_{\rm max}$, a periodically repeating FRB with an active period could be
reproduced if $r_{\rm min}<r_{\rm c}<r_{\rm max}$. However, if $r_{\rm
max}<r_{\rm c}$, the modulation of orbital motion will not work due to
persistent interaction, and this kind of repeating FRBs should be nonperiodic.
We test relevant NS-companion binary scenarios on the basis of FRB
180916.J0158+65 and FRB 121102 under this geometrical frame. It is found that
the pulsar-asteroid belt impact model is more suitable to explain these two
FRBs since this model is compatible with different companions (e.g., massive
stars and black holes). At last, we point out that FRB 121102-like samples are
potential objects which can reveal the evolution of star-forming region.

High Energy Astrophysical Phenomena;High Energy Physics - Phenomenology